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Sample records for riemann theta function

  1. Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions

    OpenAIRE

    Biane, P.; Pitman, J.; Yor, M.

    1999-01-01

    This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these probability laws, and some approximations of Riemann's zeta function which are related to these laws.

  2. Riemann-Theta Boltzmann Machine arXiv

    CERN Document Server

    Krefl, Daniel; Haghighat, Babak; Kahlen, Jens

    A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riemann-Theta functions. The conditional expectation of a hidden state for given visible states can also be calculated analytically, yielding a derivative of the logarithmic Riemann-Theta function. The conditional expectation can be used as activation function in a feedforward neural network, thereby increasing the modelling capacity of the network. Both the Boltzmann machine and the derived feedforward neural network can be successfully trained via standard gradient- and non-gradient-based optimization techniques.

  3. Theta vectors and quantum theta functions

    International Nuclear Information System (INIS)

    Chang-Young, Ee; Kim, Hoil

    2005-01-01

    In this paper, we clarify the relation between Manin's quantum theta function and Schwarz's theta vector. We do this in comparison with the relation between the kq representation, which is equivalent to the classical theta function, and the corresponding coordinate space wavefunction. We first explain the equivalence relation between the classical theta function and the kq representation in which the translation operators of the phase space are commuting. When the translation operators of the phase space are not commuting, then the kq representation is no longer meaningful. We explain why Manin's quantum theta function, obtained via algebra (quantum torus) valued inner product of the theta vector, is a natural choice for the quantum version of the classical theta function. We then show that this approach holds for a more general theta vector containing an extra linear term in the exponent obtained from a holomorphic connection of constant curvature than the simple Gaussian one used in Manin's construction

  4. A pedagogical introduction to theta functions

    International Nuclear Information System (INIS)

    Koh, I.G.; Shin, H.J.

    1988-01-01

    This paper reports on revolutions in physics that have been frequently accompanied by new developments in mathematics. In seventeenth century, Newton has initiated a program of describing celestial motion by classical mechanics. Integral and differential calculus was essential tool. Orbits of the moon and the earth are given by solving the differential equation of Newton's equation. Imagine a situation where one tries to solve such orbits without integral and differential calculus. Similar revolutions in understanding quantum gravity and in making deep connections between statistical and string physics are under progresses. One of indispensible tools are the theory of theta functions on Riemann surfaces. Since the literature of theta functions is mainly written by professional mathematician, physicists feel somewhat uneasy to begin to read a long chapters of lemmas and theorems, but it is now generally accepted that theta function is essential in understanding two-dimensional conformal field theory as the integral and differential calculus was indispensible in Newtonian mechanics

  5. Exploring the Riemann zeta function 190 years from Riemann's birth

    CERN Document Server

    Nikeghbali, Ashkan; Rassias, Michael

    2017-01-01

    This book is concerned with the Riemann Zeta Function, its generalizations, and various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis and Probability Theory. Eminent experts in the field illustrate both old and new results towards the solution of long-standing problems and include key historical remarks. Offering a unified, self-contained treatment of broad and deep areas of research, this book will be an excellent tool for researchers and graduate students working in Mathematics, Mathematical Physics, Engineering and Cryptography.

  6. Ramanujan's theta functions

    CERN Document Server

    Cooper, Shaun

    2017-01-01

    Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research. Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter.

  7. Ramanujan's mock theta functions.

    Science.gov (United States)

    Griffin, Michael; Ono, Ken; Rolen, Larry

    2013-04-09

    In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. Recent work by Zwegers [Zwegers S (2001) Contemp Math 291:268-277 and Zwegers S (2002) PhD thesis (Univ of Utrecht, Utrecht, The Netherlands)] has elucidated the theory encompassing these examples. They are holomorphic parts of special harmonic weak Maass forms. Despite this understanding, little attention has been given to Ramanujan's original definition. Here, we prove that Ramanujan's examples do indeed satisfy his original definition.

  8. Functionals of finite Riemann surfaces

    CERN Document Server

    Schiffer, Menahem

    1954-01-01

    This advanced monograph on finite Riemann surfaces, based on the authors' 1949-50 lectures at Princeton University, remains a fundamental book for graduate students. The Bulletin of the American Mathematical Society hailed the self-contained treatment as the source of ""a plethora of ideas, each interesting in its own right,"" noting that ""the patient reader will be richly rewarded."" Suitable for graduate-level courses, the text begins with three chapters that offer a development of the classical theory along historical lines, examining geometrical and physical considerations, existence theo

  9. Lectures on the Riemann zeta function

    CERN Document Server

    Iwaniec, H

    2014-01-01

    The Riemann zeta function was introduced by L. Euler (1737) in connection with questions about the distribution of prime numbers. Later, B. Riemann (1859) derived deeper results about the prime numbers by considering the zeta function in the complex variable. The famous Riemann Hypothesis, asserting that all of the non-trivial zeros of zeta are on a critical line in the complex plane, is one of the most important unsolved problems in modern mathematics. The present book consists of two parts. The first part covers classical material about the zeros of the Riemann zeta function with applications to the distribution of prime numbers, including those made by Riemann himself, F. Carlson, and Hardy-Littlewood. The second part gives a complete presentation of Levinson's method for zeros on the critical line, which allows one to prove, in particular, that more than one-third of non-trivial zeros of zeta are on the critical line. This approach and some results concerning integrals of Dirichlet polynomials are new. Th...

  10. Algebraic geometry and theta functions

    CERN Document Server

    Coble, Arthur B

    1929-01-01

    This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and

  11. A Theta lift representation for the Kawazumi-Zhang and Faltings invariants of genus-two Riemann surfaces

    CERN Document Server

    Pioline, Boris

    2016-01-01

    The Kawazumi-Zhang invariant $\\varphi$ for compact genus-two Riemann surfaces was recently shown to be a eigenmode of the Laplacian on the Siegel upper half-plane, away from the separating degeneration divisor. Using this fact and the known behavior of $\\varphi$ in the non-separating degeneration limit, it is shown that $\\varphi$ is equal to the Theta lift of the unique (up to normalization) weak Jacobi form of weight $-2$. This identification provides the complete Fourier-Jacobi expansion of $\\varphi$ near the non-separating node, gives full control on the asymptotics of $\\varphi$ in the various degeneration limits, and provides a efficient numerical procedure to evaluate $\\varphi$ to arbitrary accuracy. It also reveals a mock-type holomorphic Siegel modular form of weight $-2$ underlying $\\varphi$. From the general relation between the Faltings invariant, the Kawazumi-Zhang invariant and the discriminant for hyperelliptic Riemann surfaces, a Theta lift representation for the Faltings invariant in genus two ...

  12. Meromorphic functions and cohomology on a Riemann surface

    International Nuclear Information System (INIS)

    Gomez-Mont, X.

    1989-01-01

    The objective of this set of notes is to introduce a series of concepts of Complex Analytic Geometry on a Riemann Surface. We motivate the introduction of cohomology groups through the analysis of meromorphic functions. We finish by showing that the set of infinitesimal deformations of a Riemann surface (the tangent space to Teichmueller space) may be computed as a Cohomology group. (author). 6 refs

  13. Theta function identities associated with Ramanujan's modular ...

    Indian Academy of Sciences (India)

    In Chapter 20 of his second notebook [6], Ramanujan recorded several theta function identities associated with modular equations of composite degree 15. These identities have previously been proved by Berndt in [3]. But he proved most of these theta function identities using modular equations. These identities can also ...

  14. The sewing technique and correlation functions on arbitrary Riemann surfaces

    International Nuclear Information System (INIS)

    Di Vecchia, P.

    1989-01-01

    We describe in the case of free bosonic and fermionic theories the sewing procedure, that is a very convenient way for constructing correlation functions of these theories on an arbitrary Riemann surface from their knowledge on the sphere. The fundamental object that results from this construction is the N-point g-loop vertex. It summarizes the information of all correlation functions of the theory on an arbitrary Riemann surface. We then check explicitly the bosonization rules and derive some useful formulas. (orig.)

  15. Riemann zeta function from wave-packet dynamics

    DEFF Research Database (Denmark)

    Mack, R.; Dahl, Jens Peder; Moya-Cessa, H.

    2010-01-01

    We show that the time evolution of a thermal phase state of an anharmonic oscillator with logarithmic energy spectrum is intimately connected to the generalized Riemann zeta function zeta(s, a). Indeed, the autocorrelation function at a time t is determined by zeta (sigma + i tau, a), where sigma...... index of JWKB. We compare and contrast exact and approximate eigenvalues of purely logarithmic potentials. Moreover, we use a numerical method to find a potential which leads to exact logarithmic eigenvalues. We discuss possible realizations of Riemann zeta wave-packet dynamics using cold atoms...

  16. Cubic metaplectic forms and theta functions

    CERN Document Server

    Proskurin, Nikolai

    1998-01-01

    The book is an introduction to the theory of cubic metaplectic forms on the 3-dimensional hyperbolic space and the author's research on cubic metaplectic forms on special linear and symplectic groups of rank 2. The topics include: Kubota and Bass-Milnor-Serre homomorphisms, cubic metaplectic Eisenstein series, cubic theta functions, Whittaker functions. A special method is developed and applied to find Fourier coefficients of the Eisenstein series and cubic theta functions. The book is intended for readers, with beginning graduate-level background, interested in further research in the theory of metaplectic forms and in possible applications.

  17. The Riemann zeta-function theory and applications

    CERN Document Server

    Ivic, Aleksandar

    2003-01-01

    ""A thorough and easily accessible account.""-MathSciNet, Mathematical Reviews on the Web, American Mathematical Society. This extensive survey presents a comprehensive and coherent account of Riemann zeta-function theory and applications. Starting with elementary theory, it examines exponential integrals and exponential sums, the Voronoi summation formula, the approximate functional equation, the fourth power moment, the zero-free region, mean value estimates over short intervals, higher power moments, and omega results. Additional topics include zeros on the critical line, zero-density estim

  18. Method of construction of the Riemann function for a second-order hyperbolic equation

    Science.gov (United States)

    Aksenov, A. V.

    2017-12-01

    A linear hyperbolic equation of the second order in two independent variables is considered. The Riemann function of the adjoint equation is shown to be invariant with respect to the fundamental solutions transformation group. Symmetries and symmetries of fundamental solutions of the Euler-Poisson-Darboux equation are found. The Riemann function is constructed with the aid of fundamental solutions symmetries. Examples of the application of the algorithm for constructing Riemann function are given.

  19. On the $a$-points of the derivatives of the Riemann zeta function

    OpenAIRE

    Onozuka, Tomokazu

    2016-01-01

    We prove three results on the $a$-points of the derivatives of the Riemann zeta function. The first result is a formula of the Riemann-von Mangoldt type; we estimate the number of the $a$-points of the derivatives of the Riemann zeta function. The second result is on certain exponential sum involving $a$-points. The third result is an analogue of the zero density theorem. We count the $a$-points of the derivatives of the Riemann zeta function in $1/2-(\\log\\log T)^2/\\log T

  20. Indefinite theta series and generalized error functions

    CERN Document Server

    Alexandrov, Sergei; Manschot, Jan; Pioline, Boris

    2016-01-01

    Theta series for lattices with indefinite signature $(n_+,n_-)$ arise in many areas of mathematics including representation theory and enumerative algebraic geometry. Their modular properties are well understood in the Lorentzian case ($n_+=1$), but have remained obscure when $n_+\\geq 2$. Using a higher-dimensional generalization of the usual (complementary) error function, discovered in an independent physics project, we construct the modular completion of a class of `conformal' holomorphic theta series ($n_+=2$). As an application, we determine the modular properties of a generalized Appell-Lerch sum attached to the lattice ${\\operatorname A}_2$, which arose in the study of rank 3 vector bundles on $\\mathbb{P}^2$. The extension of our method to $n_+>2$ is outlined.

  1. Ramanujan’s mock theta functions

    Science.gov (United States)

    Griffin, Michael; Ono, Ken; Rolen, Larry

    2013-01-01

    In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. Recent work by Zwegers [Zwegers S (2001) Contemp Math 291:268–277 and Zwegers S (2002) PhD thesis (Univ of Utrecht, Utrecht, The Netherlands)] has elucidated the theory encompassing these examples. They are holomorphic parts of special harmonic weak Maass forms. Despite this understanding, little attention has been given to Ramanujan’s original definition. Here, we prove that Ramanujan’s examples do indeed satisfy his original definition. PMID:23536292

  2. Minimal models on Riemann surfaces: The partition functions

    International Nuclear Information System (INIS)

    Foda, O.

    1990-01-01

    The Coulomb gas representation of the A n series of c=1-6/[m(m+1)], m≥3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius) 2 of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.)

  3. Minimal models on Riemann surfaces: The partition functions

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O. (Katholieke Univ. Nijmegen (Netherlands). Inst. voor Theoretische Fysica)

    1990-06-04

    The Coulomb gas representation of the A{sub n} series of c=1-6/(m(m+1)), m{ge}3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius){sup 2} of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.).

  4. Orbifold Riemann surfaces: Teichmueller spaces and algebras of geodesic functions

    Energy Technology Data Exchange (ETDEWEB)

    Mazzocco, Marta [Loughborough University, Loughborough (United Kingdom); Chekhov, Leonid O [Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow (Russian Federation)

    2009-12-31

    A fat graph description is given for Teichmueller spaces of Riemann surfaces with holes and with Z{sub 2}- and Z{sub 3}-orbifold points (conical singularities) in the Poincare uniformization. The corresponding mapping class group transformations are presented, geodesic functions are constructed, and the Poisson structure is introduced. The resulting Poisson algebras are then quantized. In the particular cases of surfaces with n Z{sub 2}-orbifold points and with one and two holes, the respective algebras A{sub n} and D{sub n} of geodesic functions (classical and quantum) are obtained. The infinite-dimensional Poisson algebra D{sub n}, which is the semiclassical limit of the twisted q-Yangian algebra Y'{sub q}(o{sub n}) for the orthogonal Lie algebra o{sub n}, is associated with the algebra of geodesic functions on an annulus with n Z{sub 2}-orbifold points, and the braid group action on this algebra is found. From this result the braid group actions are constructed on the finite-dimensional reductions of this algebra: the p-level reduction and the algebra D{sub n}. The central elements for these reductions are found. Also, the algebra D{sub n} is interpreted as the Poisson algebra of monodromy data of a Frobenius manifold in the vicinity of a non-semisimple point. Bibliography: 36 titles.

  5. Superconformal algebras and mock theta functions

    International Nuclear Information System (INIS)

    Eguchi, Tohru; Hikami, Kazuhiro

    2009-01-01

    It is known that characters of BPS representations of extended superconformal algebras do not have good modular properties due to extra singular vectors coming from the BPS condition. In order to improve their modular properties we apply the method of Zwegers which has recently been developed to analyze modular properties of mock theta functions. We consider the case of the N=4 superconformal algebra at general levels and obtain the decomposition of characters of BPS representations into a sum of simple Jacobi forms and an infinite series of non-BPS representations. We apply our method to study elliptic genera of hyper-Kaehler manifolds in higher dimensions. In particular, we determine the elliptic genera in the case of complex four dimensions of the Hilbert scheme of points on K3 surfaces K [2] and complex tori A [[3

  6. Superconformal algebras and mock theta functions

    Energy Technology Data Exchange (ETDEWEB)

    Eguchi, Tohru [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Hikami, Kazuhiro [Department of Mathematics, Naruto University of Education, Tokushima 772-8502 (Japan)], E-mail: eguchi@yukawa.kyoto-u.ac.jp, E-mail: hikami@naruto-u.ac.jp

    2009-07-31

    It is known that characters of BPS representations of extended superconformal algebras do not have good modular properties due to extra singular vectors coming from the BPS condition. In order to improve their modular properties we apply the method of Zwegers which has recently been developed to analyze modular properties of mock theta functions. We consider the case of the N=4 superconformal algebra at general levels and obtain the decomposition of characters of BPS representations into a sum of simple Jacobi forms and an infinite series of non-BPS representations. We apply our method to study elliptic genera of hyper-Kaehler manifolds in higher dimensions. In particular, we determine the elliptic genera in the case of complex four dimensions of the Hilbert scheme of points on K3 surfaces K{sup [2]} and complex tori A{sup [[3

  7. Eisenstein Series Identities Involving the Borweins' Cubic Theta Functions

    Directory of Open Access Journals (Sweden)

    Ernest X. W. Xia

    2012-01-01

    Full Text Available Based on the theories of Ramanujan's elliptic functions and the (p, k-parametrization of theta functions due to Alaca et al. (2006, 2007, 2006 we derive certain Eisenstein series identities involving the Borweins' cubic theta functions with the help of the computer. Some of these identities were proved by Liu based on the fundamental theory of elliptic functions and some of them may be new. One side of each identity involves Eisenstein series, the other products of the Borweins' cubic theta functions. As applications, we evaluate some convolution sums. These evaluations are different from the formulas given by Alaca et al.

  8. Functional models for commutative systems of linear operators and de Branges spaces on a Riemann surface

    International Nuclear Information System (INIS)

    Zolotarev, Vladimir A

    2009-01-01

    Functional models are constructed for commutative systems {A 1 ,A 2 } of bounded linear non-self-adjoint operators which do not contain dissipative operators (which means that ξ 1 A 1 +ξ 2 A 2 is not a dissipative operator for any ξ 1 , ξ 2 element of R). A significant role is played here by the de Branges transform and the function classes occurring in this context. Classes of commutative systems of operators {A 1 ,A 2 } for which such a construction is possible are distinguished. Realizations of functional models in special spaces of meromorphic functions on Riemann surfaces are found, which lead to reasonable analogues of de Branges spaces on these Riemann surfaces. It turns out that the functions E(p) and E-tilde(p) determining the order of growth in de Branges spaces on Riemann surfaces coincide with the well-known Baker-Akhiezer functions. Bibliography: 11 titles.

  9. Local Extrema of the $\\Xi(t)$ Function and The Riemann Hypothesis

    OpenAIRE

    Kobayashi, Hisashi

    2016-01-01

    In the present paper we obtain a necessary and sufficient condition to prove the Riemann hypothesis in terms of certain properties of local extrema of the function $\\Xi(t)=\\xi(\\tfrac{1}{2}+it)$. First, we prove that positivity of all local maxima and negativity of all local minima of $\\Xi(t)$ form a necessary condition for the Riemann hypothesis to be true. After showing that any extremum point of $\\Xi(t)$ is a saddle point of the function $\\Re\\{\\xi(s)\\}$, we prove that the above properties o...

  10. Quantized Dirac field in curved Riemann--Cartan background. I. Symmetry properties, Green's function

    International Nuclear Information System (INIS)

    Nieh, H.T.; Yan, M.L.

    1982-01-01

    In the present series of papers, we study the properties of quantized Dirac field in curved Riemann--Cartan space, with particular attention on the role played by torsion. In this paper, we give, in the spirit of the original work of Weyl, a systematic presentation of Dirac's theory in curved Riemann--Cartan space. We discuss symmetry properties of the system, and derive conservation laws as direct consequences of these symmetries. Also discussed is conformal gauge symmetry, with torsion effectively playing the role of a conformal gauge field. To obtain short-distance behavior, we calculate the spinor Green's function, in curved Riemann--Cartan background, using the Schwinger--DeWitt method of proper-time expansion. The calculation corresponds to a generalization of DeWitt's calculation for a Riemannian background

  11. Combinatorial identities for tenth order mock theta functions

    Indian Academy of Sciences (India)

    44

    which lead us to one 4-way and one 3-way combinatorial identity. ... mock theta functions, partition identities and different combinatorial parameters, see for ... 3. Example 1.1. There are twelve (n + 1)–color partitions of 2: 21, 21 + 01, 11 + 11, ...

  12. Averages of ratios of the Riemann zeta-function and correlations of divisor sums

    Science.gov (United States)

    Conrey, Brian; Keating, Jonathan P.

    2017-10-01

    Nonlinearity has published articles containing a significant number-theoretic component since the journal was first established. We examine one thread, concerning the statistics of the zeros of the Riemann zeta function. We extend this by establishing a connection between the ratios conjecture for the Riemann zeta-function and a conjecture concerning correlations of convolutions of Möbius and divisor functions. Specifically, we prove that the ratios conjecture and an arithmetic correlations conjecture imply the same result. This provides new support for the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe. Our main theorem generalises a recent calculation pertaining to the special case of two-over-two ratios.

  13. Donaldson-Witten theory and indefinite theta functions

    Science.gov (United States)

    Korpas, Georgios; Manschot, Jan

    2017-11-01

    We consider partition functions with insertions of surface operators of topologically twisted N=2 , SU(2) supersymmetric Yang-Mills theory, or Donaldson-Witten theory for short, on a four-manifold. If the metric of the compact four-manifold has positive scalar curvature, Moore and Witten have shown that the partition function is completely determined by the integral over the Coulomb branch parameter a, while more generally the Coulomb branch integral captures the wall-crossing behavior of both Donaldson polynomials and Seiberg-Witten invariants. We show that after addition of a \\overlineQ -exact surface operator to the Moore-Witten integrand, the integrand can be written as a total derivative to the anti-holomorphic coordinate ā using Zwegers' indefinite theta functions. In this way, we reproduce Göttsche's expressions for Donaldson invariants of rational surfaces in terms of indefinite theta functions for any choice of metric.

  14. Combinatorics of tenth-order mock theta functions

    Indian Academy of Sciences (India)

    θ(q) there is some root of unity ζ for which f (q) − θ(q) is unbounded as q → ζ rapidly. In the long list of 17 mock theta functions given by Ramanujan, few have been interpreted combinatorially. For example, (q) defined by (1.1) below, has been interpreted by Fine. [8] as a generating function for partitions into odd parts without ...

  15. Lee weight enumerators of self-dual codes and theta functions

    NARCIS (Netherlands)

    Asch, van A.G.; Martens, F.J.L.

    2008-01-01

    The theory of modular forms, in particular theta functions, and coding theory are in a remarkable way connected. The connection is established by defining a suitable lattice corresponding to the given code, and considering its theta function. First we define some special theta functions, and

  16. Applications of Wirtinger Inequalities on the Distribution of Zeros of the Riemann Zeta-Function

    Directory of Open Access Journals (Sweden)

    Saker SamirH

    2010-01-01

    Full Text Available On the hypothesis that the th moments of the Hardy -function are correctly predicted by random matrix theory and the moments of the derivative of are correctly predicted by the derivative of the characteristic polynomials of unitary matrices, we establish new large spaces between the zeros of the Riemann zeta-function by employing some Wirtinger-type inequalities. In particular, it is obtained that which means that consecutive nontrivial zeros often differ by at least 6.1392 times the average spacing.

  17. Brandt matrices and theta series over global function fields

    CERN Document Server

    Chuang, Chih-Yun; Wei, Fu-Tsun; Yu, Jing

    2015-01-01

    The aim of this article is to give a complete account of the Eichler-Brandt theory over function fields and the basis problem for Drinfeld type automorphic forms. Given arbitrary function field k together with a fixed place \\infty, the authors construct a family of theta series from the norm forms of "definite" quaternion algebras, and establish an explicit Hecke-module homomorphism from the Picard group of an associated definite Shimura curve to a space of Drinfeld type automorphic forms. The "compatibility" of these homomorphisms with different square-free levels is also examined. These Heck

  18. Fractional parts and their relations to the values of the Riemann zeta function

    KAUST Repository

    Alabdulmohsin, Ibrahim

    2017-09-06

    A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem.

  19. Fractional parts and their relations to the values of the Riemann zeta function

    KAUST Repository

    Alabdulmohsin, Ibrahim

    2017-01-01

    A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem.

  20. Completely X-symmetric S-matrices corresponding to theta functions

    International Nuclear Information System (INIS)

    Chudnovsky, D.V.

    1981-01-01

    We consider the realization of the classical Weyl commutation relations using THETA-functions. The representations of the Heisenberg group enable us to realize completely symmetric factorized S-matrices in terms of THETA-functions corresponding to the torsion subgroup of an abelian variety. (orig.)

  1. On the irrationality of Ramanujan's mock theta functions and other q-series at an infinite number of points

    OpenAIRE

    Mingarelli, Angelo B.

    2007-01-01

    We show that all of Ramanujan's mock theta functions of order 3, Watson's three additional mock theta functions of order 3, the Rogers-Ramanujan q-series, and 6 mock theta functions of order 5 take on irrational values at the points q=\\pm 1/2,\\pm 1/3,\\pm 1/4,...

  2. Bernhard Riemann

    Indian Academy of Sciences (India)

    the basis for various fields of mathematics and the general relativity theory of Einstein. In 1857 ... This idea explained the work on algebraic ... theory, Riemann found the key to the problem of the distribution of primes, in that he associated it ...

  3. Some theorems on the explicit evaluation of Ramanujan's theta-functions

    Directory of Open Access Journals (Sweden)

    Nayandeep Deka Baruah

    2004-01-01

    Full Text Available Bruce C. Berndt et al. and Soon-Yi Kang have proved many of Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions in terms of Weber-Ramanujan class invariants. In this note, we give alternative proofs of some of these identities of theta-functions recorded by Ramanujan in his notebooks and deduce some formulas for the explicit evaluation of his theta-functions in terms of Weber-Ramanujan class invariants.

  4. Deformations of super Riemann surfaces

    International Nuclear Information System (INIS)

    Ninnemann, H.

    1992-01-01

    Two different approaches to (Konstant-Leites-) super Riemann surfaces are investigated. In the local approach, i.e. glueing open superdomains by superconformal transition functions, deformations of the superconformal structure are discussed. On the other hand, the representation of compact super Riemann surfaces of genus greater than one as a fundamental domain in the Poincare upper half-plane provides a simple description of super Laplace operators acting on automorphic p-forms. Considering purely odd deformations of super Riemann surfaces, the number of linear independent holomorphic sections of arbitrary holomorphic line bundles will be shown to be independent of the odd moduli, leading to a simple proof of the Riemann-Roch theorem for compact super Riemann surfaces. As a further consequence, the explicit connections between determinants of super Laplacians and Selberg's super zeta functions can be determined, allowing to calculate at least the 2-loop contribution to the fermionic string partition function. (orig.)

  5. Deformations of super Riemann surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Ninnemann, H [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    1992-11-01

    Two different approaches to (Konstant-Leites-) super Riemann surfaces are investigated. In the local approach, i.e. glueing open superdomains by superconformal transition functions, deformations of the superconformal structure are discussed. On the other hand, the representation of compact super Riemann surfaces of genus greater than one as a fundamental domain in the Poincare upper half-plane provides a simple description of super Laplace operators acting on automorphic p-forms. Considering purely odd deformations of super Riemann surfaces, the number of linear independent holomorphic sections of arbitrary holomorphic line bundles will be shown to be independent of the odd moduli, leading to a simple proof of the Riemann-Roch theorem for compact super Riemann surfaces. As a further consequence, the explicit connections between determinants of super Laplacians and Selberg's super zeta functions can be determined, allowing to calculate at least the 2-loop contribution to the fermionic string partition function. (orig.).

  6. Dynamic links between theta executive functions and alpha storage buffers in auditory and visual working memory.

    Science.gov (United States)

    Kawasaki, Masahiro; Kitajo, Keiichi; Yamaguchi, Yoko

    2010-05-01

    Working memory (WM) tasks require not only distinct functions such as a storage buffer and central executive functions, but also coordination among these functions. Neuroimaging studies have revealed the contributions of different brain regions to different functional roles in WM tasks; however, little is known about the neural mechanism governing their coordination. Electroencephalographic (EEG) rhythms, especially theta and alpha, are known to appear over distributed brain regions during WM tasks, but the rhythms associated with task-relevant regional coupling have not been obtained thus far. In this study, we conducted time-frequency analyses for EEG data in WM tasks that include manipulation periods and memory storage buffer periods. We used both auditory WM tasks and visual WM tasks. The results successfully demonstrated function-specific EEG activities. The frontal theta amplitudes increased during the manipulation periods of both tasks. The alpha amplitudes increased during not only the manipulation but also the maintenance periods in the temporal area for the auditory WM and the parietal area for the visual WM. The phase synchronization analyses indicated that, under the relevant task conditions, the temporal and parietal regions show enhanced phase synchronization in the theta bands with the frontal region, whereas phase synchronization between theta and alpha is significantly enhanced only within the individual areas. Our results suggest that WM task-relevant brain regions are coordinated by distant theta synchronization for central executive functions, by local alpha synchronization for the memory storage buffer, and by theta-alpha coupling for inter-functional integration.

  7. Explicit solution of Riemann-Hilbert problems for the Ernst equation

    Science.gov (United States)

    Klein, C.; Richter, O.

    1998-01-01

    Riemann-Hilbert problems are an important solution technique for completely integrable differential equations. They are used to introduce a free function in the solutions which can be used at least in principle to solve initial or boundary value problems. But even if the initial or boundary data can be translated into a Riemann-Hilbert problem, it is in general impossible to obtain explicit solutions. In the case of the Ernst equation, however, this is possible for a large class because the matrix problem can be shown to be gauge equivalent to a scalar one on a hyperelliptic Riemann surface that can be solved in terms of theta functions. As an example we discuss the rigidly rotating dust disk.

  8. What is the functional relevance of prefrontal cortex entrainment to hippocampal theta rhythms?

    Directory of Open Access Journals (Sweden)

    James Michael Hyman

    2011-03-01

    Full Text Available There has been considerable interest in the importance of oscillations in the brain and in how these oscillations relate to the firing of single neurons. Recently a number of studies have shown that the spiking of individual neurons in the medial prefrontal cortex (mPFC become entrained to the hippocampal (HPC theta rhythm. We recently showed that theta-entrained mPFC cells lost theta-entrainment specifically on error trials even though the firing rates of these cells did not change (Hyman et al., 2010. This implied that the level of HPC theta-entrainment of mPFC units was more predictive of trial outcome than differences in firing rates and that there is more information encoded by the mPFC on working memory tasks than can be accounted for by a simple rate code. Nevertheless, the functional meaning of mPFC entrainment to HPC theta remains a mystery. It is also unclear as to whether there are any differences in the nature of the information encoded by theta-entrained and non-entrained mPFC cells. In this review we discuss mPFC entrainment to HPC theta within the context of previous results as well as provide a more detailed analysis of the Hyman et al. (2010 data set. This re-analysis revealed that theta-entrained mPFC cells selectively encoded a variety of task relevant behaviors and stimuli while never theta-entrained mPFC cells were most strongly attuned to errors or the lack of expected rewards. In fact, these error responsive neurons were responsible for the error representations exhibited by the entire ensemble of mPFC neurons. A theta reset was also detected in the post-error period. While it is becoming increasingly evident that mPFC neurons exhibit correlates to virtually all cues and behaviors, perhaps phase-locking directs attention to the task-relevant representations required to solve a spatially based working memory task while the loss of theta-entrainment at the start of error trials may represent a shift of attention away from

  9. Conformal mapping on Riemann surfaces

    CERN Document Server

    Cohn, Harvey

    2010-01-01

    The subject matter loosely called ""Riemann surface theory"" has been the starting point for the development of topology, functional analysis, modern algebra, and any one of a dozen recent branches of mathematics; it is one of the most valuable bodies of knowledge within mathematics for a student to learn.Professor Cohn's lucid and insightful book presents an ideal coverage of the subject in five pans. Part I is a review of complex analysis analytic behavior, the Riemann sphere, geometric constructions, and presents (as a review) a microcosm of the course. The Riemann manifold is introduced in

  10. Fuzzy Riemann surfaces

    International Nuclear Information System (INIS)

    Arnlind, Joakim; Hofer, Laurent; Hoppe, Jens; Bordemann, Martin; Shimada, Hidehiko

    2009-01-01

    We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear, Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For a continuous class of quartic constraints, we explicitly work out finite dimensional representations of the corresponding C-Algebras.

  11. Completely X-symmetric S-matrices corresponding to theta functions and models of statistical mechanics

    International Nuclear Information System (INIS)

    Chudnovsky, D.V.; Chudnovsky, G.V.

    1981-01-01

    We consider general expressions of factorized S-matrices with Abelian symmetry expressed in terms of theta-functions. These expressions arise from representations of the Heisenberg group. New examples of factorized S-matrices lead to a large class of completely integrable models of statistical mechanics which generalize the XYZ-model of the eight-vertex model. (orig.)

  12. Riemann surfaces with boundaries and string theory

    International Nuclear Information System (INIS)

    Morozov, A.Yu.; Roslyj, A.A.

    1989-01-01

    A consideration of the cutting and joining operations for Riemann surfaces permits one to express the functional integral on a Riemann surface in terms of integrals over its pieces which are suarfaces with boundaries. This yields an expression for the determinant of the Laplacian on a Riemann surface in terms of Krichever maps for its pieces. Possible applications of the methods proposed to a study of the string perturbation theory in terms of an universal moduli space are mentioned

  13. Maass waveforms arising from sigma and related indefinite theta functions

    OpenAIRE

    Zwegers, Sander

    2010-01-01

    In this paper we consider an example of a Maass waveform which was constructed by Cohen from a function $\\sigma$, studied by Andrews, Dyson and Hickerson, and it's companion $\\sigma^*$. We put this example in a more general framework.

  14. The Euler–Riemann gases, and partition identities

    International Nuclear Information System (INIS)

    Chair, Noureddine

    2013-01-01

    The Euler theorem in partition theory and its generalization are derived from a non-interacting quantum field theory in which each bosonic mode with a given frequency is equivalent to a sum of bosonic mode whose frequency is twice (s-times) as much, and a fermionic (parafermionic) mode with the same frequency. Explicit formulas for the graded parafermionic partition functions are obtained, and the inverse of the graded partition function (IGPPF), turns out to be bosonic (fermionic) partition function depending on the parity of the order s of the parafermions. It is also shown that these partition functions are generating functions of partitions of integers with restrictions, the Euler generating function is identified with the inverse of the graded parafermionic partition function of order 2. As a result we obtain new sequences of partitions of integers with given restrictions. If the parity of the order s is even, then mixing a system of parafermions with a system whose partition function is (IGPPF), results in a system of fermions and bosons. On the other hand, if the parity of s is odd, then, the system we obtain is still a mixture of fermions and bosons but the corresponding Fock space of states is truncated. It turns out that these partition functions are given in terms of the Jacobi theta function θ 4 , and generate sequences in partition theory. Our partition functions coincide with the overpartitions of Corteel and Lovejoy, and jagged partitions in conformal field theory. Also, the partition functions obtained are related to the Ramond characters of the superconformal minimal models, and in the counting of the Moore–Read edge spectra that appear in the fractional quantum Hall effect. The different partition functions for the Riemann gas that are the counter parts of the Euler gas are obtained by a simple change of variables. In particular the counter part of the Jacobi theta function is (ζ(2t))/(ζ(t) 2 ) . Finally, we propose two formulas which brings

  15. Functional localization and effective connectivity of cortical theta and alpha oscillatory activity during an attention task

    Directory of Open Access Journals (Sweden)

    Yuichi Kitaura

    Full Text Available Objectives: The aim of this paper is to investigate cortical electric neuronal activity as an indicator of brain function, in a mental arithmetic task that requires sustained attention, as compared to the resting state condition. The two questions of interest are the cortical localization of different oscillatory activities, and the directional effective flow of oscillatory activity between regions of interest, in the task condition compared to resting state. In particular, theta and alpha activity are of interest here, due to their important role in attention processing. Methods: We adapted mental arithmetic as an attention ask in this study. Eyes closed 61-channel EEG was recorded in 14 participants during resting and in a mental arithmetic task (“serial sevens subtraction”. Functional localization and connectivity analyses were based on cortical signals of electric neuronal activity estimated with sLORETA (standardized low resolution electromagnetic tomography. Functional localization was based on the comparison of the cortical distributions of the generators of oscillatory activity between task and resting conditions. Assessment of effective connectivity was based on the iCoh (isolated effective coherence method, which provides an appropriate frequency decomposition of the directional flow of oscillatory activity between brain regions. Nine regions of interest comprising nodes from the dorsal and ventral attention networks were selected for the connectivity analysis. Results: Cortical spectral density distribution comparing task minus rest showed significant activity increase in medial prefrontal areas and decreased activity in left parietal lobe for the theta band, and decreased activity in parietal-occipital regions for the alpha1 band. At a global level, connections among right hemispheric nodes were predominantly decreased during the task condition, while connections among left hemispheric nodes were predominantly increased. At more

  16. Super Riemann surfaces

    International Nuclear Information System (INIS)

    Rogers, Alice

    1990-01-01

    A super Riemann surface is a particular kind of (1,1)-dimensional complex analytic supermanifold. From the point of view of super-manifold theory, super Riemann surfaces are interesting because they furnish the simplest examples of what have become known as non-split supermanifolds, that is, supermanifolds where the odd and even parts are genuinely intertwined, as opposed to split supermanifolds which are essentially the exterior bundles of a vector bundle over a conventional manifold. However undoubtedly the main motivation for the study of super Riemann surfaces has been their relevance to the Polyakov quantisation of the spinning string. Some of the papers on super Riemann surfaces are reviewed. Although recent work has shown all super Riemann surfaces are algebraic, some areas of difficulty remain. (author)

  17. Statistical properties of the zeros of zeta functions - beyond the Riemann case

    International Nuclear Information System (INIS)

    Bogomolny, E.; Leboeuf, P.

    1993-09-01

    The statistical distribution of the zeros of Dirichlet L-functions is investigated both analytically and numerically. Using the Hardy-Littlewood conjecture about the distribution of primes it is shown that the two-point correlation function of these zeros coincides with that for eigenvalues of the Gaussian unitary ensemble of random matrices, and that the distributions of zeros of different L-functions are statistically independent. Applications of these results to Epstein's zeta functions are shortly discussed. (authors) 30 refs., 3 figs., 1 tab

  18. Generalized Riemann zeta-function regularization and Casimir energy for a piecewise uniform string

    International Nuclear Information System (INIS)

    Li Xinzhou; Shi Xin; Zhang Jianzu.

    1990-12-01

    The generalized zeta-function techniques will be utilized to investigate the Casimir energy for the transverse oscillations of a piecewise uniform closed string. We find that zeta-function regularization method can lead straightforwardly to a correct result. (author). 6 refs

  19. Poisson sigma model with branes and hyperelliptic Riemann surfaces

    International Nuclear Information System (INIS)

    Ferrario, Andrea

    2008-01-01

    We derive the explicit form of the superpropagators in the presence of general boundary conditions (coisotropic branes) for the Poisson sigma model. This generalizes the results presented by Cattaneo and Felder [''A path integral approach to the Kontsevich quantization formula,'' Commun. Math. Phys. 212, 591 (2000)] and Cattaneo and Felder ['Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model', Lett. Math. Phys. 69, 157 (2004)] for Kontsevich's angle function [Kontsevich, M., 'Deformation quantization of Poisson manifolds I', e-print arXiv:hep.th/0101170] used in the deformation quantization program of Poisson manifolds. The relevant superpropagators for n branes are defined as gauge fixed homotopy operators of a complex of differential forms on n sided polygons P n with particular ''alternating'' boundary conditions. In the presence of more than three branes we use first order Riemann theta functions with odd singular characteristics on the Jacobian variety of a hyperelliptic Riemann surface (canonical setting). In genus g the superpropagators present g zero mode contributions

  20. Fractal supersymmetric QM, Geometric Probability and the Riemann Hypothesis

    CERN Document Server

    Castro, C

    2004-01-01

    The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form $ s_n =1/2+i\\lambda_n $. Earlier work on the RH based on supersymmetric QM, whose potential was related to the Gauss-Jacobi theta series, allows to provide the proper framework to construct the well defined algorithm to compute the probability to find a zero (an infinity of zeros) in the critical line. Geometric probability theory furnishes the answer to the very difficult question whether the probability that the RH is true is indeed equal to unity or not. To test the validity of this geometric probabilistic framework to compute the probability if the RH is true, we apply it directly to the the hyperbolic sine function $ \\sinh (s) $ case which obeys a trivial analog of the RH (the HSRH). Its zeros are equally spaced in the imaginary axis $ s_n = 0 + i n \\pi $. The geometric probability to find a zero (and an infinity of zeros) in the imaginary axis is exactly unity. We proceed with a fractal supersymme...

  1. Intermittent Theta-Burst Stimulation of the Lateral Cerebellum Increases Functional Connectivity of the Default Network

    Science.gov (United States)

    Farzan, Faranak; Eldaief, Mark C.; Schmahmann, Jeremy D.; Pascual-Leone, Alvaro

    2014-01-01

    Cerebral cortical intrinsic connectivity networks share topographically arranged functional connectivity with the cerebellum. However, the contribution of cerebellar nodes to distributed network organization and function remains poorly understood. In humans, we applied theta-burst transcranial magnetic stimulation, guided by subject-specific connectivity, to regions of the cerebellum to evaluate the functional relevance of connections between cerebellar and cerebral cortical nodes in different networks. We demonstrate that changing activity in the human lateral cerebellar Crus I/II modulates the cerebral default mode network, whereas vermal lobule VII stimulation influences the cerebral dorsal attention system. These results provide novel insights into the distributed, but anatomically specific, modulatory impact of cerebellar effects on large-scale neural network function. PMID:25186750

  2. Operator bosonization on Riemann surfaces: new vertex operators

    International Nuclear Information System (INIS)

    Semikhatov, A.M.

    1989-01-01

    A new formalism is proposed for the construction of an operator theory of generalized ghost systems (bc theories of spin J) on Riemann surfaces (loop diagrams of the theory of closed strings). The operators of the bc system are expressed in terms of operators of the bosonic conformal theory on a Riemann surface. In contrast to the standard bosonization formulas, which have meaning only locally, operator Baker-Akhiezer functions, which are well defined globally on a Riemann surface of arbitrary genus, are introduced. The operator algebra of the Baker-Akhiezer functions generates explicitly the algebraic-geometric τ function and correlation functions of bc systems on Riemann surfaces

  3. Riemann, topology, and physics

    CERN Document Server

    Monastyrsky, Michael I

    2008-01-01

    This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, "fake" differential structures on 4-dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemann’s name appears prom...

  4. PKC-theta in regulatory and effector T-cell functions

    Directory of Open Access Journals (Sweden)

    Vedran eBrezar

    2015-10-01

    Full Text Available One of the major goals in immunology research is to understand the regulatory mechanisms that underpin the rapid switch on/off of robust and efficient effector (Teff or regulatory (Tregs T-cell responses. Understanding the molecular mechanisms underlying the regulation of such responses is critical for the development of effective therapies. T-cell activation involves the engagement of T-cell receptor and co-stimulatory signals, but the subsequent recruitment of serine/threonine-specific protein Kinase C-theta (PKC-θ to the immunological synapse is instrumental for the formation of signalling complexes, that ultimately lead to a transcriptional network in T cells. Recent studies demonstrated that major differences between Teffs and Tregs occurred at the immunological synapse where its formation induces altered signalling pathways in Tregs. These pathways are characterized by reduced recruitment of PKC-θ, suggesting that PKC-θ inhibits Tregs suppressive function in a negative feedback loop. As the balance of Teffs and Tregs has been shown to be central in several diseases, it was not surprising that some studies revealed that PKC-θ plays a major role in the regulation of this balance.This review will examine recent knowledge on the role of PKC-θ in T-cell transcriptional responses and how this protein can impact on the function of both Tregs and Teffs.

  5. Riemann quasi-invariants

    International Nuclear Information System (INIS)

    Pokhozhaev, Stanislav I

    2011-01-01

    The notion of Riemann quasi-invariants is introduced and their applications to several conservation laws are considered. The case of nonisentropic flow of an ideal polytropic gas is analysed in detail. Sufficient conditions for gradient catastrophes are obtained. Bibliography: 16 titles.

  6. A theory of alpha/theta neurofeedback, creative performance enhancement, long distance functional connectivity and psychological integration.

    Science.gov (United States)

    Gruzelier, John

    2009-02-01

    Professionally significant enhancement of music and dance performance and mood has followed training with an EEG-neurofeedback protocol which increases the ratio of theta to alpha waves using auditory feedback with eyes closed. While originally the protocol was designed to induce hypnogogia, a state historically associated with creativity, the outcome was psychological integration, while subsequent applications focusing on raising the theta-alpha ratio, reduced depression and anxiety in alcoholism and resolved post traumatic stress syndrome (PTSD). In optimal performance studies we confirmed associations with creativity in musical performance, but effects also included technique and communication. We extended efficacy to dance and social anxiety. Diversity of outcome has a counterpart in wide ranging associations between theta oscillations and behaviour in cognitive and affective neuroscience: in animals with sensory-motor activity in exploration, effort, working memory, learning, retention and REM sleep; in man with meditative concentration, reduced anxiety and sympathetic autonomic activation, as well as task demands in virtual spatial navigation, focussed and sustained attention, working and recognition memory, and having implications for synaptic plasticity and long term potentiation. Neuroanatomical circuitry involves the ascending mescencephalic-cortical arousal system, and limbic circuits subserving cognitive as well as affective/motivational functions. Working memory and meditative bliss, representing cognitive and affective domains, respectively, involve coupling between frontal and posterior cortices, exemplify a role for theta and alpha waves in mediating the interaction between distal and widely distributed connections. It is posited that this mediation in part underpins the integrational attributes of alpha-theta training in optimal performance and psychotherapy, creative associations in hypnogogia, and enhancement of technical, communication and

  7. Chiral bosonization on a Riemann surface

    International Nuclear Information System (INIS)

    Eguchi, Tohru; Ooguri, Hirosi

    1987-01-01

    We point out that the basic addition theorem of θ-functions, Fay's identity, implies an equivalence between bosons and chiral fermions on Riemann surfaces with arbitrary genus. We present a rule for a bosonized calculation of correlation functions. We also discuss ghost systems of n and (1-n) tensors and derive formulas for their chiral determinants. (orig.)

  8. On calculation of zeta function of integral matrix

    Czech Academy of Sciences Publication Activity Database

    Janáček, Jiří

    2009-01-01

    Roč. 134, č. 1 (2009), s. 49-58 ISSN 0862-7959 R&D Projects: GA AV ČR(CZ) IAA100110502 Institutional research plan: CEZ:AV0Z50110509 Keywords : Epstein zeta function * integral lattice * Riemann theta function Subject RIV: BA - General Mathematics

  9. Interpolating and sampling sequences in finite Riemann surfaces

    OpenAIRE

    Ortega-Cerda, Joaquim

    2007-01-01

    We provide a description of the interpolating and sampling sequences on a space of holomorphic functions on a finite Riemann surface, where a uniform growth restriction is imposed on the holomorphic functions.

  10. Fermion Wavefunctions in Magnetized branes Theta identities and Yukawa couplings

    CERN Document Server

    Antoniadis, Ignatios; Panda, Binata

    2009-01-01

    Computation of Yukawa couplings, determining superpotentials as well as the Kähler metric, with oblique (non-commuting) fluxes in magnetized brane constructions is an interesting unresolved issue, in view of the importance of such fluxes for obtaining phenomenologically viable models. In order to perform this task, fermion (scalar) wavefunctions on toroidally compactified spaces are presented for general fluxes, parameterized by Hermitian matrices with eigenvalues of arbitrary signatures. We also give explicit mappings among fermion wavefunctions, of different internal chiralities on the tori, which interchange the role of the flux components with the complex structure of the torus. By evaluating the overlap integral of the wavefunctions, we give the expressions for Yukawa couplings among chiral multiplets arising from an arbitrary set of branes (or their orientifold images). The method is based on constructing certain mathematical identities for general Riemann theta functions with matrix valued modular par...

  11. Deficits of entropy modulation in schizophrenia are predicted by functional connectivity strength in the theta band and structural clustering.

    Science.gov (United States)

    Gomez-Pilar, Javier; de Luis-García, Rodrigo; Lubeiro, Alba; de Uribe, Nieves; Poza, Jesús; Núñez, Pablo; Ayuso, Marta; Hornero, Roberto; Molina, Vicente

    2018-01-01

    Spectral entropy (SE) allows comparing task-related modulation of electroencephalogram (EEG) between patients and controls, i.e. spectral changes of the EEG associated to task performance. A SE modulation deficit has been replicated in different schizophrenia samples. To investigate the underpinnings of SE modulation deficits in schizophrenia, we applied graph-theory to EEG recordings during a P300 task and fractional anisotropy (FA) data from diffusion tensor imaging in 48 patients (23 first episodes) and 87 healthy controls. Functional connectivity was assessed from phase-locking values among sensors in the theta band, and structural connectivity was based on FA values for the tracts connecting pairs of regions. From those data, averaged clustering coefficient (CLC), characteristic path-length (PL) and connectivity strength (CS, also known as density) were calculated for both functional and structural networks. The corresponding functional modulation values were calculated as the difference in SE and CLC, PL and CS between the pre-stimulus and response windows during the task. The results revealed a higher functional CS in the pre-stimulus window in patients, predictive of smaller modulation of SE in this group. The amount of increase in theta CS from pre-stimulus to response related to SE modulation in patients and controls. Structural CLC was associated with SE modulation in the patients. SE modulation was predictive of negative symptoms, whereas CLC and PL modulation was associated with cognitive performance in the patients. These results support that a hyperactive functional connectivity and/or structural connective deficits in the patients hamper the dynamical modulation of connectivity underlying cognition.

  12. Computational approach to Riemann surfaces

    CERN Document Server

    Klein, Christian

    2011-01-01

    This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first...

  13. The concept of a Riemann surface

    CERN Document Server

    Weyl, Hermann

    2009-01-01

    This classic on the general history of functions was written by one of the twentieth century's best-known mathematicians. Hermann Weyl, who worked with Einstein at Princeton, combined function theory and geometry in this high-level landmark work, forming a new branch of mathematics and the basis of the modern approach to analysis, geometry, and topology.The author intended this book not only to develop the basic ideas of Riemann's theory of algebraic functions and their integrals but also to examine the related ideas and theorems with an unprecedented degree of rigor. Weyl's two-part treatment

  14. [Cortical functional connectivity during retention of affective pictures in working memory: EEG-source theta coherence analysis].

    Science.gov (United States)

    Machinskaya, R I; Rozovskaya, R I; Kurgansky, A V; Pechenkova, E V

    2016-01-01

    A pattern of cortical functional connectivity in the source space was studied in a group of right-handed adult participants (N = 44:17 women, 27 men, aged M = 29.61 ± 6.45 years) who retained in their working memory (WM) traces of realistic pictures of positive, neutral, and negative emotional valence while in their working memory (WM) while performing same different task in which participants had to compare an etalon picture against a target picture that followed after a specified delay. A coherence (COH) between pairs of cortical sources chosen in advance according to fMRI data was estimated in the theta frequency range for the period of time preceding the etalon stimulus, distinct sets of functional links are found. The links of the first type that presumably reflect the involvement of sustained attention were between the dorsal anterior cingulate cortex, the prefrontal areas, and temporal areas of the right hemispheres. When compared to the rest period, links of this type showed strengthening not only during the retention period but also during the period preceding the etalon picture. The links of the second type presumably reflecting a progressive neocortex-to-hippocampus functional integration with increasing memory load and strengthened exclusively during retention period. Those links were between parietal, temporal and prefrontal cortices in the lateral surface of both hemispheres with the additional inclusion of the posterior cingulate cortex and the medial parietal cortex in the left hemisphere. An impact of emotional valence onto the strength and topography of the functional links of the second type was found. In the left hemisphere, an increase in the strength of cortical interaction was more pronounced for pictures of positive valence than for pictures of either neutral or negative valences. When compared to the pictures of neutral valence, the retention of pictorial information of both positive and negative valence showed some extraneous integration

  15. DOES THE INFERIOR FRONTAL SULCUS PLAY A FUNCTIONAL ROLE IN DECEPTION? A NEURONAVIGATED THETA-BURST TRANSCRANIAL MAGNETIC STIMULATION STUDY

    Directory of Open Access Journals (Sweden)

    Bruno eVerschuere

    2012-10-01

    Full Text Available Background. By definition, lying involves withholding the truth. Response inhibition may therefore be the cognitive function at the heart of deception. Neuroimaging research has shown that the same brain region that is activated during response inhibition tasks, namely the inferior frontal region, is also activated during deception paradigms. This led to the hypothesis that the inferior frontal region is the neural substrate critically involved in withholding the truth. Objective. We critically examine the functional necessity of the inferior frontal region in withholding the truth during deception. Method. We experimentally manipulated the neural activity level in right inferior frontal sulcus (IFS by means of neuronavigated continuous theta burst stimulation (cTBS. Individual structural magnetic resonance brain images (MRI were used to allow precise stimulation in each participant. Twenty-six participants answered autobiographical questions truthfully or deceptively before and after sham and real cTBS. Results. Deception was reliably associated with more errors, longer and more variable response times than truth telling. Despite the potential role of IFS in deception as suggested by neuroimaging data, the cTBS-induced disruption of right IFS did not affect response times or error rates, when compared to sham stimulation. Conclusions. The present findings do not support the hypothesis that the right inferior frontal sulcus is critically involved in deception.

  16. Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods

    International Nuclear Information System (INIS)

    Ernst, Frederick J

    2007-01-01

    metric tensor components. The first two chapters of this book are devoted to some basic ideas: in the introductory chapter 1 the authors discuss the concept of integrability, comparing the integrability of the vacuum Ernst equation with the integrability of nonlinear equations of Korteweg-de Vries (KdV) type, while in chapter 2 they describe various circumstances in which the vacuum Ernst equation has been determined to be relevant, not only in connection with gravitation but also, for example, in the construction of solutions of the self-dual Yang-Mills equations. It is also in this chapter that one of several equivalent linear systems for the Ernst equation is described. The next two chapters are devoted to Dmitry Korotkin's concept of algebro-geometric solutions of a linear system: in chapter 3 the structure of such solutions of the vacuum Ernst equation, which involve Riemann theta functions of hyperelliptic algebraic curves of any genus, is contrasted with the periodic structure of such solutions of the KdV equation. How such solutions can be obtained, for example, by solving a matrix Riemann-Hilbert problem and how the metric tensor of the associated spacetime can be evaluated is described in detail. In chapter 4 the asymptotic behaviour and the similarity structure of the general algebro-geometric solutions of the Ernst equation are described, and the relationship of such solutions to the perhaps more familiar multi-soliton solutions is discussed. The next three chapters are based upon the authors' own published research: in chapter 5 it is shown that a problem involving counter-rotating infinitely thin disks of matter can be solved in terms of genus two Riemann theta functions, while in chapter 6 the authors describe numerical methods that facilitate the construction of such solutions, and in chapter 7 three-dimensional graphs are displayed that depict all metrical fields of the associated spacetime. Finally, in chapter 8, the difficulties associated with

  17. Supermanifolds and super Riemann surfaces

    International Nuclear Information System (INIS)

    Rabin, J.M.

    1986-09-01

    The theory of super Riemann surfaces is rigorously developed using Rogers' theory of supermanifolds. The global structures of super Teichmueller space and super moduli space are determined. The super modular group is shown to be precisely the ordinary modular group. Super moduli space is shown to be the gauge-fixing slice for the fermionic string path integral

  18. Riemann surfaces, Clifford algebras and infinite dimensional groups

    International Nuclear Information System (INIS)

    Carey, A.L.; Eastwood, M.G.; Hannabuss, K.C.

    1990-01-01

    We introduce of class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a 'gauge' group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces. (orig.)

  19. On Riemann zeroes, lognormal multiplicative chaos, and Selberg integral

    International Nuclear Information System (INIS)

    Ostrovsky, Dmitry

    2016-01-01

    Rescaled Mellin-type transforms of the exponential functional of the Bourgade–Kuan–Rodgers statistic of Riemann zeroes are conjecturally related to the distribution of the total mass of the limit lognormal stochastic measure of Mandelbrot–Bacry–Muzy. The conjecture implies that a non-trivial, log-infinitely divisible probability distribution is associated with Riemann zeroes. For application, integral moments, covariance structure, multiscaling spectrum, and asymptotics associated with the exponential functional are computed in closed form using the known meromorphic extension of the Selberg integral. (paper)

  20. Parietal theta burst TMS: Functional fractionation observed during bistable perception not evident in attention tasks.

    Science.gov (United States)

    Schauer, Georg; Kanai, Ryota; Brascamp, Jan W

    2016-02-01

    When visual input is ambiguous, perception spontaneously alternates between interpretations: bistable perception. Studies have identified two distinct sites near the right intraparietal sulcus where inhibitory transcranial magnetic stimulation (TMS) affects the frequency of occurrence of these alternations, but strikingly with opposite directions of effect for the two sites. Lesion and TMS studies on spatial and sustained attention have also indicated a parcellation of right parietal cortex, into areas serving distinct attentional functions. We used the exact TMS procedure previously employed to affect bistable perception, yet measured its effect on spatial and sustained attention tasks. Although there was a trend for TMS to affect performance, trends were consistently similar for both parietal sites, with no indication of opposite effects. We interpret this as signifying that the previously observed parietal fractionation of function regarding the perception of ambiguous stimuli is not due to TMS-induced modification of spatial or sustained attention. Copyright © 2016 Elsevier Inc. All rights reserved.

  1. Differential downstream functions of protein kinase Ceta and -theta in EL4 mouse thymoma cells.

    Science.gov (United States)

    Resnick, M S; Kang, B S; Luu, D; Wickham, J T; Sando, J J; Hahn, C S

    1998-10-16

    Sensitive EL4 mouse thymoma cells (s-EL4) respond to phorbol esters with growth inhibition, adherence to substrate, and production of cytokines including interleukin 2. Since these cells express several of the phorbol ester-sensitive protein kinase C (PKC) isozymes, the function of each isozyme remains unclear. Previous studies demonstrated that s-EL4 cells expressed substantially more PKCeta and PKCtheta than did EL4 cells resistant to phorbol esters (r-EL4). To examine potential roles for PKCeta and PKCtheta in EL4 cells, wild type and constitutively active versions of the isozymes were transiently expressed using a Sindbis virus system. Expression of constitutively active PKCeta, but not PKCtheta, in s- and r-EL4 cells altered cell morphology and cytoskeletal structure in a manner similar to that of phorbol ester treatment, suggesting a role for PKCeta in cytoskeletal organization. Prolonged treatment of s-EL4 cells with phorbol esters results in inhibition of cell cycling along with a decreased expression of most of the PKC isozymes, including PKCtheta. Introduction of virally expressed PKCtheta, but not PKCeta, overcame the inhibitory effects of the prolonged phorbol ester treatment on cell cycle progression, suggesting a possible involvement of PKCtheta in cell cycle regulation. These results support differential functions for PKCeta and PKCtheta in T cell activation.

  2. Quantum thetas on noncommutative T4 from embeddings into lattice

    International Nuclear Information System (INIS)

    Chang-Young, Ee; Kim, Hoil

    2007-01-01

    In this paper, we investigate the theta vector and quantum theta function over noncommutative T 4 from the embedding of RxZ 2 . Manin has constructed the quantum theta functions from the lattice embedding into vector space (x finite group). We extend Manin's construction of the quantum theta function to the embedding of vector space x lattice case. We find that the holomorphic theta vector exists only over the vector space part of the embedding, and over the lattice part we can only impose the condition for the Schwartz function. The quantum theta function built on this partial theta vector satisfies the requirement of the quantum theta function. However, two subsequent quantum translations from the embedding into the lattice part are nonadditive, contrary to the additivity of those from the vector space part

  3. Extended Riemann-Liouville type fractional derivative operator with applications

    Directory of Open Access Journals (Sweden)

    Agarwal P.

    2017-12-01

    Full Text Available The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented.

  4. Getting superstring amplitudes by degenerating Riemann surfaces

    International Nuclear Information System (INIS)

    Matone, Marco; Volpato, Roberto

    2010-01-01

    We explicitly show how the chiral superstring amplitudes can be obtained through factorisation of the higher genus chiral measure induced by suitable degenerations of Riemann surfaces. This powerful tool also allows to derive, at any genera, consistency relations involving the amplitudes and the measure. A key point concerns the choice of the local coordinate at the node on degenerate Riemann surfaces that greatly simplifies the computations. As a first application, starting from recent ansaetze for the chiral measure up to genus five, we compute the chiral two-point function for massless Neveu-Schwarz states at genus two, three and four. For genus higher than three, these computations include some new corrections to the conjectural formulae appeared so far in the literature. After GSO projection, the two-point function vanishes at genus two and three, as expected from space-time supersymmetry arguments, but not at genus four. This suggests that the ansatz for the superstring measure should be corrected for genus higher than four.

  5. Genetic influences on functional connectivity associated with feedback processing and prediction error: Phase coupling of theta-band oscillations in twins.

    Science.gov (United States)

    Demiral, Şükrü Barış; Golosheykin, Simon; Anokhin, Andrey P

    2017-05-01

    Detection and evaluation of the mismatch between the intended and actually obtained result of an action (reward prediction error) is an integral component of adaptive self-regulation of behavior. Extensive human and animal research has shown that evaluation of action outcome is supported by a distributed network of brain regions in which the anterior cingulate cortex (ACC) plays a central role, and the integration of distant brain regions into a unified feedback-processing network is enabled by long-range phase synchronization of cortical oscillations in the theta band. Neural correlates of feedback processing are associated with individual differences in normal and abnormal behavior, however, little is known about the role of genetic factors in the cerebral mechanisms of feedback processing. Here we examined genetic influences on functional cortical connectivity related to prediction error in young adult twins (age 18, n=399) using event-related EEG phase coherence analysis in a monetary gambling task. To identify prediction error-specific connectivity pattern, we compared responses to loss and gain feedback. Monetary loss produced a significant increase of theta-band synchronization between the frontal midline region and widespread areas of the scalp, particularly parietal areas, whereas gain resulted in increased synchrony primarily within the posterior regions. Genetic analyses showed significant heritability of frontoparietal theta phase synchronization (24 to 46%), suggesting that individual differences in large-scale network dynamics are under substantial genetic control. We conclude that theta-band synchronization of brain oscillations related to negative feedback reflects genetically transmitted differences in the neural mechanisms of feedback processing. To our knowledge, this is the first evidence for genetic influences on task-related functional brain connectivity assessed using direct real-time measures of neuronal synchronization. Copyright © 2016

  6. Search for the exotic $\\Theta^+$ resonance in the NOMAD experiment

    CERN Document Server

    Samoylov, O; Autiero, D; Baldisseri, Alberto; Baldo-Ceolin, M; Banner, M; Bassompierre, G; Benslama, K; Besson, N; Bird, I; Blumenfeld, B; Bobisut, F; Bouchez, J; Boyd, S; Bueno, A; Bunyatov, S; Camilleri, L L; Cardini, A; Cattaneo, P W; Cavasinni, V; Cervera-Villanueva, A; Challis, R; Chukanov, A; Collazuol, G; Conforto, G; Conta, C; Contalbrigo, M; Cousins, R; Daniels, D; De Santo, A; Degaudenzi, H M; Del Prete, T; Di Lella, L; Dignan, T; Do Couto e Silva, E; Dumarchez, J; Ellis, M; Feldman, G J; Ferrari, R; Ferrère, D; Flaminio, V; Fraternali, M; Gaillard, J M; Gangler, E; Geiser, A; Geppert, D; Gibin, D; Gninenko, S; Godley, A; Gosset, J; Gouanère, M; Grant, A; Graziani, G; Guglielmi, A M; Gómez-Cadenas, J J; Gössling, C; Hagner, C; Hernando, J; Hubbard, D; Hurst, P; Hyett, N; Iacopini, E; Joseph, C; Juget, F; Kent, N; Kirsanov, M; Klimov, O; Kokkonen, J; Kovzelev, A; Krasnoperov, A V; La Rotonda, L; Lacaprara, S; Lachaud, C; Lakic, B; Lanza, A; Laveder, M; Letessier-Selvon, A A; Linssen, L; Ljubicic, A; Long, J; Lupi, A; Lyubushkin, V; Lévy, J M; Marchionni, A; Martelli, F; Mendiburu, J P; Meyer, J P; Mezzetto, M; Mishra, S R; Moorhead, G F; Méchain, X; Naumov, D; Nefedov, Yu; Nguyen-Mau, C; Nédélec, P; Orestano, D; Pastore, F; Peak, L S; Pennacchio, E; Pessard, H; Petti, R; Placci, A; Polesello, G; Pollmann, D; Polyarush, A Yu; Popov, B; Poulsen, C; Rebuffi, L; Rico, J; Riemann, P; Roda, C; Rubbia, André; Salvatore, F; Schahmaneche, K; Schmidt, B; Schmidt, T; Sconza, A; Sevior, M; Sillou, D; Soler, F J P; Sozzi, G; Steele, D; Stiegler, U; Stipcevic, M; Stolarczyk, T; Tareb-Reyes, M; Taylor, G N; Tereshchenko, V V; Toropin, A; Touchard, A M; Tovey, S N; Tran, M T; Tsesmelis, E; Ulrichs, J; Vacavant, L; Valdata-Nappi, M; Valuev, V; Vannucci, F; Varvell, K E; Veltri, M; Vercesi, V; Vidal-Sitjes, G; Vieira, J M; Vinogradova, T; Weber, F V; Weisse, T; Wilson, F F; Winton, L J; Yabsley, B D; Zaccone, Henri; Zuber, K; Zuccon, P

    2007-01-01

    A search for exotic Theta baryon via Theta -> proton +Ks decay mode in the NOMAD muon neutrino DIS data is reported. The special background generation procedure was developed. The proton identification criteria are tuned to maximize the sensitivity to the Theta signal as a function of xF which allows to study the Theta production mechanism. We do not observe any evidence for the Theta state in the NOMAD data. We provide an upper limit on Theta production rate at 90% CL as 2.13 per 1000 of neutrino interactions.

  7. Traveling Theta Waves in the Human Hippocampus

    Science.gov (United States)

    Zhang, Honghui

    2015-01-01

    The hippocampal theta oscillation is strongly correlated with behaviors such as memory and spatial navigation, but we do not understand its specific functional role. One hint of theta's function came from the discovery in rodents that theta oscillations are traveling waves that allow parts of the hippocampus to simultaneously exhibit separate oscillatory phases. Because hippocampal theta oscillations in humans have different properties compared with rodents, we examined these signals directly using multielectrode recordings from neurosurgical patients. Our findings confirm that human hippocampal theta oscillations are traveling waves, but also show that these oscillations appear at a broader range of frequencies compared with rodents. Human traveling waves showed a distinctive pattern of spatial propagation such that there is a consistent phase spread across the hippocampus regardless of the oscillations' frequency. This suggests that traveling theta oscillations are important functionally in humans because they coordinate phase coding throughout the hippocampus in a consistent manner. SIGNIFICANCE STATEMENT We show for the first time in humans that hippocampal theta oscillations are traveling waves, moving along the length of the hippocampus in a posterior–anterior direction. The existence of these traveling theta waves is important for understanding hippocampal neural coding because they cause neurons at separate positions in the hippocampus to experience different theta phases simultaneously. The theta phase that a neuron measures is a key factor in how that cell represents behavioral information. Therefore, the existence of traveling theta waves indicates that, to fully understand how a hippocampal neuron represents information, it is vital to also account for that cell's location in addition to conventional measures of neural activity. PMID:26354915

  8. The Riemann-Lovelock Curvature Tensor

    OpenAIRE

    Kastor, David

    2012-01-01

    In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D

  9. Fermion wavefunctions in magnetized branes: Theta identities and Yukawa couplings

    International Nuclear Information System (INIS)

    Antoniadis, Ignatios; Kumar, Alok; Panda, Binata

    2009-01-01

    Computation of Yukawa couplings, determining superpotentials as well as the Kaehler metric, with oblique (non-commuting) fluxes in magnetized brane constructions is an interesting unresolved issue, in view of the importance of such fluxes for obtaining phenomenologically viable models. In order to perform this task, fermion (scalar) wavefunctions on toroidally compactified spaces are presented for general fluxes, parameterized by Hermitian matrices with eigenvalues of arbitrary signatures. We also give explicit mappings among fermion wavefunctions, of different internal chiralities on the tori, which interchange the role of the flux components with the complex structure of the torus. By evaluating the overlap integral of the wavefunctions, we give the expressions for Yukawa couplings among chiral multiplets arising from an arbitrary set of branes (or their orientifold images). The method is based on constructing certain mathematical identities for general Riemann theta functions with matrix valued modular parameter. We briefly discuss an application of the result, for the mass generation of non-chiral fermions, in the SU(5) GUT model presented by us in Antoniadis, Kumar and Panda (2008) .

  10. A Polyakov action on Riemann surfaces

    International Nuclear Information System (INIS)

    Zucchini, R.

    1991-02-01

    A calculation of the effective action for induced conformal gravity on higher genus Riemann surfaces is presented. Our expression, generalizing Polyakov's formula, depends holomorphically on the Beltrami and integrates the diffeomorphism anomaly. A solution of the conformal Ward identity on an arbitrary compact Riemann surfaces without boundary is presented, and its remarkable properties are studied. (K.A.) 16 refs., 2 figs

  11. Ice cream and orbifold Riemann-Roch

    International Nuclear Information System (INIS)

    Buckley, Anita; Reid, Miles; Zhou Shengtian

    2013-01-01

    We give an orbifold Riemann-Roch formula in closed form for the Hilbert series of a quasismooth polarized n-fold (X,D), under the assumption that X is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of the same canonical weight; the orbifold parts are called ice cream functions. This form of the Hilbert series is particularly useful for computer algebra, and we illustrate it on examples of K3 surfaces and Calabi-Yau 3-folds. These results apply also with higher dimensional orbifold strata (see [1] and [2]), although the precise statements are considerably trickier. We expect to return to this in future publications.

  12. Ice cream and orbifold Riemann-Roch

    Science.gov (United States)

    Buckley, Anita; Reid, Miles; Zhou, Shengtian

    2013-06-01

    We give an orbifold Riemann-Roch formula in closed form for the Hilbert series of a quasismooth polarized n-fold (X,D), under the assumption that X is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of the same canonical weight; the orbifold parts are called ice cream functions. This form of the Hilbert series is particularly useful for computer algebra, and we illustrate it on examples of {K3} surfaces and Calabi-Yau 3-folds. These results apply also with higher dimensional orbifold strata (see [1] and [2]), although the precise statements are considerably trickier. We expect to return to this in future publications.

  13. The Riemann-Lovelock curvature tensor

    International Nuclear Information System (INIS)

    Kastor, David

    2012-01-01

    In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are 'Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature. (paper)

  14. Riemann y los Números Primos

    Directory of Open Access Journals (Sweden)

    José Manuel Sánchez Muñoz

    2011-10-01

    Full Text Available En el mes de noviembre de 1859, durante la presentación mensual de losinformes de la Academia de Berlín, el alemán Bernhard Riemann presentóun trabajo que cambiaría los designios futuros de la ciencia matemática. El tema central de su informe se centraba en los números primos, presentando el que hoy día, una vez demostrada la Conjetura de Poincaré, puede ser considerado el problema matemático abierto más importante. El presente artículo muestra en su tercera sección una traducción al castellano de dicho trabajo.

  15. Conformal algebra of Riemann surfaces

    International Nuclear Information System (INIS)

    Vafa, C.

    1988-01-01

    It has become clear over the last few years that 2-dimensional conformal field theories are a crucial ingredient of string theory. Conformal field theories correspond to vacuum solutions of strings; or more precisely we know how to compute string spectrum and scattering amplitudes by starting from a formal theory (with a proper value of central charge of the Virasoro algebra). Certain non-linear sigma models do give rise to conformal theories. A lot of progress has been made in the understanding of conformal theories. The author discusses a different view of conformal theories which was motivated by the development of operator formalism on Riemann surfaces. The author discusses an interesting recent work from this point of view

  16. Conformal scalar fields and chiral splitting on super Riemann surfaces

    International Nuclear Information System (INIS)

    D'Hoker, E.; Phong, D.H.

    1989-01-01

    We provide a complete description of correlation functions of scalar superfields on a super Riemann surface, taking into account zero modes and non-trivial topology. They are built out of chirally split correlation functions, or conformal blocks at fixed internal momenta. We formulate effective rules which determine these completely in terms of geometric invariants of the super Riemann surface. The chirally split correlation functions have non-trivial monodromy and produce single-valued amplitudes only upon integration over loop momenta. Our discussion covers the even spin structure as well as the odd spin structure case which had been the source of many difficulties in the past. Super analogues of Green's functions, holomorphic spinors, and prime forms emerge which should pave the way to function theory on super Riemann surfaces. In superstring theories, chirally split amplitudes for scalar superfields are crucial in enforcing the GSO projection required for consistency. However one really knew how to carry this out only in the operator formalism to one-loop order. Our results provide a way of enforcing the GSO projection to any loop. (orig.)

  17. Super differential forms on super Riemann surfaces

    International Nuclear Information System (INIS)

    Konisi, Gaku; Takahasi, Wataru; Saito, Takesi.

    1994-01-01

    Line integral on the super Riemann surface is discussed. A 'super differential operator' which possesses both properties of differential and of differential operator is proposed. With this 'super differential operator' a new theory of differential form on the super Riemann surface is constructed. We call 'the new differentials on the super Riemann surface' 'the super differentials'. As the applications of our theory, the existency theorems of singular 'super differentials' such as 'super abelian differentials of the 3rd kind' and of a super projective connection are examined. (author)

  18. Current direction-dependent modulation of human hand motor function by intermittent theta burst stimulation (iTBS).

    Science.gov (United States)

    Shirota, Yuichiro; Dhaka, Suman; Paulus, Walter; Sommer, Martin

    2017-05-22

    Transcranial magnetic stimulation (TMS) with different current directions can activate different sets of neurons. Current direction can also affect the results of repetitive TMS. To test the influence of uni-directional intermittent theta burst stimulation (iTBS) using different current directions, namely posteroanterior (PA) and anteroposterior (AP), on motor behaviour. In a cross-over design, PA- and AP-iTBS was applied over the left primary motor cortex in 19 healthy, right-handed volunteers. Performance of a finger-tapping task was recorded before and 0, 10, 20, and 30min after the iTBS. The task was conducted with the right and left hands separately at each time point. As a control, AP-iTBS with reduced intensity was applied to 14 participants in a separate session (AP weak condition). The finger-tapping count with the left hand was decreased after PA-iTBS. Neither AP- nor AP weak -iTBS altered the performance. Current direction had a significant impact on the after-effects of iTBS. Copyright © 2017 Elsevier B.V. All rights reserved.

  19. Quantum thetas on noncommutative Td with general embeddings

    International Nuclear Information System (INIS)

    Chang-Young, Ee; Kim, Hoil

    2008-01-01

    In this paper, we construct quantum theta functions over noncommutative T d with general embeddings. Manin has constructed quantum theta functions from the lattice embedding into vector space x finite group. We extend Manin's construction of quantum thetas to the case of general embedding of vector space x lattice x torus. It turns out that only for the vector space part of the embedding there exists the holomorphic theta vector, while for the lattice part there does not. Furthermore, the so-called quantum translations from embedding into the lattice part become non-additive, while those from the vector space part are additive

  20. Quantum Thetas on Noncommutative T^d with General Embeddings

    OpenAIRE

    Chang-Young, Ee; Kim, Hoil

    2007-01-01

    In this paper we construct quantum theta functions over noncommutative T^d with general embeddings. Manin has constructed quantum theta functions from the lattice embedding into vector space x finite group. We extend Manin's construction of quantum thetas to the case of general embedding of vector space x lattice x torus. It turns out that only for the vector space part of the embedding there exists the holomorphic theta vector, while for the lattice part there does not. Furthermore, the so-c...

  1. Bosonization in a two-dimensional Riemann Cartan geometry

    International Nuclear Information System (INIS)

    Denardo, G.; Spallucci, E.

    1987-01-01

    We study the vacuum functional for a Dirac field in a two dimensional Riemann-Cartan geometry. Torsion is treated as a quantum variable while the metric is considered as a classical background field. Decoupling spinors from the non-Riemannian part of the geometry introduces a chiral Jacobian into the vacuum generating functional. We compute this functional Jacobian determinant by means of the Alvarez method. Finally, we show that the effective action for the background geometry is of the Liouville type and does not preserve any memory of the initial torsion field. (author)

  2. Quantum Hall effect on Riemann surfaces

    Science.gov (United States)

    Tejero Prieto, Carlos

    2009-06-01

    We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic charge transport on Riemann surfaces, we prove that Hall conductivity is proportional to the intersection product on the first homology group of S and therefore it is quantized. Finally, by using the theory of determinant bundles developed by Bismut, Gillet and Soul, we compute the adiabatic curvature of the spectral bundles defined by the holomorphic Landau levels. We prove that it is given by the polarization of the jacobian variety of the Riemann surface, plus a term depending on the relative analytic torsion.

  3. Quantum Hall effect on Riemann surfaces

    International Nuclear Information System (INIS)

    Tejero Prieto, Carlos

    2009-01-01

    We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic charge transport on Riemann surfaces, we prove that Hall conductivity is proportional to the intersection product on the first homology group of S and therefore it is quantized. Finally, by using the theory of determinant bundles developed by Bismut, Gillet and Soul, we compute the adiabatic curvature of the spectral bundles defined by the holomorphic Landau levels. We prove that it is given by the polarization of the jacobian variety of the Riemann surface, plus a term depending on the relative analytic torsion.

  4. Stage theta pinch experiments

    International Nuclear Information System (INIS)

    Linford, R.K.; Downing, J.N.; Gribble, R.F.; Jacobson, A.R.; Platts, D.A.; Thomas, K.S.

    1975-01-01

    The Staged Theta Pinch program is designed to study the technological and physics problems associated with producing fat plasmas and separating the implosion heating from the adiabatic compression. Several methods of implosion heating are discussed. Circuit diagrams and theoretical magnetic field behavior are described for the STP and resonant heating experiments. (MOW)

  5. Structural stability of solutions to the Riemann problem for a non-strictly hyperbolic system with flux approximation

    Directory of Open Access Journals (Sweden)

    Meina Sun

    2016-05-01

    Full Text Available We study the Riemann problem for a non-strictly hyperbolic system of conservation laws under the linear approximations of flux functions with three parameters. The approximated system also belongs to the type of triangular systems of conservation laws and this approximation does not change the structure of Riemann solutions to the original system. Furthermore, it is proven that the Riemann solutions to the approximated system converge to the corresponding ones to the original system as the perturbation parameter tends to zero.

  6. Improvement of language functions in a chronic non-fluent post-stroke aphasic patient following bilateral sequential theta burst magnetic stimulation.

    Science.gov (United States)

    Vuksanović, Jasmina; Jelić, Milan B; Milanović, Sladjan D; Kačar, Katarina; Konstantinović, Ljubica; Filipović, Saša R

    2015-01-01

    In chronic non-fluent aphasia patients, inhibition of the intact right hemisphere (RH), by transcranial magnetic stimulation (TMS) or similar methods, can induce improvement in language functions. The supposed mechanism behind this improvement is a release of preserved left hemisphere (LH) language networks from RH transcallosal inhibition. Direct stimulation of the damaged LH can sometimes bring similar results too. Therefore, we developed a novel treatment approach that combined direct LH (Broca's area (BA)) stimulation, by intermittent theta burst stimulation (TBS), with homologue RH area's inhibition, by continuous TBS. We present the results of application of 15 daily sessions of the described treatment approach in a right-handed patient with chronic post-stroke non-fluent aphasia. The intervention appeared to improve several language functions, but most notably propositional speech, semantic fluency, short-term verbal memory, and verbal learning. Bilateral TBS modulation of activation of the language-related areas of both hemispheres seems to be a feasible and promising way to induce recovery in chronic aphasic patients. Due to potentially cumulative physiological effects of bilateral stimulation, the improvements may be even greater than following unilateral interventions.

  7. Gaussian curvature on hyperelliptic Riemann surfaces

    Indian Academy of Sciences (India)

    Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 2, May 2014, pp. 155–167. c Indian Academy of Sciences. Gaussian curvature on hyperelliptic Riemann surfaces. ABEL CASTORENA. Centro de Ciencias Matemáticas (Universidad Nacional Autónoma de México,. Campus Morelia) Apdo. Postal 61-3 Xangari, C.P. 58089 Morelia,.

  8. Conformal deformation of Riemann space and torsion

    International Nuclear Information System (INIS)

    Pyzh, V.M.

    1981-01-01

    Method for investigating conformal deformations of Riemann spaces using torsion tensor, which permits to reduce the second ' order equations for Killing vectors to the system of the first order equations, is presented. The method is illustrated using conformal deformations of dimer sphere as an example. A possibility of its use when studying more complex deformations is discussed [ru

  9. Study Paths, Riemann Surfaces, and Strebel Differentials

    Science.gov (United States)

    Buser, Peter; Semmler, Klaus-Dieter

    2017-01-01

    These pages aim to explain and interpret why the late Mika Seppälä, a conformal geometer, proposed to model student study behaviour using concepts from conformal geometry, such as Riemann surfaces and Strebel differentials. Over many years Mika Seppälä taught online calculus courses to students at Florida State University in the United States, as…

  10. Hysteresis rarefaction in the Riemann problem

    Czech Academy of Sciences Publication Activity Database

    Krejčí, Pavel

    2008-01-01

    Roč. 138, - (2008), s. 1-10 ISSN 1742-6588. [International Workshop on Multi-Rate Processes and Hysteresis. Cork , 31.03.2008-05.04.2008] Institutional research plan: CEZ:AV0Z10190503 Keywords : Preisach hysteresis * Riemann problem Subject RIV: BA - General Mathematics http://iopscience.iop.org/1742-6596/138/1/012010

  11. Generalized Riemann problem for reactive flows

    International Nuclear Information System (INIS)

    Ben-Artzi, M.

    1989-01-01

    A generalized Riemann problem is introduced for the equations of reactive non-viscous compressible flow in one space dimension. Initial data are assumed to be linearly distributed on both sides of a jump discontinuity. The resolution of the singularity is studied and the first-order variation (in time) of flow variables is given in exact form. copyright 1989 Academic Press, Inc

  12. Staged theta pinch experiments

    International Nuclear Information System (INIS)

    Linford, R.K.; Downing, J.N.; Gribble, R.F.; Jacobson, A.R.; Platts, D.A.; Thomas, K.S.

    1976-01-01

    Two implosion heating circuits are being experimentally tested. The principal experiment in the program is the 4.5-m-long Staged Theta Pinch (STP). It uses two relatively low energy (50kJ and 100 kJ), high voltage (125 kV) capacitor banks to produce the theta pinch plasma inside the 20 cm i.d. quartz discharge tube. A lower voltage (50 kV), higher energy (750 kJ) capacitor bank is used to contain the plasma and provide a variable amount of adiabatic compression. Because the experiment produces a higher ratio of implosion heating to compressional heating than conventional theta pinches, it should be capable of producing high temperature plasmas with a much larger ratio of plasma radius to discharge tube radius than has been possible in the past. The Resonant Heating Experiment (RHX) in its initial configuration is the same as a 0.9-m-long section of the high voltage part of the STP experiment and all the plasma results here were obtained with the experiment in that configuration. Part of the implosion bank will be removed and a low inductance crowbar added to convert it to the resonant heating configuration. (U.K.)

  13. SO(N) WZNW models on higher-genus Riemann surfaces

    International Nuclear Information System (INIS)

    Alimohammadi, M.; Arfaei, H.; Bonn Univ.

    1993-08-01

    With the help of the string functions and fusion rules of SO(2N) 1 , we show that the results on SU(N) 1 correlators on higher-genus Riemann surfaces (HGRS) can be extended to the SO(2N) 1 and other level-one simply-laced WZNW models. Using modular invariance and factorization properties of Green functions we find multipoint correlators of primary and descendant fields of SO(2N+1) 1 WZNW models on higher genus Riemann surfaces. (orig.)

  14. Reassessing Riemann's paper on the number of primes less than a given magnitude

    CERN Document Server

    Dittrich, Walter

    2018-01-01

    In this book, the author pays tribute to Bernhard Riemann (1826–1866), mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. This book concentrates in particular on Riemann’s only work on prime numbers, including such then new ideas as analytical continuation in the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta function is presented. The impact of Riemann’s ideas on regularizing infinite values in field theory is also emphasized.

  15. Reversed Effects of Intermittent Theta Burst Stimulation following Motor Training That Vary as a Function of Training-Induced Changes in Corticospinal Excitability

    Directory of Open Access Journals (Sweden)

    Tino Stöckel

    2015-01-01

    Full Text Available Intermittent theta burst stimulation (iTBS has the potential to enhance corticospinal excitability (CSE and subsequent motor learning. However, the effects of iTBS following motor learning are unknown. The purpose of the present study was to explore the effect of iTBS on CSE and performance following motor learning. Therefore twenty-four healthy participants practiced a ballistic motor task for a total of 150 movements. iTBS was subsequently applied to the trained motor cortex (STIM group or the vertex (SHAM group. Performance and CSE were assessed before motor learning and before and after iTBS. Training significantly increased performance and CSE in both groups. In STIM group participants, subsequent iTBS significantly reduced motor performance with smaller reductions in CSE. CSE changes as a result of motor learning were negatively correlated with both the CSE changes and performance changes as a result of iTBS. No significant effects of iTBS were found for SHAM group participants. We conclude that iTBS has the potential to degrade prior motor learning as a function of training-induced CSE changes. That means the expected LTP-like effects of iTBS are reversed following motor learning.

  16. Reversed Effects of Intermittent Theta Burst Stimulation following Motor Training That Vary as a Function of Training-Induced Changes in Corticospinal Excitability.

    Science.gov (United States)

    Stöckel, Tino; Summers, Jeffery J; Hinder, Mark R

    2015-01-01

    Intermittent theta burst stimulation (iTBS) has the potential to enhance corticospinal excitability (CSE) and subsequent motor learning. However, the effects of iTBS following motor learning are unknown. The purpose of the present study was to explore the effect of iTBS on CSE and performance following motor learning. Therefore twenty-four healthy participants practiced a ballistic motor task for a total of 150 movements. iTBS was subsequently applied to the trained motor cortex (STIM group) or the vertex (SHAM group). Performance and CSE were assessed before motor learning and before and after iTBS. Training significantly increased performance and CSE in both groups. In STIM group participants, subsequent iTBS significantly reduced motor performance with smaller reductions in CSE. CSE changes as a result of motor learning were negatively correlated with both the CSE changes and performance changes as a result of iTBS. No significant effects of iTBS were found for SHAM group participants. We conclude that iTBS has the potential to degrade prior motor learning as a function of training-induced CSE changes. That means the expected LTP-like effects of iTBS are reversed following motor learning.

  17. Mapping the after-effects of theta burst stimulation on the human auditory cortex with functional imaging.

    Science.gov (United States)

    Andoh, Jamila; Zatorre, Robert J

    2012-09-12

    Auditory cortex pertains to the processing of sound, which is at the basis of speech or music-related processing. However, despite considerable recent progress, the functional properties and lateralization of the human auditory cortex are far from being fully understood. Transcranial Magnetic Stimulation (TMS) is a non-invasive technique that can transiently or lastingly modulate cortical excitability via the application of localized magnetic field pulses, and represents a unique method of exploring plasticity and connectivity. It has only recently begun to be applied to understand auditory cortical function. An important issue in using TMS is that the physiological consequences of the stimulation are difficult to establish. Although many TMS studies make the implicit assumption that the area targeted by the coil is the area affected, this need not be the case, particularly for complex cognitive functions which depend on interactions across many brain regions. One solution to this problem is to combine TMS with functional Magnetic resonance imaging (fMRI). The idea here is that fMRI will provide an index of changes in brain activity associated with TMS. Thus, fMRI would give an independent means of assessing which areas are affected by TMS and how they are modulated. In addition, fMRI allows the assessment of functional connectivity, which represents a measure of the temporal coupling between distant regions. It can thus be useful not only to measure the net activity modulation induced by TMS in given locations, but also the degree to which the network properties are affected by TMS, via any observed changes in functional connectivity. Different approaches exist to combine TMS and functional imaging according to the temporal order of the methods. Functional MRI can be applied before, during, after, or both before and after TMS. Recently, some studies interleaved TMS and fMRI in order to provide online mapping of the functional changes induced by TMS. However, this

  18. On Lovelock analogs of the Riemann tensor

    Science.gov (United States)

    Camanho, Xián O.; Dadhich, Naresh

    2016-03-01

    It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.

  19. Large chiral diffeomorphisms on Riemann surfaces and W-algebras

    International Nuclear Information System (INIS)

    Bandelloni, G.; Lazzarini, S.

    2006-01-01

    The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented through a Becchi-Rouet-Stora (BRS) formulation (for a given order of truncation) leading to a more algebraic setup. In this context the ghost fields behave as holomorphically covariant jets. Subsequently, the link with the so-called W-algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones. We give a general solution with the help of the structure functions pertaining to all the possible truncations lower or equal to the given order. This provides another contribution to the relationship between Korteweg-de Vries (KdV) flows and W-diffeomorphims

  20. The KZB equations on Riemann surfaces

    OpenAIRE

    Felder, Giovanni

    1996-01-01

    In this paper, based on the author's lectures at the 1995 les Houches Summer school, explicit expressions for the Friedan--Shenker connection on the vector bundle of WZW conformal blocks on the moduli space of curves with tangent vectors at $n$ marked points are given. The covariant derivatives are expressed in terms of ``dynamical $r$-matrices'', a notion borrowed from integrable systems. The case of marked points moving on a fixed Riemann surface is studied more closely. We prove a universa...

  1. Arc Length Coding by Interference of Theta Frequency Oscillations May Underlie Context-Dependent Hippocampal Unit Data and Episodic Memory Function

    Science.gov (United States)

    Hasselmo, Michael E.

    2007-01-01

    Many memory models focus on encoding of sequences by excitatory recurrent synapses in region CA3 of the hippocampus. However, data and modeling suggest an alternate mechanism for encoding of sequences in which interference between theta frequency oscillations encodes the position within a sequence based on spatial arc length or time. Arc length…

  2. Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

    Science.gov (United States)

    Bender, Carl M.; Brody, Dorje C.

    2018-04-01

    The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.

  3. Jacob's ladders, Riemann's oscillators, quotient of two oscillating multiforms and set of metamorphoses of this system

    OpenAIRE

    Moser, Jan

    2015-01-01

    In this paper we introduce complicated oscillating system, namely quotient of two multiforms based on Riemann-Siegel formula. We prove that there is an infinite set of metamorphoses of this system (=chrysalis) on critical line $\\sigma=\\frac 12$ into a butterfly (=infinite series of M\\" obius functions in the region of absolute convergence $\\sigma>1$).

  4. Post-Quantum Cryptography: Riemann Primitives and Chrysalis

    OpenAIRE

    Malloy, Ian; Hollenbeck, Dennis

    2018-01-01

    The Chrysalis project is a proposed method for post-quantum cryptography using the Riemann sphere. To this end, Riemann primitives are introduced in addition to a novel implementation of this new method. Chrysalis itself is the first cryptographic scheme to rely on Holomorphic Learning with Errors, which is a complex form of Learning with Errors relying on the Gauss Circle Problem within the Riemann sphere. The principle security reduction proposed by this novel cryptographic scheme applies c...

  5. Inverse Scattering, the Coupling Constant Spectrum, and the Riemann Hypothesis

    International Nuclear Information System (INIS)

    Khuri, N. N.

    2002-01-01

    It is well known that the s-wave Jost function for a potential, λV, is an entire function of λ with an infinite number of zeros extending to infinity. For a repulsive V, and at zero energy, these zeros of the 'coupling constant', λ, will all be real and negative, λ n (0) n n =1/2+iγ n . Thus, finding a repulsive V whose coupling constant spectrum coincides with the Riemann zeros will establish the Riemann hypothesis, but this will be a very difficult and unguided search.In this paper we make a significant enlargement of the class of potentials needed for a generalization of the above idea. We also make this new class amenable to construction via inverse scattering methods. We show that all one needs is a one parameter class of potentials, U(s;x), which are analytic in the strip, 0≤Res≤1, Ims>T 0 , and in addition have an asymptotic expansion in powers of [s(s-1)] -1 , i.e. U(s;x)=V 0 (x)+gV 1 (x)+g 2 V 2 (x)+...+O(g N ), with g=[s(s-1)] -1 . The potentials V n (x) are real and summable. Under suitable conditions on the V n 's and the O(g N ) term we show that the condition, ∫ 0 ∞ vertical bar f 0 (x) vertical bar 2 V 1 (x) dx≠0, where f 0 is the zero energy and g=0 Jost function for U, is sufficient to guarantee that the zeros g n are real and, hence, s n =1/2+iγ n , for γ n ≥T 0 .Starting with a judiciously chosen Jost function, M(s,k), which is constructed such that M(s,0) is Riemann's ξ(s) function, we have used inverse scattering methods to actually construct a U(s;x) with the above properties. By necessity, we had to generalize inverse methods to deal with complex potentials and a nonunitary S-matrix. This we have done at least for the special cases under consideration.For our specific example, ∫ 0 ∞ vertical bar f 0 (x) vertical bar 2 V 1 (x) dx=0 and, hence, we get no restriction on Img n or Res n . The reasons for the vanishing of the above integral are given, and they give us hints on what one needs to proceed further. The problem

  6. Resolution improvement by nonconfocal theta microscopy.

    Science.gov (United States)

    Lindek, S; Stelzer, E H

    1999-11-01

    We present a novel scanning fluorescence microscopy technique, nonconfocal theta microscopy (NCTM), that provides almost isotropic resolution. In NCTM, multiphoton absorption from two orthogonal illumination directions is used to induce fluorescence emission. Therefore the point-spread function of the microscope is described by the product of illumination point-spread functions with reduced spatial overlap, which provides the resolution improvement and the more isotropic observation volume. We discuss the technical details of this new method.

  7. Riemann monodromy problem and conformal field theories

    International Nuclear Information System (INIS)

    Blok, B.

    1989-01-01

    A systematic analysis of the use of the Riemann monodromy problem for determining correlators (conformal blocks) on the sphere is presented. The monodromy data is constructed in terms of the braid matrices and gives a constraint on the noninteger part of the conformal dimensions of the primary fields. To determine the conformal blocks we need to know the order of singularities. We establish a criterion which tells us when the knowledge of the conformal dimensions of primary fields suffice to determine the blocks. When zero modes of the extended algebra are present the analysis is more difficult. In this case we give a conjecture that works for the SU(2) WZW case. (orig.)

  8. Cortical theta wanes for language.

    Science.gov (United States)

    Hermes, Dora; Miller, Kai J; Vansteensel, Mariska J; Edwards, Erik; Ferrier, Cyrille H; Bleichner, Martin G; van Rijen, Peter C; Aarnoutse, Erik J; Ramsey, Nick F

    2014-01-15

    The role of low frequency oscillations in language areas is not yet understood. Using ECoG in six human subjects, we studied whether different language regions show prominent power changes in a specific rhythm, in similar manner as the alpha rhythm shows the most prominent power changes in visual areas. Broca's area and temporal language areas were localized in individual subjects using fMRI. In these areas, the theta rhythm showed the most pronounced power changes and theta power decreased significantly during verb generation. To better understand the role of this language-related theta decrease, we then studied the interaction between low frequencies and local neuronal activity reflected in high frequencies. Amplitude-amplitude correlations showed that theta power correlated negatively with high frequency activity, specifically across verb generation trials. Phase-amplitude coupling showed that during control trials, high frequency power was coupled to theta phase, but this coupling decreased significantly during verb generation trials. These results suggest a dynamic interaction between the neuronal mechanisms underlying the theta rhythm and local neuronal activity in language areas. As visual areas show a pronounced alpha rhythm that may reflect pulsed inhibition, language regions show a pronounced theta rhythm with highly similar features. © 2013.

  9. Quantum field theory on higher-genus Riemann surfaces

    International Nuclear Information System (INIS)

    Kubo, Reijiro; Yoshii, Hisahiro; Ojima, Shuichi; Paul, S.K.

    1989-07-01

    Quantum field theory for b-c systems is formulated on Riemann surfaces with arbitrary genus. We make use of the formalism recently developed by Krichever and Novikov. Hamiltonian is defined properly, and the Ward-Takahashi identities are derived on higher-genus Riemann surfaces. (author)

  10. Non-abelian bosonization in higher genus Riemann surfaces

    International Nuclear Information System (INIS)

    Koh, I.G.; Yu, M.

    1988-01-01

    We propose a generalization of the character formulas of the SU(2) Kac-Moody algebra to higher genus Riemann surfaces. With this construction, we show that the modular invariant partition funciton of the SO(4) k = 1 Wess-Zumino model is equivalent, in arbitrary genus Riemann surfaces, to that of free fermion theory. (orig.)

  11. Collisionless analogs of Riemann S ellipsoids with halo

    International Nuclear Information System (INIS)

    Abramyan, M.G.

    1987-01-01

    A spheroidal halo ensures equilibrium of the collisionless analogs of the Riemann S ellipsoids with oscillations of the particles along the direction of their rotation. Sequences of collisionless triaxial ellipsoids begin and end with dynamically stable members of collisionless embedded spheroids. Both liquid and collisionless Riemann S ellipsoids with weak halo have properties that resemble those of bars of SB galaxies

  12. A Riemann problem with small viscosity and dispersion

    Directory of Open Access Journals (Sweden)

    Kayyunnapara Thomas Joseph

    2006-09-01

    Full Text Available In this paper we prove existence of global solutions to a hyperbolic system in elastodynamics, with small viscosity and dispersion terms and derive estimates uniform in the viscosity-dispersion parameters. By passing to the limit, we prove the existence of solution the Riemann problem for the hyperbolic system with arbitrary Riemann data.

  13. Impairment of cognitive function and synaptic plasticity associated with alteration of information flow in theta and gamma oscillations in melamine-treated rats.

    Directory of Open Access Journals (Sweden)

    Xiaxia Xu

    Full Text Available Changes of neural oscillations at a variety of physiological rhythms are effectively associated with cognitive performance. The present study investigated whether the directional indices of neural information flow (NIF could be used to symbolize the synaptic plasticity impairment in hippocampal CA3-CA1 network in a rat model of melamine. Male Wistar rats were employed while melamine was administered at a dose of 300 mg/kg/day for 4 weeks. Behavior was measured by the Morris water maze(MWMtest. Local field potentials (LFPs were recorded before long-term potentiation (LTP induction. Generalized partial directed coherence (gPDC and phase-amplitude coupling conditional mutual information (PAC_CMI were used to measure the unidirectional indices in both theta and low gamma oscillations (LG, ~ 30-50 Hz. Our results showed that melamine induced the cognition deficits consistent with the reduced LTP in CA1 area. Phase locking values (PLVs showed that the synchronization between CA3 and CA1 in both theta and LG rhythms was reduced by melamine. In both theta and LG rhythms, unidirectional indices were significantly decreased in melamine treated rats while a similar variation trend was observed in LTP reduction, implying that the effects of melamine on cognitive impairment were possibly mediated via profound alterations of NIF on CA3-CA1 pathway in hippocampus. The results suggested that LFPs activities at these rhythms were most likely involved in determining the alterations of information flow in the hippocampal CA3-CA1 network, which might be associated with the alteration of synaptic transmission to some extent.

  14. E-string theory on Riemann surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Hee-Cheol; Vafa, Cumrun [Jefferson Physical Laboratory, Harvard University, Cambridge, MA (United States); Razamat, Shlomo S. [Physics Department, Technion, Haifa (Israel); Zafrir, Gabi [Kavli IPMU (WPI), UTIAS, the University of Tokyo, Kashiwa, Chiba (Japan)

    2018-01-15

    We study compactifications of the 6d E-string theory, the theory of a small E{sub 8} instanton, to four dimensions. In particular we identify N = 1 field theories in four dimensions corresponding to compactifications on arbitrary Riemann surfaces with punctures and with arbitrary non-abelian flat connections as well as fluxes for the abelian sub-groups of the E{sub 8} flavor symmetry. This sheds light on emergent symmetries in a number of 4d N = 1 SCFTs (including the 'E7 surprise' theory) as well as leads to new predictions for a large number of 4-dimensional exceptional dualities and symmetries. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  15. Moduli of Riemann surfaces, transcendental aspects

    International Nuclear Information System (INIS)

    Hain, R.

    2000-01-01

    These notes are an informal introduction to moduli spaces of compact Riemann surfaces via complex analysis, topology and Hodge Theory. The prerequisites for the first lecture are just basic complex variables, basic Riemann surface theory up to at least the Riemann-Roch formula, and some algebraic topology, especially covering space theory. The first lecture covers moduli in genus 0 and genus 1 as these can be understood using relatively elementary methods, but illustrate many of the points which arise in higher genus. The notes cover more material than was covered in the lectures, and sometimes the order of topics in the notes differs from that in the lectures. We have seen in genus 1 case that M 1 is the quotient Γ 1 /X 1 of a contractible complex manifold X 1 = H by a discrete group Γ 1 = SL 2 (Z). The action of Γ 1 on X 1 is said to be virtually free - that is, Γ 1 has a finite index subgroup which acts (fixed point) freely on X 1 . In this section we will generalize this to all g >= 1 - we will sketch a proof that there is a contractible complex manifold Xg, called Teichmueller space, and a group Γ g , called the mapping class group, which acts virtually freely on X g . The moduli space of genus g compact Riemann surfaces is the quotient: M g = Γ g /X g . This will imply that M g has the structure of a complex analytic variety with finite quotient singularities. Teichmueller theory is a difficult and technical subject. Because of this, it is only possible to give an overview. In this lecture, we compute the orbifold Picard group of M g for all g >= 1. Recall that an orbifold line bundle over M g is a holomorphic line bundle L over Teichmueller space X g together with an action of the mapping class group Γ g on it such that the projection L → X g is Γ g -equivariant. An orbifold section of this line bundle is a holomorphic Γ g -equivariant section X g → L of L. This is easily seen to be equivalent to fixing a level l>= 3 and considering holomorphic

  16. Transformation optics with artificial Riemann sheets

    Science.gov (United States)

    Xu, Lin; Chen, Huanyang

    2013-11-01

    The two original versions of ‘invisibility’ cloaks (Leonhardt 2006 Science 312 1777-80 and Pendry et al 2006 Science 312 1780-2) show perfect cloaking but require unphysical singularities in material properties. A non-Euclidean version of cloaking (Leonhardt 2009 Science 323 110-12) was later presented to address these problems, using a very complicated non-Euclidean geometry. In this work, we combine the two original approaches to transformation optics into a more general concept: transformation optics with artificial Riemann sheets. Our method is straightforward and can be utilized to design new kinds of cloaks that can work not only in the realm of geometric optics but also using wave optics. The physics behind this design is similar to that of the conformal cloak for waves. The resonances in the interior region make the phase delay disappear and induce the cloaking effect. Numerical simulations confirm our theoretical results.

  17. Transformation optics with artificial Riemann sheets

    International Nuclear Information System (INIS)

    Xu, Lin; Chen, Huanyang

    2013-01-01

    The two original versions of ‘invisibility’ cloaks (Leonhardt 2006 Science 312 1777–80 and Pendry et al 2006 Science 312 1780–2) show perfect cloaking but require unphysical singularities in material properties. A non-Euclidean version of cloaking (Leonhardt 2009 Science 323 110–12) was later presented to address these problems, using a very complicated non-Euclidean geometry. In this work, we combine the two original approaches to transformation optics into a more general concept: transformation optics with artificial Riemann sheets. Our method is straightforward and can be utilized to design new kinds of cloaks that can work not only in the realm of geometric optics but also using wave optics. The physics behind this design is similar to that of the conformal cloak for waves. The resonances in the interior region make the phase delay disappear and induce the cloaking effect. Numerical simulations confirm our theoretical results. (paper)

  18. From Riemann to differential geometry and relativity

    CERN Document Server

    Papadopoulos, Athanase; Yamada, Sumio

    2017-01-01

    This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.

  19. From Euclidean to Minkowski space with the Cauchy-Riemann equations

    International Nuclear Information System (INIS)

    Gimeno-Segovia, Mercedes; Llanes-Estrada, Felipe J.

    2008-01-01

    We present an elementary method to obtain Green's functions in non-perturbative quantum field theory in Minkowski space from Green's functions calculated in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes often is unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore, we suggest to use the Cauchy-Riemann equations, which perform the analytical continuation without assuming global information on the function in the entire complex plane, but only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge quantum chromodynamics, which is known from lattice and Dyson-Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy-Riemann equations against high-frequency noise,which makes it difficult to achieve good accuracy. We also point out a few curious details related to the Wick rotation. (orig.)

  20. Distinct slow and fast cortical theta dynamics in episodic memory retrieval.

    Science.gov (United States)

    Pastötter, Bernhard; Bäuml, Karl-Heinz T

    2014-07-01

    Brain oscillations in the theta frequency band (3-8 Hz) have been shown to be critically involved in human episodic memory retrieval. In prior work, both positive and negative relationships between cortical theta power and retrieval success have been reported. This study examined the hypothesis that slow and fast cortical theta oscillations at the edges of the traditional theta frequency band are differentially related to retrieval success. Scalp EEG was recorded in healthy human participants as they performed a cued-recall episodic memory task. Slow (~3 Hz) and fast (~7 Hz) theta oscillations at retrieval were examined as a function of whether an item was recalled or not and as a function of the items' output position at test. Recall success typically declines with output position, due to increases in interference level. The results showed that slow theta power was positively related but fast theta power was negatively related to retrieval success. Concurrent positive and negative episodic memory effects for slow and fast theta oscillations were dissociable in time and space, showing different time courses and different spatial locations on the scalp. Moreover, fast theta power increased from early to late output positions, whereas slow theta power was unaffected by items' output position. Together with prior work, the results suggest that slow and fast theta oscillations have distinct functional roles in episodic memory retrieval, with slow theta oscillations being related to processes of recollection and conscious awareness, and fast theta oscillations being linked to processes of interference and interference resolution. Copyright © 2014 Elsevier Inc. All rights reserved.

  1. Riemann zeros and phase transitions via the spectral operator on fractal strings

    International Nuclear Information System (INIS)

    Herichi, Hafedh; Lapidus, Michel L

    2012-01-01

    The spectral operator was introduced by Lapidus and van Frankenhuijsen (2006 Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings) in their reinterpretation of the earlier work of Lapidus and Maier (1995 J. Lond. Math. Soc. 52 15–34) on inverse spectral problems and the Riemann hypothesis. In essence, it is a map that sends the geometry of a fractal string onto its spectrum. In this review, we present the rigorous functional analytic framework given by Herichi and Lapidus (2012) and within which to study the spectral operator. Furthermore, we give a necessary and sufficient condition for the invertibility of the spectral operator (in the critical strip) and therefore obtain a new spectral and operator-theoretic reformulation of the Riemann hypothesis. More specifically, we show that the spectral operator is quasi-invertible (or equivalently, that its truncations are invertible) if and only if the Riemann zeta function ζ(s) does not have any zeros on the vertical line Re(s) = c. Hence, it is not invertible in the mid-fractal case when c= 1/2 , and it is quasi-invertible everywhere else (i.e. for all c ∈ (0, 1) with c≠ 1/2 ) if and only if the Riemann hypothesis is true. We also show the existence of four types of (mathematical) phase transitions occurring for the spectral operator at the critical fractal dimension c= 1/2 and c = 1 concerning the shape of the spectrum, its boundedness, its invertibility as well as its quasi-invertibility. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (review)

  2. Riemann-Hilbert treatment of Liouville theory on the torus: the general case

    International Nuclear Information System (INIS)

    Menotti, Pietro

    2011-01-01

    We extend the previous treatment of Liouville theory on the torus to the general case in which the distribution of charges is not necessarily symmetric. This requires the concept of Fuchsian differential equation on Riemann surfaces. We show through a group theoretic argument that the Heun parameter and a weight constant are sufficient to satisfy all monodromy conditions. We then apply the technique of differential equations on a Riemann surface to the two-point function on the torus in which one source is arbitrary and the other small. As a byproduct, we give in terms of quadratures the exact Green function on the square and on the rhombus with opening angle 2π/6 in the background of the field generated by an arbitrary charge.

  3. Long-term plasticity is proportional to theta-activity.

    Directory of Open Access Journals (Sweden)

    Marian Tsanov

    Full Text Available BACKGROUND: Theta rhythm in the hippocampal formation is a main feature of exploratory behaviour and is believed to enable the encoding of new spatial information and the modification of synaptic weights. Cyclic changes of dentate gyrus excitability during theta rhythm are related to its function, but whether theta epochs per se are able to alter network properties of dentate gyrus for long time-periods is still poorly understood. METHODOLOGY/PRINCIPAL FINDINGS: We used low-frequency stimulation protocols that amplify the power of endogenous theta oscillations, in order to estimate the plasticity effect of endogenous theta oscillations on a population level. We found that stimulation-induced augmentation of the theta rhythm is linked to a subsequent increase of neuronal excitability and decrease of the synaptic response. This EPSP-to-Spike uncoupling is related to an increased postsynaptic spiking on the positive phases of theta frequency oscillations. Parallel increase of the field EPSP slope and the population spike occurs only after concurrent pre- and postsynaptic activation. Furthermore, we observed that long-term potentiation (>24 h occurs in the dentate gyrus of freely behaving adult rats after phasic activity of entorhinal afferents in the theta-frequency range. This plasticity is proportional to the field bursting activity of granule cells during the stimulation, and may comprise a key step in spatial information transfer. Long-term potentiation of the synaptic component occurs only when the afferent stimulus precedes the evoked population burst, and is input-specific. CONCLUSIONS/SIGNIFICANCE: Our data confirm the role of the dentate gyrus in filtering information to the subsequent network during the activated state of the hippocampus.

  4. Theta power is reduced in healthy cognitive aging.

    Science.gov (United States)

    Cummins, Tarrant D R; Finnigan, Simon

    2007-10-01

    The effects of healthy cognitive aging on electroencephalographic (EEG) theta (4.9-6.8 Hz) power were examined during performance of a modified Sternberg, S., 1966. High-speed scanning in human memory. Science 153, 652-654.) word recognition task. In a sample of fourteen young (mean age 21.9 years, range=18-27) and fourteen older (mean age 68.4 years, range=60-80) participants, theta power was found to be significantly lower in older adults during both the retention and recognition intervals. This theta power difference was greatest at the fronto-central midline electrode and occurred in parallel with a small, non-significant decrease in recognition accuracy in the older sample. A significant decrease in older adults' mean theta power was also observed in resting EEG, however, it was of substantially smaller magnitude than the task-related theta difference. It is proposed that a neurophysiological measure(s), such as task-specific frontal midline theta (fmtheta) power, may be a more sensitive marker of cognitive aging than task performance measures. Furthermore, as recent research indicates that fmtheta is generated primarily in the anterior cingulate cortex, the current findings support evidence that the function of brain networks incorporating this structure may be affected in cognitive aging.

  5. A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation

    Directory of Open Access Journals (Sweden)

    Abdon Atangana

    2014-01-01

    Full Text Available The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions u as function of time and space. The function u accounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method.

  6. Integrable equations, addition theorems, and the Riemann-Schottky problem

    International Nuclear Information System (INIS)

    Buchstaber, Viktor M; Krichever, I M

    2006-01-01

    The classical Weierstrass theorem claims that, among the analytic functions, the only functions admitting an algebraic addition theorem are the elliptic functions and their degenerations. This survey is devoted to far-reaching generalizations of this result that are motivated by the theory of integrable systems. The authors discovered a strong form of the addition theorem for theta functions of Jacobian varieties, and this form led to new approaches to known problems in the geometry of Abelian varieties. It is shown that strong forms of addition theorems arise naturally in the theory of the so-called trilinear functional equations. Diverse aspects of the approaches suggested here are discussed, and some important open problems are formulated.

  7. Theta variation and spatiotemporal scaling along the septotemporal axis of the hippocampus

    Directory of Open Access Journals (Sweden)

    Lauren L Long

    2015-03-01

    Full Text Available Hippocampal theta has been related to locomotor speed, attention, anxiety, sensorimotor integration and memory among other emergent phenomena. One difficulty in understanding the function of theta is that the hippocampus (HPC modulates voluntary behavior at the same time that it processes sensory input. Both functions are correlated with characteristic changes in theta indices. The current review highlights a series of studies examining theta local field potential (LFP signals across the septotemporal or longitudinal axis of the HPC. While the theta signal is coherent throughout the entirety of the HPC, the amplitude, but not the frequency, of theta varies significantly across its three-dimensional expanse. We suggest that the theta signal offers a rich vein of information about how distributed neuronal ensembles support emergent function. Further, we speculate that emergent function across the long axis varies with respect to spatiotemporal scale. Thus, septal hippocampus processes details of the proximal spatiotemporal environment while more temporal aspects process larger spaces and wider time-scales. The degree to which emergent functions are supported by the synchronization of theta across the septotemporal axis is an open question. Our working model is that theta synchrony serves to bind ensembles representing varying resolutions of spatiotemporal information at interdependent septotemporal areas of the HPC. Such synchrony and cooperative interactions along the septotemporal axis likely support memory formation and subsequent consolidation and retrieval.

  8. The Differential-Algebraic Analysis of Symplectic and Lax Structures Related with New Riemann-Type Hydrodynamic Systems

    Science.gov (United States)

    Prykarpatsky, Yarema A.; Artemovych, Orest D.; Pavlov, Maxim V.; Prykarpatski, Anatolij K.

    2013-06-01

    A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic hierarchy, proposed recently by O. D. Artemovych, M. V. Pavlov, Z. Popowicz and A. K. Prykarpatski, is developed. In addition to the Lax-type representation, found before by Z. Popowicz, a closely related representation is constructed in exact form by means of a new differential-functional technique. The bi-Hamiltonian integrability and compatible Poisson structures of the generalized Riemann type hierarchy are analyzed by means of the symplectic and gradient-holonomic methods. An application of the devised differential-algebraic approach to other Riemann and Vakhnenko type hydrodynamic systems is presented.

  9. On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

    Science.gov (United States)

    Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

    2018-01-01

    The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

  10. Fermions on a Riemann surface and the Kadomtsev-Petviashvili equation

    International Nuclear Information System (INIS)

    Zabrodin, A.V.

    1989-01-01

    It is shown that the S matrix of free massless fermions on a Riemann surface of finite genus generates quasiperiodic solutions of the Kadomtsev-Petviashvili equation. An operator that changes the genus of a solution is constructed, and the law of composition of such operators is discussed. The construction is a generalization of the well-known operator approach in the case of soliton solutions to the general case of quasiperiodic τ functions

  11. Two-dimensional time dependent Riemann solvers for neutron transport

    International Nuclear Information System (INIS)

    Brunner, Thomas A.; Holloway, James Paul

    2005-01-01

    A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem

  12. The exchange algebra for Liouville theory on punctured Riemann sphere

    International Nuclear Information System (INIS)

    Shen Jianmin; Sheng Zhengmao

    1991-11-01

    We consider in this paper the classical Liouville field theory on the Riemann sphere with n punctures. In terms of the uniformization theorem of Riemann surface, we show explicitly the classical exchange algebra (CEA) for the chiral components of the Liouville fields. We find that the matrice which dominate the CEA is related to the symmetry of the Lie group SL(n) in a nontrivial manner with n>3. (author). 10 refs

  13. Bernhard Riemann 1826-1866 Turning Points in the Conception of Mathematics

    CERN Document Server

    Laugwitz, Detlef

    2008-01-01

    The name of Bernard Riemann is well known to mathematicians and physicists around the world. College students encounter the Riemann integral early in their studies. Real and complex function theories are founded on Riemann’s work. Einstein’s theory of gravitation would be unthinkable without Riemannian geometry. In number theory, Riemann’s famous conjecture stands as one of the classic challenges to the best mathematical minds and continues to stimulate deep mathematical research. The name is indelibly stamped on the literature of mathematics and physics. This book, originally written in German and presented here in an English-language translation, examines Riemann’s scientific work from a single unifying perspective. Laugwitz describes Riemann’s development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hi...

  14. Robinson manifolds and Cauchy-Riemann spaces

    CERN Document Server

    Trautman, A

    2002-01-01

    A Robinson manifold is defined as a Lorentz manifold (M, g) of dimension 2n >= 4 with a bundle N subset of C centre dot TM such that the fibres of N are maximal totally null and there holds the integrability condition [Sec N, Sec N] subset of Sec N. The real part of N intersection N-bar is a bundle of null directions tangent to a congruence of null geodesics. This generalizes the notion of a shear-free congruence of null geodesics (SNG) in dimension 4. Under a natural regularity assumption, the set M of all these geodesics has the structure of a Cauchy-Riemann manifold of dimension 2n - 1. Conversely, every such CR manifold lifts to many Robinson manifolds. Three definitions of a CR manifold are described here in considerable detail; they are equivalent under the assumption of real analyticity, but not in the smooth category. The distinctions between these definitions have a bearing on the validity of the Robinson theorem on the existence of null Maxwell fields associated with SNGs. This paper is largely a re...

  15. Kinetic description of linear theta-pinch equilibria

    International Nuclear Information System (INIS)

    Batchelor, D.B.; Davidson, R.C.

    1975-01-01

    Equilibrium properties of linear theta-pinch plasmas are studied within the framework of the steady-state (o/x=0) Vlasov-Maxwell equations. The analysis is carried out for an infinitely long plasma column aligned parallel to an externally applied axial magnetic field Bsub(z)sup(ext)esub(z). Equilibrium properties are calculated for the class of rigid-rotor Vlasov equilibria, in which the th component distribution function (Hsub(perpendicular), Psub(theta), upsilonsub(z) depends on perpendicular energy H and canonical angular momentum Psub(theta), exclusively through the linear combination Hsub(perpendicular)-ωsub(j)Psub(theta), where ω;=const.=angular velocity of mean rotation. General equilibrium relations that pertain to the entire class of rigid-rotor Vlasov equilibria are discussed; and specific examples of sharp- and diffuse-boundary equilibrium configurations are considered. Rigid-rotor density and magnetic field profiles are compared with experimentally observed profiles. A general prescription is given for determining the functional dependence of the equilibrium distribution function on Hsub(perpendicular)-ωsub(j)Psub(theta) in circumstances, where the density profile or magnetic field profile is specified. (author)

  16. Eta Products and Theta Series Identities

    CERN Document Server

    Kohler, Gunter

    2011-01-01

    This monograph deals with products of Dedekind's eta function, with Hecke theta series on quadratic number fields, and with "Eisenstein series." The author brings to the public the large number of identities that have been discovered over the past 20 years, the majority of which have not been published elsewhere. This book will be of interest to graduate students and scholars in the field of number theory and, in particular, modular forms. It is not an introductory text in this field. Nevertheless, some theoretical background material is presented that is important for understanding

  17. Power of theta waves in the EEG of human subjects increases during recall of haptic information.

    Science.gov (United States)

    Grunwald, M; Weiss, T; Krause, W; Beyer, L; Rost, R; Gutberlet, I; Gertz, H J

    1999-02-05

    Several studies have reported a functional relationship between spectral power within the theta-band of the EEG (theta-power) and memory load while processing visual or semantic information. We investigated theta power during the processing of different complex haptic stimuli using a delayed recall design. The haptic explorations consisted of palpating the structure of twelve sunken reliefs with closed eyes. Subjects had to reproduce each relief by drawing it 10 s after the end of the exploration. The relationship between mean theta power and mean exploration time was analysed using a regression model. A linear relationship was found between the exploration time and theta power over fronto-central regions (Fp1, Fp2, F3, F7, F8, Fz, C3) directly before the recall of the relief. This result is interpreted in favour of the hypothesis that fronto-central theta power of the EEG correlates with the load of working memory independent of stimulus modality.

  18. Multidimensional Riemann problem with self-similar internal structure - part III - a multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems

    Science.gov (United States)

    Balsara, Dinshaw S.; Nkonga, Boniface

    2017-10-01

    Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The fastest way of endowing such sub-structure consists of making a multidimensional extension of the HLLI Riemann solver for hyperbolic conservation laws. Presenting such a multidimensional analogue of the HLLI Riemann solver with linear sub-structure for use on structured meshes is the goal of this work. The multidimensional MuSIC Riemann solver documented here is universal in the sense that it can be applied to any hyperbolic conservation law. The multidimensional Riemann solver is made to be consistent with constraints that emerge naturally from the Galerkin projection of the self-similar states within the wave model. When the full eigenstructure in both directions is used in the present Riemann solver, it becomes a complete Riemann solver in a multidimensional sense. I.e., all the intermediate waves are represented in the multidimensional wave model. The work also presents, for the very first time, an important analysis of the dissipation characteristics of multidimensional Riemann solvers. The present Riemann solver results in the most efficient implementation of a multidimensional Riemann solver with sub-structure. Because it preserves stationary linearly degenerate waves, it might also help with well-balancing. Implementation-related details are presented in pointwise fashion for the one-dimensional HLLI Riemann solver as well as the multidimensional MuSIC Riemann solver.

  19. Solution of Riemann problem for ideal polytropic dusty gas

    International Nuclear Information System (INIS)

    Nath, Triloki; Gupta, R.K.; Singh, L.P.

    2017-01-01

    Highlights : • A direct approach is used to solve the Riemann problem for dusty ideal polytropic gas. • An analytical solution to the Riemann problem for dusty gas flow is obtained. • The existence and uniqueness of the solution in dusty gas is discussed. • Properties of elementary wave solutions of Riemann problem are discussed. • Effect of mass fraction of solid particles on the solution is presented. - Abstract: The Riemann problem for a quasilinear hyperbolic system of equations governing the one dimensional unsteady flow of an ideal polytropic gas with dust particles is solved analytically without any restriction on magnitude of the initial states. The elementary wave solutions of the Riemann problem, that is shock waves, rarefaction waves and contact discontinuities are derived explicitly and their properties are discussed, for a dusty gas. The existence and uniqueness of the solution for Riemann problem in dusty gas is discussed. Also the conditions leading to the existence of shock waves or simple waves for a 1-family and 3-family curves in the solution of the Riemann problem are discussed. It is observed that the presence of dust particles in an ideal polytropic gas leads to more complex expression as compared to the corresponding ideal case; however all the parallel results remain same. Also, the effect of variation of mass fraction of dust particles with fixed volume fraction (Z) and the ratio of specific heat of the solid particles and the specific heat of the gas at constant pressure on the variation of velocity and density across the shock wave, rarefaction wave and contact discontinuities are discussed.

  20. Conformal fields. From Riemann surfaces to integrable hierarchies

    International Nuclear Information System (INIS)

    Semikhatov, A.M.

    1991-01-01

    I discuss the idea of translating ingredients of conformal field theory into the language of hierarchies of integrable differential equations. Primary conformal fields are mapped into (differential or matrix) operators living on the phase space of the hierarchy, whereas operator insertions of, e.g., a current or the energy-momentum tensor, become certain vector fields on the phase space and thus acquire a meaning independent of a given Riemann surface. A number of similarities are observed between the structures arising on the hierarchy and those of the theory on the world-sheet. In particular, there is an analogue of the operator product algebra with the Cauchy kernel replaced by its 'off-shell' hierarchy version. Also, hierarchy analogues of certain operator insertions admit two (equivalent, but distinct) forms, resembling the 'bosonized' and 'fermionized' versions respectively. As an application, I obtain a useful reformulation of the Virasoro constraints of the type that arise in matrix models, as a system of equations on dressing (or Lax) operators (rather than correlation functions, i.e., residues or traces). This also suggests an interpretation in terms of a 2D topological field theory, which might be extended to a correspondence between Virasoro-constrained hierarchies and topological theories. (orig.)

  1. Riemann solvers and undercompressive shocks of convex FPU chains

    International Nuclear Information System (INIS)

    Herrmann, Michael; Rademacher, Jens D M

    2010-01-01

    We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space–time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We allow the flux to have a turning point, and observe a third type of elementary wave (conservative shocks) in the atomistic simulations. These waves are heteroclinic travelling waves and correspond to non-classical, undercompressive shocks of the p-system. We analyse such shocks for fluxes with one or more turning points. Depending on the convexity properties of the flux we propose FPU-Riemann solvers. Our numerical simulations confirm that Lax shocks are replaced by so-called dispersive shocks. For convex–concave flux we provide numerical evidence that convex FPU chains follow the p-system in generating conservative shocks that are supersonic. For concave–convex flux, however, the conservative shocks of the p-system are subsonic and do not appear in FPU-Riemann solutions

  2. swot: Super W Of Theta

    Science.gov (United States)

    Coupon, Jean; Leauthaud, Alexie; Kilbinger, Martin; Medezinski, Elinor

    2017-07-01

    SWOT (Super W Of Theta) computes two-point statistics for very large data sets, based on “divide and conquer” algorithms, mainly, but not limited to data storage in binary trees, approximation at large scale, parellelization (open MPI), and bootstrap and jackknife resampling methods “on the fly”. It currently supports projected and 3D galaxy auto and cross correlations, galaxy-galaxy lensing, and weighted histograms.

  3. The Riemann problem for the relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation

    Science.gov (United States)

    Shao, Zhiqiang

    2018-04-01

    The relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation is studied. The Riemann problem is solved constructively. The delta shock wave arises in the Riemann solutions, provided that the initial data satisfy some certain conditions, although the system is strictly hyperbolic and the first and third characteristic fields are genuinely nonlinear, while the second one is linearly degenerate. There are five kinds of Riemann solutions, in which four only consist of a shock wave and a centered rarefaction wave or two shock waves or two centered rarefaction waves, and a contact discontinuity between the constant states (precisely speaking, the solutions consist in general of three waves), and the other involves delta shocks on which both the rest mass density and the proper energy density simultaneously contain the Dirac delta function. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy condition, we establish the existence and uniqueness of solutions involving delta shocks for the Riemann problem.

  4. A computational study on altered theta-gamma coupling during learning and phase coding.

    Directory of Open Access Journals (Sweden)

    Xuejuan Zhang

    Full Text Available There is considerable interest in the role of coupling between theta and gamma oscillations in the brain in the context of learning and memory. Here we have used a neural network model which is capable of producing coupling of theta phase to gamma amplitude firstly to explore its ability to reproduce reported learning changes and secondly to memory-span and phase coding effects. The spiking neural network incorporates two kinetically different GABA(A receptor-mediated currents to generate both theta and gamma rhythms and we have found that by selective alteration of both NMDA receptors and GABA(A,slow receptors it can reproduce learning-related changes in the strength of coupling between theta and gamma either with or without coincident changes in theta amplitude. When the model was used to explore the relationship between theta and gamma oscillations, working memory capacity and phase coding it showed that the potential storage capacity of short term memories, in terms of nested gamma-subcycles, coincides with the maximal theta power. Increasing theta power is also related to the precision of theta phase which functions as a potential timing clock for neuronal firing in the cortex or hippocampus.

  5. Impaired theta-gamma coupling during working memory performance in schizophrenia.

    Science.gov (United States)

    Barr, Mera S; Rajji, Tarek K; Zomorrodi, Reza; Radhu, Natasha; George, Tony P; Blumberger, Daniel M; Daskalakis, Zafiris J

    2017-11-01

    Working memory deficits represent a core feature of schizophrenia. These deficits have been associated with dysfunctional dorsolateral prefrontal cortex (DLPFC) cortical oscillations. Theta-gamma coupling describes the modulation of gamma oscillations by theta phasic activity that has been directly associated with the ordering of information during working memory performance. Evaluating theta-gamma coupling may provide greater insight into the neural mechanisms mediating working memory deficits in this disorder. Thirty-eight patients diagnosed with schizophrenia or schizoaffective disorder and 38 healthy controls performed the verbal N-Back task administered at 4 levels, while EEG was recorded. Theta (4-7Hz)-gamma (30-50Hz) coupling was calculated for target and non-target correct trials for each working memory load. The relationship between theta-gamma coupling and accuracy was determined. Theta-gamma coupling was significantly and selectively impaired during correct responses to target letters among schizophrenia patients compared to healthy controls. A significant and positive relationship was found between theta-gamma coupling and 3-Back accuracy in controls, while this relationship was not observed in patients. These findings suggest that impaired theta-gamma coupling contribute to working memory dysfunction in schizophrenia. Future work is needed to evaluate the predictive utility of theta-gamma coupling as a neurophysiological marker for functional outcomes in this disorder. Copyright © 2017. Published by Elsevier B.V.

  6. The fermion boundary condition and the THETA-angle in QED2

    International Nuclear Information System (INIS)

    Hrasko, P.

    1983-09-01

    The order parameter of the Schwinger model is calculated in the Euclidean functional integral approach. It is shown that the symmetry breaking angle THETA is intimately connected to the boundary condition imposed on the fermions. The transition to the Euclidean description involves both imaginary time and imaginary THETA. (author)

  7. BRST quantization of superconformal theories on higher genus Riemann surfaces

    International Nuclear Information System (INIS)

    Leman Kuang

    1992-01-01

    A complex contour integral method is constructed and applied to the Becchi-Rouet-Stora-Tyutin (BRST) quantization procedure of string theories on higher genus Riemann surfaces with N=0 and 1 Krichever-Novikov (KN) algebras. This method makes calculations very simple. It is shown that the critical spacetime dimension of the string theories on a genus-g Riemann surface equals that of the string theories on a genus-zero Riemann surface, and that the 'Regge intercepts' in the genus-g case are α(g)=1-3/4g-9/8g 2 and 1/2-3/4g-17/16g 2 for bosonic strings and superstrings, respectively. (orig.)

  8. Compact Riemann surfaces an introduction to contemporary mathematics

    CERN Document Server

    Jost, Jürgen

    2006-01-01

    Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

  9. Line operators from M-branes on compact Riemann surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Amariti, Antonio [Physics Department, The City College of the CUNY, 160 Convent Avenue, New York, NY 10031 (United States); Orlando, Domenico [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Reffert, Susanne, E-mail: sreffert@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland)

    2016-12-15

    In this paper, we determine the charge lattice of mutually local Wilson and 't Hooft line operators for class S theories living on M5-branes wrapped on compact Riemann surfaces. The main ingredients of our analysis are the fundamental group of the N-cover of the Riemann surface, and a quantum constraint on the six-dimensional theory. The latter plays a central role in excluding some of the possible lattices and imposing consistency conditions on the charges. This construction gives a geometric explanation for the mutual locality among the lines, fixing their charge lattice and the structure of the four-dimensional gauge group.

  10. Investigation of plasma turbulence in a theta-pinch-discharge

    International Nuclear Information System (INIS)

    Lins, G.

    1980-01-01

    This thesis is concerned with investigations of plasma turbulence in a 3 KJ Theta-Pinch during implosion by high-frequency Stark-effect and Thomson scattering. The next points are modifications of electron-distribution function by ionization in low preionizized turbulent plasma and energy losses by particle flow and heat flow at the ends. (HT)

  11. Riemann-Hilbert approach to the time-dependent generalized sine kernel

    Energy Technology Data Exchange (ETDEWEB)

    Kozlowski, K.K.

    2010-12-15

    We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models described by a six-vertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann-Hilbert based analysis. (orig.)

  12. Transmitter release in the neuromuscular synapse of the protein kinase C theta-deficient adult mouse.

    Science.gov (United States)

    Besalduch, Núria; Santafé, Manel M; Garcia, Neus; Gonzalez, Carmen; Tomás, Marta; Tomás, Josep; Lanuza, Maria A

    2011-04-01

    We studied structural and functional features of the neuromuscular junction in adult mice (P30) genetically deficient in the protein kinase C (PKC) theta isoform. Confocal and electron microscopy shows that there are no differences in the general morphology of the endplates between PKC theta-deficient and wild-type (WT) mice. Specifically, there is no difference in the density of the synaptic vesicles. However, the myelin sheath is not as thick in the intramuscular nerve fibers of the PKC theta-deficient mice. We found a significant reduction in the size of evoked endplate potentials and in the frequency of spontaneous, asynchronous, miniature endplate potentials in the PKC theta-deficient neuromuscular preparations in comparison with the WT, but the mean amplitude of the spontaneous potentials is not different. These changes indicate that PKC theta has a presynaptic role in the function of adult neuromuscular synapses. Copyright © 2010 Wiley-Liss, Inc.

  13. Theta dynamics in rat: speed and acceleration across the Septotemporal axis.

    Directory of Open Access Journals (Sweden)

    Lauren L Long

    Full Text Available Theta (6-12 Hz rhythmicity in the local field potential (LFP reflects a clocking mechanism that brings physically isolated neurons together in time, allowing for the integration and segregation of distributed cell assemblies. Variation in the theta signal has been linked to locomotor speed, sensorimotor integration as well as cognitive processing. Previously, we have characterized the relationship between locomotor speed and theta power and how that relationship varies across the septotemporal (long axis of the hippocampus (HPC. The current study investigated the relationship between whole body acceleration, deceleration and theta indices at CA1 and dentate gyrus (DG sites along the septotemporal axis of the HPC in rats. Results indicate that whole body acceleration and deceleration predicts a significant amount of variability in the theta signal beyond variation in locomotor speed. Furthermore, deceleration was more predictive of variation in theta amplitude as compared to acceleration as rats traversed a linear track. Such findings highlight key variables that systematically predict the variability in the theta signal across the long axis of the HPC. A better understanding of the relative contribution of these quantifiable variables and their variation as a function of experience and environmental conditions should facilitate our understanding of the relationship between theta and sensorimotor/cognitive functions.

  14. Patterns of coupled theta activity in amygdala-hippocampal-prefrontal cortical circuits during fear extinction.

    Directory of Open Access Journals (Sweden)

    Jörg Lesting

    Full Text Available Signals related to fear memory and extinction are processed within brain pathways involving the lateral amygdala (LA for formation of aversive stimulus associations, the CA1 area of the hippocampus for context-dependent modulation of these associations, and the infralimbic region of the medial prefrontal cortex (mPFC for extinction processes. While many studies have addressed the contribution of each of these modules individually, little is known about their interactions and how they function as an integrated system. Here we show, by combining multiple site local field potential (LFP and unit recordings in freely behaving mice in a fear conditioning paradigm, that theta oscillations may provide a means for temporally and functionally connecting these modules. Theta oscillations occurred with high specificity in the CA1-LA-mPFC network. Theta coupling increased between all areas during retrieval of conditioned fear, and declined during extinction learning. During extinction recall, theta coupling partly rebounded in LA-mPFC and CA1-mPFC, and remained at a low level in CA1-LA. Interfering with theta coupling through local electrical microstimulation in CA1-LA affected conditioned fear and extinction recall depending on theta phase. These results support the hypothesis that theta coupling provides a means for inter-areal coordination in conditioned behavioral responsiveness. More specifically, theta oscillations seem to contribute to a population code indicating conditioned stimuli during recall of fear memory before and after extinction.

  15. Integrability of Liouville system on high genus Riemann surface: Pt. 1

    International Nuclear Information System (INIS)

    Chen Yixin; Gao Hongbo

    1992-01-01

    By using the theory of uniformization of Riemann-surfaces, we study properties of the Liouville equation and its general solution on a Riemann surface of genus g>1. After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices, we prove the classical integrability of Liouville system on high genus Riemann surface

  16. Oscillatory frontal theta responses are increased upon bisensory stimulation.

    Science.gov (United States)

    Sakowitz, O W; Schürmann, M; Başar, E

    2000-05-01

    To investigate the functional correlation of oscillatory EEG components with the interaction of sensory modalities following simultaneous audio-visual stimulation. In an experimental study (15 subjects) we compared auditory evoked potentials (AEPs) and visual evoked potentials (VEPs) to bimodal evoked potentials (BEPs; simultaneous auditory and visual stimulation). BEPs were assumed to be brain responses to complex stimuli as a marker for intermodal associative functioning. Frequency domain analysis of these EPs showed marked theta-range components in response to bimodal stimulation. These theta components could not be explained by linear addition of the unimodal responses in the time domain. Considering topography the increased theta-response showed a remarkable frontality in proximity to multimodal association cortices. Referring to methodology we try to demonstrate that, even if various behavioral correlates of brain oscillations exist, common patterns can be extracted by means of a systems-theoretical approach. Serving as an example of functionally relevant brain oscillations, theta responses could be interpreted as an indicator of associative information processing.

  17. Movement-related theta rhythm in humans: coordinating self-directed hippocampal learning.

    Directory of Open Access Journals (Sweden)

    Raphael Kaplan

    Full Text Available The hippocampus is crucial for episodic or declarative memory and the theta rhythm has been implicated in mnemonic processing, but the functional contribution of theta to memory remains the subject of intense speculation. Recent evidence suggests that the hippocampus might function as a network hub for volitional learning. In contrast to human experiments, electrophysiological recordings in the hippocampus of behaving rodents are dominated by theta oscillations reflecting volitional movement, which has been linked to spatial exploration and encoding. This literature makes the surprising cross-species prediction that the human hippocampal theta rhythm supports memory by coordinating exploratory movements in the service of self-directed learning. We examined the links between theta, spatial exploration, and memory encoding by designing an interactive human spatial navigation paradigm combined with multimodal neuroimaging. We used both non-invasive whole-head Magnetoencephalography (MEG to look at theta oscillations and Functional Magnetic Resonance Imaging (fMRI to look at brain regions associated with volitional movement and learning. We found that theta power increases during the self-initiation of virtual movement, additionally correlating with subsequent memory performance and environmental familiarity. Performance-related hippocampal theta increases were observed during a static pre-navigation retrieval phase, where planning for subsequent navigation occurred. Furthermore, periods of the task showing movement-related theta increases showed decreased fMRI activity in the parahippocampus and increased activity in the hippocampus and other brain regions that strikingly overlap with the previously observed volitional learning network (the reverse pattern was seen for stationary periods. These fMRI changes also correlated with participant's performance. Our findings suggest that the human hippocampal theta rhythm supports memory by coordinating

  18. On an isospectrality question over compact Riemann surfaces

    International Nuclear Information System (INIS)

    Srinivas Rau, S.

    1990-01-01

    It is proved that for a generic compact Riemann surface X of genus g>1,(i) there are at most 2 2g unitary characters of π 1 (X) whose associated line bundles have laplacians of identical spectrum, (ii) generating cycles for π 1 (X) can be chosen to be closed geodesics whose length multiplicity is 1. (author). 5 refs

  19. Quantum Riemann surfaces. Pt. 2; The discrete series

    Energy Technology Data Exchange (ETDEWEB)

    Klimek, S. (Dept. of Mathematics, IUPUI, Indianapolis, IN (United States)); Lesniewski, A. (Dept. of Physics, Harvard Univ., Cambridge, MA (United States))

    1992-02-01

    We continue our study of noncommutative deformations of two-dimensional hyperbolic manifolds which we initiated in Part I. We construct a sequence of C{sup *}-algebras which are quantizations of a compact Riemann surface of genus g corresponding to special values of the Planck constant. These algebras are direct integrals of finite-dimensional C{sup *}-algebras. (orig.).

  20. Colliding holes in Riemann surfaces and quantum cluster algebras

    Science.gov (United States)

    Chekhov, Leonid; Mazzocco, Marta

    2018-01-01

    In this paper, we describe a new type of surgery for non-compact Riemann surfaces that naturally appears when colliding two holes or two sides of the same hole in an orientable Riemann surface with boundary (and possibly orbifold points). As a result of this surgery, bordered cusps appear on the boundary components of the Riemann surface. In Poincaré uniformization, these bordered cusps correspond to ideal triangles in the fundamental domain. We introduce the notion of bordered cusped Teichmüller space and endow it with a Poisson structure, quantization of which is achieved with a canonical quantum ordering. We give a complete combinatorial description of the bordered cusped Teichmüller space by introducing the notion of maximal cusped lamination, a lamination consisting of geodesic arcs between bordered cusps and closed geodesics homotopic to the boundaries such that it triangulates the Riemann surface. We show that each bordered cusp carries a natural decoration, i.e. a choice of a horocycle, so that the lengths of the arcs in the maximal cusped lamination are defined as λ-lengths in Thurston-Penner terminology. We compute the Goldman bracket explicitly in terms of these λ-lengths and show that the groupoid of flip morphisms acts as a generalized cluster algebra mutation. From the physical point of view, our construction provides an explicit coordinatization of moduli spaces of open/closed string worldsheets and their quantization.

  1. Weyl transforms associated with the Riemann-Liouville operator

    Directory of Open Access Journals (Sweden)

    N. B. Hamadi

    2006-01-01

    Full Text Available For the Riemann-Liouville transform ℛα, α∈ℝ+, associated with singular partial differential operators, we define and study the Weyl transforms Wσ connected with ℛα, where σ is a symbol in Sm, m∈ℝ. We give criteria in terms of σ for boundedness and compactness of the transform Wσ.

  2. Weyl and Riemann-Liouville multifractional Ornstein-Uhlenbeck processes

    International Nuclear Information System (INIS)

    Lim, S C; Teo, L P

    2007-01-01

    This paper considers two new multifractional stochastic processes, namely the Weyl multifractional Ornstein-Uhlenbeck process and the Riemann-Liouville multifractional Ornstein-Uhlenbeck process. Basic properties of these processes such as locally self-similar property and Hausdorff dimension are studied. The relationship between the multifractional Ornstein-Uhlenbeck processes and the corresponding multifractional Brownian motions is established

  3. Toeplitz operators on higher Cauchy-Riemann spaces

    Czech Academy of Sciences Publication Activity Database

    Engliš, Miroslav; Zhang, G.

    2017-01-01

    Roč. 22, č. 22 (2017), s. 1081-1116 ISSN 1431-0643 Institutional support: RVO:67985840 Keywords : Toeplitz operator * Hankel operator * Cauchy-Riemann operators Subject RIV: BA - General Math ematics OBOR OECD: Pure math ematics Impact factor: 0.800, year: 2016 https://www. math .uni-bielefeld.de/documenta/vol-22/32.html

  4. The beauty of the Riemann-Silberstein vector

    International Nuclear Information System (INIS)

    Bialynicki-Birula, I.

    2005-01-01

    Beams of light carrying angular momentum have recently been widely studied theoretically and experimentally. In my talk I will show that the description of these beams in terms of the Riemann-Silberstein vector offers many advantages. In particular, it provides a natural bridge between the classical and the quantum description. (author)

  5. Riemann surfaces of complex classical trajectories and tunnelling splitting in one-dimensional systems

    Science.gov (United States)

    Harada, Hiromitsu; Mouchet, Amaury; Shudo, Akira

    2017-10-01

    The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann surface provides complete information on the topology of complex paths, which allows us to enumerate all the possible candidates contributing to the semiclassical sum formula for tunnelling splittings. This naturally leads to action relations among classically disjoined regions, revealing entirely non-local nature in the quantization condition. The importance of the proper treatment of Stokes phenomena is also discussed in Hamiltonians in the normal form.

  6. Approximate Riemann solver for the two-fluid plasma model

    International Nuclear Information System (INIS)

    Shumlak, U.; Loverich, J.

    2003-01-01

    An algorithm is presented for the simulation of plasma dynamics using the two-fluid plasma model. The two-fluid plasma model is more general than the magnetohydrodynamic (MHD) model often used for plasma dynamic simulations. The two-fluid equations are derived in divergence form and an approximate Riemann solver is developed to compute the fluxes of the electron and ion fluids at the computational cell interfaces and an upwind characteristic-based solver to compute the electromagnetic fields. The source terms that couple the fluids and fields are treated implicitly to relax the stiffness. The algorithm is validated with the coplanar Riemann problem, Langmuir plasma oscillations, and the electromagnetic shock problem that has been simulated with the MHD plasma model. A numerical dispersion relation is also presented that demonstrates agreement with analytical plasma waves

  7. Exploration and extension of an improved Riemann track fitting algorithm

    Science.gov (United States)

    Strandlie, A.; Frühwirth, R.

    2017-09-01

    Recently, a new Riemann track fit which operates on translated and scaled measurements has been proposed. This study shows that the new Riemann fit is virtually as precise as popular approaches such as the Kalman filter or an iterative non-linear track fitting procedure, and significantly more precise than other, non-iterative circular track fitting approaches over a large range of measurement uncertainties. The fit is then extended in two directions: first, the measurements are allowed to lie on plane sensors of arbitrary orientation; second, the full error propagation from the measurements to the estimated circle parameters is computed. The covariance matrix of the estimated track parameters can therefore be computed without recourse to asymptotic properties, and is consequently valid for any number of observation. It does, however, assume normally distributed measurement errors. The calculations are validated on a simulated track sample and show excellent agreement with the theoretical expectations.

  8. Pseudo-periodic maps and degeneration of Riemann surfaces

    CERN Document Server

    Matsumoto, Yukio

    2011-01-01

    The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen’s incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one-parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.

  9. Towards a theory of chaos explained as travel on Riemann surfaces

    International Nuclear Information System (INIS)

    Calogero, F; Santini, P M; Gomez-Ullate, D; Sommacal, M

    2009-01-01

    We investigate the dynamics defined by a set of three coupled first-order ODEs. It is shown that the system can be reduced to quadratures which can be expressed in terms of elementary functions. Despite the integrable character of the model, the general solution is a multiple-valued function of time (considered as a complex variable), and we investigate the position and nature of its branch points. In the semi-symmetric case (g 1 = g 2 ≠ g 3 ), for rational values of the coupling constants the system is isochronous and explicit formulae for the period of the solutions can be given. For irrational values, the motions are confined but feature aperiodic motion with sensitive dependence on initial conditions. The system shows a rich dynamical behaviour that can be understood in quantitative detail since a global description of the Riemann surface associated with the solutions can be achieved. The details of the description of the Riemann surface are postponed to a forthcoming publication. This toy model is meant to provide a paradigmatic first step towards understanding a certain novel kind of chaotic behaviour

  10. Non-supersymmetric matrix strings from generalized Yang-Mills theory on arbitrary Riemann surfaces

    International Nuclear Information System (INIS)

    Billo, M.; D'Adda, A.; Provero, P.

    2000-01-01

    We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the gauge where the field strength is diagonal. Twisted sectors originate, as in Matrix string theory, from permutations of the eigenvalues around homotopically non-trivial loops. These sectors, that must be discarded in the usual quantization due to divergences occurring when two eigenvalues coincide, can be consistently kept if one modifies the action by introducing a coupling of the field strength to the space-time curvature. This leads to a generalized Yang-Mills theory whose action reduces to the usual one in the limit of zero curvature. After integrating over the non-diagonal components of the gauge fields, the theory becomes a free string theory (sum over unbranched coverings) with a U(1) gauge theory on the world-sheet. This is shown to be equivalent to a lattice theory with a gauge group which is the semi-direct product of S N and U(1) N . By using well known results on the statistics of coverings, the partition function on arbitrary Riemann surfaces and the kernel functions on surfaces with boundaries are calculated. Extensions to include branch points and non-abelian groups on the world-sheet are briefly commented upon

  11. Quantum field theory on higher-genus Riemann surfaces, 2

    International Nuclear Information System (INIS)

    Kubo, Reijiro; Ojima, Shuichi.

    1990-08-01

    Quantum field theory for closed bosonic string systems is formulated on arbitrary higher-genus Riemann surfaces in global operator formalism. Canonical commutation relations between bosonic string field X μ and their conjugate momenta P ν are derived in the framework of conventional quantum field theory. Problems arising in quantizing bosonic systems are considered in detail. Applying the method exploited in the preceding paper we calculate Ward-Takahashi identities. (author)

  12. A contribution to the great Riemann solver debate

    Science.gov (United States)

    Quirk, James J.

    1992-01-01

    The aims of this paper are threefold: to increase the level of awareness within the shock capturing community to the fact that many Godunov-type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very high resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.

  13. Study on creep behavior of Grade 91 heat-resistant steel using theta projection method

    Science.gov (United States)

    Ren, Facai; Tang, Xiaoying

    2017-10-01

    Creep behavior of Grade 91 heat-resistant steel used for steam cooler was characterized using the theta projection method. Creep tests were conducted at the temperature of 923K under the stress ranging from 100-150MPa. Based on the creep curve results, four theta parameters were established using a nonlinear least square fitting method. Four theta parameters showed a good linearity as a function of stress. The predicted curves coincided well with the experimental data and creep curves were also modeled to the low stress level of 60MPa.

  14. Submaximal Riemann-Roch expected curves and symplectic packing.

    Directory of Open Access Journals (Sweden)

    Wioletta Syzdek

    2007-06-01

    Full Text Available We study Riemann-Roch expected curves on $mathbb{P}^1 imes mathbb{P}^1$ in the context of the Nagata-Biran conjecture. This conjecture predicts that for sufficiently large number of points multiple points Seshadri constants of an ample line bundle on algebraic surface are maximal. Biran gives an effective lower bound $N_0$. We construct examples verifying to the effect that the assertions of the Nagata-Biran conjecture can not hold for small number of points. We discuss cases where our construction fails. We observe also that there exists a strong relation between Riemann-Roch expected curves on $mathbb{P}^1 imes mathbb{P}^1$ and the symplectic packing problem. Biran relates the packing problem to the existence of solutions of certain Diophantine equations. We construct such solutions for any ample line bundle on $mathbb{P}^1 imes mathbb{P}^1$ and a relatively smallnumber of points. The solutions geometrically correspond to Riemann-Roch expected curves. Finally we discuss in how far the Biran number $N_0$ is optimal in the case of mathbb{P}^1 imes mathbb{P}^1. In fact we conjecture that it can be replaced by a lower number and we provide evidence justifying this conjecture.

  15. Testing the effects of adolescent alcohol use on adult conflict-related theta dynamics.

    Science.gov (United States)

    Harper, Jeremy; Malone, Stephen M; Iacono, William G

    2017-11-01

    Adolescent alcohol use (AAU) is associated with brain anomalies, but less is known about long-term neurocognitive effects. Despite theoretical models linking AAU to diminished cognitive control, empirical work testing this relationship with specific cognitive control neural correlates (e.g., prefrontal theta-band EEG dynamics) remains scarce. A longitudinal twin design was used to test the hypothesis that greater AAU is associated with reduced conflict-related EEG theta-band dynamics in adulthood, and to examine the genetic/environmental etiology of this association. In a large (N=718) population-based prospective twin sample, AAU was assessed at ages 11/14/17. Twins completed a flanker task at age 29 to elicit EEG theta-band medial frontal cortex (MFC) power and medial-dorsal prefrontal cortex (MFC-dPFC) connectivity. Two complementary analytic methods (cotwin control analysis; biometric modeling) were used to disentangle the genetic/shared environmental risk towards AAU from possible alcohol exposure effects on theta dynamics. AAU was negatively associated with adult cognitive control-related theta-band MFC power and MFC-dPFC functional connectivity. Genetic influences primarily underlie these associations. Findings provide strong evidence that genetic factors underlie the comorbidity between AAU and diminished cognitive control-related theta dynamics in adulthood. Conflict-related theta-band dynamics appear to be candidate brain-based endophenotypes/mechanisms for AAU. Copyright © 2017 International Federation of Clinical Neurophysiology. Published by Elsevier B.V. All rights reserved.

  16. Independent delta/theta rhythms in the human hippocampus and entorhinal cortex

    Directory of Open Access Journals (Sweden)

    Florian Mormann

    2008-05-01

    Full Text Available Theta oscillations in the medial temporal lobe (MTL of mammals are involved in various functions such as spatial navigation, sensorimotor integration, and cognitive processing. While the theta rhythm was originally assumed to originate in the medial septum, more recent studies suggest autonomous theta generation in the MTL. Although coherence between entorhinal and hippocampal theta activity has been found to influence memory formation, it remains unclear whether these two structures can generate theta independently. In this study we analyzed intracranial electroencephalographic (EEG recordings from 22 patients with unilateral hippocampal sclerosis undergoing presurgical evaluation prior to resection of the epileptic focus. Using a wavelet-based, frequency-band-specific measure of phase synchronization, we quantified synchrony between 10 different recording sites along the longitudinal axis of the hippocampal formation in the non-epileptic brain hemisphere. We compared EEG synchrony between adjacent recording sites (i within the entorhinal cortex, (ii within the hippocampus, and (iii between the hippocampus and entorhinal cortex. We observed a significant interregional gap in synchrony for the delta and theta band, indicating the existence of independent delta/theta rhythms in different subregions of the human MTL. The interaction of these rhythms could represent the temporal basis for the information processing required for mnemonic encoding and retrieval.

  17. Theta series, wall-crossing and quantum dilogarithm identities

    CERN Document Server

    Alexandrov, Sergei

    2016-01-01

    Motivated by mathematical structures which arise in string vacua and gauge theories with N=2 supersymmetry, we study the properties of certain generalized theta series which appear as Fourier coefficients of functions on a twisted torus. In Calabi-Yau string vacua, such theta series encode instanton corrections from $k$ Neveu-Schwarz five-branes. The theta series are determined by vector-valued wave-functions, and in this work we obtain the transformation of these wave-functions induced by Kontsevich-Soibelman symplectomorphisms. This effectively provides a quantum version of these transformations, where the quantization parameter is inversely proportional to the five-brane charge $k$. Consistency with wall-crossing implies a new five-term relation for Faddeev's quantum dilogarithm $\\Phi_b$ at $b=1$, which we prove. By allowing the torus to be non-commutative, we obtain a more general five-term relation valid for arbitrary $b$ and $k$, which may be relevant for the physics of five-branes at finite chemical po...

  18. Fast entrainment of human electroencephalogram to a theta-band photic flicker during successful memory encoding

    Directory of Open Access Journals (Sweden)

    Naoyuki eSato

    2013-05-01

    Full Text Available Theta band power (4-8Hz in the scalp electroencephalogram (EEG is thought to be stronger during memory encoding for subsequently remembered items than for forgotten items. According to simultaneous EEG-functional magnetic resonance imaging (fMRI measurements, the memory-dependent EEG theta is associated with multiple regions of the brain. This suggests that the multiple regions cooperate with EEG theta synchronization during successful memory encoding. However, a question still remains: What kind of neural dynamic organizes such a memory-dependent global network? In this study, the modulation of the EEG theta entrainment property during successful encoding was hypothesized to lead to EEG theta synchronization among a distributed network. Then, a transient response of EEG theta to a theta-band photic flicker with a short duration was evaluated during memory encoding. In the results, flicker-induced EEG power increased and decreased with a time constant of several hundred milliseconds following the onset and the offset of the flicker, respectively. Importantly, the offset response of EEG power was found to be significantly decreased during successful encoding. Moreover, the offset response of the phase locking index was also found to associate with memory performance. According to computational simulations, the results are interpreted as a smaller time constant (i.e., faster response of a driven harmonic oscillator rather than a change in the spontaneous oscillatory input. This suggests that the fast response of EEG theta forms a global EEG theta network among memory-related regions during successful encoding, and it contributes to a flexible formation of the network along the time course.

  19. Fast entrainment of human electroencephalogram to a theta-band photic flicker during successful memory encoding.

    Science.gov (United States)

    Sato, Naoyuki

    2013-01-01

    Theta band power (4-8 Hz) in the scalp electroencephalogram (EEG) is thought to be stronger during memory encoding for subsequently remembered items than for forgotten items. According to simultaneous EEG-functional magnetic resonance imaging (fMRI) measurements, the memory-dependent EEG theta is associated with multiple regions of the brain. This suggests that the multiple regions cooperate with EEG theta synchronization during successful memory encoding. However, a question still remains: What kind of neural dynamic organizes such a memory-dependent global network? In this study, the modulation of the EEG theta entrainment property during successful encoding was hypothesized to lead to EEG theta synchronization among a distributed network. Then, a transient response of EEG theta to a theta-band photic flicker with a short duration was evaluated during memory encoding. In the results, flicker-induced EEG power increased and decreased with a time constant of several hundred milliseconds following the onset and the offset of the flicker, respectively. Importantly, the offset response of EEG power was found to be significantly decreased during successful encoding. Moreover, the offset response of the phase locking index was also found to associate with memory performance. According to computational simulations, the results are interpreted as a smaller time constant (i.e., faster response) of a driven harmonic oscillator rather than a change in the spontaneous oscillatory input. This suggests that the fast response of EEG theta forms a global EEG theta network among memory-related regions during successful encoding, and it contributes to a flexible formation of the network along the time course.

  20. Theta-Generalized closed sets in fuzzy topological spaces

    International Nuclear Information System (INIS)

    El-Shafei, M.E.; Zakari, A.

    2006-01-01

    In this paper we introduce the concepts of theta-generalized closed fuzzy sets and generalized fuzzy sets in topological spaces. Furthermore, generalized fuzzy sets are extended to theta-generalized fuzzy sets. Also, we introduce the concepts of fuzzy theta-generalized continuous and fuzzy theta-generalized irresolute mappings. (author)

  1. Other characterizations of $\\beta$-$\\theta$-R0 topological spaces

    OpenAIRE

    Miguel Caldas Cueva

    2013-01-01

    In this paper we give other characterizations of $\\beta$-$\\theta$-$%R_0$ and also introduce a new separation axiom called$\\beta$-$\\theta$-$R_1$. It turns out that $\\beta$-$\\theta$-$R_1$ isstronger that $\\beta$-$\\theta$-$R_0$

  2. Derivative-Based Trapezoid Rule for the Riemann-Stieltjes Integral

    Directory of Open Access Journals (Sweden)

    Weijing Zhao

    2014-01-01

    Full Text Available The derivative-based trapezoid rule for the Riemann-Stieltjes integral is presented which uses 2 derivative values at the endpoints. This kind of quadrature rule obtains an increase of two orders of precision over the trapezoid rule for the Riemann-Stieltjes integral and the error term is investigated. At last, the rationality of the generalization of derivative-based trapezoid rule for Riemann-Stieltjes integral is demonstrated.

  3. Bi-Directional Theta Modulation between the Septo-Hippocampal System and the Mammillary Area in Free-Moving Rats

    Directory of Open Access Journals (Sweden)

    Ming Ruan

    2017-09-01

    Full Text Available Hippocampal (HPC theta oscillations have long been linked to various functions of the brain. Many cortical and subcortical areas that also exhibit theta oscillations have been linked to functional circuits with the hippocampus on the basis of coupled activities at theta frequencies. We examine, in freely moving rats, the characteristics of diencephalic theta local field potentials (LFPs recorded in the supramammillary/mammillary (SuM/MM areas that are bi-directionally connected to the HPC through the septal complex. Using partial directed coherence (PDC, we find support for previous suggestions that SuM modulates HPC theta at higher frequencies. We find weak separation of SuM and MM by dominant theta frequency recorded locally. Contrary to oscillatory cell activities under anesthesia where SuM is insensitive, but MM is sensitive to medial septal (MS inactivation, theta LFPs persisted and became indistinguishable after MS-inactivation. However, MS-inactivation attenuated SuM/MM theta power, while increasing the frequency of SuM/MM theta. MS-inactivation also reduced root mean squared power in both HPC and SuM/MM equally, but reduced theta power differentially in the time domain. We provide converging evidence that SuM is preferentially involved in coding HPC theta at higher frequencies, and that the MS-HPC circuit normally imposes a frequency-limiting modulation over the SuM/MM area as suggested by cell-based recordings in anesthetized animals. In addition, we provide evidence that the postulated SuM-MS-HPC-MM circuit is under complex bi-directional control, rather than SuM and MM having roles as unidirectional relays in the network.

  4. Integrable systems twistors, loop groups, and Riemann surfaces

    CERN Document Server

    Hitchin, NJ; Ward, RS

    2013-01-01

    This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians and renowned expositors. It is written in an accessible and informal style, and fills a gap in the existing literature. The introduction by Nigel Hitchin addresses the meaning of integrability: how do werecognize an integrable system? His own contribution then develops connections with algebraic geometry, and inclu

  5. Riemann-Roch Spaces and Linear Network Codes

    DEFF Research Database (Denmark)

    Hansen, Johan P.

    We construct linear network codes utilizing algebraic curves over finite fields and certain associated Riemann-Roch spaces and present methods to obtain their parameters. In particular we treat the Hermitian curve and the curves associated with the Suzuki and Ree groups all having the maximal...... number of points for curves of their respective genera. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possibly altered vector space. Ralf Koetter and Frank R. Kschischang %\\cite{DBLP:journals/tit/KoetterK08} introduced...... in the above metric making them suitable for linear network coding....

  6. Theta-alpha EEG phase distributions in the frontal area for dissociation of visual and auditory working memory.

    Science.gov (United States)

    Akiyama, Masakazu; Tero, Atsushi; Kawasaki, Masahiro; Nishiura, Yasumasa; Yamaguchi, Yoko

    2017-03-07

    Working memory (WM) is known to be associated with synchronization of the theta and alpha bands observed in electroencephalograms (EEGs). Although frontal-posterior global theta synchronization appears in modality-specific WM, local theta synchronization in frontal regions has been found in modality-independent WM. How frontal theta oscillations separately synchronize with task-relevant sensory brain areas remains an open question. Here, we focused on theta-alpha phase relationships in frontal areas using EEG, and then verified their functional roles with mathematical models. EEG data showed that the relationship between theta (6 Hz) and alpha (12 Hz) phases in the frontal areas was about 1:2 during both auditory and visual WM, and that the phase distributions between auditory and visual WM were different. Next, we used the differences in phase distributions to construct FitzHugh-Nagumo type mathematical models. The results replicated the modality-specific branching by orthogonally of the trigonometric functions for theta and alpha oscillations. Furthermore, mathematical and experimental results were consistent with regards to the phase relationships and amplitudes observed in frontal and sensory areas. These results indicate the important role that different phase distributions of theta and alpha oscillations have in modality-specific dissociation in the brain.

  7. Extended KN algebras and extended conformal field theories over higher genus Riemann surfaces

    International Nuclear Information System (INIS)

    Ceresole, A.; Huang Chaoshang

    1990-01-01

    A global operator formalism for extended conformal field theories over higher genus Riemann surfaces is introduced and extended KN algebra are obtained by means of the KN bases. The BBSS construction of the spin-3 operator is carried out for Kac-Moody algebra A 2 over a Riemann surface of arbitrary genus. (orig.)

  8. Superconformal structures and holomorphic 1/2-superdifferentials on N=1 super Riemann surfaces

    International Nuclear Information System (INIS)

    Kachkachi, H.; Kachkachi, M.

    1992-07-01

    Using the Super Riemann-Roch theorem we give a local expression for a holomorphic 1/2-superdifferential in a superconformal structure parametrized by special isothermal coordinates on an N=1 Super Riemann Surface (SRS). This construction is done by choosing a suitable origin for these coordinates. The holomorphy of the latter with respect to super Beltrami differentials is proven. (author). 26 refs

  9. Superconformal algebra on meromorphic vector fields with three poles on super-Riemann sphere

    International Nuclear Information System (INIS)

    Wang Shikun; Xu Kaiwen.

    1989-07-01

    Based upon the Riemann-Roch theorem, we construct superconformal algebra of meromorphic vector fields with three poles and the relevant abelian differential of the third kind on super Riemann sphere. The algebra includes two Ramond sectors as subalgebra, and implies a picture of interaction of three superstrings. (author). 14 refs

  10. Brain Responses to a 6-Hz Binaural Beat: Effects on General Theta Rhythm and Frontal Midline Theta Activity.

    Science.gov (United States)

    Jirakittayakorn, Nantawachara; Wongsawat, Yodchanan

    2017-01-01

    A binaural beat is a beat phenomenon that is generated by the dichotic presentation of two almost equivalent pure tones but with slightly different frequencies. The brain responses to binaural beats remain controversial; therefore, the aim of this study was to investigate theta activity responses to a binaural beat by controlling factors affecting localization, including beat frequency, carrier tone frequency, exposure duration, and recording procedure. Exposure to a 6-Hz binaural beat on a 250 Hz carrier tone for 30 min was utilized in this study. Quantitative electroencephalography (QEEG) was utilized as the recording modality. Twenty-eight participants were divided into experimental and control groups. Emotional states were evaluated by Brunel Mood Scale (BRMUS) before and after exposing to the stimulus. The results showed that theta activity was induced in the entire cortex within 10 min of exposure to the stimulus in the experimental group. Compared to the control group, theta activity was also induced at the frontal and parietal-central regions, which included the Fz position, and left hemisphere dominance was presented for other exposure durations. The pattern recorded for 10 min of exposure appeared to be brain functions of a meditative state. Moreover, tension factor of BRUMS was decreased in experimental group compared to control group which resembled the meditation effect. Thus, a 6-Hz binaural beat on a 250 Hz carrier tone was suggested as a stimulus for inducing a meditative state.

  11. Brain Responses to a 6-Hz Binaural Beat: Effects on General Theta Rhythm and Frontal Midline Theta Activity

    Directory of Open Access Journals (Sweden)

    Nantawachara Jirakittayakorn

    2017-06-01

    Full Text Available A binaural beat is a beat phenomenon that is generated by the dichotic presentation of two almost equivalent pure tones but with slightly different frequencies. The brain responses to binaural beats remain controversial; therefore, the aim of this study was to investigate theta activity responses to a binaural beat by controlling factors affecting localization, including beat frequency, carrier tone frequency, exposure duration, and recording procedure. Exposure to a 6-Hz binaural beat on a 250 Hz carrier tone for 30 min was utilized in this study. Quantitative electroencephalography (QEEG was utilized as the recording modality. Twenty-eight participants were divided into experimental and control groups. Emotional states were evaluated by Brunel Mood Scale (BRMUS before and after exposing to the stimulus. The results showed that theta activity was induced in the entire cortex within 10 min of exposure to the stimulus in the experimental group. Compared to the control group, theta activity was also induced at the frontal and parietal-central regions, which included the Fz position, and left hemisphere dominance was presented for other exposure durations. The pattern recorded for 10 min of exposure appeared to be brain functions of a meditative state. Moreover, tension factor of BRUMS was decreased in experimental group compared to control group which resembled the meditation effect. Thus, a 6-Hz binaural beat on a 250 Hz carrier tone was suggested as a stimulus for inducing a meditative state.

  12. Two-Loop Scattering Amplitudes from the Riemann Sphere

    CERN Document Server

    Geyer, Yvonne; Monteiro, Ricardo; Tourkine, Piotr

    2016-01-01

    The scattering equations give striking formulae for massless scattering amplitudes at tree level and, as shown recently, at one loop. The progress at loop level was based on ambitwistor string theory, which naturally yields the scattering equations. We proposed that, for ambitwistor strings, the standard loop expansion in terms of the genus of the worldsheet is equivalent to an expansion in terms of nodes of a Riemann sphere, with the nodes carrying the loop momenta. In this paper, we show how to obtain two-loop scattering equations with the correct factorization properties. We adapt genus-two integrands from the ambitwistor string to the nodal Riemann sphere and show that these yield correct answers, by matching standard results for the four-point two-loop amplitudes of maximal supergravity and super-Yang-Mills theory. In the Yang-Mills case, this requires the loop analogue of the Parke-Taylor factor carrying the colour dependence, which includes non-planar contributions.

  13. Zeros da função zeta de Riemann e o teorema dos números primos

    OpenAIRE

    Oliveira, Willian Diego [UNESP

    2013-01-01

    We studied various properties of the Riemann’s zeta function. Three proofs of the Prime Number Theorem were provides. Classical results on zero-free region of the zeta function, as well as their relation to the error term in the Prime Number Theorem, were studied in details Estudamos várias propriedades da função zeta de Riemann. Três provas do Teorema dos Números Primos foram fornecidas. Resultados clássicos sobre regiões livres de zeros da função zeta, bem como sua relação com o termo do...

  14. A Riemann-Hilbert formulation for the finite temperature Hubbard model

    Energy Technology Data Exchange (ETDEWEB)

    Cavaglià, Andrea [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); Cornagliotto, Martina [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); DESY Hamburg, Theory Group,Notkestrasse 85, D-22607 Hamburg (Germany); Mattelliano, Massimo; Tateo, Roberto [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy)

    2015-06-03

    Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results by Jüttner, Klümper and Suzuki based on the Quantum Transfer Matrix method. We also comment on the analytic continuation mechanism leading to excited states and on the mirror equations describing the finite-size Hubbard model with twisted boundary conditions.

  15. A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

    Science.gov (United States)

    Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira

    2014-06-01

    Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.

  16. Riemann surfaces and algebraic curves a first course in Hurwitz theory

    CERN Document Server

    Cavalieri, Renzo

    2016-01-01

    Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.

  17. Engineering prototypes for theta-pinch devices

    International Nuclear Information System (INIS)

    Hansborough, L.D.; Hammer, C.F.; Hanks, K.W.; McDonald, T.E.; Nunnally, W.C.

    1975-01-01

    Past, present, and future engineering prototypes for theta-pinch plasma-physics devices at Los Alamos Scientific Laboratory are discussed. Engineering prototypes are designed to test and evaluate all components under system conditions expected on actual plasma-physics experimental devices. The importance of engineering prototype development increases as the size and complexity of the plasma-physics device increases. Past experiences with the Scyllac prototype and the Staged Theta-Pinch prototype are discussed and evaluated. The design of the proposed Staged Scyllac prototype and the Large Staged Scyllac implosion prototype assembly are discussed

  18. Better than sleep: theta neurofeedback training accelerates memory consolidation.

    Science.gov (United States)

    Reiner, Miriam; Rozengurt, Roman; Barnea, Anat

    2014-01-01

    Consistent empirical results showed that both night and day sleep enhanced memory consolidation. In this study we explore processes of consolidation of memory during awake hours. Since theta oscillations have been shown to play a central role in exchange of information, we hypothesized that elevated theta during awake hours will enhance memory consolidation. We used a neurofeedback protocol, to enhance the relative power of theta or beta oscillations. Participants trained on a tapping task, were divided into three groups: neurofeedback theta; neurofeedback beta; control. We found a significant improvement in performance in the theta group, relative to the beta and control groups, immediately after neurofeedback. Performance was further improved after night sleep in all groups, with a significant advantage favoring the theta group. Theta power during training was correlated with the level of improvement, indicating a clear relationship between memory consolidation, and theta neurofeedback. Copyright © 2013 Elsevier B.V. All rights reserved.

  19. Leptogenesis, $\\mu - \\tau$ Symmetry and $\\theta_{13}$

    CERN Document Server

    Mohapatra, Rabindra N; Yu, H; Yu, Haibo

    2005-01-01

    We show that in theories where neutrino masses arise from type I seesaw formula with three right handed neutrinos and where large atmospheric mixing angle owes its origin to an approximate leptonic $\\mu-\\tau$ interchange symmetry, the primordial lepton asymmetry of the Universe, $\\epsilon_l$ can be expressed in a simple form in terms of low energy neutrino oscillation parameters as $\\epsilon_l = (a \\Delta m^2_\\odot+ b \\Delta m^2_A \\theta^2_{13})$, where $a$ and $b$ are parameters characterizing high scale physics and are each of order $\\leq 10^{-2} $ eV$^{-2}$. We also find that for the case of two right handed neutrinos, $\\epsilon_l \\propto \\theta^2_{13}$ as a result of which, the observed value of baryon to photon ratio implies a lower limit on $\\theta_{13}$. For specific choices of the CP phase $\\delta$ we find $\\theta_{13}$ is predicted to be between $0.10-0.15$.

  20. Hippocampal theta frequency shifts and operant behaviour

    NARCIS (Netherlands)

    Lopes da Silva, F.H.; Kamp, A.

    1. 1. A shift of hippocampal dominant theta frequency to 6 c/sec has been demonstrated in the post-reward period in two dogs, which occurs consistently related in time to a well defined behavioural pattern in the course of an operant conditioning paradigm. 2. 2. The frequency shift was detected and

  1. Scylla IV-P theta pinch

    International Nuclear Information System (INIS)

    Bailey, A.G.; Chandler, G.I.; Ekdahl, C.A. Jr.; Lillberg, J.W.; Machalek, M.D.; Seibel, F.T.

    1976-01-01

    Scylla IV-P is a flexible, linear theta pinch designed to investigate high-density linear concepts, end-stoppering, alternate heating methods, and plasma injection techniques relevant to a pure fusion reactor and/or a fusion-fission hybrid system. The construction and experimental arrangement of the device are briefly described

  2. Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis.

    Science.gov (United States)

    Lapidus, Michel L

    2015-08-06

    This research expository article not only contains a survey of earlier work but also contains a main new result, which we first describe. Given c≥0, the spectral operator [Formula: see text] can be thought of intuitively as the operator which sends the geometry onto the spectrum of a fractal string of dimension not exceeding c. Rigorously, it turns out to coincide with a suitable quantization of the Riemann zeta function ζ=ζ(s): a=ζ(∂), where ∂=∂(c) is the infinitesimal shift of the real line acting on the weighted Hilbert space [Formula: see text]. In this paper, we establish a new asymmetric criterion for the Riemann hypothesis (RH), expressed in terms of the invertibility of the spectral operator for all values of the dimension parameter [Formula: see text] (i.e. for all c in the left half of the critical interval (0,1)). This corresponds (conditionally) to a mathematical (and perhaps also, physical) 'phase transition' occurring in the midfractal case when [Formula: see text]. Both the universality and the non-universality of ζ=ζ(s) in the right (resp., left) critical strip [Formula: see text] (resp., [Formula: see text]) play a key role in this context. These new results are presented here. We also briefly discuss earlier joint work on the complex dimensions of fractal strings, and we survey earlier related work of the author with Maier and with Herichi, respectively, in which were established symmetric criteria for the RH, expressed, respectively, in terms of a family of natural inverse spectral problems for fractal strings of Minkowski dimension D∈(0,1), with [Formula: see text], and of the quasi-invertibility of the family of spectral operators [Formula: see text] (with [Formula: see text]). © 2015 The Author(s) Published by the Royal Society. All rights reserved.

  3. Three-dimensional ideal theta(1)/theta(2) angular transformer and its uses in fiber optics.

    Science.gov (United States)

    Ning, X

    1988-10-01

    A 3-D ideal theta(1)/theta(2) angular transformer in nonimaging optics is introduced. The axially symmetric transformer, combining a portion of a hyperbolic concentrator with two lenses, transforms an input limited Lambertian over an angle theta(1) to an output limited Lambertian over an angle theta(2) without losing throughput. This is the first known transformer with such ideal properties. Results of computer simulations of a transformer with planospherical lenses are presented. Because of its ideal angular transforming property, the transformer offers an excellent solution for power launching and fiber-fiber coupling in optical fiber systems. In principle, the theoretical maximum coupling efficiency based on radiance conservation can be achieved with this transformer. Several conceptual designs of source-fiber and fiber-fiber couplers using the transformer are given.

  4. Age-related changes of frontal-midline theta is predictive of efficient memory maintenance.

    Science.gov (United States)

    Kardos, Z; Tóth, B; Boha, R; File, B; Molnár, M

    2014-07-25

    Frontal areas are thought to be the coordinators of working memory processes by controlling other brain areas reflected by oscillatory activities like frontal-midline theta (4-7 Hz). With aging substantial changes can be observed in the frontal brain areas, presumably leading to age-associated changes in cortical correlates of cognitive functioning. The present study aimed to test whether altered frontal-midline theta dynamics during working memory maintenance may underlie the capacity deficits observed in older adults. 33-channel EEG was recorded in young (18-26 years, N=20) and old (60-71 years, N=16) adults during the retention period of a visual delayed match-to-sample task, in which they had to maintain arrays of 3 or 5 colored squares. An additional visual odd-ball task was used to be able to measure the electrophysiological indices of sustained attentional processes. Old participants showed reduced frontal theta activity during both tasks compared to the young group. In the young memory maintenance-related frontal-midline theta activity was shown to be sensitive both to the increased memory demands and to efficient subsequent memory performance, whereas the old adults showed no such task-related difference in the frontal theta activity. The decrease of frontal-midline theta activity in the old group indicates that cerebral aging may alter the cortical circuitries of theta dynamics, thereby leading to age-associated decline of working memory maintenance function. Copyright © 2014 IBRO. Published by Elsevier Ltd. All rights reserved.

  5. The theta-structure in string theories - 1: bosonic strings

    International Nuclear Information System (INIS)

    Li Miao.

    1985-09-01

    We explored the theta-structures in bosonic string theories which are similar to those in gauge field theories. The theta-structure of string is due to the multiply connected spatial compact subspace of space-time. The work of this paper shows that there is an energy band E(theta) in the string theory and one may move the tachyon out in theory by choosing some proper theta parameters. (author)

  6. Contribution of non integer integro-differential operators (NIDO) to the geometrical understanding of Riemann's conjecture-(II)

    International Nuclear Information System (INIS)

    Le Mehaute, Alain; El Kaabouchi, Abdelaziz; Nivanen, Laurent

    2008-01-01

    Advances in fractional analysis suggest a new way for the physics understanding of Riemann's conjecture. It asserts that, if s is a complex number, the non trivial zeros of zeta function 1/(ζ(s)) =Σ n=1 ∞ (μ(n))/(n s ) in the gap [0, 1], is characterized by s=1/2 (1+2iθ). This conjecture can be understood as a consequence of 1/2-order fractional differential characteristics of automorph dynamics upon opened punctuated torus with an angle at infinity equal to π/4. This physical interpretation suggests new opportunities for revisiting the cryptographic methodologies

  7. Dynamical stability of the alpha and theta phases of alumina

    DEFF Research Database (Denmark)

    Lodziana, Zbigniew; Parlinski, K.

    2003-01-01

    Using density functional calculations the phonon dispersion relations, phonon density of states, and free energy of theta and alpha phases of alumina are investigated. The temperature dependence of the free energy indicates that entropy contributes to the destabilization of the alpha phase...... cations in alumina, and suggest that some other than entropic mechanism exists, which stabilizes transition aluminas up to 1400 K. The present calculations go beyond the ground state energy calculations [C. Wolverton and K.C. Hass, Phys. Rev. B 63, 24102 (2001)], and give an additional understanding...... of the stability of transition alumina at finite temperatures....

  8. Polynomials, Riemann surfaces, and reconstructing missing-energy events

    CERN Document Server

    Gripaios, Ben; Webber, Bryan

    2011-01-01

    We consider the problem of reconstructing energies, momenta, and masses in collider events with missing energy, along with the complications introduced by combinatorial ambiguities and measurement errors. Typically, one reconstructs more than one value and we show how the wrong values may be correlated with the right ones. The problem has a natural formulation in terms of the theory of Riemann surfaces. We discuss examples including top quark decays in the Standard Model (relevant for top quark mass measurements and tests of spin correlation), cascade decays in models of new physics containing dark matter candidates, decays of third-generation leptoquarks in composite models of electroweak symmetry breaking, and Higgs boson decay into two tau leptons.

  9. Supersymmetric Dirac particles in Riemann-Cartan space-time

    International Nuclear Information System (INIS)

    Rumpf, H.

    1981-01-01

    A natural extension of the supersymmetric model of Di Vecchia and Ravndal yields a nontrivial coupling of classical spinning particles to torsion in a Riemann-Cartan geometry. The equations of motion implied by this model coincide with a consistent classical limit of the Heisenberg equations derived from the minimally coupled Dirac equation. Conversely, the latter equation is shown to arise from canonical quantization of the classical system. The Heisenberg equations are obtained exact in all powers of h/2π and thus complete the partial results of previous WKB calculations. The author also considers such matters of principle as the mathematical realization of anticommuting variables, the physical interpretation of supersymmetry transformations, and the effective variability of rest mass. (Auth.)

  10. A New Riemann Type Hydrodynamical Hierarchy and its Integrability Analysis

    International Nuclear Information System (INIS)

    Golenia, Jolanta Jolanta; Bogolubov, Nikolai N. Jr.; Popowicz, Ziemowit; Pavlov, Maxim V.; Prykarpatsky, Anatoliy K.

    2009-12-01

    Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible co-symplectic structures and Lax type representations for the special cases N = 2, 3 and N = 4 are constructed. (author)

  11. Decreased rhythmic GABAergic septal activity and memory-associated theta oscillations after hippocampal amyloid-beta pathology in the rat.

    Science.gov (United States)

    Villette, Vincent; Poindessous-Jazat, Frédérique; Simon, Axelle; Léna, Clément; Roullot, Elodie; Bellessort, Brice; Epelbaum, Jacques; Dutar, Patrick; Stéphan, Aline

    2010-08-18

    The memory deficits associated with Alzheimer's disease result to a great extent from hippocampal network dysfunction. The coordination of this network relies on theta (symbol) oscillations generated in the medial septum. Here, we investigated in rats the impact of hippocampal amyloid beta (Abeta) injections on the physiological and cognitive functions that depend on the septohippocampal system. Hippocampal Abeta injections progressively impaired behavioral performances, the associated hippocampal theta power, and theta frequency response in a visuospatial recognition test. These alterations were associated with a specific reduction in the firing of the identified rhythmic bursting GABAergic neurons responsible for the propagation of the theta rhythm to the hippocampus, but without loss of medial septal neurons. Such results indicate that hippocampal Abeta treatment leads to a specific functional depression of inhibitory projection neurons of the medial septum, resulting in the functional impairment of the temporal network.

  12. The Picard group of the moduli space of r-Spin Riemann surfaces

    DEFF Research Database (Denmark)

    Randal-Williams, Oscar

    2012-01-01

    An r-Spin Riemann surface is a Riemann surface equipped with a choice of rth root of the (co)tangent bundle. We give a careful construction of the moduli space (orbifold) of r-Spin Riemann surfaces, and explain how to establish a Madsen–Weiss theorem for it. This allows us to prove the “Mumford...... conjecture” for these moduli spaces, but more interestingly allows us to compute their algebraic Picard groups (for g≥10, or g≥9 in the 2-Spin case). We give a complete description of these Picard groups, in terms of explicitly constructed line bundles....

  13. Structural stability of Riemann solutions for strictly hyperbolic systems with three piecewise constant states

    Directory of Open Access Journals (Sweden)

    Xuefeng Wei

    2016-12-01

    Full Text Available This article concerns the wave interaction problem for a strictly hyperbolic system of conservation laws whose Riemann solutions involve delta shock waves. To cover all situations, the global solutions are constructed when the initial data are taken as three piecewise constant states. It is shown that the Riemann solutions are stable with respect to a specific small perturbation of the Riemann initial data. In addition, some interesting nonlinear phenomena are captured during the process of constructing the solutions, such as the generation and decomposition of delta shock waves.

  14. The Riemann zeros as energy levels of a Dirac fermion in a potential built from the prime numbers in Rindler spacetime

    International Nuclear Information System (INIS)

    Sierra, Germán

    2014-01-01

    We construct a Hamiltonian H R whose discrete spectrum contains, in a certain limit, the Riemann zeros. H R is derived from the action of a massless Dirac fermion living in a domain of Rindler spacetime, in 1 + 1 dimensions, which has a boundary given by the world line of a uniformly accelerated observer. The action contains a sum of delta function potentials that can be viewed as partially reflecting moving mirrors. An appropriate choice of the accelerations of the mirrors, provide primitive periodic orbits that are associated with the prime numbers p, whose periods, as measured by the observer's clock, are logp. Acting on the chiral components of the fermion χ ∓ , H R becomes the Berry–Keating Hamiltonian ±(x p-hat + p-hat x)/2, where x is identified with the Rindler spatial coordinate and p-hat with the conjugate momentum. The delta function potentials give the matching conditions of the fermion wave functions on both sides of the mirrors. There is also a phase shift e iϑ for the reflection of the fermions at the boundary where the observer sits. The eigenvalue problem is solved by transfer matrix methods in the limit where the reflection amplitudes become infinitesimally small. We find that, for generic values of ϑ, the spectrum is a continuum where the Riemann zeros are missing, as in the adelic Connes model. However, for some values of ϑ, related to the phase of the zeta function, the Riemann zeros appear as discrete eigenvalues that are immersed in the continuum. We generalize this result to the zeros of Dirichlet L-functions, which are associated to primitive characters, that are encoded in the reflection coefficients of the mirrors. Finally, we show that the Hamiltonian associated to the Riemann zeros belongs to class AIII, or chiral GUE, of the Random Matrix Theory. (paper)

  15. Self-regulation of frontal-midline theta facilitates memory updating and mental set shifting

    Directory of Open Access Journals (Sweden)

    Stefanie eEnriquez-Geppert

    2014-12-01

    Full Text Available Frontal-midline (fm theta oscillations as measured via the electroencephalogram (EEG have been suggested as neural working language of executive functioning. Their power has been shown to increase when cognitive processing or task performance is enhanced. Thus, the question arises whether learning to increase fm-theta amplitudes would functionally impact the behavioral performance in tasks probing executive functions (EFs. Here, the effects of neurofeedback, a learning method to self-up-regulate fm-theta over frontal-midline electrodes, on the four most representative EFs, memory updating, set shifting, conflict monitoring, and motor inhibition are presented. Before beginning and after completing an individualized, eight-session gap-spaced neurofeedback intervention, the three-back, letter/number task-switching, Stroop, and stop-signal tasks were tested while measuring the EEG. Self-determined up-regulation of fm-theta and its putative role for executive functioning were compared to an active control group, the so-called pseudo-neurofeedback group. Task-related fm-theta activity after training differed significantly between groups. More importantly, though, after neurofeedback significantly enhanced behavioral performance was observed. The training group showed higher accuracy scores in the three-back task and reduced mixing and shifting costs in letter/number task-switching. However, this specific protocol type did not affect performance in tasks probing conflict monitoring and motor inhibition. Thus, our results suggest a modulation of proactive but not reactive mechanisms of cognitive control. In sum, the modulation of fm-theta via neurofeedback may serve as potent treatment approach for executive dysfunctions.

  16. Statistical properties of multi-theta polymer chains

    Science.gov (United States)

    Uehara, Erica; Deguchi, Tetsuo

    2018-04-01

    We study statistical properties of polymer chains with complex structures whose chemical connectivities are expressed by graphs. The multi-theta curve of m subchains with two branch points connected by them is one of the simplest graphs among those graphs having closed paths, i.e. loops. We denoted it by θm , and for m  =  2 it is given by a ring. We derive analytically the pair distribution function and the scattering function for the θm -shaped polymer chains consisting of m Gaussian random walks of n steps. Surprisingly, it is shown rigorously that the mean-square radius of gyration for the Gaussian θm -shaped polymer chain does not depend on the number m of subchains if each subchain has the same fixed number of steps. For m  =  3 we show the Kratky plot for the theta-shaped polymer chain consisting of hard cylindrical segments by the Monte-Carlo method including reflection at trivalent vertices.

  17. Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature

    OpenAIRE

    Loveridge, Lee C.

    2004-01-01

    Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.

  18. Existence and Nonexistence of Positive Solutions for Coupled Riemann-Liouville Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Johnny Henderson

    2016-01-01

    Full Text Available We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.

  19. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

    National Research Council Canada - National Science Library

    Derbyshire, John

    2003-01-01

    .... Is the hypothesis true or false?Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic defining a precise formula to track and identify the occurrence...

  20. Nontrivial Solution of Fractional Differential System Involving Riemann-Stieltjes Integral Condition

    Directory of Open Access Journals (Sweden)

    Ge-Feng Yang

    2012-01-01

    differential system involving the Riemann-Stieltjes integral condition, by using the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle, some sufficient conditions of the existence and uniqueness of a nontrivial solution of a system are obtained.

  1. Abnormal-induced theta activity supports early directed-attention network deficits in progressive MCI.

    Science.gov (United States)

    Deiber, Marie-Pierre; Ibañez, Vicente; Missonnier, Pascal; Herrmann, François; Fazio-Costa, Lara; Gold, Gabriel; Giannakopoulos, Panteleimon

    2009-09-01

    The electroencephalography (EEG) theta frequency band reacts to memory and selective attention paradigms. Global theta oscillatory activity includes a posterior phase-locked component related to stimulus processing and a frontal-induced component modulated by directed attention. To investigate the presence of early deficits in the directed attention-related network in elderly individuals with mild cognitive impairment (MCI), time-frequency analysis at baseline was used to assess global and induced theta oscillatory activity (4-6Hz) during n-back working memory tasks in 29 individuals with MCI and 24 elderly controls (EC). At 1-year follow-up, 13 MCI patients were still stable and 16 had progressed. Baseline task performance was similar in stable and progressive MCI cases. Induced theta activity at baseline was significantly reduced in progressive MCI as compared to EC and stable MCI in all n-back tasks, which were similar in terms of directed attention requirements. While performance is maintained, the decrease of induced theta activity suggests early deficits in the directed-attention network in progressive MCI, whereas this network is functionally preserved in stable MCI.

  2. A variational approach to closed bosonic strings on bordered Riemann surfaces

    International Nuclear Information System (INIS)

    Ohrndorf, T.

    1987-01-01

    Polyakov's path integral for bosonic closed strings defined on a bordered Riemann surface is investigated by variational methods. It is demonstrated that boundary variations are generated by the Virasoro operators. The investigation is performed for both, simply connected Riemann surfaces as well as ringlike domains. It is shown that the form of the variational operator is the same on both kinds of surfaces. The Virasoro algebra arises as a consistency condition for the variation. (orig.)

  3. Essay on Fractional Riemann-Liouville Integral Operator versus Mikusinski’s

    Directory of Open Access Journals (Sweden)

    Ming Li

    2013-01-01

    Full Text Available This paper presents the representation of the fractional Riemann-Liouville integral by using the Mikusinski operators. The Mikusinski operators discussed in the paper may yet provide a new view to describe and study the fractional Riemann-Liouville integral operator. The present result may be useful for applying the Mikusinski operational calculus to the study of fractional calculus in mathematics and to the theory of filters of fractional order in engineering.

  4. Theta oscillations during holeboard training in rats: different learning strategies entail different context-dependent modulations in the hippocampus.

    Science.gov (United States)

    Woldeit, M L; Korz, V

    2010-02-03

    A functional connection between theta rhythms, information processing, learning and memory formation is well documented by studies focusing on the impact of theta waves on motor activity, global context or phase coding in spatial learning. In the present study we analyzed theta oscillations during a spatial learning task and assessed which specific behavioral contexts were connected to changes in theta power and to the formation of memory. Therefore, we measured hippocampal dentate gyrus theta modulations in male rats that were allowed to establish a long-term spatial reference memory in a holeboard (fixed pattern of baited holes) in comparison to rats that underwent similar training conditions but could not form a reference memory (randomly baited holes). The first group established a pattern specific learning strategy, while the second developed an arbitrary search strategy, visiting increasingly more holes during training. Theta power was equally influenced during the training course in both groups, but was significantly higher when compared to untrained controls. A detailed behavioral analysis, however, revealed behavior- and context-specific differences within the experimental groups. In spatially trained animals theta power correlated with the amounts of reference memory errors in the context of the inspection of unbaited holes and exploration in which, as suggested by time frequency analyses, also slow wave (delta) power was increased. In contrast, in randomly trained animals positive correlations with working memory errors were found in the context of rearing behavior. These findings indicate a contribution of theta/delta to long-lasting memory formation in spatially trained animals, whereas in pseudo trained animals theta seems to be related to attention in order to establish trial specific short-term working memory. Implications for differences in neuronal plasticity found in earlier studies are discussed. Copyright 2010 IBRO. Published by Elsevier Ltd

  5. Riemann's and Helmholtz-Lie's problems of space from Weyl's relativistic perspective

    Science.gov (United States)

    Bernard, Julien

    2018-02-01

    I reconstruct Riemann's and Helmholtz-Lie's problems of space, from some perspectives that allow for a fruitful comparison with Weyl. In Part II. of his inaugural lecture, Riemann justifies that the infinitesimal metric is the square root of a quadratic form. Thanks to Finsler geometry, I clarify both the implicit and explicit hypotheses used for this justification. I explain that Riemann-Finsler's kind of method is also appropriate to deal with indefinite metrics. Nevertheless, Weyl shares with Helmholtz a strong commitment to the idea that the notion of group should be at the center of the foundations of geometry. Riemann missed this point, and that is why, according to Weyl, he dealt with the problem of space in a "too formal" way. As a consequence, to solve the problem of space, Weyl abandoned Riemann-Finsler's methods for group-theoretical ones. However, from a philosophical point of view, I show that Weyl and Helmholtz are in strong opposition. The meditation on Riemann's inaugural lecture, and its clear methodological separation between the infinitesimal and the finite parts of the problem of space, must have been crucial for Weyl, while searching for strong epistemological foundations for the group-theoretical methods, avoiding Helmholtz's unjustified transition from the finite to the infinitesimal.

  6. RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

    International Nuclear Information System (INIS)

    Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.

    2010-01-01

    We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.

  7. Numerical implication of Riemann problem theory for fluid dynamics

    International Nuclear Information System (INIS)

    Menikoff, R.

    1988-01-01

    The Riemann problem plays an important role in understanding the wave structure of fluid flow. It is also crucial step in some numerical algorithms for accurately and efficiently computing fluid flow; Godunov method, random choice method, and from tracking method. The standard wave structure consists of shock and rarefaction waves. Due to physical effects such as phase transitions, which often are indistinguishable from numerical errors in an equation of state, anomalkous waves may occur, ''rarefaction shocks'', split waves, and composites. The anomalous waves may appear in numerical calculations as waves smeared out by either too much artificial viscosity or insufficient resolution. In addition, the equation of state may lead to instabilities of fluid flow. Since these anomalous effects due to the equation of state occur for the continuum equations, they can be expected to occur for all computational algorithms. The equation of state may be characterized by three dimensionless variables: the adiabatic exponent γ, the Grueneisen coefficient Γ, and the fundamental derivative G. The fluid flow anomalies occur when inequalities relating these variables are violated. 18 refs

  8. Deduction of Einstein equation from homogeneity of Riemann spacetime

    Science.gov (United States)

    Ni, Jun

    2012-03-01

    The symmetry of spacetime translation leads to the energy-momentum conservation. However, the Lagrange depends on spacetime coordinates, which makes the symmetry of spacetime translation different with other symmetry invariant explicitly under symmetry transformation. We need an equation to guarantee the symmetry of spacetime translation. In this talk, I will show that the Einstein equation can be deduced purely from the general covariant principle and the homogeneity of spacetime in the frame of quantum field theory. The Einstein equation is shown to be the equation to guarantee the symmetry of spacetime translation. Gravity is an apparent force due to the curvature of spacetime resulted from the conservation of energy-momentum. In the action of quantum field, only electroweak-strong interactions appear with curved spacetime metric determined by the Einstein equation.. The general covariant principle and the homogeneity of spacetime are merged into one basic principle: Any Riemann spacetime metric guaranteeing the energy-momentum conservation are equivalent, which can be called as the conserved general covariant principle. [4pt] [1] Jun Ni, Chin. Phys. Lett. 28, 110401 (2011).

  9. Seasonal variation of Sigma sub(Theta) with wind speed, direction and stability

    Digital Repository Service at National Institute of Oceanography (India)

    Sadhuram, Y.

    For an airport site near Visakhapatnam, India, and based on 10 years of data for the months of January, April, August and October, values of Sigma sub(Theta) are given as a function of wind speed, wind direction and Pasquill diffusion category...

  10. Lower trait frontal theta activity in mindfulness meditators

    Directory of Open Access Journals (Sweden)

    Guaraci Ken Tanaka

    2014-09-01

    Full Text Available Acute and long-term effects of mindfulness meditation on theta-band activity are not clear. The aim of this study was to investigate frontal theta differences between long- and short-term mindfulness practitioners before, during, and after mindfulness meditation. Twenty participants were recruited, of which 10 were experienced Buddhist meditators. Despite an acute increase in the theta activity during meditation in both the groups, the meditators showed lower trait frontal theta activity. Therefore, we suggested that this finding is a neural correlate of the expert practitioners’ ability to limit the processing of unnecessary information (e.g., discursive thought and increase the awareness of the essential content of the present experience. In conclusion, acute changes in the theta band throughout meditation did not appear to be a specific correlate of mindfulness but were rather related to the concentration properties of the meditation. Notwithstanding, lower frontal theta activity appeared to be a trait of mindfulness practices.

  11. {theta}-Compactness in L-topological spaces

    Energy Technology Data Exchange (ETDEWEB)

    Hanafy, I.M. [Department of Mathematics, Faculty of Education, Suez Canal University, El-Arish (Egypt)], E-mail: ihanafy@hotmail.com

    2009-12-15

    Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum particle physics in connection with string theory and e{sup {infinity}} theory. In 2005, Caldas and Jafari have introduced {theta}-compact fuzzy topological spaces. In this paper, the concepts of{theta}-compactness, countable{theta}-compactness and the{theta}-Lindeloef property are introduced and studied in L-topological spaces, where L is a complete de Morgan algebra. They are defined by means of{theta}-openL-sets and their inequalities. They does not rely on the structure of basis lattice L and no distributivity in L is required. They can also be characterized by{theta}-closedL-sets and their inequalities. When L is a completely de Morgan algebra, their many characterizations are presented.

  12. Genetic variability in the human cannabinoid receptor 1 is associated with resting state EEG theta power in humans.

    Science.gov (United States)

    Heitland, I; Kenemans, J L; Böcker, K B E; Baas, J M P

    2014-11-01

    It has long been postulated that exogenous cannabinoids have a profound effect on human cognitive functioning. These cannabinoid effects are thought to depend, at least in parts, on alterations of phase-locking of local field potential neuronal firing. The latter can be measured as activity in the theta frequency band (4-7Hz) by electroencephalogram. Theta oscillations are supposed to serve as a mechanism in neural representations of behaviorally relevant information. However, it remains unknown whether variability in endogenous cannabinoid activity is involved in theta rhythms and therefore, may serve as an individual differences index of human cognitive functioning. To clarify this issue, we recorded resting state EEG activity in 164 healthy human subjects and extracted EEG power across frequency bands (δ, θ, α, and β). To assess variability in the endocannabinoid system, two genetic polymorphisms (rs1049353, rs2180619) within the cannabinoid receptor 1 (CB1) were determined in all participants. As expected, we observed significant effects of rs1049353 on EEG power in the theta band at frontal, central and parietal electrode regions. Crucially, these effects were specific for the theta band, with no effects on activity in the other frequency bands. Rs2180619 showed no significant associations with theta power after Bonferroni correction. Taken together, we provide novel evidence in humans showing that genetic variability in the cannabinoid receptor 1 is associated with resting state EEG power in the theta frequency band. This extends prior findings of exogenous cannabinoid effects on theta power to the endogenous cannabinoid system. Copyright © 2014 Elsevier B.V. All rights reserved.

  13. Frontal Theta Activity Supports Detecting Mismatched Information in Visual Working Memory.

    Science.gov (United States)

    Liang, Tengfei; Hu, Zhonghua; Liu, Qiang

    2017-01-01

    During the comparison stage of visual working memory (VWM) processing, detecting the mismatch between the external sensory input and internal representations is a crucial cognitive ability for human, but the neural mechanism behind it remains largely unclear. The present study investigated the role of frontal theta power in detecting the mismatched information in VWM in a delayed matching task. A control task required to compare two simultaneously presented visual figures was also designed as a contrast to exclude the possibility that frontal theta activity just reflecting the non-memory-related behavioral conflicts. To better characterize the control mechanisms shaped by the frontal theta oscillation in human VWM, colored shapes were adopted as materials while both the task-relevant shape feature and task-irrelevant color feature could be mismatched. We found that the response times of participants were significantly delayed under the relevant- and irrelevant-mismatch conditions in both tasks and the conjunction-mismatch condition in delayed matching task. While our EEG data showed that increased frontal theta power was only observed under the relevant- and conjunction-mismatch conditions in the delayed matching task, but not the control task. These findings suggest that the frontal distributed theta activity observed here reflects the detection of mismatched information during the comparison stage of VWM, rather than the response-related conflicts. Furthermore, it is consistent with the proposal that theta-band oscillation can act as a control mechanism in working memory function so that the target-mismatched information in VWM could be successfully tracked. We also propose a possible processing structure to explain the neural dynamics underlying the mismatch detection process in VWM.

  14. Theta oscillations are sensitive to both early and late conflict processing stages: effects of alcohol intoxication.

    Science.gov (United States)

    Kovacevic, Sanja; Azma, Sheeva; Irimia, Andrei; Sherfey, Jason; Halgren, Eric; Marinkovic, Ksenija

    2012-01-01

    Prior neuroimaging evidence indicates that decision conflict activates medial and lateral prefrontal and parietal cortices. Theoretical accounts of cognitive control highlight anterior cingulate cortex (ACC) as a central node in this network. However, a better understanding of the relative primacy and functional contributions of these areas to decision conflict requires insight into the neural dynamics of successive processing stages including conflict detection, response selection and execution. Moderate alcohol intoxication impairs cognitive control as it interferes with the ability to inhibit dominant, prepotent responses when they are no longer correct. To examine the effects of moderate intoxication on successive processing stages during cognitive control, spatio-temporal changes in total event-related theta power were measured during Stroop-induced conflict. Healthy social drinkers served as their own controls by participating in both alcohol (0.6 g/kg ethanol for men, 0.55 g/kg women) and placebo conditions in a counterbalanced design. Anatomically-constrained magnetoencephalography (aMEG) approach was applied to complex power spectra for theta (4-7 Hz) frequencies. The principal generator of event-related theta power to conflict was estimated to ACC, with contributions from fronto-parietal areas. The ACC was uniquely sensitive to conflict during both early conflict detection, and later response selection and execution stages. Alcohol attenuated theta power to conflict across successive processing stages, suggesting that alcohol-induced deficits in cognitive control may result from theta suppression in the executive network. Slower RTs were associated with attenuated theta power estimated to ACC, indicating that alcohol impairs motor preparation and execution subserved by the ACC. In addition to their relevance for the currently prevailing accounts of cognitive control, our results suggest that alcohol-induced impairment of top-down strategic processing

  15. Frontal Theta Activity Supports Detecting Mismatched Information in Visual Working Memory

    Directory of Open Access Journals (Sweden)

    Tengfei Liang

    2017-10-01

    Full Text Available During the comparison stage of visual working memory (VWM processing, detecting the mismatch between the external sensory input and internal representations is a crucial cognitive ability for human, but the neural mechanism behind it remains largely unclear. The present study investigated the role of frontal theta power in detecting the mismatched information in VWM in a delayed matching task. A control task required to compare two simultaneously presented visual figures was also designed as a contrast to exclude the possibility that frontal theta activity just reflecting the non-memory-related behavioral conflicts. To better characterize the control mechanisms shaped by the frontal theta oscillation in human VWM, colored shapes were adopted as materials while both the task-relevant shape feature and task-irrelevant color feature could be mismatched. We found that the response times of participants were significantly delayed under the relevant- and irrelevant-mismatch conditions in both tasks and the conjunction-mismatch condition in delayed matching task. While our EEG data showed that increased frontal theta power was only observed under the relevant- and conjunction-mismatch conditions in the delayed matching task, but not the control task. These findings suggest that the frontal distributed theta activity observed here reflects the detection of mismatched information during the comparison stage of VWM, rather than the response-related conflicts. Furthermore, it is consistent with the proposal that theta-band oscillation can act as a control mechanism in working memory function so that the target-mismatched information in VWM could be successfully tracked. We also propose a possible processing structure to explain the neural dynamics underlying the mismatch detection process in VWM.

  16. Artificial theta stimulation impairs encoding of contextual fear memory.

    Directory of Open Access Journals (Sweden)

    Arto Lipponen

    Full Text Available Several experiments have demonstrated an intimate relationship between hippocampal theta rhythm (4-12 Hz and memory. Lesioning the medial septum or fimbria-fornix, a fiber track connecting the hippocampus and the medial septum, abolishes the theta rhythm and results in a severe impairment in declarative memory. To assess whether there is a causal relationship between hippocampal theta and memory formation we investigated whether restoration of hippocampal theta by electrical stimulation during the encoding phase also restores fimbria-fornix lesion induced memory deficit in rats in the fear conditioning paradigm. Male Wistar rats underwent sham or fimbria-fornix lesion operation. Stimulation electrodes were implanted in the ventral hippocampal commissure and recording electrodes in the septal hippocampus. Artificial theta stimulation of 8 Hz was delivered during 3-min free exploration of the test cage in half of the rats before aversive conditioning with three foot shocks during 2 min. Memory was assessed by total freezing time in the same environment 24 h and 28 h after fear conditioning, and in an intervening test session in a different context. As expected, fimbria-fornix lesion impaired fear memory and dramatically attenuated hippocampal theta power. Artificial theta stimulation produced continuous theta oscillations that were almost similar to endogenous theta rhythm in amplitude and frequency. However, contrary to our predictions, artificial theta stimulation impaired conditioned fear response in both sham and fimbria-fornix lesioned animals. These data suggest that restoration of theta oscillation per se is not sufficient to support memory encoding after fimbria-fornix lesion and that universal theta oscillation in the hippocampus with a fixed frequency may actually impair memory.

  17. Numerical studies of the linear theta pinch

    International Nuclear Information System (INIS)

    Brackbill, J.U.; Menzel, M.T.; Barnes, D.C.

    1975-01-01

    Aspects of several physical problems associated with linear theta pinches were studied using recently developed numerical methods for the solution of the nonlinear equations for time-dependent magnetohydrodynamic flow in two- and three-dimensions. The problems studied include the propagation of end-loss produced rarefaction waves, the flow produced in a proposed injection experiment geometry, and the linear growth and nonlinear saturation of instabilities in rotating plasmas, all in linear geometries. The studies illustrate how numerical computations aid in flow visualization, and how the small amplitude behavior and nonlinear fate of plasmas in unstable equilibria can be connected through the numerical solution of the dynamical equations. (auth)

  18. Material testing in a linear theta pinch

    International Nuclear Information System (INIS)

    Alani, R.; Azodi, H.; Naraghi, M.; Safaii, B.; Torabi-Fard, A.

    1983-01-01

    The interaction of stainless steel 316 and Inconel 625 alloys has been investigated with a thermonuclear-like plasma, n = 10 16 cm -3 and Tsub(i) = 1 keV, generated in the Alvand I linear theta pinch. The average power flux is 10 7 W/cm 2 and the interaction time nearly one μs. A theoretical analysis based on the formation of an observed impurity layer near the material, has been used to determine the properties of the impurity layer and the extent of the damage on the material. Although arcing has been observed, the dominant damage mechanism has been assessed to be due to evaporation. Exposure to single shots has produced very heavily defective areas and even surface cracks on the SS 316 sample, but no cracks were observed on Inconel 625 after exposure to even 18 shots. On the basis of temperature rise and evaporation a comparison is made among materials exposed to plasmas of a theta pinch, shock tube, present generation tokamak and an anticipated tokamak reactor. (orig.)

  19. Intrahemispheric theta rhythm desynchronization impairs working memory.

    Science.gov (United States)

    Alekseichuk, Ivan; Pabel, Stefanie Corinna; Antal, Andrea; Paulus, Walter

    2017-01-01

    There is a growing interest in large-scale connectivity as one of the crucial factors in working memory. Correlative evidence has revealed the anatomical and electrophysiological players in the working memory network, but understanding of the effective role of their connectivity remains elusive. In this double-blind, placebo-controlled study we aimed to identify the causal role of theta phase connectivity in visual-spatial working memory. The frontoparietal network was over- or de-synchronized in the anterior-posterior direction by multi-electrode, 6 Hz transcranial alternating current stimulation (tACS). A decrease in memory performance and increase in reaction time was caused by frontoparietal intrahemispheric desynchronization. According to the diffusion drift model, this originated in a lower signal-to-noise ratio, known as the drift rate index, in the memory system. The EEG analysis revealed a corresponding decrease in phase connectivity between prefrontal and parietal areas after tACS-driven desynchronization. The over-synchronization did not result in any changes in either the behavioral or electrophysiological levels in healthy participants. Taken together, we demonstrate the feasibility of manipulating multi-site large-scale networks in humans, and the disruptive effect of frontoparietal desynchronization on theta phase connectivity and visual-spatial working memory.

  20. Riemann-Christoffel Tensor in Differential Geometry of Fractional Order Application to Fractal Space-Time

    Science.gov (United States)

    Jumarie, Guy

    2013-04-01

    By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.

  1. On membrane interactions and a three-dimensional analog of Riemann surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Kovacs, Stefano [Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); ICTP South American Institute for Fundamental Research, IFT-UNESP,São Paulo, SP 01440-070 (Brazil); Sato, Yuki [National Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical Physics, University of the Witwartersrand,Wits 2050 (South Africa); Shimada, Hidehiko [Okayama Institute for Quantum Physics,Okayama (Japan)

    2016-02-08

    Membranes in M-theory are expected to interact via splitting and joining processes. We study these effects in the pp-wave matrix model, in which they are associated with transitions between states in sectors built on vacua with different numbers of membranes. Transition amplitudes between such states receive contributions from BPS instanton configurations interpolating between the different vacua. Various properties of the moduli space of BPS instantons are known, but there are very few known examples of explicit solutions. We present a new approach to the construction of instanton solutions interpolating between states containing arbitrary numbers of membranes, based on a continuum approximation valid for matrices of large size. The proposed scheme uses functions on a two-dimensional space to approximate matrices and it relies on the same ideas behind the matrix regularisation of membrane degrees of freedom in M-theory. We show that the BPS instanton equations have a continuum counterpart which can be mapped to the three-dimensional Laplace equation through a sequence of changes of variables. A description of configurations corresponding to membrane splitting/joining processes can be given in terms of solutions to the Laplace equation in a three-dimensional analog of a Riemann surface, consisting of multiple copies of ℝ{sup 3} connected via a generalisation of branch cuts. We discuss various general features of our proposal and we also present explicit analytic solutions.

  2. On membrane interactions and a three-dimensional analog of Riemann surfaces

    International Nuclear Information System (INIS)

    Kovacs, Stefano; Sato, Yuki; Shimada, Hidehiko

    2016-01-01

    Membranes in M-theory are expected to interact via splitting and joining processes. We study these effects in the pp-wave matrix model, in which they are associated with transitions between states in sectors built on vacua with different numbers of membranes. Transition amplitudes between such states receive contributions from BPS instanton configurations interpolating between the different vacua. Various properties of the moduli space of BPS instantons are known, but there are very few known examples of explicit solutions. We present a new approach to the construction of instanton solutions interpolating between states containing arbitrary numbers of membranes, based on a continuum approximation valid for matrices of large size. The proposed scheme uses functions on a two-dimensional space to approximate matrices and it relies on the same ideas behind the matrix regularisation of membrane degrees of freedom in M-theory. We show that the BPS instanton equations have a continuum counterpart which can be mapped to the three-dimensional Laplace equation through a sequence of changes of variables. A description of configurations corresponding to membrane splitting/joining processes can be given in terms of solutions to the Laplace equation in a three-dimensional analog of a Riemann surface, consisting of multiple copies of ℝ"3 connected via a generalisation of branch cuts. We discuss various general features of our proposal and we also present explicit analytic solutions.

  3. The Equation Δ u + ∇φ· ∇u = 8πc(1-heu) on a Riemann Surface

    International Nuclear Information System (INIS)

    Wang Meng

    2009-12-01

    Let M be a compact Riemann surface, h(x) a positive smooth function on M, and φ(x) a smooth function on M which satisfies that ∫ M e φ dV g = 1. In this paper, we consider the functional J(u) = 2 1 ∫ M |∇u| 2 e φ dV g +8πc ∫ M ue φ dV g -8πclog ∫ M he u+φ dV g . We give a sufficient condition under which J achieves its minimum for c ≤ inf xelement ofM Φ(x). (author)

  4. Chasing theta-13 with the Double Chooz experiment

    Energy Technology Data Exchange (ETDEWEB)

    Lasserre, Thierry [CEA/DSM/IRFU/SPP, Gif-sur-Yvette (France)

    2009-07-01

    Neutrino oscillation physics is entering a precision measurement area. The smallness of the theta-13 neutrino mixing angle is still enigmatic and should be resolved. Double Chooz will use two identical detectors near the Chooz nuclear power station to search for a non vanishing theta-13, and hopefully open the way to experiments aspiring to discover CP violation in the leptonic sector.

  5. The continuous determination of spacetime geometry by the Riemann curvature tensor

    International Nuclear Information System (INIS)

    Rendall, A.D.

    1988-01-01

    It is shown that generically the Riemann tensor of a Lorentz metric on an n-dimensional manifold (n ≥ 4) determines the metric up to a constant factor and hence determines the associated torsion-free connection uniquely. The resulting map from Riemann tensors to connections is continuous in the Whitney Csup(∞) topology but, at least for some manifolds, constant factors cannot be chosen so as to make the map from Riemann tensors to metrics continuous in that topology. The latter map is, however, continuous in the compact open Csup(∞) topology so that estimates of the metric and its derivatives on a compact set can be obtained from similar estimates on the curvature and its derivatives. (author)

  6. Frontal theta and beta synchronizations for monetary reward increase visual working memory capacity.

    Science.gov (United States)

    Kawasaki, Masahiro; Yamaguchi, Yoko

    2013-06-01

    Visual working memory (VWM) capacity is affected by motivational influences; however, little is known about how reward-related brain activities facilitate the VWM systems. To investigate the dynamic relationship between VWM- and reward-related brain activities, we conducted time-frequency analyses using electroencephalograph (EEG) data obtained during a monetary-incentive delayed-response task that required participants to memorize the position of colored disks. In case of a correct answer, participants received a monetary reward (0, 10 or 50 Japanese yen) announced at the beginning of each trial. Behavioral results showed that VWM capacity under high-reward condition significantly increased compared with that under low- or no-reward condition. EEG results showed that frontal theta (6 Hz) amplitudes enhanced during delay periods and positively correlated with VWM capacity, indicating involvement of theta local synchronizations in VWM. Moreover, frontal beta activities (24 Hz) were identified as reward-related activities, because delay-period amplitudes correlated with increases in VWM capacity between high-reward and no-reward conditions. Interestingly, cross-frequency couplings between frontal theta and beta phases were observed only under high-reward conditions. These findings suggest that the functional dynamic linking between VWM-related theta and reward-related beta activities on the frontal regions plays an integral role in facilitating increases in VWM capacity.

  7. Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

    Science.gov (United States)

    Chiodaroli, Elisabetta; Kreml, Ondřej

    2018-04-01

    We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157–90), and based on the techniques of De Lellis and Székelyhidi (2010 Arch. Ration. Mech. Anal. 195 225–60), we extend the results of Chiodaroli and Kreml (2014 Arch. Ration. Mech. Anal. 214 1019–49) and prove that it is possible to characterize a set of Riemann data, giving rise to a self-similar solution consisting of one admissible shock and one rarefaction wave, for which the problem also admits infinitely many admissible weak solutions.

  8. Modular transformations of conformal blocks in WZW models on Riemann surfaces of higher genus

    International Nuclear Information System (INIS)

    Miao Li; Ming Yu.

    1989-05-01

    We derive the modular transformations for conformal blocks in Wess-Zumino-Witten models on Riemann surfaces of higher genus. The basic ingredient consists of using the Chern-Simons theory developed by Witten. We find that the modular transformations generated by Dehn twists are linear combinations of Wilson line operators, which can be expressed in terms of braiding matrices. It can also be shown that modular transformation matrices for g > 0 Riemann surfaces depend only on those for g ≤ 3. (author). 13 refs, 15 figs

  9. A fast Cauchy-Riemann solver. [differential equation solution for boundary conditions by finite difference approximation

    Science.gov (United States)

    Ghil, M.; Balgovind, R.

    1979-01-01

    The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.

  10. Exact Riemann solutions of the Ripa model for flat and non-flat bottom topographies

    Science.gov (United States)

    Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

    2018-03-01

    This article is concerned with the derivation of exact Riemann solutions for Ripa model considering flat and non-flat bottom topographies. The Ripa model is a system of shallow water equations accounting for horizontal temperature gradients. In the case of non-flat bottom topography, the mass, momentum and energy conservation principles are utilized to relate the left and right states across the step-type bottom topography. The resulting system of algebraic equations is solved iteratively. Different numerical case studies of physical interest are considered. The solutions obtained from developed exact Riemann solvers are compared with the approximate solutions of central upwind scheme.

  11. Riemann problems and their application to ultra-relativistic heavy ion collisions

    International Nuclear Information System (INIS)

    Plohr, B.J.; Sharp, D.H.

    1986-07-01

    Heavy ion collisions at sufficiently high energies to form quark-gluon plasma are considered. The phase transformation from a quark-gluon phase to hadrons as the nuclear matter cools is modeled as a hydrodynamical flow. Nonlinear waves are the predominant feature of this type of flow and the Riemann problem of a relativistic gas undergoing a phase transformation is explored as a method to numerically model this phase transition process in nuclear matter. The solution of the Riemann problem is outlined and results of preliminary numerical computations of the flow are presented. 10 refs., 2 figs

  12. Reduction of 4-dim self dual super Yang-Mills onto super Riemann surfaces

    International Nuclear Information System (INIS)

    Mendoza, A.; Restuccia, A.; Martin, I.

    1990-05-01

    Recently self dual super Yang-Mills over a super Riemann surface was obtained as the zero set of a moment map on the space of superconnections to the dual of the super Lie algebra of gauge transformations. We present a new formulation of 4-dim Euclidean self dual super Yang-Mills in terms of constraints on the supercurvature. By dimensional reduction we obtain the same set of superconformal field equations which define self dual connections on a super Riemann surface. (author). 10 refs

  13. Coupling between Theta Oscillations and Cognitive Control Network during Cross-Modal Visual and Auditory Attention: Supramodal vs Modality-Specific Mechanisms.

    Science.gov (United States)

    Wang, Wuyi; Viswanathan, Shivakumar; Lee, Taraz; Grafton, Scott T

    2016-01-01

    Cortical theta band oscillations (4-8 Hz) in EEG signals have been shown to be important for a variety of different cognitive control operations in visual attention paradigms. However the synchronization source of these signals as defined by fMRI BOLD activity and the extent to which theta oscillations play a role in multimodal attention remains unknown. Here we investigated the extent to which cross-modal visual and auditory attention impacts theta oscillations. Using a simultaneous EEG-fMRI paradigm, healthy human participants performed an attentional vigilance task with six cross-modal conditions using naturalistic stimuli. To assess supramodal mechanisms, modulation of theta oscillation amplitude for attention to either visual or auditory stimuli was correlated with BOLD activity by conjunction analysis. Negative correlation was localized to cortical regions associated with the default mode network and positively with ventral premotor areas. Modality-associated attention to visual stimuli was marked by a positive correlation of theta and BOLD activity in fronto-parietal area that was not observed in the auditory condition. A positive correlation of theta and BOLD activity was observed in auditory cortex, while a negative correlation of theta and BOLD activity was observed in visual cortex during auditory attention. The data support a supramodal interaction of theta activity with of DMN function, and modality-associated processes within fronto-parietal networks related to top-down theta related cognitive control in cross-modal visual attention. On the other hand, in sensory cortices there are opposing effects of theta activity during cross-modal auditory attention.

  14. Alcohol Hits You When It Is Hard: Intoxication, Task Difficulty, and Theta Brain Oscillations.

    Science.gov (United States)

    Rosen, Burke Q; Padovan, Nevena; Marinkovic, Ksenija

    2016-04-01

    Alcohol intoxication is known to impair decision making in a variety of situations. Previous neuroimaging evidence suggests that the neurofunctional system subserving controlled processing is especially vulnerable to alcohol in conflict-evoking tasks. The present study investigated the effects of moderate alcohol intoxication on the spatiotemporal neural dynamics of event-related total theta (4 to 7 Hz) power as a function of task difficulty. Two variants of the Simon task manipulated incongruity via simple spatial stimulus-response mismatch and, in a more difficult version, by combining spatial and semantic interference. Healthy social drinkers participated in both alcohol (0.6 g/kg ethanol for men, 0.55 g/kg for women) and placebo conditions in a counterbalanced design. Whole-head magnetoencephalography (MEG) signals were acquired and event-related total theta power was calculated on each trial with Morlet wavelets. MEG sources were estimated using anatomically constrained, noise-normalized, spectral dynamic statistical parametric mapping. Longer reaction times and lower accuracy confirmed the difficulty manipulation. Response conflict (incongruity) increased and alcohol intoxication decreased event-related theta power overall during both tasks bilaterally in the medial and ventrolateral prefrontal cortices. However, alcohol-induced theta suppression was selective for conflict only in the more difficult task which engaged the dorsal anterior cingulate (dAC) and anterior inferolateral prefrontal cortices. Theta power correlated negatively with drinking levels and disinhibition, suggesting that cognitive control is susceptible in more impulsive individuals with higher alcohol intake. The spatiotemporal theta profile across the 2 tasks supports the concept of a rostrocaudal activity gradient in the medial prefrontal cortex that is modulated by task difficulty, with the dAC as the key node in the network subserving cognitive control. Conflict-related theta power was

  15. Creep curve modeling of hastelloy-X alloy by using the theta projection method

    International Nuclear Information System (INIS)

    Woo Gon, Kim; Woo-Seog, Ryu; Jong-Hwa, Chang; Song-Nan, Yin

    2007-01-01

    To model the creep curves of the Hastelloy-X alloy which is being considered as a candidate material for the VHTR (Very High Temperature gas-cooled Reactor) components, full creep curves were obtained by constant-load creep tests for different stress levels at 950 C degrees. Using the experimental creep data, the creep curves were modeled by applying the Theta projection method. A number of computing processes of a nonlinear least square fitting (NLSF) analysis was carried out to establish the suitably of the four Theta parameters. The results showed that the Θ 1 and Θ 2 parameters could not be optimized well with a large error during the fitting of the full creep curves. On the other hand, the Θ 3 and Θ 4 parameters were optimized well without an error. For this result, to find a suitable cutoff strain criterion, the NLSF analysis was performed with various cutoff strains for all the creep curves. An optimum cutoff strain range for defining the four Theta parameters accurately was found to be a 3% cutoff strain. At the 3% cutoff strain, the predicted curves coincided well with the experimental ones. The variation of the four Theta parameters as the function of a stress showed a good linearity, and the creep curves were modeled well for the low stress levels. Predicted minimum creep rate showed a good agreement with the experimental data. Also, for a design usage of the Hastelloy-X alloy, the plot of the log stress versus log the time to a 1% strain was predicted, and the creep rate curves with time and a cutoff strain at 950 C degrees were constructed numerically for a wide rang of stresses by using the Theta projection method. (authors)

  16. Super-quasi-conformal transformation and Schiffer variation on super-Riemann surface

    International Nuclear Information System (INIS)

    Takahasi, Wataru

    1990-01-01

    A set of equations which characterizes the super-Teichmueller deformations is proposed. It is a supersymmetric extension of the Beltrami equation. Relations between the set of equations and the Schiffer variations with the KN bases are discussed. This application of the KN bases shows the powerfulness of the KN theory in the study of super-Riemann surfaces. (author)

  17. The Great Gorilla Jump: An Introduction to Riemann Sums and Definite Integrals

    Science.gov (United States)

    Sealey, Vicki; Engelke, Nicole

    2012-01-01

    The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as…

  18. Riemann type algebraic structures and their differential-algebraic integrability analysis

    Directory of Open Access Journals (Sweden)

    Prykarpatsky A.K.

    2010-06-01

    Full Text Available The differential-algebraic approach to studying the Lax type integrability of generalized Riemann type equations is devised. The differentiations and the associated invariant differential ideals are analyzed in detail. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.

  19. Infinite conformal symmetries and Riemann-Hilbert transformation in super principal chiral model

    International Nuclear Information System (INIS)

    Hao Sanru; Li Wei

    1989-01-01

    This paper shows a new symmetric transformation - C transformation in super principal chiral model and discover an infinite dimensional Lie algebra related to the Virasoro algebra without central extension. By using the Riemann-Hilbert transformation, the physical origination of C transformation is discussed

  20. Superconformal algebra and central extension of meromorphic vector fields with multipoles on super-Riemann sphere

    International Nuclear Information System (INIS)

    Wang Shikun; Xu Kaiwen.

    1989-12-01

    The superconformal algebras of meromorphic vector fields with multipoles, the central extension and the relevant abelian differential of the third kind on super Riemann sphere were constructed. The background of our theory is concerned with the interaction of closed superstrings. (author). 9 refs

  1. Seeley-De Witt coefficients in a Riemann-Cartan manifold

    International Nuclear Information System (INIS)

    Cognola, G.; Zerbini, S.; Istituto Nazionale di Fisica Nucleare, Povo

    1988-01-01

    A new derivation of the first two coefficients of the heat kernel expansion for a second-order elliptic differential operator on a Riemann-Cartan manifold with arbitrary torsion is given. The expressions are presented in a very compact and tractable form useful for physical applications. Comparisons with other similar results that appeared in the literature are briefly discussed. (orig.)

  2. Regular Riemann-Hilbert transforms, Baecklund transformations and hidden symmetry algebra for some linearization systems

    International Nuclear Information System (INIS)

    Chau Ling-Lie; Ge Mo-Lin; Teh, Rosy.

    1984-09-01

    The Baecklund Transformations and the hidden symmetry algebra for Self-Dual Yang-Mills Equations, Landau-Lifshitz equations and the Extended Super Yang-Mills fields (N>2) are discussed on the base of the Regular Riemann-Hilbert Transform and the linearization equations. (author)

  3. Representation theory of current algebra and conformal field theory on Riemann surfaces

    International Nuclear Information System (INIS)

    Yamada, Yasuhiko

    1989-01-01

    We study conformal field theories with current algebra (WZW-model) on general Riemann surfaces based on the integrable representation theory of current algebra. The space of chiral conformal blocks defined as solutions of current and conformal Ward identities is shown to be finite dimensional and satisfies the factorization properties. (author)

  4. Quadratic algebras and noncommutative integration of Klein-Gordon equations in non-steckel Riemann spaces

    International Nuclear Information System (INIS)

    Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.; Shirokov, I.V.

    1995-01-01

    The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented

  5. Classical and quantum Liouville theory on the Riemann sphere with n>3 punctures (III)

    International Nuclear Information System (INIS)

    Shen Jianmin; Sheng Zhengmao; Wang Zhonghua

    1992-02-01

    We study the Classical and Quantum Liouville theory on the Riemann sphere with n>3 punctures. We get the quantum exchange algebra relations between the chiral components in the Liouville theory from our assumption on the principle of quantization. (author). 5 refs

  6. Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere

    International Nuclear Information System (INIS)

    Sabbah, C

    2004-01-01

    It is shown that the Fourier-Laplace transform of an irreducible regular differential system on the Riemann sphere underlies a polarizable regular twistor D-module if one considers only the part at finite distance. The associated holomorphic bundle defined away from the origin of the complex plane is therefore equipped with a natural harmonic metric having a tame behaviour near the origin

  7. Alpha and theta brain oscillations index dissociable processes in spoken word recognition.

    Science.gov (United States)

    Strauß, Antje; Kotz, Sonja A; Scharinger, Mathias; Obleser, Jonas

    2014-08-15

    Slow neural oscillations (~1-15 Hz) are thought to orchestrate the neural processes of spoken language comprehension. However, functional subdivisions within this broad range of frequencies are disputed, with most studies hypothesizing only about single frequency bands. The present study utilizes an established paradigm of spoken word recognition (lexical decision) to test the hypothesis that within the slow neural oscillatory frequency range, distinct functional signatures and cortical networks can be identified at least for theta- (~3-7 Hz) and alpha-frequencies (~8-12 Hz). Listeners performed an auditory lexical decision task on a set of items that formed a word-pseudoword continuum: ranging from (1) real words over (2) ambiguous pseudowords (deviating from real words only in one vowel; comparable to natural mispronunciations in speech) to (3) pseudowords (clearly deviating from real words by randomized syllables). By means of time-frequency analysis and spatial filtering, we observed a dissociation into distinct but simultaneous patterns of alpha power suppression and theta power enhancement. Alpha exhibited a parametric suppression as items increasingly matched real words, in line with lowered functional inhibition in a left-dominant lexical processing network for more word-like input. Simultaneously, theta power in a bilateral fronto-temporal network was selectively enhanced for ambiguous pseudowords only. Thus, enhanced alpha power can neurally 'gate' lexical integration, while enhanced theta power might index functionally more specific ambiguity-resolution processes. To this end, a joint analysis of both frequency bands provides neural evidence for parallel processes in achieving spoken word recognition. Copyright © 2014 Elsevier Inc. All rights reserved.

  8. Rotational instability in a linear theta pinch

    International Nuclear Information System (INIS)

    Ekdahl, C.; Bartsch, R.R.; Commisso, R.J.; Gribble, R.F.; McKenna, K.F.; Miller, G.; Siemon, R.E.

    1980-01-01

    The m=1 ''wobble'' instability of the plasma column in a 5-m linear theta pinch has been studied using an axial array of orthogonally viewing position detectors to resolve the wavelength and frequency of the column motion. The experimental results are compared with recent theoretical predictions that include finite Larmor orbit effects. The frequency and wavelength characteristics at saturation agree with the predicted dispersion relation for a plasma rotating faster than the diamagnetic drift speed. Measurements of the magnetic fields at the ends of the pinch establish the existence of currents flowing in such a way that they short out the radial electric fields in the plasma column. The magnitude of rotation, the observed delay in the onset of m=1 motion, and the magnitude of end-shorting currents can all be understood in terms of the torsional Alfven waves that communicate to the central plasma column the information that the ends have been shorted. The same waves are responsible for the torque which rotates the plasma and leads to the observed m=1 instability. Observations of the plasma in the presence of solid end plugs indicate a stabilization of high-m number modes and a reduction of the m=1 amplitude

  9. Theta oscillations locked to intended actions rhythmically modulate perception.

    Science.gov (United States)

    Tomassini, Alice; Ambrogioni, Luca; Medendorp, W Pieter; Maris, Eric

    2017-07-07

    Ongoing brain oscillations are known to influence perception, and to be reset by exogenous stimulations. Voluntary action is also accompanied by prominent rhythmic activity, and recent behavioral evidence suggests that this might be coupled with perception. Here, we reveal the neurophysiological underpinnings of this sensorimotor coupling in humans. We link the trial-by-trial dynamics of EEG oscillatory activity during movement preparation to the corresponding dynamics in perception, for two unrelated visual and motor tasks. The phase of theta oscillations (~4 Hz) predicts perceptual performance, even >1 s before movement. Moreover, theta oscillations are phase-locked to the onset of the movement. Remarkably, the alignment of theta phase and its perceptual relevance unfold with similar non-monotonic profiles, suggesting their relatedness. The present work shows that perception and movement initiation are automatically synchronized since the early stages of motor planning through neuronal oscillatory activity in the theta range.

  10. Simple UHV offset manipulator with independent theta and phi rotations

    International Nuclear Information System (INIS)

    Jamison, K.D.; Dunning, F.B.

    1984-01-01

    A simple UHV offset manipulator is described that not only allows a target crystal to be moved to any point on a circle centered on the manipulator axis but also provides indepedent theta and phi rotations at each position

  11. The theta/gamma discrete phase code occuring during the hippocampal phase precession may be a more general brain coding scheme.

    Science.gov (United States)

    Lisman, John

    2005-01-01

    In the hippocampus, oscillations in the theta and gamma frequency range occur together and interact in several ways, indicating that they are part of a common functional system. It is argued that these oscillations form a coding scheme that is used in the hippocampus to organize the readout from long-term memory of the discrete sequence of upcoming places, as cued by current position. This readout of place cells has been analyzed in several ways. First, plots of the theta phase of spikes vs. position on a track show a systematic progression of phase as rats run through a place field. This is termed the phase precession. Second, two cells with nearby place fields have a systematic difference in phase, as indicated by a cross-correlation having a peak with a temporal offset that is a significant fraction of a theta cycle. Third, several different decoding algorithms demonstrate the information content of theta phase in predicting the animal's position. It appears that small phase differences corresponding to jitter within a gamma cycle do not carry information. This evidence, together with the finding that principle cells fire preferentially at a given gamma phase, supports the concept of theta/gamma coding: a given place is encoded by the spatial pattern of neurons that fire in a given gamma cycle (the exact timing within a gamma cycle being unimportant); sequential places are encoded in sequential gamma subcycles of the theta cycle (i.e., with different discrete theta phase). It appears that this general form of coding is not restricted to readout of information from long-term memory in the hippocampus because similar patterns of theta/gamma oscillations have been observed in multiple brain regions, including regions involved in working memory and sensory integration. It is suggested that dual oscillations serve a general function: the encoding of multiple units of information (items) in a way that preserves their serial order. The relationship of such coding to

  12. Are the iota(1440) and theta(1640) glueballs or quarkonia

    International Nuclear Information System (INIS)

    Ono, S.; Pene, O.

    1982-01-01

    We study the possibility that the iota (1440) and theta (1640) are radially excited quarkonium states (2S and 2P). Their masses, total decay rates and psi → iotaγ, thetaγ branching ratios are roughly in agreement with this hypothesis but deltaπ dominance in iota decay is difficult to explain. We propose clear tests to check if they are quarkonium states. (orig.)

  13. Modification of the Riemann problem and the application for the boundary conditions in computational fluid dynamics

    Directory of Open Access Journals (Sweden)

    Kyncl Martin

    2017-01-01

    Full Text Available We work with the system of partial differential equations describing the non-stationary compressible turbulent fluid flow. It is a characteristic feature of the hyperbolic equations, that there is a possible raise of discontinuities in solutions, even in the case when the initial conditions are smooth. The fundamental problem in this area is the solution of the so-called Riemann problem for the split Euler equations. It is the elementary problem of the one-dimensional conservation laws with the given initial conditions (LIC - left-hand side, and RIC - right-hand side. The solution of this problem is required in many numerical methods dealing with the 2D/3D fluid flow. The exact (entropy weak solution of this hyperbolical problem cannot be expressed in a closed form, and has to be computed by an iterative process (to given accuracy, therefore various approximations of this solution are being used. The complicated Riemann problem has to be further modified at the close vicinity of boundary, where the LIC is given, while the RIC is not known. Usually, this boundary problem is being linearized, or roughly approximated. The inaccuracies implied by these simplifications may be small, but these have a huge impact on the solution in the whole studied area, especially for the non-stationary flow. Using the thorough analysis of the Riemann problem we show, that the RIC for the local problem can be partially replaced by the suitable complementary conditions. We suggest such complementary conditions accordingly to the desired preference. This way it is possible to construct the boundary conditions by the preference of total values, by preference of pressure, velocity, mass flow, temperature. Further, using the suitable complementary conditions, it is possible to simulate the flow in the vicinity of the diffusible barrier. On the contrary to the initial-value Riemann problem, the solution of such modified problems can be written in the closed form for some

  14. Transient Global Amnesia Deteriorates the Network Efficiency of the Theta Band.

    Directory of Open Access Journals (Sweden)

    Young Ho Park

    Full Text Available Acute perturbation of the hippocampus, one of the connector hubs in the brain, is a key step in the pathophysiological cascade of transient global amnesia (TGA. We tested the hypothesis that network efficiency, meaning the efficiency of information exchange over a network, is impaired during the acute stage of TGA. Graph theoretical analysis was applied to resting-state EEG data collected from 21 patients with TGA. The EEG data were obtained twice, once during the acute stage ( 2 months after symptom onset of TGA. Characteristic path lengths and clustering coefficients of functional networks constructed using phase-locking values were computed and normalized as a function of the degree in the delta, theta, alpha, beta 1, beta 2 and gamma frequency bands of the EEG. We investigated whether the normalized characteristic path length (nCPL and normalized clustering coefficients (nCC differed significantly between the acute and resolved stages of TGA at each frequency band using the Wilcoxon signed-rank test. For networks where the nCPL or nCC differed significantly between the two stages, we also evaluated changes in the connections of the brain networks. During the acute stage of TGA, the nCPL of the theta band networks with mean degrees of 8, 8.5, 9 and 9.5 significantly increased (P < 0.05. During the acute stage, the lost edges for these networks were mostly found between the anterior (frontal and anterior temporal and posterior (parieto-occipital and posterior temporal brain regions, whereas newly developed edges were primarily found between the left and right frontotemporal regions. The nCC of the theta band with a mean degree of 5.5 significantly decreased during the acute stage (P < 0.05. Our results indicate that TGA deteriorates the network efficiency of the theta frequency band. This effect might be related to the desynchronization between the anterior and posterior brain areas.

  15. Selberg trace formula for bordered Riemann surfaces: Hyperbolic, elliptic and parabolic conjugacy classes, and determinants of Maass-Laplacians

    International Nuclear Information System (INIS)

    Bolte, J.

    1992-08-01

    The Selberg trace formula for automorphic forms of weight m ε- Z, on bordered Riemann surfaces is developed. The trace formula is formulated for arbitrary Fuchsian groups of the first kind which include hyperbolic, elliptic and parabolic conjugacy classes. In the case of compact bordered Riemann surfaces we can explicitly evaluate determinants of Maass-Laplacians for both Dirichlet and Neumann boundary-conditions, respectively. Some implications for the open bosonic string theory are mentioned. (orig.)

  16. Generalization of the fejer-hadamard type inequalities for p-convex functions via k-fractional integrals

    Directory of Open Access Journals (Sweden)

    Ghulam Farid

    2017-10-01

    Full Text Available The aim of this paper is to obtain some more general fractional integral inequalities of Fejer Hadamard type for p-convex functions via Riemann-Liouville k-fractional integrals. Also in particular fractional inequalities for p-convex functions via Riemann-Liouville fractional integrals have been deduced.

  17. A variational principle giving gravitational 'superpotentials', the affine connection, Riemann tensor, and Einstein field equations

    International Nuclear Information System (INIS)

    Stachel, J.

    1977-01-01

    A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensor Rsub(μνkappalambda) in terms of the affine connection and metric; the definition of the affine connection in terms of the metric; the Einstein field equations; and the definition of a set of gravitational 'superpotentials' closely connected with the Komar conservation laws (Phys. Rev.; 113:934 (1959)). Substitution of the definition of the affine connection into this Lagrangian results in a second-order Lagrangian, from which follow the definition of the fully covariant Riemann tensor in terms of the metric, the Einstein equations, and the definition of the gravitational 'superpotentials'. (author)

  18. An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State

    Energy Technology Data Exchange (ETDEWEB)

    Kamm, James Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-03-05

    This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equation of state and for the JWL equation of state.

  19. Ship-induced solitary Riemann waves of depression in Venice Lagoon

    International Nuclear Information System (INIS)

    Parnell, Kevin E.; Soomere, Tarmo; Zaggia, Luca; Rodin, Artem; Lorenzetti, Giuliano; Rapaglia, John; Scarpa, Gian Marco

    2015-01-01

    We demonstrate that ships of moderate size, sailing at low depth Froude numbers (0.37–0.5) in a navigation channel surrounded by shallow banks, produce depressions with depths up to 2.5 m. These depressions (Bernoulli wakes) propagate as long-living strongly nonlinear solitary Riemann waves of depression substantial distances into Venice Lagoon. They gradually become strongly asymmetric with the rear of the depression becoming extremely steep, similar to a bore. As they are dynamically similar, air pressure fluctuations moving over variable-depth coastal areas could generate meteorological tsunamis with a leading depression wave followed by a devastating bore-like feature. - Highlights: • Unprecedently deep long-living ship-induced waves of depression detected. • Such waves are generated in channels with side banks under low Froude numbers. • The propagation of these waves is replicated using Riemann waves. • Long-living waves of depression form bore-like features at rear slope

  20. Instanton calculus without equations of motion: semiclassics from monodromies of a Riemann surface

    Science.gov (United States)

    Gulden, Tobias; Janas, Michael; Kamenev, Alex

    2015-02-01

    Instanton calculations in semiclassical quantum mechanics rely on integration along trajectories which solve classical equations of motion. However in systems with higher dimensionality or complexified phase space these are rarely attainable. A prime example are spin-coherent states which are used e.g. to describe single molecule magnets (SMM). We use this example to develop instanton calculus which does not rely on explicit solutions of the classical equations of motion. Energy conservation restricts the complex phase space to a Riemann surface of complex dimension one, allowing to deform integration paths according to Cauchy’s integral theorem. As a result, the semiclassical actions can be evaluated without knowing actual classical paths. Furthermore we show that in many cases such actions may be solely derived from monodromy properties of the corresponding Riemann surface and residue values at its singular points. As an example, we consider quenching of tunneling processes in SMM by an applied magnetic field.

  1. Ship-induced solitary Riemann waves of depression in Venice Lagoon

    Energy Technology Data Exchange (ETDEWEB)

    Parnell, Kevin E. [College of Marine and Environmental Sciences and Centre for Tropical Environmental and Sustainability Sciences, James Cook University, Queensland 4811 (Australia); Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Soomere, Tarmo, E-mail: soomere@cs.ioc.ee [Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Estonian Academy of Sciences, Kohtu 6, 10130 Tallinn (Estonia); Zaggia, Luca [Institute of Marine Sciences, National Research Council, Castello 2737/F, 30122 Venice (Italy); Rodin, Artem [Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Lorenzetti, Giuliano [Institute of Marine Sciences, National Research Council, Castello 2737/F, 30122 Venice (Italy); Rapaglia, John [Sacred Heart University Department of Biology, 5151 Park Avenue, Fairfield, CT 06825 (United States); Scarpa, Gian Marco [Università Ca' Foscari, Dorsoduro 3246, 30123 Venice (Italy)

    2015-03-06

    We demonstrate that ships of moderate size, sailing at low depth Froude numbers (0.37–0.5) in a navigation channel surrounded by shallow banks, produce depressions with depths up to 2.5 m. These depressions (Bernoulli wakes) propagate as long-living strongly nonlinear solitary Riemann waves of depression substantial distances into Venice Lagoon. They gradually become strongly asymmetric with the rear of the depression becoming extremely steep, similar to a bore. As they are dynamically similar, air pressure fluctuations moving over variable-depth coastal areas could generate meteorological tsunamis with a leading depression wave followed by a devastating bore-like feature. - Highlights: • Unprecedently deep long-living ship-induced waves of depression detected. • Such waves are generated in channels with side banks under low Froude numbers. • The propagation of these waves is replicated using Riemann waves. • Long-living waves of depression form bore-like features at rear slope.

  2. Flux quantization and quantum mechanics on Riemann surfaces in an external magnetic field

    International Nuclear Information System (INIS)

    Bolte, J.; Steiner, F.

    1990-10-01

    We investigate the possibility to apply an external constant magnetic field to a quantum mechanical system consisting of a particle moving on a compact or non-compact two-dimensional manifold of constant negative Gaussian curvature and of finite volume. For the motion on compact Riemann surfaces we find that a consistent formulation is only possible if the magnetic flux is quantized, as it is proportional to the (integrated) first Chern class of a certain complex line bundle over the manifold. In the case of non-compact surfaces of finite volume we obtain the striking result that the magnetic flux has to vanish identically due to the theorem that any holomorphic line bundle over a non-compact Riemann surface is holomorphically trivial. (orig.)

  3. Integral relations for invariants constructed from three Riemann tensors and their applications in quantum gravity

    International Nuclear Information System (INIS)

    van Nieuwenhuizen, P.; Wu, C.C.

    1977-01-01

    The lowest order quantum corrections to pure gravitation are finite because there exists an integral relation between products of two Riemann tensors (the Gauss--Bonnet theorem). In this article several algebraic and integral relations are determined between products of three Riemann tensors in four- and six-dimensional spacetime. In both cases, one is left with only one invariant when R/sub μ//sub ν/=0, viz., ∫ (-g) 1 / 2 (R/sub b//sub β//sub μ//sub ν/R/sup μ//sup ν//sup rho//sup sigma/R/sub rho//sub sigma/ /sup α//sup β/).It is explicitly shown that this invariant does not vanish, even when R/sub μ//sub ν/=0. Consequently, the two-loop quantum corrections to pure gravitation will only be finite if, due to miraculous cancellation, the coefficient of this invariant vanishes

  4. Multi-loop string amplitudes and Riemann surfaces

    International Nuclear Information System (INIS)

    Taylor, J.G.

    1986-01-01

    The paper was presented at the workshop on 'Supersymmetry and its applications', Cambridge, United Kingdom, 1985. Super-string theory is discussed under the following topic headings: the functional approach to the string amplitude, Rieman surfaces, the determinants Δsub(epsilon)(1) and Δsub(epsilon)(2), Green's functions, total amplitude, and divergence analysis. (U.K.)

  5. Quantum Riemann surfaces. Pt. 1. The unit disc

    Energy Technology Data Exchange (ETDEWEB)

    Klimek, S.; Lesniewski, A. (Harvard Univ., Cambridge, MA (United States))

    1992-05-01

    We construct a non-commutative C{sup *}-algebra C{sub {mu}}(anti U) which is a quantum deformation of the algebra of continuous functions on the closed unit disc anti U.C{sub {mu}}(anti U) is generated by the Toeplitz operators on a suitable Hilbert space of holomorphic functions on U. (orig.).

  6. Distinguishing stimulus and response codes in theta oscillations in prefrontal areas during inhibitory control of automated responses.

    Science.gov (United States)

    Mückschel, Moritz; Dippel, Gabriel; Beste, Christian

    2017-11-01

    Response inhibition mechanisms are mediated via cortical and subcortical networks. At the cortical level, the superior frontal gyrus, including the supplementary motor area (SMA) and inferior frontal areas, is important. There is an ongoing debate about the functional roles of these structures during response inhibition as it is unclear whether these structures process different codes or contents of information during response inhibition. In the current study, we examined this question with a focus on theta frequency oscillations during response inhibition processes. We used a standard Go/Nogo task in a sample of human participants and combined different EEG signal decomposition methods with EEG beamforming approaches. The results suggest that stimulus coding during inhibitory control is attained by oscillations in the upper theta frequency band (∼7 Hz). In contrast, response selection codes during inhibitory control appear to be attained by the lower theta frequency band (∼4 Hz). Importantly, these different codes seem to be processed in distinct functional neuroanatomical structures. Although the SMA may process stimulus codes and response selection codes, the inferior frontal cortex may selectively process response selection codes during inhibitory control. Taken together, the results suggest that different entities within the functional neuroanatomical network associated with response inhibition mechanisms process different kinds of codes during inhibitory control. These codes seem to be reflected by different oscillations within the theta frequency band. Hum Brain Mapp 38:5681-5690, 2017. © 2017 Wiley-Liss, Inc. © 2017 Wiley Periodicals, Inc.

  7. Jet Riemann-Lagrange Geometry Applied to Evolution DEs Systems from Economy

    OpenAIRE

    Neagu, Mircea

    2007-01-01

    The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet Yang-Mills energies, starting from some given non-linear evolution DEs systems modelling economic phenomena, like the Kaldor model of the bussines cycle or the Tobin-Benhabib-Miyao model regarding the role of money on economic growth.

  8. Temperature duality on Riemann surface and cosmological solutions for genus g = 1 and 2

    International Nuclear Information System (INIS)

    Yan Jun; Wang Shunjin

    1999-01-01

    A bosonic string model at finite temperature on the gravitation g μν and the dilaton φ background field is examined. Moreover, the duality relation of energy momentum tensor on high genus Riemann surface is derived. At the same time, the temperature duality invariance for the action of string gas matter is proved in 4-D Robertson-Walker metric, the string cosmological solutions and temperature duality of the equations of motion for genus g = 1 and 2 are also investigated

  9. Stability of the isentropic Riemann solutions of the full multidimensional Euler system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Kreml, Ondřej; Vasseur, A.

    2015-01-01

    Roč. 47, č. 3 (2015), s. 2416-2425 ISSN 0036-1410 R&D Projects: GA ČR GA13-00522S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Euler system * isentropic solutions * Riemann problem * rarefaction wave Subject RIV: BA - General Mathematics Impact factor: 1.486, year: 2015 http://epubs.siam.org/doi/abs/10.1137/140999827

  10. Codomains for the Cauchy-Riemann and Laplace operators in ℝ2

    Directory of Open Access Journals (Sweden)

    Lloyd Edgar S. Moyo

    2008-01-01

    Full Text Available A codomain for a nonzero constant-coefficient linear partial differential operator P(∂ with fundamental solution E is a space of distributions T for which it is possible to define the convolution E*T and thus solving the equation P(∂S=T. We identify codomains for the Cauchy-Riemann operator in ℝ2 and Laplace operator in ℝ2 . The convolution is understood in the sense of the S′-convolution.

  11. Representation of symmetric metric connection via Riemann-Christoffel curvature tensor

    International Nuclear Information System (INIS)

    Selikhov, A.V.

    1989-01-01

    Bivector σ-bar μ ν ' which is the Jacoby matrix of the transformation to the Riemanian coordinates is considered in the paper. Basing on the dual nature of σ-bar μ ν ' the representation of metric connection (Christoffel symbols) have been obtained at the Riemanian coordinates via Riemann-Christoffel curvature tensor; the covariant conserved four-momentum in the general theory of relativity have been constructed. 11 refs

  12. The mass-damped Riemann problem and the aerodynamic surface force calculation for an accelerating body

    International Nuclear Information System (INIS)

    Tan, Zhiqiang; Wilson, D.; Varghese, P.L.

    1997-01-01

    We consider an extension of the ordinary Riemann problem and present an efficient approximate solution that can be used to improve the calculations of aerodynamic forces on an accelerating body. The method is demonstrated with one-dimensional examples where the Euler equations and the body motion are solved in the non-inertial co-ordinate frame fixed to the accelerating body. 8 refs., 6 figs

  13. A novel supersymmetry in 2-dimensional Yang-Mills theory on Riemann surfaces

    International Nuclear Information System (INIS)

    Soda, Jiro

    1991-02-01

    We find a novel supersymmetry in 2-dimensional Maxwell and Yang-Mills theories. Using this supersymmetry, it is shown that the 2-dimensional Euclidean pure gauge theory on a closed Riemann surface Σ can be reduced to a topological field theory which is the 3-dimensional Chern-Simons gauge theory in the special space-time topology Σ x R. Related problems are also discussed. (author)

  14. Cálculo de áreas mediante la suma de Riemann con la TI-83

    OpenAIRE

    Lupiáñez, José Luis

    2002-01-01

    En este artículo presentamos una actividad para introducir el cálculo del área que encierra una curva, basada en la Suma de Riemann, y que puede realizarse con la calculadora TI-83. El planteamiento de la actividad permite estudiar varias funciones sin perder tiempo en tediosos cálculos, con idea de observar lo acertado de este método de aproximación.

  15. Vertex operators, non-abelian orbifolds and the Riemann-Hilbert problem

    International Nuclear Information System (INIS)

    Gato, B.; Massachusetts Inst. of Tech., Cambridge

    1990-01-01

    We show how to construct the oscillator part of vertex operators for the bosonic string moving on non-abelian orbifolds, using the conserved charges method. When the three-string vertices are twisted by non-commuting group elements, the construction of the conserved charges becomes the Riemann-Hilbert problem with monodromy matrices given by the twists. This is solvable for any given configuration and any non-abelian orbifold. (orig.)

  16. Non-uniqueness of admissible weak solutions to the Riemann problem for the isentropic Euler equations

    Czech Academy of Sciences Publication Activity Database

    Chiodaroli, E.; Kreml, Ondřej

    2018-01-01

    Roč. 31, č. 4 (2018), s. 1441-1460 ISSN 0951-7715 R&D Projects: GA ČR(CZ) GJ17-01694Y Institutional support: RVO:67985840 Keywords : Riemann problem * non-uniqueness * weak solutions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.767, year: 2016 http://iopscience.iop.org/ article /10.1088/1361-6544/aaa10d/meta

  17. Non-uniqueness of admissible weak solutions to the Riemann problem for the isentropic Euler equations

    Czech Academy of Sciences Publication Activity Database

    Chiodaroli, E.; Kreml, Ondřej

    2018-01-01

    Roč. 31, č. 4 (2018), s. 1441-1460 ISSN 0951-7715 R&D Projects: GA ČR(CZ) GJ17-01694Y Institutional support: RVO:67985840 Keywords : Riemann problem * non-uniqueness * weak solutions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.767, year: 2016 http://iopscience.iop.org/article/10.1088/1361-6544/aaa10d/meta

  18. The morphology of midcingulate cortex predicts frontal-midline theta neurofeedback success

    Directory of Open Access Journals (Sweden)

    Stefanie eEnriquez-Geppert

    2013-08-01

    Full Text Available Humans differ in their ability to learn how to control their own brain activity by neurofeedback. However, neural mechanisms underlying these inter-individual differences, which may determine training success and associated cognitive enhancement, are not well understood. Here, it is asked whether neurofeedback success of frontal-midline (fm theta, an oscillation related to higher cognitive functions, could be predicted by the morphology of brain structures known to be critically involved in fm-theta generation. Nineteen young, right-handed participants underwent magnetic resonance imaging of T1-weighted brain images, and took part in an individualized, eight-session neurofeedback training in order to learn how to enhance activity in their fm-theta frequency band. Initial training success, measured at the second training session, was correlated with the final outcome measure. We found that the inferior, superior and middle frontal cortices were not associated with training success. However, volume of the midcingulate cortex as well as volume and concentration of the underlying white matter structures act as predictor variables for the general responsiveness to training. These findings suggest a neuroanatomical foundation for the ability to learn to control one’s own brain activity.

  19. Lateralized theta wave connectivity and language performance in 2- to 5-year-old children.

    Science.gov (United States)

    Kikuchi, Mitsuru; Shitamichi, Kiyomi; Yoshimura, Yuko; Ueno, Sanae; Remijn, Gerard B; Hirosawa, Tetsu; Munesue, Toshio; Tsubokawa, Tsunehisa; Haruta, Yasuhiro; Oi, Manabu; Higashida, Haruhiro; Minabe, Yoshio

    2011-10-19

    Recent neuroimaging studies support the view that a left-lateralized brain network is crucial for language development in children. However, no previous studies have demonstrated a clear link between lateralized brain functional network and language performance in preschool children. Magnetoencephalography (MEG) is a noninvasive brain imaging technique and is a practical neuroimaging method for use in young children. MEG produces a reference-free signal, and is therefore an ideal tool to compute coherence between two distant cortical rhythms. In the present study, using a custom child-sized MEG system, we investigated brain networks while 78 right-handed preschool human children (32-64 months; 96% were 3-4 years old) listened to stories with moving images. The results indicated that left dominance of parietotemporal coherence in theta band activity (6-8 Hz) was specifically correlated with higher performance of language-related tasks, whereas this laterality was not correlated with nonverbal cognitive performance, chronological age, or head circumference. Power analyses did not reveal any specific frequencies that contributed to higher language performance. Our results suggest that it is not the left dominance in theta oscillation per se, but the left-dominant phase-locked connectivity via theta oscillation that contributes to the development of language ability in young children.

  20. Semantic congruence enhances memory of episodic associations: role of theta oscillations.

    Science.gov (United States)

    Atienza, Mercedes; Crespo-Garcia, Maite; Cantero, Jose L

    2011-01-01

    Growing evidence suggests that theta oscillations play a crucial role in episodic encoding. The present study evaluates whether changes in electroencephalographic theta source dynamics mediate the positive influence of semantic congruence on incidental associative learning. Here we show that memory for episodic associations (face-location) is more accurate when studied under semantically congruent contexts. However, only participants showing RT priming effect in a conceptual priming test (priming group) also gave faster responses when recollecting source information of semantically congruent faces as compared with semantically incongruent faces. This improved episodic retrieval was positively correlated with increases in theta power during the study phase mainly in the bilateral parahippocampal gyrus, left superior temporal gyrus, and left lateral posterior parietal lobe. Reconstructed signals from the estimated sources showed higher theta power for congruent than incongruent faces and also for the priming than the nonpriming group. These results are in agreement with the attention to memory model. Besides directing top-down attention to goal-relevant semantic information during encoding, the dorsal parietal lobe may also be involved in redirecting attention to bottom-up-driven memories thanks to connections between the medial-temporal and the left ventral parietal lobe. The latter function can either facilitate or interfere with encoding of face-location associations depending on whether they are preceded by semantically congruent or incongruent contexts, respectively, because only in the former condition retrieved representations related to the cue and the face are both coherent with the person identity and are both associated with the same location.

  1. Theta frequency background tunes transmission but not summation of spiking responses.

    Directory of Open Access Journals (Sweden)

    Dhanya Parameshwaran

    Full Text Available Hippocampal neurons are known to fire as a function of frequency and phase of spontaneous network rhythms, associated with the animal's behaviour. This dependence is believed to give rise to precise rate and temporal codes. However, it is not well understood how these periodic membrane potential fluctuations affect the integration of synaptic inputs. Here we used sinusoidal current injection to the soma of CA1 pyramidal neurons in the rat brain slice to simulate background oscillations in the physiologically relevant theta and gamma frequency range. We used a detailed compartmental model to show that somatic current injection gave comparable results to more physiological synaptically driven theta rhythms incorporating excitatory input in the dendrites, and inhibitory input near the soma. We systematically varied the phase of synaptic inputs with respect to this background, and recorded changes in response and summation properties of CA1 neurons using whole-cell patch recordings. The response of the cell was dependent on both the phase of synaptic inputs and frequency of the background input. The probability of the cell spiking for a given synaptic input was up to 40% greater during the depolarized phases between 30-135 degrees of theta frequency current injection. Summation gain on the other hand, was not affected either by the background frequency or the phasic afferent inputs. This flat summation gain, coupled with the enhanced spiking probability during depolarized phases of the theta cycle, resulted in enhanced transmission of summed inputs during the same phase window of 30-135 degrees. Overall, our study suggests that although oscillations provide windows of opportunity to selectively boost transmission and EPSP size, summation of synaptic inputs remains unaffected during membrane oscillations.

  2. Harnessing the power of theta: natural manipulations of cognitive performance during hippocampal theta-contingent eyeblink conditioning

    Science.gov (United States)

    Hoffmann, Loren C.; Cicchese, Joseph J.; Berry, Stephen D.

    2015-01-01

    Neurobiological oscillations are regarded as essential to normal information processing, including coordination and timing of cells and assemblies within structures as well as in long feedback loops of distributed neural systems. The hippocampal theta rhythm is a 3–12 Hz oscillatory potential observed during cognitive processes ranging from spatial navigation to associative learning. The lower range, 3–7 Hz, can occur during immobility and depends upon the integrity of cholinergic forebrain systems. Several studies have shown that the amount of pre-training theta in the rabbit strongly predicts the acquisition rate of classical eyeblink conditioning and that impairment of this system substantially slows the rate of learning. Our lab has used a brain-computer interface (BCI) that delivers eyeblink conditioning trials contingent upon the explicit presence or absence of hippocampal theta. A behavioral benefit of theta-contingent training has been demonstrated in both delay and trace forms of the paradigm with a two- to four-fold increase in learning speed. This behavioral effect is accompanied by enhanced amplitude and synchrony of hippocampal local field potential (LFP)s, multi-unit excitation, and single-unit response patterns that depend on theta state. Additionally, training in the presence of hippocampal theta has led to increases in the salience of tone-induced unit firing patterns in the medial prefrontal cortex, followed by persistent multi-unit activity during the trace interval. In cerebellum, rhythmicity and precise synchrony of stimulus time-locked LFPs with those of hippocampus occur preferentially under the theta condition. Here we review these findings, integrate them into current models of hippocampal-dependent learning and suggest how improvement in our understanding of neurobiological oscillations is critical for theories of medial temporal lobe processes underlying intact and pathological learning. PMID:25918501

  3. Harnessing the power of theta: natural manipulations of cognitive performance during hippocampal theta-contingent eyeblink conditioning.

    Science.gov (United States)

    Hoffmann, Loren C; Cicchese, Joseph J; Berry, Stephen D

    2015-01-01

    Neurobiological oscillations are regarded as essential to normal information processing, including coordination and timing of cells and assemblies within structures as well as in long feedback loops of distributed neural systems. The hippocampal theta rhythm is a 3-12 Hz oscillatory potential observed during cognitive processes ranging from spatial navigation to associative learning. The lower range, 3-7 Hz, can occur during immobility and depends upon the integrity of cholinergic forebrain systems. Several studies have shown that the amount of pre-training theta in the rabbit strongly predicts the acquisition rate of classical eyeblink conditioning and that impairment of this system substantially slows the rate of learning. Our lab has used a brain-computer interface (BCI) that delivers eyeblink conditioning trials contingent upon the explicit presence or absence of hippocampal theta. A behavioral benefit of theta-contingent training has been demonstrated in both delay and trace forms of the paradigm with a two- to four-fold increase in learning speed. This behavioral effect is accompanied by enhanced amplitude and synchrony of hippocampal local field potential (LFP)s, multi-unit excitation, and single-unit response patterns that depend on theta state. Additionally, training in the presence of hippocampal theta has led to increases in the salience of tone-induced unit firing patterns in the medial prefrontal cortex, followed by persistent multi-unit activity during the trace interval. In cerebellum, rhythmicity and precise synchrony of stimulus time-locked LFPs with those of hippocampus occur preferentially under the theta condition. Here we review these findings, integrate them into current models of hippocampal-dependent learning and suggest how improvement in our understanding of neurobiological oscillations is critical for theories of medial temporal lobe processes underlying intact and pathological learning.

  4. Chasing {theta}{sub 13} with new reactor neutrino experiments

    Energy Technology Data Exchange (ETDEWEB)

    Lasserre, Th. [DSM/DAPNIA/SPP, CEA/Saclay, 91191 Gif-sur-Yvette (France)

    2005-12-15

    It is now widely accepted that a new middle baseline disappearance reactor neutrino experiment with multiple detectors could provide a clean measurement of the {theta}{sub 13} mixing angle, free from any parameter degeneracies and correlations induced by matter effect and the unknown leptonic Dirac CP phase. The current best constraint on the third mixing angle comes from the Chooz reactor neutrino experiment sin{sup 2}(2{theta}{sub 13})<0.2 (90 % C.L., {delta}m{sub atm}{sup 2}=2.010{sup -3} eV{sup 2}). Several projects of experiment, with different timescales, have been proposed over the last two years all around the world. Their sensitivities range from sin{sup 2}(2{theta}{sub 13})<0.01 to 0.03, having thus an excellent discovery potential of the {nu}{sub e} fraction of {nu}{sub 3}.

  5. Continuous theta burst stimulation of angular gyrus reduces subjective recollection.

    Directory of Open Access Journals (Sweden)

    Yasemin Yazar

    Full Text Available The contribution of lateral parietal regions such as the angular gyrus to human episodic memory has been the subject of much debate following widespread observations of left parietal activity in healthy volunteers during functional neuroimaging studies of memory retrieval. Patients with lateral parietal lesions are not amnesic, but recent evidence indicates that their memory abilities may not be entirely preserved. Whereas recollection appears intact when objective measures such as source accuracy are used, patients often exhibit reduced subjective confidence in their accurate recollections. When asked to recall autobiographical memories, they may produce spontaneous narratives that lack richness and specificity, but can remember specific details when prompted. Two distinct theoretical accounts have been proposed to explain these results: that the patients have a deficit in the bottom-up capturing of attention by retrieval output, or that they have an impairment in the subjective experience of recollection. The present study aimed to differentiate between these accounts using continuous theta burst stimulation (cTBS in healthy participants to disrupt function of specific left parietal subregions, including angular gyrus. Inconsistent with predictions of the attentional theory, angular gyrus cTBS did not result in greater impairment of free recall than cued recall. Supporting predictions of the subjective recollection account, temporary disruption of angular gyrus was associated with highly accurate source recollection accuracy but a selective reduction in participants' rated source confidence. The findings are consistent with a role for angular gyrus in the integration of memory features into a conscious representation that enables the subjective experience of remembering.

  6. Modelling the transition between fixed and mobile bed conditions in two-phase free-surface flows: The Composite Riemann Problem and its numerical solution

    Science.gov (United States)

    Rosatti, Giorgio; Zugliani, Daniel

    2015-03-01

    In a two-phase free-surface flow, the transition from a mobile-bed condition to a fixed-bed one (and vice versa) occurs at a sharp interface across which the relevant system of partial differential equations changes abruptly. This leads to the possibility of conceiving a new type of Riemann Problem (RP), which we have called Composite Riemann Problem (CRP), where not only the initial constant values of the variables but also the system of equations change from left to right of a discontinuity. In this paper, we present a strategy for solving a CRP by reducing it to a standard RP of a single, composite system of equations. This can be obtained by combining the two original systems by means of a suitable weighting function, namely the erodibility variable, and the introduction of an appropriate differential equation for this quantity. In this way, the CRP problem can be analyzed theoretically with standard methods, and the features of the solutions can be clearly identified. In particular, a stationary contact wave is able to correctly describe the sharp transition between mobile- and fixed-bed conditions. A finite volume scheme based on the Multiple Averages Generalized Roe approach (Rosatti and Begnudelli (2013) [22]) was used to numerically solve the fixed-mobile CRP. Several test cases demonstrate the effectiveness, exact well balanceness and high accuracy of the scheme when applied to problems that fall within the physical range of applicability of the relevant mathematical model.

  7. Pre-stimulus thalamic theta power predicts human memory formation.

    Science.gov (United States)

    Sweeney-Reed, Catherine M; Zaehle, Tino; Voges, Jürgen; Schmitt, Friedhelm C; Buentjen, Lars; Kopitzki, Klaus; Richardson-Klavehn, Alan; Hinrichs, Hermann; Heinze, Hans-Jochen; Knight, Robert T; Rugg, Michael D

    2016-09-01

    Pre-stimulus theta (4-8Hz) power in the hippocampus and neocortex predicts whether a memory for a subsequent event will be formed. Anatomical studies reveal thalamus-hippocampal connectivity, and lesion, neuroimaging, and electrophysiological studies show that memory processing involves the dorsomedial (DMTN) and anterior thalamic nuclei (ATN). The small size and deep location of these nuclei have limited real-time study of their activity, however, and it is unknown whether pre-stimulus theta power predictive of successful memory formation is also found in these subcortical structures. We recorded human electrophysiological data from the DMTN and ATN of 7 patients receiving deep brain stimulation for refractory epilepsy. We found that greater pre-stimulus theta power in the right DMTN was associated with successful memory encoding, predicting both behavioral outcome and post-stimulus correlates of successful memory formation. In particular, significant correlations were observed between right DMTN theta power and both frontal theta and right ATN gamma (32-50Hz) phase alignment, and frontal-ATN theta-gamma cross-frequency coupling. We draw the following primary conclusions. Our results provide direct electrophysiological evidence in humans of a role for the DMTN as well as the ATN in memory formation. Furthermore, prediction of subsequent memory performance by pre-stimulus thalamic oscillations provides evidence that post-stimulus differences in thalamic activity that index successful and unsuccessful encoding reflect brain processes specifically underpinning memory formation. Finally, the findings broaden the understanding of brain states that facilitate memory encoding to include subcortical as well as cortical structures. Copyright © 2016 Elsevier Inc. All rights reserved.

  8. Resting-state theta band connectivity and graph analysis in generalized social anxiety disorder.

    Science.gov (United States)

    Xing, Mengqi; Tadayonnejad, Reza; MacNamara, Annmarie; Ajilore, Olusola; DiGangi, Julia; Phan, K Luan; Leow, Alex; Klumpp, Heide

    2017-01-01

    Functional magnetic resonance imaging (fMRI) resting-state studies show generalized social anxiety disorder (gSAD) is associated with disturbances in networks involved in emotion regulation, emotion processing, and perceptual functions, suggesting a network framework is integral to elucidating the pathophysiology of gSAD. However, fMRI does not measure the fast dynamic interconnections of functional networks. Therefore, we examined whole-brain functional connectomics with electroencephalogram (EEG) during resting-state. Resting-state EEG data was recorded for 32 patients with gSAD and 32 demographically-matched healthy controls (HC). Sensor-level connectivity analysis was applied on EEG data by using Weighted Phase Lag Index (WPLI) and graph analysis based on WPLI was used to determine clustering coefficient and characteristic path length to estimate local integration and global segregation of networks. WPLI results showed increased oscillatory midline coherence in the theta frequency band indicating higher connectivity in the gSAD relative to HC group during rest. Additionally, WPLI values positively correlated with state anxiety levels within the gSAD group but not the HC group. Our graph theory based connectomics analysis demonstrated increased clustering coefficient and decreased characteristic path length in theta-based whole brain functional organization in subjects with gSAD compared to HC. Theta-dependent interconnectivity was associated with state anxiety in gSAD and an increase in information processing efficiency in gSAD (compared to controls). Results may represent enhanced baseline self-focused attention, which is consistent with cognitive models of gSAD and fMRI studies implicating emotion dysregulation and disturbances in task negative networks (e.g., default mode network) in gSAD.

  9. The small mixing angle $\\theta_{13}$ and the lepton asymmetry

    CERN Document Server

    Lee, S H; Lee, Song-Haeng; Siyeon, Kim

    2005-01-01

    We present the correlation of low energy CP phases, both Dirac and Majorana, and the lepton asymmetry for the baryon asymmetry in the universe, with a certain class of Yukawa matrices that consist of two right-handed neutrinos and include one texture zero in themselves. For cases in which the amount of the lepton asymmetry $Y_L$ turns out to be proportional to $\\theta_{13}^2$, we consider the relation between two types of CP phases and the relation of $Y_L$ versus the Jarlskog invariant or the amplitude of neutrinoless double beta decay as $\\theta_{13}$ varies.

  10. Simplified scaling model for the THETA-pinch

    Science.gov (United States)

    Ewing, K. J.; Thomson, D. B.

    1982-02-01

    A simple ID scaing model for the fast Theta pinch was developed and written as a code that would be flexible, inexpensive in computer time, and readily available for use with the Los Alamos explosive-driven high magnetic field program. The simplified model uses three successive separate stages: (1) a snowplow-like radial implosion, (2) an idealized resistive annihilation of reverse bias field, and (3) an adiabatic compression stage of a Beta = 1 plasma for which ideal pressure balance is assumed to hold. The code uses one adjustable fitting constant whose value was first determined by comparison with results from the Los Alamos Scylla III, Scyllacita, and Scylla IA Theta pinches.

  11. Energy transfer efficiency measurements in a theta-pinch

    International Nuclear Information System (INIS)

    Cavalcanti, G.H.; Luna, F.R.T.; Trigueiros, A.G.

    1993-01-01

    An increase in energy transfer efficiency of the capacitor bank to the plasma was obtained when the electrical system of a theta-pinch was changed so that the ratio of total inductance to coil inductance was switched of 1/6 to 1/2. A further increase about 20% was obtained for 16/1 ratio. The measurements were made through the current discharge decay, and the spectral analysis of the emitted light from theta-pinch shows a correspondent efficiency increase. (author)

  12. Working memory performance inversely predicts spontaneous delta and theta-band scaling relations.

    Science.gov (United States)

    Euler, Matthew J; Wiltshire, Travis J; Niermeyer, Madison A; Butner, Jonathan E

    2016-04-15

    Electrophysiological studies have strongly implicated theta-band activity in human working memory processes. Concurrently, work on spontaneous, non-task-related oscillations has revealed the presence of long-range temporal correlations (LRTCs) within sub-bands of the ongoing EEG, and has begun to demonstrate their functional significance. However, few studies have yet assessed the relation of LRTCs (also called scaling relations) to individual differences in cognitive abilities. The present study addressed the intersection of these two literatures by investigating the relation of narrow-band EEG scaling relations to individual differences in working memory ability, with a particular focus on the theta band. Fifty-four healthy adults completed standardized assessments of working memory and separate recordings of their spontaneous, non-task-related EEG. Scaling relations were quantified in each of the five classical EEG frequency bands via the estimation of the Hurst exponent obtained from detrended fluctuation analysis. A multilevel modeling framework was used to characterize the relation of working memory performance to scaling relations as a function of general scalp location in Cartesian space. Overall, results indicated an inverse relationship between both delta and theta scaling relations and working memory ability, which was most prominent at posterior sensors, and was independent of either spatial or individual variability in band-specific power. These findings add to the growing literature demonstrating the relevance of neural LRTCs for understanding brain functioning, and support a construct- and state-dependent view of their functional implications. Copyright © 2016 Elsevier B.V. All rights reserved.

  13. The noncommutative standard model. Construction beyond leading order in {theta} and collider phenomenology

    Energy Technology Data Exchange (ETDEWEB)

    Alboteanu, A.M.

    2007-07-01

    Within this work we study the phenomenological consequences of a possible realization of QFT on noncommutative space-time. In the first part we performed a phenomenological analysis of the hadronic process pp {yields} Z{sub {gamma}} {yields} l{sup +}l{sup -}{gamma} at the LHC and of electron-positron pair annihilation into a Z boson and a photon at the International Linear Collider (ILC). The noncommutative extension of the SM considered within this work relies on two building blocks: the Moyal-Weyl *-product of functions on ordinary space-time and the Seiberg-Witten maps. A consequence of the noncommutativity of space-time is the violation of rotational invariance with respect to the beam axis. This effect shows up in the azimuthal dependence of cross sections, which is absent in the SM as well as in other models beyond the SM. We have found this dependence to be best suited for deriving the sensitivity bounds on the noncommutative scale NC. By studying pp{yields}Z{sub {gamma}} {yields}l{sup +}l{sup -}{gamma} to first order in the noncommutative parameter {theta}, we show in the first part of this work that measurements at the LHC are sensitive to noncommutative effects only in certain cases, giving bounds on the noncommutative scale of {lambda}{sub NC} >or similar 1.2 TeV. By means of e{sup +}e{sup -} {yields} Z{sub {gamma}} {yields} l{sup +}l{sup -}{gamma} to O({theta}) we have shown that ILC measurements are complementary to LHC measurements of the noncommutative parameters. In addition, the bounds on {lambda}{sub NC} derived from the ILC are significantly higher and reach {lambda}{sub NC} >or similar 6 TeV. In the second part of this work we expand the neutral current sector of the noncommutative SM to second order in {theta}. We found that, against the general expectation, the theory must be enlarged by additional parameters. The new parameters enter the theory as ambiguities of the Seiberg-Witten maps. The latter are not uniquely determined and differ by

  14. Histamine Enhances Theta-Coupled Spiking and Gamma Oscillations in the Medial Entorhinal Cortex Consistent With Successful Spatial Recognition.

    Science.gov (United States)

    Chen, Quanhui; Luo, Fenlan; Yue, Faguo; Xia, Jianxia; Xiao, Qin; Liao, Xiang; Jiang, Jun; Zhang, Jun; Hu, Bo; Gao, Dong; He, Chao; Hu, Zhian

    2017-06-07

    Encoding of spatial information in the superficial layers of the medial entorhinal cortex (sMEC) involves theta-modulated spiking and gamma oscillations, as well as spatially tuned grid cells and border cells. Little is known about the role of the arousal-promoting histaminergic system in the modification of information encoded in the sMEC in vivo, and how such histamine-regulated information correlates with behavioral functions. Here, we show that histamine upregulates the neural excitability of a significant proportion of neurons (16.32%, 39.18%, and 52.94% at 30 μM, 300 μM, and 3 mM, respectively) and increases local theta (4-12 Hz) and gamma power (low: 25-48 Hz; high: 60-120 Hz) in the sMEC, through activation of histamine receptor types 1 and 3. During spatial exploration, the strength of theta-modulated firing of putative principal neurons and high gamma oscillations is enhanced about 2-fold by histamine. The histamine-mediated increase of theta phase-locking of spikes and high gamma power is consistent with successful spatial recognition. These results, for the first time, reveal possible mechanisms involving the arousal-promoting histaminergic system in the modulation of spatial cognition. Published by Oxford University Press 2017. This work is written by (a) US Government employee(s) and is in the public domain in the US.

  15. Classical Conditioning of Hippocampal Theta Patterns in the Rat.

    Science.gov (United States)

    1976-08-01

    associated with changes in performance of learned tasks , 1,4,5, 8,9 there have been very few studies of neurona l plasticity of the hippocampus It self...rapid development of a conditioned hippocampal theta response to a visual sti mulus demonstrates tha t there is considerable neurona l plasticity in the

  16. Double-Chooz: a search for {theta}{sub 13}

    Energy Technology Data Exchange (ETDEWEB)

    Lasserre, Th. [DSM/DAPNIA/SPP, CEA/Saclay, 91191 Gif-sur-Yvette (France)

    2005-12-15

    The Double-Chooz experiment goal is to search for a non-vanishing value of the {theta}{sub 13} neutrino mixing angle. This is the last step to accomplish prior moving towards a new era of precision measurements in the lepton sector. The current best constraint on the third mixing angle comes from the CHOOZ reactor neutrino experiment sin{sup 2}(2{theta}{sub 13})<0.2 (90% C.L., {delta}m{sub atm}{sup 2}=2.0eV{sup 2}). Double-Chooz will explore the range of sin{sup 2}(2{theta}{sub 13}) from 0.2 to 0.03-0.02, within three years of data taking. The improvement of the CHOOZ result requires an increase in the statistics, a reduction of the systematic error below one percent, and a careful control of the backgrounds. Therefore, Double-Chooz will use two identical detectors, one at 150 m and another at 1.05 km distance from the Chooz nuclear cores. In addition, we will use the near detector as a ''state of the art'' prototype to investigate the potential of neutrinos for monitoring the civil nuclear power plants. The plan is to start operation with two detectors in 2008, and to reach a sensitivity sin{sup 2}(2{theta}{sub 13}) of 0.05 in 2009, and 0.03-0.02 in 2011.

  17. Instability study during implosion in the Tupa Theta-Pinch

    International Nuclear Information System (INIS)

    Kayama, M.E.; Boeckelmann, H.K.

    1986-01-01

    The importance of instabilities which occur during plasma heating in a Theta Pinch, in the implosion phase, is analysed. The plasma diagnostic was done by ultrafast photography and diamagnetic probe. The implosion time and the current layer thickness were calculated using a hybrid code for plasma simulation. The theoretical data were compared with the experimental ones. (M.C.K.) [pt

  18. Steady state theta pinch concept for slow formation of FRC

    International Nuclear Information System (INIS)

    Hirano, K.

    1987-05-01

    A steady state high beta plasma flow through a channel along the magnetic field increasing downstream can be regarded as a ''steady state theta pinch'', because if we see the plasma riding on the flow we should observe very similar process taking place in a theta pinch. Anticipating to produce an FRC without using very high voltage technics such as the ones required in a conventional theta pinch, we have studied after the analogy a ''steady state reversed field theta pinch'' which is brought about by steady head-on collision of counter plasma streams along the channel as ejected from two identical co-axial plasma sources mounted at the both ends of the apparatus. The ideal Poisson and shock adiabatic flow models are employed for the analysis of the steady colliding process. It is demonstrated that an FRC involving large numbers of particles is produced only by the weak shock mode which is achieved in case energetic plasma flow is decelerated almost to be stagnated through Poisson adiabatic process before the streams are collided. (author)

  19. Electrical insulators for the theta-pinch fusion reactor

    International Nuclear Information System (INIS)

    Clinard, F.W. Jr.

    1976-01-01

    The five major applications for electrical insulators in the Reference Theta Pinch Reactor are as follows: (1) first-wall insulator, (2) blanket intersegment insulator, (3) graphite encapsulating insulator, (4) implosion coil insulator, and (5) compression coil insulator. Insulator design proposals and some preliminary test results are given for each application

  20. Multidimensional Riemann problem with self-similar internal structure. Part II - Application to hyperbolic conservation laws on unstructured meshes

    Science.gov (United States)

    Balsara, Dinshaw S.; Dumbser, Michael

    2015-04-01

    Multidimensional Riemann solvers that have internal sub-structure in the strongly-interacting state have been formulated recently (D.S. Balsara (2012, 2014) [5,16]). Any multidimensional Riemann solver operates at the grid vertices and takes as its input all the states from its surrounding elements. It yields as its output an approximation of the strongly interacting state, as well as the numerical fluxes. The multidimensional Riemann problem produces a self-similar strongly-interacting state which is the result of several one-dimensional Riemann problems interacting with each other. To compute this strongly interacting state and its higher order moments we propose the use of a Galerkin-type formulation to compute the strongly interacting state and its higher order moments in terms of similarity variables. The use of substructure in the Riemann problem reduces numerical dissipation and, therefore, allows a better preservation of flow structures, like contact and shear waves. In this second part of a series of papers we describe how this technique is extended to unstructured triangular meshes. All necessary details for a practical computer code implementation are discussed. In particular, we explicitly present all the issues related to computational geometry. Because these Riemann solvers are Multidimensional and have Self-similar strongly-Interacting states that are obtained by Consistency with the conservation law, we call them MuSIC Riemann solvers. (A video introduction to multidimensional Riemann solvers is available on http://www.elsevier.com/xml/linking-roles/text/html". The MuSIC framework is sufficiently general to handle general nonlinear systems of hyperbolic conservation laws in multiple space dimensions. It can also accommodate all self-similar one-dimensional Riemann solvers and subsequently produces a multidimensional version of the same. In this paper we focus on unstructured triangular meshes. As examples of different systems of conservation laws we

  1. Study of the Riemann problem and construction of multidimensional Godunov-type schemes for two-phase flow models

    International Nuclear Information System (INIS)

    Toumi, I.

    1990-04-01

    This thesis is devoted to the study of the Riemann problem and the construction of Godunov type numerical schemes for one or two dimensional two-phase flow models. In the first part, we study the Riemann problem for the well-known Drift-Flux, model which has been widely used for the analysis of thermal hydraulics transients. Then we use this study to construct approximate Riemann solvers and we describe the corresponding Godunov type schemes for simplified equation of state. For computation of complex two-phase flows, a weak formulation of Roe's approximate Riemann solver, which gives a method to construct a Roe-averaged jacobian matrix with a general equation of state, is proposed. For two-dimensional flows, the developed methods are based upon an approximate solver for a two-dimensional Riemann problem, according to Harten-Lax-Van Leer principles. The numerical results for standard test problems show the good behaviour of these numerical schemes for a wide range of flow conditions [fr

  2. Impaired theta phase-resetting underlying auditory N1 suppression in chronic alcoholism.

    Science.gov (United States)

    Fuentemilla, Lluis; Marco-Pallarés, Josep; Gual, Antoni; Escera, Carles; Polo, Maria Dolores; Grau, Carles

    2009-02-18

    It has been suggested that chronic alcoholism may lead to altered neural mechanisms related to inhibitory processes. Here, we studied auditory N1 suppression phenomena (i.e. amplitude reduction with repetitive stimuli) in chronic alcoholic patients as an early-stage information-processing brain function involving inhibition by the analysis of the N1 event-related potential and time-frequency computation (spectral power and phase-resetting). Our results showed enhanced neural theta oscillatory phase-resetting underlying N1 generation in suppressed N1 event-related potential. The present findings suggest that chronic alcoholism alters neural oscillatory synchrony dynamics at very early stages of information processing.

  3. Riemann solvers for multi-component gas mixtures with temperature dependent heat capacities

    International Nuclear Information System (INIS)

    Beccantini, A.

    2001-01-01

    This thesis represents a contribution to the development of upwind splitting schemes for the Euler equations for ideal gaseous mixtures and their investigation in computing multidimensional flows in irregular geometries. In the preliminary part we develop and investigate the parameterization of the shock and rarefaction curves in the phase space. Then, we apply them to perform some field-by-field decompositions of the Riemann problem: the entropy-respecting one, the one which supposes that genuinely-non-linear (GNL) waves are both shocks (shock-shock one) and the one which supposes that GNL waves are both rarefactions (rarefaction-rarefaction one). We emphasize that their analysis is fundamental in Riemann solvers developing: the simpler the field-by-field decomposition, the simpler the Riemann solver based on it. As the specific heat capacities of the gases depend on the temperature, the shock-shock field-by-field decomposition is the easiest to perform. Then, in the second part of the thesis, we develop an upwind splitting scheme based on such decomposition. Afterwards, we investigate its robustness, precision and CPU-time consumption, with respect to some of the most popular upwind splitting schemes for polytropic/non-polytropic ideal gases. 1-D test-cases show that this scheme is both precise (exact capturing of stationary shock and stationary contact) and robust in dealing with strong shock and rarefaction waves. Multidimensional test-cases show that it suffers from some of the typical deficiencies which affect the upwind splitting schemes capable of exact capturing stationary contact discontinuities i.e the developing of non-physical instabilities in computing strong shock waves. In the final part, we use the high-order multidimensional solver here developed to compute fully-developed detonation flows. (author)

  4. A family of high-order gas-kinetic schemes and its comparison with Riemann solver based high-order methods

    Science.gov (United States)

    Ji, Xing; Zhao, Fengxiang; Shyy, Wei; Xu, Kun

    2018-03-01

    Most high order computational fluid dynamics (CFD) methods for compressible flows are based on Riemann solver for the flux evaluation and Runge-Kutta (RK) time stepping technique for temporal accuracy. The advantage of this kind of space-time separation approach is the easy implementation and stability enhancement by introducing more middle stages. However, the nth-order time accuracy needs no less than n stages for the RK method, which can be very time and memory consuming due to the reconstruction at each stage for a high order method. On the other hand, the multi-stage multi-derivative (MSMD) method can be used to achieve the same order of time accuracy using less middle stages with the use of the time derivatives of the flux function. For traditional Riemann solver based CFD methods, the lack of time derivatives in the flux function prevents its direct implementation of the MSMD method. However, the gas kinetic scheme (GKS) provides such a time accurate evolution model. By combining the second-order or third-order GKS flux functions with the MSMD technique, a family of high order gas kinetic methods can be constructed. As an extension of the previous 2-stage 4th-order GKS, the 5th-order schemes with 2 and 3 stages will be developed in this paper. Based on the same 5th-order WENO reconstruction, the performance of gas kinetic schemes from the 2nd- to the 5th-order time accurate methods will be evaluated. The results show that the 5th-order scheme can achieve the theoretical order of accuracy for the Euler equations, and present accurate Navier-Stokes solutions as well due to the coupling of inviscid and viscous terms in the GKS formulation. In comparison with Riemann solver based 5th-order RK method, the high order GKS has advantages in terms of efficiency, accuracy, and robustness, for all test cases. The 4th- and 5th-order GKS have the same robustness as the 2nd-order scheme for the capturing of discontinuous solutions. The current high order MSMD GKS is a

  5. Modulation of Hippocampal Theta Oscillations and Spatial Memory by Relaxin-3 Neurons of the Nucleus Incertus

    Science.gov (United States)

    Ma, Sherie; Olucha-Bordonau, Francisco E.; Hossain, M. Akhter; Lin, Feng; Kuei, Chester; Liu, Changlu; Wade, John D.; Sutton, Steven W.; Nunez, Angel; Gundlach, Andrew L.

    2009-01-01

    Hippocampal theta rhythm is thought to underlie learning and memory, and it is well established that "pacemaker" neurons in medial septum (MS) modulate theta activity. Recent studies in the rat demonstrated that brainstem-generated theta rhythm occurs through a multisynaptic pathway via the nucleus incertus (NI), which is the primary source of the…

  6. Loss of hyperbolicity changes the number of wave groups in Riemann problems

    OpenAIRE

    Vítor Matos; Julio D. Silva; Dan Marchesin

    2016-01-01

    Themain goal of ourwork is to showthat there exists a class of 2×2 Riemann problems for which the solution comprises a singlewave group for an open set of initial conditions. This wave group comprises a 1-rarefaction joined to a 2-rarefaction, not by an intermediate state, but by a doubly characteristic shock, 1-left and 2-right characteristic. In order to ensure that perturbations of initial conditions do not destroy the adjacency of the waves, local transversality between a composite curve ...

  7. The motion of a classical spinning point particle in a Riemann-Cartan space-time

    International Nuclear Information System (INIS)

    Amorim, R.

    1983-01-01

    A consistent set of equations of motion for classical charged point particles with spin and magnetic dipole moment in a Riemann-Cartan space-time is generated from a generalized Lagrangean formalism. The equations avoid the spurius free helicoidal solutions and at the same time conserve the canonical condition of normalization of the 4-velocity. The 4-velocity and the mechanical moment are paralell in this theory, where the condition of orthogonality between the spin and the 4-velocity is treated as a non-holonomic one. (Author) [pt

  8. A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line

    Science.gov (United States)

    Its, A.; Sukhanov, V.

    2016-05-01

    The paper is concerned with the inverse scattering problem for the Stark operator on the line with a potential from the Schwartz class. In our study of the inverse problem, we use the Riemann-Hilbert formalism. This allows us to overcome the principal technical difficulties which arise in the more traditional approaches based on the Gel’fand-Levitan-Marchenko equations, and indeed solve the problem. We also produce a complete description of the relevant scattering data (which have not been obtained in the previous works on the Stark operator) and establish the bijection between the Schwartz class potentials and the scattering data.

  9. The transition from regular to irregular motions, explained as travel on Riemann surfaces

    International Nuclear Information System (INIS)

    Calogero, F; Santini, P M; Gomez-Ullate, D; Sommacal, M

    2005-01-01

    We introduce and discuss a simple Hamiltonian dynamical system, interpretable as a three-body problem in the (complex) plane and providing the prototype of a mechanism explaining the transition from regular to irregular motions as travel on Riemann surfaces. The interest of this phenomenology-illustrating the onset in a deterministic context of irregular motions-is underlined by its generality, suggesting its eventual relevance to understand natural phenomena and experimental investigations. Here only some of our main findings are reported, without detailing their proofs: a more complete presentation will be published elsewhere

  10. Arithmetical Fourier and Limit values of elliptic modular functions

    Indian Academy of Sciences (India)

    2

    In order to remove singularities, Riemann used a well-known device of taking the odd part (3.2) or an alternate sum (3.3) to be stated in §3. In §2 of this note we shall reveal that the limit values of elliptic modular functions in Riemann's fragment II evaluated by the differences of polyloga- rithm function l1(x) of order 1 (cf.

  11. Do extended objects move along the geodesics in the Riemann space-time

    International Nuclear Information System (INIS)

    Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.

    1981-01-01

    Movement of an extended self-gravitating body in the gravitational field of another distant body is studied in the postnewtonian approximation of arbitrary metrical gravitational theory. Comparison of the mass center acceleration of the extended body with the acceleration of a point body moving in the Riemann space-time, the metrics of which is formally equivalent to the metrics of two moving extended bodies, shows that in any metrical gravitation theory with conservation laws of energy and momentum of the matter and gravitational field taken together, the mass center of the extended body does not, in general case, move along the geodesics of the Riemann space-time. Application of the general formulas obtained to the system Sun-Earth combined with the experimental data of the lunar laser ranging, shows that the Earth in its orbital motion is oscillating with respect to reference geodesics, with the period about one hour and the amplitude not less than 10 -2 cm. This amplitude is of the postnewtonian magnitude and as a consequence, the deviation of the Earth movement from the geodesical movement can be observed in the experiment possessing the postnewtonian accuracy. The difference between the acceleration of the Earth mass center and that of a test body in the postnewtonian approximation is equal to 10 -7 part of the Earth acceleration. The ratio of the passive gravitational mass of the Earth (defined according to Will) and its inert mass differs from 1 by 10 -8 approximately [ru

  12. Riemann Integration

    Indian Academy of Sciences (India)

    and that this should be true, no matter how the in- terval [a, b] is subdivided. ..... Moreover, J: 1 is the unique number with this property. We do not know which ..... as some of our previous demonstrations illustrate, the details of the argument ...

  13. Event-related theta synchronization predicts deficit in facial affect recognition in schizophrenia.

    Science.gov (United States)

    Csukly, Gábor; Stefanics, Gábor; Komlósi, Sarolta; Czigler, István; Czobor, Pál

    2014-02-01

    Growing evidence suggests that abnormalities in the synchronized oscillatory activity of neurons in schizophrenia may lead to impaired neural activation and temporal coding and thus lead to neurocognitive dysfunctions, such as deficits in facial affect recognition. To gain an insight into the neurobiological processes linked to facial affect recognition, we investigated both induced and evoked oscillatory activity by calculating the Event Related Spectral Perturbation (ERSP) and the Inter Trial Coherence (ITC) during facial affect recognition. Fearful and neutral faces as well as nonface patches were presented to 24 patients with schizophrenia and 24 matched healthy controls while EEG was recorded. The participants' task was to recognize facial expressions. Because previous findings with healthy controls showed that facial feature decoding was associated primarily with oscillatory activity in the theta band, we analyzed ERSP and ITC in this frequency band in the time interval of 140-200 ms, which corresponds to the N170 component. Event-related theta activity and phase-locking to facial expressions, but not to nonface patches, predicted emotion recognition performance in both controls and patients. Event-related changes in theta amplitude and phase-locking were found to be significantly weaker in patients compared with healthy controls, which is in line with previous investigations showing decreased neural synchronization in the low frequency bands in patients with schizophrenia. Neural synchrony is thought to underlie distributed information processing. Our results indicate a less effective functioning in the recognition process of facial features, which may contribute to a less effective social cognition in schizophrenia. PsycINFO Database Record (c) 2014 APA, all rights reserved.

  14. Kinesthetic motor imagery training modulates frontal midline theta during imagination of a dart throw.

    Science.gov (United States)

    Weber, E; Doppelmayr, M

    2016-12-01

    Motor imagery (MI) is a frequently used and effective method for motor learning in sports as well as in other domains. Electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) studies indicated that experts within a certain sport exhibit a more pronounced brain activity during MI as compared to novices. Similar to the execution, during MI the motor sequence has to be planned. Thus, the frontal attentional system, in part represented by the frontal midline theta (4-7Hz), is closely related to these processes and presumably plays a major role in MI as well. In this study, a MI dart training and its impact on frontal midline theta activity (fmt) during MI are examined. 53 healthy subjects with no prior dart experience were randomly allocated to a kinesthetic training group (KinVis) or to a control group (Control). Both groups performed 15 training sessions. While in the KinVis group dart throwing was accompanied by MI, the Control group trained without MI. Dart performance and fmt activity during MI within the first and the 15th session were compared. As expected, the performance increase was more pronounced in the KinVis group. Furthermore, frontal theta amplitude was significantly increased in the KinVis group during MI in the 15th training session as compared to the baseline. These results confirm the effectivity of MI. The enhanced fmt activity in the KinVis group can be interpreted as a better allocation of the requested resources in the frontal attentional network after MI. Copyright © 2016 Elsevier B.V. All rights reserved.

  15. (No) time for control: Frontal theta dynamics reveal the cost of temporally guided conflict anticipation.

    Science.gov (United States)

    van Driel, Joram; Swart, Jennifer C; Egner, Tobias; Ridderinkhof, K Richard; Cohen, Michael X

    2015-12-01

    During situations of response conflict, cognitive control is characterized by prefrontal theta-band (3- to 8-Hz) activity. It has been shown that cognitive control can be triggered proactively by contextual cues that predict conflict. Here, we investigated whether a pretrial preparation interval could serve as such a cue. This would show that the temporal contingencies embedded in the task can be used to anticipate upcoming conflict. To this end, we recorded electroencephalography (EEG) from 30 human subjects while they performed a version of a Simon task in which the duration of a fixation cross between trials predicted whether the next trial would contain response conflict. Both their behavior and EEG activity showed a consistent but unexpected pattern of results: The conflict effect (increased reaction times and decreased accuracy on conflict as compared to nonconflict trials) was stronger when conflict was cued, and this was associated with stronger conflict-related midfrontal theta activity and functional connectivity. Interestingly, intervals that predicted conflict did show a pretarget increase in midfrontal theta power. These findings suggest that temporally guided expectations of conflict do heighten conflict anticipation, but also lead to less efficiently applied reactive control. We further explored this post-hoc interpretation by means of three behavioral follow-up experiments, in which we used nontemporal cues, semantically informative cues, and neutral cues. Together, this body of results suggests that the counterintuitive cost of conflict cueing may not be uniquely related to the temporal domain, but may instead be related to the implicitness and validity of the cue.

  16. Imploding to equilibrium of helically symmetric theta pinches

    International Nuclear Information System (INIS)

    Sharky, N.N.

    1978-01-01

    The time-dependent, single-fluid, dissipative magnetohydrodynamic equations are solved in helical coordinates (r,phi), where phi = THETA-kz, k = 2π/L and L is the periodicity length in the z-direction. The two-dimensional numerical calculations simulate theta pinches which have an l = 1 helical field added to them. Given the applied magnetic fields and the initial state of the plasma, we study the time evolution of the system. The plasma is found to experience two kinds of oscillations, occurring on different time scales. These are the radial compression oscillations, and the slower helical oscillations of the plasma column. The plasma motion is followed until these oscillations disappear and an equilibrium is nearly reached. Hence given the amplitude and the rise time of the applied magnetic fields, the calculations allow one to relate the initial state of a cold, homogeneous plasma to its final equilibrium state where it is heated and compressed

  17. Theta, mental flexibility, and post-traumatic stress disorder: connecting in the parietal cortex.

    Directory of Open Access Journals (Sweden)

    Benjamin T Dunkley

    Full Text Available Post-traumatic stress disorder (PTSD is a mental health injury characterised by re-experiencing, avoidance, numbing and hyperarousal. Whilst the aetiology of the disorder is relatively well understood, there is debate about the prevalence of cognitive sequelae that manifest in PTSD. In particular, there are conflicting reports about deficits in executive function and mental flexibility. Even less is known about the neural changes that underlie such deficits. Here, we used magnetoencephalography to study differences in functional connectivity during a mental flexibility task in combat-related PTSD (all males, mean age = 37.4, n = 18 versus a military control (all males, mean age = 33.05, n = 19 group. We observed large-scale increases in theta connectivity in the PTSD group compared to controls. The PTSD group performance was compromised in the more attentionally-demanding task and this was characterised by 'late-stage' theta hyperconnectivity, concentrated in network connections involving right parietal cortex. Furthermore, we observed significant correlations with the connectivity strength in this region with a number of cognitive-behavioural outcomes, including measures of attention, depression and anxiety. These findings suggest atypical coordination of neural synchronisation in large scale networks contributes to deficits in mental flexibility for PTSD populations in timed, attentionally-demanding tasks, and this propensity toward network hyperconnectivity may play a more general role in the cognitive sequelae evident in this disorder.

  18. The role of REM theta activity in emotional memory

    Directory of Open Access Journals (Sweden)

    Isabel Camilla Hutchison

    2015-10-01

    Full Text Available While NREM sleep has been strongly implicated in the reactivation and consolidation of memory traces, the role of REM sleep remains unclear. A growing body of research on humans and animals provide behavioral evidence for a role of REM sleep in the strengthening and modulation of emotional memories. Theta activity – which describes low frequency oscillations in the local field potential within the hippocampus, amygdala and neocortex – is a prominent feature of both wake and REM sleep in humans and rodents. Theta coherence between the hippocampus and amygdala drives large-scale PGO waves, the density of which predicts increases in plasticity-related gene expression. This could potentially facilitate the processing of emotional memory traces within the hippocampus during REM sleep. Further, the timing of hippocampal activity in relation to theta phase is vital in determining subsequent potentiation of neuronal activity. This could allow the emotionally modulated strengthening of novel and the gradual weakening of consolidated hippocampal memory traces observed in both wake and REM sleep. Hippocampal theta activity is also correlated with REM sleep acetylcholine levels – which are thought to reduce hippocampal afferent inputs in the neocortex. The additional low levels of noradrenaline during REM sleep, which facilitate recurrent activation within the neocortex, could allow the integration of novel memory traces previously consolidated during NREM sleep. We therefore propose that REM sleep mediates the prioritized processing of emotional memories within the hippocampus, the integration of previously consolidated memory traces within the neocortex, as well as the disengagement of consolidated neocortical memory traces from the hippocampus.

  19. Double-Chooz: a search for {theta}{sub 13}

    Energy Technology Data Exchange (ETDEWEB)

    Mention, G. [APC/PCC, College de France, 75005 Paris (France)

    2005-08-15

    The Double-Chooz experiment goal is to search for a non-vanishing value of the {theta}{sub 13} neutrino mixing angle. This is the last step to accomplish prior moving towards a new era of precision measurements in the lepton sector. The current best constraint on the third mixing angle comes from the CHOOZ reactor neutrino experiment sin{sup 2}(2{theta}{sub 13}) < 0.2-0.14 (90% C.L., {delta}m{sub atm}{sup 2}=2.0-2.410{sup -3} eV{sup 2}). Double-Chooz will explore the range of sin{sup 2}(2{theta}{sub 13}) from 0.2 to 0.03-0.02, within three years of data taking. The improvement of the CHOOZ result requires an increase in the statistics, a reduction of the systematic error below one percent, and a careful control of the backgrounds. Therefore, Double-Chooz will use two identical detectors, one at 150 m and another at 1.05 km distance from the Chooz nuclear cores. In addition, we will use the near detector as a 'state of the art' prototype to investigate the potential of neutrinos for monitoring the civil nuclear power plants. The plan is to start operation with two detectors in 2008, and to reach a sin{sup 2}(2{theta}{sub 13}) sensitivity of 0.05 in 2009, and 0.03-0.02 in 2011.

  20. A reversed-field theta-pinch plasma machine

    International Nuclear Information System (INIS)

    Yasojima, Yoshiyuki; Ueda, Yoshihiro; Sasao, Hiroyuki; Ueno, Noboru; Tanaka, Toshihide

    1984-01-01

    Mitsubishi Electric has constructed a reversed-field theta-pinch machine at its Central Research Laboratory and initiated a series of plasma diagnostics and control studies for development of nuclear-fusion technology. Although the device has a linear configuration, a stable high-temperature, high-density toroidal plasma can be generated. The article describes the overall structure, vacuum system, power-supply system, and diagnostics and control system of the plasma machine. (author)

  1. Theta coordinated error-driven learning in the hippocampus.

    Directory of Open Access Journals (Sweden)

    Nicholas Ketz

    Full Text Available The learning mechanism in the hippocampus has almost universally been assumed to be Hebbian in nature, where individual neurons in an engram join together with synaptic weight increases to support facilitated recall of memories later. However, it is also widely known that Hebbian learning mechanisms impose significant capacity constraints, and are generally less computationally powerful than learning mechanisms that take advantage of error signals. We show that the differential phase relationships of hippocampal subfields within the overall theta rhythm enable a powerful form of error-driven learning, which results in significantly greater capacity, as shown in computer simulations. In one phase of the theta cycle, the bidirectional connectivity between CA1 and entorhinal cortex can be trained in an error-driven fashion to learn to effectively encode the cortical inputs in a compact and sparse form over CA1. In a subsequent portion of the theta cycle, the system attempts to recall an existing memory, via the pathway from entorhinal cortex to CA3 and CA1. Finally the full theta cycle completes when a strong target encoding representation of the current input is imposed onto the CA1 via direct projections from entorhinal cortex. The difference between this target encoding and the attempted recall of the same representation on CA1 constitutes an error signal that can drive the learning of CA3 to CA1 synapses. This CA3 to CA1 pathway is critical for enabling full reinstatement of recalled hippocampal memories out in cortex. Taken together, these new learning dynamics enable a much more robust, high-capacity model of hippocampal learning than was available previously under the classical Hebbian model.

  2. Instantons, theta-vacua, confinement..... a pedagogical introduction

    International Nuclear Information System (INIS)

    Teper, M.J.

    1980-01-01

    In this series of lectures the concept of the instanton and its various ramifications, such as the dilute gas and theta-vacua, are introduced through the relatively simple dynamical system of 1 + 1 dimensional quantum mechanics and the 1 + 1 abelian Higgs model. Although QCD is not dealt with explicitly those aspects of the argument which are relevant to that much more complicated theory are noted. (UK)

  3. Impact of Prefrontal Theta Burst Stimulation on Clinical Neuropsychological Tasks

    Directory of Open Access Journals (Sweden)

    Raquel Viejo-Sobera

    2017-08-01

    Full Text Available Theta burst stimulation (TBS protocols hold high promise in neuropsychological rehabilitation. Nevertheless, their ability to either decrease (continuous, cTBS or increase (intermittent, iTBS cortical excitability in areas other than the primary motor cortex, and their consistency modulating human behaviors with clinically relevant tasks remain to be fully established. The behavioral effects of TBS over the dorsolateral prefrontal cortex (dlPFC are particularly interesting given its involvement in working memory (WM and executive functions (EF, often impaired following frontal brain damage. We aimed to explore the ability of cTBS and iTBS to modulate WM and EF in healthy individuals, assessed with clinical neuropsychological tests (Digits Backward, 3-back task, Stroop Test, and Tower of Hanoi. To this end, 36 participants were assessed using the four tests 1 week prior to stimulation and immediately following a single session of either cTBS, iTBS, or sham TBS, delivered to the left dlPFC. No significant differences were found across stimulation conditions in any of the clinical tasks. Nonetheless, in some of them, active stimulation induced significant pre/post performance modulations, which were not found for the sham condition. More specifically, sham stimulation yielded improvements in the 3-back task and the Color, Color-Word, and Interference Score of the Stroop Test, an effect likely caused by task practice. Both, iTBS and cTBS, produced improvements in Digits Backward and impairments in 3-back task accuracy. Moreover, iTBS increased Interference Score in the Stroop Test in spite of the improved word reading and impaired color naming, whereas cTBS decreased the time required to complete the Tower of Hanoi. Differing from TBS outcomes reported for cortico-spinal measures on the primary motor cortex, our analyses did not reveal any of the expected performance differences across stimulation protocols. However, if one considers independently

  4. Delta-gamma-theta Hedging of Crude Oil Asian Options

    Directory of Open Access Journals (Sweden)

    Juraj Hruška

    2015-01-01

    Full Text Available Since Black-Scholes formula was derived, many methods have been suggested for vanilla as well as exotic options pricing. More of investing and hedging strategies have been developed based on these pricing models. Goal of this paper is to derive delta-gamma-theta hedging strategy for Asian options and compere its efficiency with gamma-delta-theta hedging combined with predictive model. Fixed strike Asian options are type of exotic options, whose special feature is that payoff is calculated from the difference of average market price and strike price for call options and vice versa for the put options. Methods of stochastic analysis are used to determine deltas, gammas and thetas of Asian options. Asian options are cheaper than vanilla options and therefore they are more suitable for precise portfolio creation. On the other hand their deltas are also smaller as well as profits. That means that they are also less risky and more suitable for hedging. Results, conducted on chosen commodity, confirm better feasibility of Asian options compering with vanilla options in sense of gamma hedging.

  5. Dendritic brushes under theta and poor solvent conditions

    Science.gov (United States)

    Gergidis, Leonidas N.; Kalogirou, Andreas; Charalambopoulos, Antonios; Vlahos, Costas

    2013-07-01

    The effects of solvent quality on the internal stratification of polymer brushes formed by dendron polymers up to third generation were studied by means of molecular dynamics simulations with Langevin thermostat. The distributions of polymer units, of the free ends, the radii of gyration, and the back folding probabilities of the dendritic spacers were studied at the macroscopic states of theta and poor solvent. For high grafting densities we observed a small decrease in the height of the brush as the solvent quality decreases. The internal stratification in theta solvent was similar to the one we found in good solvent, with two and in some cases three kinds of populations containing short dendrons with weakly extended spacers, intermediate-height dendrons, and tall dendrons with highly stretched spacers. The differences increase as the grafting density decreases and single dendron populations were evident in theta and poor solvent. In poor solvent at low grafting densities, solvent micelles, polymeric pinned lamellae, spherical and single chain collapsed micelles were observed. The scaling dependence of the height of the dendritic brush at high density brushes for both solvents was found to be in agreement with existing analytical results.

  6. Theta signal as the neural signature of social exclusion.

    Science.gov (United States)

    Cristofori, Irene; Moretti, Laura; Harquel, Sylvain; Posada, Andres; Deiana, Gianluca; Isnard, Jean; Mauguière, François; Sirigu, Angela

    2013-10-01

    The feeling of being excluded from a social interaction triggers social pain, a sensation as intense as actual physical pain. Little is known about the neurophysiological underpinnings of social pain. We addressed this issue using intracranial electroencephalography in 15 patients performing a ball game where inclusion and exclusion blocks were alternated. Time-frequency analyses showed an increase in power of theta-band oscillations during exclusion in the anterior insula (AI) and posterior insula, the subgenual anterior cingulate cortex (sACC), and the fusiform "face area" (FFA). Interestingly, the AI showed an initial fast response to exclusion but the signal rapidly faded out. Activity in the sACC gradually increased and remained significant thereafter. This suggests that the AI may signal social pain by detecting emotional distress caused by the exclusion, whereas the sACC may be linked to the learning aspects of social pain. Theta activity in the FFA was time-locked to the observation of a player poised to exclude the participant, suggesting that the FFA encodes the social value of faces. Taken together, our findings suggest that theta activity represents the neural signature of social pain. The time course of this signal varies across regions important for processing emotional features linked to social information.

  7. Theta and Alpha Oscillations in Attentional Interaction during Distracted Driving

    Directory of Open Access Journals (Sweden)

    Yu-Kai Wang

    2018-02-01

    Full Text Available Performing multiple tasks simultaneously usually affects the behavioral performance as compared with executing the single task. Moreover, processing multiple tasks simultaneously often involve more cognitive demands. Two visual tasks, lane-keeping task and mental calculation, were utilized to assess the brain dynamics through 32-channel electroencephalogram (EEG recorded from 14 participants. A 400-ms stimulus onset asynchrony (SOA factor was used to induce distinct levels of attentional requirements. In the dual-task conditions, the deteriorated behavior reflected the divided attention and the overlapping brain resources used. The frontal, parietal and occipital components were decomposed by independent component analysis (ICA algorithm. The event- and response-related theta and alpha oscillations in selected brain regions were investigated first. The increased theta oscillation in frontal component and decreased alpha oscillations in parietal and occipital components reflect the cognitive demands and attentional requirements as executing the designed tasks. Furthermore, time-varying interactive over-additive (O-Add, additive (Add and under-additive (U-Add activations were explored and summarized through the comparison between the summation of the elicited spectral perturbations in two single-task conditions and the spectral perturbations in the dual task. Add and U-Add activations were observed while executing the dual tasks. U-Add theta and alpha activations dominated the posterior region in dual-task situations. Our results show that both deteriorated behaviors and interactive brain activations should be comprehensively considered for evaluating workload or attentional interaction precisely.

  8. Adaptive [theta]-methods for pricing American options

    Science.gov (United States)

    Khaliq, Abdul Q. M.; Voss, David A.; Kazmi, Kamran

    2008-12-01

    We develop adaptive [theta]-methods for solving the Black-Scholes PDE for American options. By adding a small, continuous term, the Black-Scholes PDE becomes an advection-diffusion-reaction equation on a fixed spatial domain. Standard implementation of [theta]-methods would require a Newton-type iterative procedure at each time step thereby increasing the computational complexity of the methods. Our linearly implicit approach avoids such complications. We establish a general framework under which [theta]-methods satisfy a discrete version of the positivity constraint characteristic of American options, and numerically demonstrate the sensitivity of the constraint. The positivity results are established for the single-asset and independent two-asset models. In addition, we have incorporated and analyzed an adaptive time-step control strategy to increase the computational efficiency. Numerical experiments are presented for one- and two-asset American options, using adaptive exponential splitting for two-asset problems. The approach is compared with an iterative solution of the two-asset problem in terms of computational efficiency.

  9. Approximate Riemann solvers and flux vector splitting schemes for two-phase flow; Solveurs de Riemann approches et schemas de decentrement de flux pour les ecoulements diphasiques

    Energy Technology Data Exchange (ETDEWEB)

    Toumi, I.; Kumbaro, A.; Paillere, H

    1999-07-01

    These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)

  10. Differential-algebraic integrability analysis of the generalized Riemann type and Korteweg-de Vries hydrodynamical equations

    Energy Technology Data Exchange (ETDEWEB)

    Prykarpatsky, Anatoliy K [Department of Mining Geodesy, AGH University of Science and Technology, Cracow 30059 (Poland); Artemovych, Orest D [Department of Algebra and Topology, Faculty of Mathematics and Informatics of the Vasyl Stefanyk Pre-Carpathian National University, Ivano-Frankivsk (Ukraine); Popowicz, Ziemowit [Institute of Theoretical Physics, University of Wroclaw (Poland); Pavlov, Maxim V, E-mail: pryk.anat@ua.f, E-mail: artemo@usk.pk.edu.p, E-mail: ziemek@ift.uni.wroc.p, E-mail: M.V.Pavlov@lboro.ac.u [Department of Mathematical Physics, P.N. Lebedev Physical Institute, 53 Leninskij Prospekt, Moscow 119991 (Russian Federation)

    2010-07-23

    A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic equations at N = 3, 4 is devised. The approach is also applied to studying the Lax-type integrability of the well-known Korteweg-de Vries dynamical system.

  11. Differential-algebraic integrability analysis of the generalized Riemann type and Korteweg-de Vries hydrodynamical equations

    International Nuclear Information System (INIS)

    Prykarpatsky, Anatoliy K; Artemovych, Orest D; Popowicz, Ziemowit; Pavlov, Maxim V

    2010-01-01

    A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic equations at N = 3, 4 is devised. The approach is also applied to studying the Lax-type integrability of the well-known Korteweg-de Vries dynamical system.

  12. Existence and Solution-representation of IVP for LFDE with Generalized Riemann-Liouville fractional derivatives and $n$ terms

    OpenAIRE

    Kim, Myong-Ha; Ri, Guk-Chol; O, Hyong-Chol

    2013-01-01

    This paper provides the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski's type. We prove that the initial value problem has the solution of if and only if some initial values should be zero.

  13. Learning curves of theta/beta neurofeedback in children with ADHD.

    Science.gov (United States)

    Janssen, Tieme W P; Bink, Marleen; Weeda, Wouter D; Geladé, Katleen; van Mourik, Rosa; Maras, Athanasios; Oosterlaan, Jaap

    2017-05-01

    Neurofeedback is widely applied as non-pharmacological intervention aimed at reducing symptoms of ADHD, even though efficacy has not been unequivocally established. Neuronal changes during the neurofeedback intervention that resemble learning can provide crucial evidence for the feasibility and specificity of this intervention. A total of 38 children (aged between 7 and 13 years) with a DSM-IV-TR diagnosis of ADHD, completed on average 29 sessions of theta (4-8 Hz)/beta (13-20 Hz) neurofeedback training. Dependent variables included training-related measures as well as theta and beta power during baseline and training runs for each session. Learning effects were analyzed both within and between sessions. To further specify findings, individual learning curves were explored and correlated with behavioral changes in ADHD symptoms. Over the course of the training, there was a linear increase in participants' mean training level, highest obtained training level and the number of earned credits (range b = 0.059, -0.750, p neurofeedback, although a lack of behavioral correlates may indicate insufficient transfer to daily functioning, or to confounding reinforcement of electromyographic activity. This trial is registered at the US National Institutes of Health (ClinicalTrials.gov, ref. no: NCT01363544); https://clinicaltrials.gov/show/NCT01363544 .

  14. The neuronal mechanisms underlying improvement of impulsivity in ADHD by theta/beta neurofeedback.

    Science.gov (United States)

    Bluschke, Annet; Broschwitz, Felicia; Kohl, Simon; Roessner, Veit; Beste, Christian

    2016-08-12

    Neurofeedback is increasingly recognized as an intervention to treat core symptoms of attention deficit hyperactivity disorder (ADHD). Despite the large number of studies having been carried out to evaluate its effectiveness, it is widely elusive what neuronal mechanisms related to the core symptoms of ADHD are modulated by neurofeedback. 19 children with ADHD undergoing 8 weeks of theta/beta neurofeedback and 17 waiting list controls performed a Go/Nogo task in a pre-post design. We used neurophysiological measures combining high-density EEG recording with source localization analyses using sLORETA. Compared to the waiting list ADHD control group, impulsive behaviour measured was reduced after neurofeedback treatment. The effects of neurofeedback were very specific for situations requiring inhibitory control over responses. The neurophysiological data shows that processes of perceptual gating, attentional selection and resource allocation processes were not affected by neurofeedback. Rather, neurofeedback effects seem to be based on the modulation of response inhibition processes in medial frontal cortices. The study shows that specific neuronal mechanisms underlying impulsivity are modulated by theta/beta neurofeedback in ADHD. The applied neurofeedback protocol could be particularly suitable to address inhibitory control. The study validates assumed functional neuroanatomical target regions of an established neurofeedback protocol on a neurophysiological level.

  15. Differential Galois theory through Riemann-Hilbert correspondence an elementary introduction

    CERN Document Server

    Sauloy, Jacques

    2017-01-01

    Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. This book offers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. Since the book studies only complex analytic linear differential equat...

  16. A boundary-fitted staggered difference method for incompressible flow using Riemann geometry

    International Nuclear Information System (INIS)

    Koshizuka, Seiichi; Kondo, Shunsuke; Oka, Yoshiaki.

    1990-01-01

    A boundary-fitted staggered difference method (BFSDM) is investigated for incompressible flow in nuclear plants. BFSDM employs control cells for scalars, staggered location of velocity components, and integrated formulation of div=0. Governing equations are written as coordinate-free forms using Riemann geometry. Flow velocity is represented with contravariant physical components in the present method. Connection terms emerge as source terms in the coordinate-free governing equations. These terms are studied from the viewpoints of physical meaning, numerical stability, and conservative property. Some flows on a round or slant boundary are solved using boundary-fitted curvilinear (BFC) grids and rectangular grids to compare the present method and the rectangular-type (R-type) staggered difference method (SDM). Supercomputing of the present method, including vector processing, is also discussed compared with the R-type method. (author)

  17. Riemann-Liouville integrals of fractional order and extended KP hierarchy

    International Nuclear Information System (INIS)

    Kamata, Masaru; Nakamula, Atsushi

    2002-01-01

    An attempt to formulate the extensions of the KP hierarchy by introducing fractional-order pseudo-differential operators is given. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered here. More general hierarchies constructed by the 1/Nth-order pseudo-differential operators, their integrability and the reduction procedure are also investigated. In addition to finding the new extensions of the KP hierarchy, a brief introduction to the Riemann-Liouville integral is provided to yield a candidate for the fractional-order pseudo-differential operators

  18. Scattering analysis of asymmetric metamaterial resonators by the Riemann-Hilbert approach

    DEFF Research Database (Denmark)

    Kaminski, Piotr Marek; Ziolkowski, Richard W.; Arslanagic, Samel

    2016-01-01

    This work presents an analytical treatment of an asymmetric metamaterial-based resonator excited by an electric line source, and explores its beam shaping capabilities. The resonator consists of two concentric cylindrical material layers covered with an infinitely thin conducting shell with an ap......This work presents an analytical treatment of an asymmetric metamaterial-based resonator excited by an electric line source, and explores its beam shaping capabilities. The resonator consists of two concentric cylindrical material layers covered with an infinitely thin conducting shell...... with an aperture. Exact analytical solution of the problem is derived; it is based on the n-series approach which is casted into the equivalent Riemann-Hilbert problem. The examined configuration leads to large enhancements of the radiated field and to steerable Huygens-like directivity patterns. Particularly...

  19. Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering

    Science.gov (United States)

    Pelinovsky, Dmitry E.; Sulem, Catherine

    A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.

  20. Comparison of the generalized Riemann solver and the gas-kinetic scheme for inviscid compressible flow simulations

    International Nuclear Information System (INIS)

    Li Jiequan; Li Qibing; Xu Kun

    2011-01-01

    The generalized Riemann problem (GRP) scheme for the Euler equations and gas-kinetic scheme (GKS) for the Boltzmann equation are two high resolution shock capturing schemes for fluid simulations. The difference is that one is based on the characteristics of the inviscid Euler equations and their wave interactions, and the other is based on the particle transport and collisions. The similarity between them is that both methods can use identical MUSCL-type initial reconstructions around a cell interface, and the spatial slopes on both sides of a cell interface involve in the gas evolution process and the construction of a time-dependent flux function. Although both methods have been applied successfully to the inviscid compressible flow computations, their performances have never been compared. Since both methods use the same initial reconstruction, any difference is solely coming from different underlying mechanism in their flux evaluation. Therefore, such a comparison is important to help us to understand the correspondence between physical modeling and numerical performances. Since GRP is so faithfully solving the inviscid Euler equations, the comparison can be also used to show the validity of solving the Euler equations itself. The numerical comparison shows that the GRP exhibits a slightly better computational efficiency, and has comparable accuracy with GKS for the Euler solutions in 1D case, but the GKS is more robust than GRP. For the 2D high Mach number flow simulations, the GKS is absent from the shock instability and converges to the steady state solutions faster than the GRP. The GRP has carbuncle phenomena, likes a cloud hanging over exact Riemann solvers. The GRP and GKS use different physical processes to describe the flow motion starting from a discontinuity. One is based on the assumption of equilibrium state with infinite number of particle collisions, and the other starts from the non-equilibrium free transport process to evolve into an

  1. Energy storage and transfer with homopolar machine for a linear theta-pinch hybrid reactor

    International Nuclear Information System (INIS)

    Vogel, H.F.; Brennan, M.; Dase, W.G.; Tolk, K.M.; Weldon, W.F.

    1975-12-01

    This report describes the energy storage and transfer system for the compression coil system of a linear theta-pinch hybrid reactor (LTPHR). High efficiency and low cost are the principal requirements for the energy storage and transfer of 25 MJ/m or 25 GJ for a 1-km LTPHR. The circuit efficiency must be approximately 90 percent, and the cost for the circuit 5 to 6 cents/J. Scaling laws and simple relationships between circuit efficiency and cost per unit energy as a function of the half cycle time are presented. Capacitors and homopolor machines are considered as energy storage elements with both functioning basically as capacitors. The advantage of the homopolar machine in this application is its relatively low cost, whereas that of capacitors is better efficiency

  2. Enhancing early consolidation of human episodic memory by theta EEG neurofeedback.

    Science.gov (United States)

    Rozengurt, Roman; Shtoots, Limor; Sheriff, Aviv; Sadka, Ofir; Levy, Daniel A

    2017-11-01

    Consolidation of newly formed memories is readily disrupted, but can it be enhanced? Given the prominent role of hippocampal theta oscillations in memory formation and retrieval, we hypothesized that upregulating theta power during early stages of consolidation might benefit memory stability and persistence. We used EEG neurofeedback to enable participants to selectively increase theta power in their EEG spectra following episodic memory encoding, while other participants engaged in low beta-focused neurofeedback or passively viewed a neutral nature movie. Free recall assessments immediately following the interventions, 24h later and 7d later all indicated benefit to memory of theta neurofeedback, relative to low beta neurofeedback or passive movie-viewing control conditions. The degree of benefit to memory was correlated with the extent of theta power modulation, but not with other spectral changes. Theta enhancement may provide optimal conditions for stabilization of new hippocampus-dependent memories. Copyright © 2017 Elsevier Inc. All rights reserved.

  3. Atmospheric, long baseline, and reactor neutrino data constraints on theta_{13}.

    Science.gov (United States)

    Roa, J E; Latimer, D C; Ernst, D J

    2009-08-07

    An atmospheric neutrino oscillation tool that uses full three-neutrino oscillation probabilities and a full three-neutrino treatment of the Mikheyev-Smirnov-Wolfenstein effect, together with an analysis of the K2K, MINOS, and CHOOZ data, is used to examine the bounds on theta_{13}. The recent, more finely binned, Super-K atmospheric data are employed. For L/E_{nu} greater, similar 10;{4} km/GeV, we previously found significant linear in theta_{13} terms. This analysis finds theta_{13} bounded from above by the atmospheric data while bounded from below by CHOOZ. The origin of this result arises from data in the previously mentioned very long baseline region; here, matter effects conspire with terms linear in theta_{13} to produce asymmetric bounds on theta_{13}. Assuming CP conservation, we find theta_{13} = -0.07_{-0.11};{+0.18} (90% C.L.).

  4. Increased theta band EEG power in sickle cell disease patients

    Directory of Open Access Journals (Sweden)

    Case M

    2017-12-01

    Full Text Available Michelle Case,1 Sina Shirinpour,1 Huishi Zhang,1 Yvonne H Datta,2 Stephen C Nelson,3 Karim T Sadak,4 Kalpna Gupta,2 Bin He1,5 1Department of Biomedical Engineering, 2Department of Medicine, University of Minnesota, 3Pediatric Hematology-Oncology, Children’s Hospitals and Clinics of Minnesota, 4Pediatric Hematology-Oncology, University of Minnesota Masonic Children’s Hospital, 5Institute for Engineering in Medicine, University of Minnesota, Minneapolis, MN, USA Objective: Pain is a major issue in the care of patients with sickle cell disease (SCD. The mechanisms behind pain and the best way to treat it are not well understood. We studied how electroencephalography (EEG is altered in SCD patients. Methods: We recruited 20 SCD patients and compared their resting state EEG to that of 14 healthy controls. EEG power was found across frequency bands using Welch’s method. Electrophysiological source imaging was assessed for each frequency band using the eLORETA algorithm. Results: SCD patients had increased theta power and decreased beta2 power compared to controls. Source localization revealed that areas of greater theta band activity were in areas related to pain processing. Imaging parameters were significantly correlated to emergency department visits, which indicate disease severity and chronic pain intensity. Conclusion: The present results support the pain mechanism referred to as thalamocortical dysrhythmia. This mechanism causes increased theta power in patients. Significance: Our findings show that EEG can be used to quantitatively evaluate differences between controls and SCD patients. Our results show the potential of EEG to differentiate between different levels of pain in an unbiased setting, where specific frequency bands could be used as biomarkers for chronic pain. Keywords: sickle cell disease, electroencephalography, chronic pain, electrophysiological source imaging, thalamocortical dysrhythmia

  5. Field reversed theta pinch TC-I UNICAMP

    International Nuclear Information System (INIS)

    Honda, R.Y.; Machida, M.; Aramaki, E.A.; Porto, P.; Berni, L.A.

    1990-01-01

    Field reversed configuration TC-I device is 16 cm diameter, 1 meter long with two mirror coils and 30 kJ field reversed theta pinch working for over two years at University of Campinas. Its implosion dynamics and field reversal parameters have been studied using flux excluded loops, internal magnetic probe, visible spectroscopy, photodiode array and image converter camera. The vacuum vessel is a pyrex tube of 14,5 cm diameter pumped with a liquid nitrogen cooled diffusion pump to a base pressure of 6 x 10 -7 Torr. The schematic view of the machine and experimental set up are shown. (Author)

  6. Resting-state theta-band connectivity and verbal memory in schizophrenia and in the high-risk state.

    Science.gov (United States)

    Andreou, Christina; Leicht, Gregor; Nolte, Guido; Polomac, Nenad; Moritz, Steffen; Karow, Anne; Hanganu-Opatz, Ileana L; Engel, Andreas K; Mulert, Christoph

    2015-02-01

    Disturbed functional connectivity is assumed to underlie neurocognitive deficits in patients with schizophrenia. As neurocognitive deficits are already present in the high-risk state, identification of the neural networks involved in this core feature of schizophrenia is essential to our understanding of the disorder. Resting-state studies enable such investigations, while at the same time avoiding the known confounder of impaired task performance in patients. The aim of the present study was to investigate EEG resting-state connectivity in high-risk individuals (HR) compared to first episode patients with schizophrenia (SZ) and to healthy controls (HC), and its association with cognitive deficits. 64-channel resting-state EEG recordings (eyes closed) were obtained for 28 HR, 19 stable SZ, and 23 HC, matched for age, education, and parental education. The imaginary coherence-based multivariate interaction measure (MIM) was used as a measure of connectivity across 80 cortical regions and six frequency bands. Mean connectivity at each region was compared across groups using the non-parametric randomization approach. Additionally, the network-based statistic was applied to identify affected networks in patients. SZ displayed increased theta-band resting-state MIM connectivity across midline, sensorimotor, orbitofrontal regions and the left temporoparietal junction. HR displayed intermediate theta-band connectivity patterns that did not differ from either SZ or HC. Mean theta-band connectivity within the above network partially mediated verbal memory deficits in SZ and HR. Aberrant theta-band connectivity may represent a trait characteristic of schizophrenia associated with neurocognitive deficits. As such, it might constitute a promising target for novel treatment applications. Copyright © 2014 Elsevier B.V. All rights reserved.

  7. Expected reward modulates encoding-related theta activity before an event.

    Science.gov (United States)

    Gruber, Matthias J; Watrous, Andrew J; Ekstrom, Arne D; Ranganath, Charan; Otten, Leun J

    2013-01-01

    Oscillatory brain activity in the theta frequency range (4-8 Hz) before the onset of an event has been shown to affect the likelihood of successfully encoding the event into memory. Recent work has also indicated that frontal theta activity might be modulated by reward, but it is not clear how reward expectancy, anticipatory theta activity, and memory formation might be related. Here, we used scalp electroencephalography (EEG) to assess the relationship between these factors. EEG was recorded from healthy adults while they memorized a series of words. Each word was preceded by a cue that indicated whether a high or low monetary reward would be earned if the word was successfully remembered in a later recognition test. Frontal theta power between the presentation of the reward cue and the onset of a word was predictive of later memory for the word, but only in the high reward condition. No theta differences were observed before word onset following low reward cues. The magnitude of prestimulus encoding-related theta activity in the high reward condition was correlated with the number of high reward words that were later confidently recognized. These findings provide strong evidence for a link between reward expectancy, theta activity, and memory encoding. Theta activity before event onset seems to be especially important for the encoding of motivationally significant stimuli. One possibility is that dopaminergic activity during reward anticipation mediates frontal theta activity related to memory. Copyright © 2012 Elsevier Inc. All rights reserved.

  8. Hippocampal theta activity in the acute cerveau isolé cat.

    Science.gov (United States)

    Gottesmann, C; Zernicki, B; Gandolfo, G

    1981-01-01

    In three cerveau isole cats, cortical and hippocampal EEG activity were recorded. In the cortical records, spindles alternated with low-voltage activity, whereas theta activity dominated in the hippocampus. The amount and frequency of theta were similar to those described previously for the pretrigeminal cat. In confirmation of previous results on rats, although cortical EEG activity differs in cerveau isole cat and pretrigeminal cat, both preparations show domination of theta activity in the hippocampus. It is concluded that the mesencephalic transection eliminates inhibitory effects from the lower brainstem on generators of the theta rhythm.

  9. On the fractional calculus of Besicovitch function

    International Nuclear Information System (INIS)

    Liang Yongshun

    2009-01-01

    Relationship between fractional calculus and fractal functions has been explored. Based on prior investigations dealing with certain fractal functions, fractal dimensions including Hausdorff dimension, Box dimension, K-dimension and Packing dimension is shown to be a linear function of order of fractional calculus. Both Riemann-Liouville fractional calculus and Weyl-Marchaud fractional derivative of Besicovitch function have been discussed.

  10. Opacity test using a neon-seeded theta pinch

    International Nuclear Information System (INIS)

    Thomson, D.B.

    1980-02-01

    Vacuum ultraviolet (VUV) emission from a neon-seeded high-density theta-pinch has been observed for comparison with theoretical radiation emission calculations. The plasma was created in a 25-cm-long theta-coil with 90-kG field having a 3.0-μs quarter period. A gas fill of 1 torr of helium + 2% neon was used. Observation of the HeII 4686 line/continuum ratio gave an electron temperature of 25 +- 4 eV. Shadowgraphs of the plasma radius, taken with a ruby laser, gave an electron density of 0.9 +- 0.09 x 10 18 cm -3 . The VUV emission was observed in radial view and with time resolution with a 2.2-m grazing-incidence monochromator equipped with a photomultiplier and p-terphenyl scintillator. Thin foils of carbon and aluminum were used as filters to absorb stray light and pass emission in the 44- to 100-A region

  11. Energy storage and transfer with homopolar machine for a linear theta-pinch hybrid reactor

    International Nuclear Information System (INIS)

    Vogel, H.F.; Brennan, M.; Dase, W.G.; Tolk, K.M.; Weldon, W.F.

    1976-01-01

    The energy storage and transfer system for the compression coils of a linear theta-pinch hybrid reactor (LTPHR) are described. High efficiency and low cost are the principal requirements for the energy storage and transfer of 25MJ/m or 25GJ for a 1-km LTPHR. The circuit efficiency must be approximately 90%, and the cost for the circuit 5-6c/J. Scaling laws and simple relationships between circuit efficiency and cost-per-unit energy as a function of the half cycle time are presented. An important consideration concerns the pulse repetition rate of 2.25 pulses per second, 70x10 6 shots/yr, or 1.7x10 9 shots over the 25-yr plant life. Current interruption to initiate energy transfer is not feasible at this rate. Therefore, a simple ringing circuit with contactors to make and break at the periodically occurring zero-current instances, is considered

  12. Glutathione-binding site of a bombyx mori theta-class glutathione transferase.

    Directory of Open Access Journals (Sweden)

    M D Tofazzal Hossain

    Full Text Available The glutathione transferase (GST superfamily plays key roles in the detoxification of various xenobiotics. Here, we report the isolation and characterization of a silkworm protein belonging to a previously reported theta-class GST family. The enzyme (bmGSTT catalyzes the reaction of glutathione with 1-chloro-2,4-dinitrobenzene, 1,2-epoxy-3-(4-nitrophenoxy-propane, and 4-nitrophenethyl bromide. Mutagenesis of highly conserved residues in the catalytic site revealed that Glu66 and Ser67 are important for enzymatic function. These results provide insights into the catalysis of glutathione conjugation in silkworm by bmGSTT and into the metabolism of exogenous chemical agents.

  13. Establishing the Thematic Structure and Investigating the most Prominent Theta Roles Used in Sindhi Language

    Directory of Open Access Journals (Sweden)

    Zahid Ali Veesar

    2015-07-01

    Full Text Available This study focuses on the thematic structure of the Sindhi verbs to find theta roles in the Sindhi language. The study tries to answer the research questions; “What are the thematic structures of Sindhi verbs?” and “What are the prominent theta roles in the Sindhi language?” It examines the argument/thematic structure of Sindhi verbs and also finds the theta roles assigned by the Sindhi verbs to their arguments along with the most prominent theta roles used in the Sindhi language. The data come from the two interviews taken from two young native Sindhi speakers, which consist of 2 hours conversation having 1,669 sentences in natural spoken version of the Sindhi language. Towards the end, it has been found that the Sindhi language has certain theta roles which are assigned by the verbs to their arguments in sentences. Each verb phrase in our data is thus examined and studied in detail in terms of Argument/Thematic structure in order to find theta roles in Sindhi language. Thus, in this regard, each verb phrase (in a sentence has been examined with the help of Carnie’s theoretical framework (Thematic Relation and Theta Roles: 2006 in order to find the prominent theta roles in the Sindhi language. The data have been examined and analysed on the basis of the Carnie’s theoretical framework. The study finds that the Sindhi language has all (09 theta roles which have been proposed by Carnie (2006. It has been found that six prominent theta roles out of nine are used prominently in Sindhi. The six prominent theta roles in Sindhi language are: agent, theme, beneficiary, recipient, locative and goal.

  14. Implicit approximate Riemann solver for two fluid two phase flow models

    International Nuclear Information System (INIS)

    Raymond, P.; Toumi, I.; Kumbaro, A.

    1993-01-01

    This paper is devoted to the description of new numerical methods developed for the numerical treatment of two phase flow models with two velocity fields which are now widely used in nuclear engineering for design or safety calculations. These methods are finite volumes numerical methods and are based on the use of Approximate Riemann Solver's concepts in order to define convective flux versus mean cell quantities. The first part of the communication will describe the numerical method for a three dimensional drift flux model and the extensions which were performed to make the numerical scheme implicit and to have fast running calculations of steady states. Such a scheme is now implemented in the FLICA-4 computer code devoted to 3-D steady state and transient core computations. We will present results obtained for a steady state flow with rod bow effect evaluation and for a Steam Line Break calculation were the 3-D core thermal computation was coupled with a 3-D kinetic calculation and a thermal-hydraulic transient calculation for the four loops of a Pressurized Water Reactor. The second part of the paper will detail the development of an equivalent numerical method based on an approximate Riemann Solver for a two fluid model with two momentum balance equations for the liquid and the gas phases. The main difficulty for these models is due to the existence of differential modelling terms such as added mass effects or interfacial pressure terms which make hyperbolic the model. These terms does not permit to write the balance equations system in a conservative form, and the classical theory for discontinuity propagation for non-linear systems cannot be applied. Meanwhile, the use of non-conservative products theory allows the study of discontinuity propagation for a non conservative model and this will permit the construction of a numerical scheme for two fluid two phase flow model. These different points will be detailed in that section which will be illustrated by

  15. GABAergic contributions to gating, timing, and phase precession of hippocampal neuronal activity during theta oscillations.

    Science.gov (United States)

    Cutsuridis, Vassilis; Hasselmo, Michael

    2012-07-01

    Successful spatial exploration requires gating, storage, and retrieval of spatial memories in the correct order. The hippocampus is known to play an important role in the temporal organization of spatial information. Temporally ordered spatial memories are encoded and retrieved by the firing rate and phase of hippocampal pyramidal cells and inhibitory interneurons with respect to ongoing network theta oscillations paced by intra- and extrahippocampal areas. Much is known about the anatomical, physiological, and molecular characteristics as well as the connectivity and synaptic properties of various cell types in the hippocampal microcircuits, but how these detailed properties of individual neurons give rise to temporal organization of spatial memories remains unclear. We present a model of the hippocampal CA1 microcircuit based on observed biophysical properties of pyramidal cells and six types of inhibitory interneurons: axo-axonic, basket, bistratistified, neurogliaform, ivy, and oriens lacunosum-moleculare cells. The model simulates a virtual rat running on a linear track. Excitatory transient inputs come from the entorhinal cortex (EC) and the CA3 Schaffer collaterals and impinge on both the pyramidal cells and inhibitory interneurons, whereas inhibitory inputs from the medial septum impinge only on the inhibitory interneurons. Dopamine operates as a gate-keeper modulating the spatial memory flow to the PC distal dendrites in a frequency-dependent manner. A mechanism for spike-timing-dependent plasticity in distal and proximal PC dendrites consisting of three calcium detectors, which responds to the instantaneous calcium level and its time course in the dendrite, is used to model the plasticity effects. The model simulates the timing of firing of different hippocampal cell types relative to theta oscillations, and proposes functional roles for the different classes of the hippocampal and septal inhibitory interneurons in the correct ordering of spatial memories

  16. Recent developments in linear theta-pinch research: experiment and theory

    International Nuclear Information System (INIS)

    McKenna, K.F.; Bartsch, R.R.; Commisso, R.J.

    1978-01-01

    High energy plasmas offusion interest can be generated in linear theta pinches. However, end losses present a fundamental limitation on the plasma containment time. This paper discusses recent progress in end-loss and end-stoppering experiments and in the theoretical understanding of linear theta-pinch physics

  17. Torus C-I field reversed theta-pinch at UNICAMP

    International Nuclear Information System (INIS)

    Machida, M.; Collares, M.P.; Honda, R.Y.; Sakanaka, P.H.; Scheid, V.H.B.

    1984-01-01

    The influence of multipole fields (octopole and quadrupole) on supressing the n=2 rotational instability, field reconnection, particle loss effects is studied, and the viability of transforming the theta-pinch from Campinas, Brazil (100Kv, 55Kj) to the field reversed theta-pinch with plasma translation program is analyzed. (E.G.) [pt

  18. Mixing angle theta and magnetic monopole in Weinberg's unified gauge theory

    International Nuclear Information System (INIS)

    Hsu, J.P.

    1975-01-01

    Gauge symmetry admits a local unit isovector and leads to the magnetic monopoles in Weinberg's unified theory. One predicts sin 2 theta = 1 / 2 for the mixing angle theta on the basis of Dirac's condition for charge quantization. This interesting result should be tested experimentally

  19. Transient reduction in theta power caused by interictal spikes in human temporal lobe epilepsy.

    Science.gov (United States)

    Manling Ge; Jundan Guo; Yangyang Xing; Zhiguo Feng; Weide Lu; Xinxin Ma; Yuehua Geng; Xin Zhang

    2017-07-01

    The inhibitory impacts of spikes on LFP theta rhythms(4-8Hz) are investigated around sporadic spikes(SSs) based on intracerebral EEG of 4 REM sleep patients with temporal lobe epilepsy(TLE) under the pre-surgical monitoring. Sequential interictal spikes in both genesis area and extended propagation pathway are collected, that, SSs genesis only in anterior hippocampus(aH)(possible propagation pathway in Entorhinal cortex(EC)), only in EC(possible propagation pathway in aH), and in both aH and EC synchronously. Instantaneous theta power was estimated by using Gabor wavelet transform, and theta power level was estimated by averaged over time and frequency before SSs(350ms pre-spike) and after SSs(350ms post-spike). The inhibitory effect around spikes was evaluated by the ratio of theta power level difference between pre-spike and post-spike to pre-spike theta power level. The findings were that theta power level was reduced across SSs, and the effects were more sever in the case of SSs in both aH and EC synchronously than either SSs only in EC or SSs only in aH. It is concluded that interictal spikes impair LFP theta rhythms transiently and directly. The work suggests that the reduction of theta power after the interictal spike might be an evaluation indicator of damage of epilepsy to human cognitive rhythms.

  20. Formulation of dynamical theory of X-ray diffraction for perfect crystals in the Laue case using the Riemann surface.

    Science.gov (United States)

    Saka, Takashi

    2016-05-01

    The dynamical theory for perfect crystals in the Laue case was reformulated using the Riemann surface, as used in complex analysis. In the two-beam approximation, each branch of the dispersion surface is specified by one sheet of the Riemann surface. The characteristic features of the dispersion surface are analytically revealed using four parameters, which are the real and imaginary parts of two quantities specifying the degree of departure from the exact Bragg condition and the reflection strength. By representing these parameters on complex planes, these characteristics can be graphically depicted on the Riemann surface. In the conventional case, the absorption is small and the real part of the reflection strength is large, so the formulation is the same as the traditional analysis. However, when the real part of the reflection strength is small or zero, the two branches of the dispersion surface cross, and the dispersion relationship becomes similar to that of the Bragg case. This is because the geometrical relationships among the parameters are similar in both cases. The present analytical method is generally applicable, irrespective of the magnitudes of the parameters. Furthermore, the present method analytically revealed many characteristic features of the dispersion surface and will be quite instructive for further numerical calculations of rocking curves.

  1. Task-related modulation of anterior theta and posterior alpha EEG reflects top-down preparation

    Directory of Open Access Journals (Sweden)

    Park Hae-Jeong

    2010-06-01

    Full Text Available Abstract Background Prestimulus EEG alpha activity in humans has been considered to reflect ongoing top-down preparation for the performance of subsequent tasks. Since theta oscillations may be related to poststimulus top-down processing, we investigated whether prestimulus EEG theta activity also reflects top-down cognitive preparation for a stimulus. Results We recorded EEG data from 15 healthy controls performing a color and shape discrimination task, and used the wavelet transformation to investigate the time course and power of oscillatory activity in the signals. We observed a relationship between both anterior theta and posterior alpha power in the prestimulus period and the type of subsequent task. Conclusions Since task-differences were reflected in both theta and alpha activities prior to stimulus onset, both prestimulus theta (particularly around the anterior region and prestimulus alpha (particularly around the posterior region activities may reflect prestimulus top-down preparation for the performance of subsequent tasks.

  2. Cylinder renormalization for Siegel disks and a constructive Measurable Riemann Mapping Theorem

    CERN Document Server

    Gaydashev, D G

    2006-01-01

    The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point with the golden mean rotation number has been observed to be self-similar. The geometry of this self-similarity is universal for a large class of holomorphic maps. A renormalization explanation of this universality has been proposed in the literature. However, one of the ingredients of this explanation, the hyperbolicity of renormalization, has not been proved yet. The present work considers a cylinder renormalization - a novel type of renormalization for holomorphic maps with a Siegel disk which is better suited for a hyperbolicity proof. A key element of a cylinder renormalization of a holomorphic map is a conformal isomorphism of a dynamical quotient of a subset of $\\field{C}$ to a bi-infinite cylinder $\\field{C} / \\field{Z}$. A construction of this conformal isomorphism is an implicit procedure which can be performed using the Measurable Riemann Mapping Theorem. We present a constructive proof of the Mea...

  3. Approximate Riemann solvers and flux vector splitting schemes for two-phase flow

    International Nuclear Information System (INIS)

    Toumi, I.; Kumbaro, A.; Paillere, H.

    1999-01-01

    These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)

  4. A geometric construction of the Riemann scalar curvature in Regge calculus

    Science.gov (United States)

    McDonald, Jonathan R.; Miller, Warner A.

    2008-10-01

    The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas.

  5. 3D staggered Lagrangian hydrodynamics scheme with cell-centered Riemann solver-based artificial viscosity

    International Nuclear Information System (INIS)

    Loubere, Raphael; Maire, Pierre-Henri; Vachal, Pavel

    2013-01-01

    The aim of the present work is the 3D extension of a general formalism to derive a staggered discretization for Lagrangian hydrodynamics on unstructured grids. The classical compatible discretization is used; namely, momentum equation is discretized using the fundamental concept of subcell forces. Specific internal energy equation is obtained using total energy conservation. The subcell force is derived by invoking the Galilean invariance and thermodynamic consistency. A general form of the subcell force is provided so that a cell entropy inequality is satisfied. The subcell force consists of a classical pressure term plus a tensorial viscous contribution proportional to the difference between the node velocity and the cell-centered velocity. This cell-centered velocity is an extra degree of freedom solved with a cell-centered approximate Riemann solver. The second law of thermodynamics is satisfied by construction of the local positive definite subcell tensor involved in the viscous term. A particular expression of this tensor is proposed. A more accurate extension of this discretization both in time and space is also provided using a piecewise linear reconstruction of the velocity field and a predictor-corrector time discretization. Numerical tests are presented in order to assess the efficiency of this approach in 3D. Sanity checks show that the 3D extension of the 2D approach reproduces 1D and 2D results. Finally, 3D problems such as Sedov, Noh, and Saltzman are simulated. (authors)

  6. A geometric construction of the Riemann scalar curvature in Regge calculus

    International Nuclear Information System (INIS)

    McDonald, Jonathan R; Miller, Warner A

    2008-01-01

    The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas

  7. On the properties of torsions in Riemann-Cartan space-times

    International Nuclear Information System (INIS)

    Baker, W.M.; Atkins, W.K.; Davis, W.R.

    1978-01-01

    This paper is the first paper in a series of three papers dealing with the physical properties of torsions in Riemann-Cartan space-times (U 4 ). Paper one deals with the particular types of torsion that can be associated with the U 4 reinterpretation of a special class of null electromagnetic solutions of the standard form of Einstein's equations. In particular, for plane null electromagnetic solutions, three types of torsion solutions are associated with this type of reinterpretation. Two of these solutions, the trivector and semi-symmetric torsions, although rather special, serve as examples of what could be done to find the associated torsions in terms of simple requirements on identities in U 4 . The third class is obtained by relating the contorsion to the Lanczos ''spin'' tensor. Paper two, dealing with gravitational radiation, provides the proper background relating to the physical significance of the Lanczos tensor. This series of papers is primarily concerned with the question of the possible physical role of all types of torsion, compatible with an extension or an U 4 reinterpretation of Einstein's theory, consistent with the broadest possible interpretation of the present form of the Einstein-Cartan-Sciama-Kibble theory. However, in paper three some consideration will be given on theories with simpler metrical generalizations of U 4 and the related types of torsion. We emphasize that the content of paper one and two should be viewed mainly as special formal results that introduce the more general considerations of paper three

  8. Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

    Energy Technology Data Exchange (ETDEWEB)

    Duca, Vittorio Del [Institute for Theoretical Physics, ETH Zürich,Hönggerberg, 8093 Zürich (Switzerland); Druc, Stefan; Drummond, James [School of Physics & Astronomy, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom); Duhr, Claude [Theoretical Physics Department, CERN,Route de Meyrin, CH-1211 Geneva 23 (Switzerland); Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium); Dulat, Falko [SLAC National Accelerator Laboratory, Stanford University,Stanford, CA 94309 (United States); Marzucca, Robin [Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium); Papathanasiou, Georgios [SLAC National Accelerator Laboratory, Stanford University,Stanford, CA 94309 (United States); Verbeek, Bram [Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium)

    2016-08-25

    We show that scattering amplitudes in planar N=4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes’ theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L+4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.

  9. Reduction in LFP cross-frequency coupling between theta and gamma rhythms associated with impaired STP and LTP in a rat model of brain ischemia

    Directory of Open Access Journals (Sweden)

    Tao eZhang

    2013-04-01

    Full Text Available The theta-gamma cross-frequency coupling (CFC in hippocampus was reported to reflect memory process. In this study, we measured the CFC of hippocampal local field potentials (LFPs in a two-vessel occlusion (2VO rat model, combined with both amplitude and phase properties and associated with short and long-term plasticity indicating the memory function. Male Wistar rats were used and a 2VO model was established. STP and LTP were recorded in hippocampal CA3-CA1 pathway after LFPs were collected in both CA3 and CA1. Based on the data of relative power spectra and phase synchronization, it suggested that both the amplitude and phase coupling of either theta or gamma rhythm were involved in modulating the neural network in 2VO rats. In order to determine whether the CFC was also implicated in neural impairment in 2VO rats, the coupling of CA3 theta–CA1 gamma was measured by both phase-phase coupling (n:m phase synchronization and phase-amplitude coupling. The attenuated CFC strength in 2VO rats implied the impaired neural communication in the coordination of theta-gamma entraining process. Moreover, compared with modulation index (MI a novel algorithm named cross frequency conditional mutual information (CF-CMI, was developed to focus on the coupling between theta phase and the phase of gamma amplitude. The results suggest that the reduced CFC strength probably attributed to the disruption of the phase of CA1 gamma envelop. In conclusion, it implied that the phase coupling and CFC of hippocampal theta and gamma played an important role in supporting functions of neural network. Furthermore, synaptic plasticity on CA3-CA1 pathway was reduced in line with the decreased CFC strength from CA3 to CA1. It partly supported our hypothesis that directional CFC indicator might probably be used as a measure of synaptic plasticity.

  10. The Dynamics of Networks of Identical Theta Neurons.

    Science.gov (United States)

    Laing, Carlo R

    2018-02-05

    We consider finite and infinite all-to-all coupled networks of identical theta neurons. Two types of synaptic interactions are investigated: instantaneous and delayed (via first-order synaptic processing). Extensive use is made of the Watanabe/Strogatz (WS) ansatz for reducing the dimension of networks of identical sinusoidally-coupled oscillators. As well as the degeneracy associated with the constants of motion of the WS ansatz, we also find continuous families of solutions for instantaneously coupled neurons, resulting from the reversibility of the reduced model and the form of the synaptic input. We also investigate a number of similar related models. We conclude that the dynamics of networks of all-to-all coupled identical neurons can be surprisingly complicated.

  11. LTPF: a linear theta-pinch neutron source

    International Nuclear Information System (INIS)

    Ellis, W.R.

    1975-07-01

    The linear theta pinch is optimized with respect to maximum neutron current on a sample located between the discharge tube and the compression coil wall. Emphasis throughout is placed on physics and technology considerations which govern the choice of parameters. Technological demands are (hopefully) kept to a minimum. Two ''point designs'' are developed which are distinguished by their compressional magnetic field (i.e., coil current) wave-forms: one is sinusoidal and continuous, the other trapezoidal and pulsed intermittently. Both point designs give an average neutron current of approximately 5 x 10 13 n/cm 2 /s. Both devices are characterized by short lengths (approximately 1 m), rapid cycling (2 to 30 kHz), and magnetic mirrors (2 to 5:1) at the ends. A crucial item is the power supply, which is discussed in detail. (U.S.)

  12. Cost estimation for a theta-pinch reactor

    International Nuclear Information System (INIS)

    Coultas, T.A.; Cook, J.M.; Crnkovich, P.; Dauzvardis, P.

    1976-02-01

    A simulation of a theta-pinch fusion power plant has been completed to the point where economic feasibility can be examined. A PL/I cost subprogram is presented for interfacing with the computer code TPFPP. This code is then used to obtain a first approximation of the costs for the reactor. Independent geometrical and plant design parameters are varied over a wide range, with simultaneous variation of magnetic field, minor first wall radius, and plasma maximum compression. The study indicates that the plant energy balance must be favorable, availability must be high, and major component costs must be low to achieve economical results. Although costing uncertainties remain, it is clear that development of easy and rapid replacement methods for reactor components is essential and that new staging concepts to reduce the implosion energy requirement must be pursued

  13. Laser--plasma interaction in a theta-pinch geometry

    International Nuclear Information System (INIS)

    Armstrong, W.T.

    1978-06-01

    Prompt stimulated Brillouin scatter (SBS) is studied in an experiment wherein a high power, pulsed CO 2 laser irradiates an independently produced, theta-pinch plasma. SBS does not significantly affect laser heating of the plasma. Measurements of density profiles and temperature histories permitted examination of laser refraction, local heating and net absorption. Refractive containment of the CO 2 laser beam by an on-axis density minimum was observed at early times during the laser pulse. However, refractive containment was lost at late times due to the diffusive loss of the density minimum. Classical modeling of the expected heating required ''bleached'' absorption to account for the observed heating. A plasma absorptivity of approximately 46% was inferred from calorimetry measurements at 250 mtorr fill pressure. These results confirm that classical heating and refraction dominated the laser-plasma interaction

  14. Simulation of the implosion of a theta pinch

    International Nuclear Information System (INIS)

    Busnardo Neto, J.; Leite Neto, J.P.; Jesus Paes, A.C. de

    1982-01-01

    A two-fluid model was used to simulate the implosion of a theta-pinch, with initial densities varying from 10 12 to 10 16 cm -3 . The gases used were hydrogen, helium, neon and argon; initial temperatures of 2 eV and total ionization were assumed. For hydrogen the anomalous resistivity is dominant everywhere when the density is low (ν sub(eff) - ω sub(pi)). For high densities both resistivities are not high enough to allow diffusion of the magnetic field during the time of the implosion (ν sub(eff) approximatelly 0.3 ω sub(pi)). For heavier gases a surprisingly high value of the anomalous resistivity was found, due to the greater mass, (ν sub(eff) approximatelly 10-12 ω sub(pi)). (Author) [pt

  15. Fluctuating inhibitory inputs promote reliable spiking at theta frequencies in hippocampal interneurons

    Directory of Open Access Journals (Sweden)

    Duluxan eSritharan

    2012-05-01

    Full Text Available Theta frequency (4-12 Hz rhythms in the hippocampus play important roles in learning and memory. CA1 interneurons located at the stratum lacunosum-moleculare and radiatum junction (LM/RAD are thought to contribute to hippocampal theta population activities by rhythmically pacing pyramidal cells with inhibitory postsynaptic potentials. This implies that LM/RAD cells need to fire reliably at theta frequencies in vivo. To determine whether this could occur, we use biophysically-based LM/RAD model cells and apply different cholinergic and synaptic inputs to simulate in vivo-like network environments. We assess spike reliabilities and spiking frequencies, identifying biophysical properties and network conditions that best promote reliable theta spiking. We find that synaptic background activities that feature large inhibitory, but not excitatory, fluctuations are essential. This suggests that strong inhibitory input to these cells is vital for them to be able to contribute to population theta activities. Furthermore, we find that Type I-like oscillator models produced by augmented persistent sodium currents (INap or diminished A type potassium currents (IA enhance reliable spiking at lower theta frequencies. These Type I-like models are also the most responsive to large inhibitory fluctuations and can fire more reliably under such conditions. In previous work, we showed that INap and IA are largely responsible for establishing LM/RAD cells’ subthreshold activities. Taken together with this study, we see that while both these currents are important for subthreshold theta fluctuations and reliable theta spiking, they contribute in different ways – INap to reliable theta spiking and subthreshold activity generation, and IA to subthreshold activities at theta frequencies. This suggests that linking subthreshold and suprathreshold activities should be done with consideration of both in vivo contexts and biophysical specifics.

  16. Impaired cognitive discrimination and discoordination of coupled theta-gamma oscillations in Fmr1 knockout mice

    Science.gov (United States)

    Radwan, Basma; Dvorak, Dino; Fenton, André

    2016-01-01

    Fragile X syndrome (FXS) patients do not make the fragile X mental retardation protein (FMRP). Absence of FMRP causes dysregulated translation, abnormal synaptic plasticity and the most common form of inherited intellectual disability. But FMRP loss has minimal effects on memory itself, making it difficult to understand why absence of FMRP impairs memory discrimination and increases risk of autistic symptoms in patients, such as exaggerated responses to environmental changes. While Fmr1 knockout (KO) and wild-type (WT) mice perform cognitive discrimination tasks, we find abnormal patterns of coupling between theta and gamma oscillations in perisomatic and dendritic hippocampal CA1 local field potentials of the KO. Perisomatic CA1 theta-gamma phase-amplitude coupling (PAC) decreases with familiarity in both the WT and KO, but activating an invisible shock zone, subsequently changing its location, or turning it off, changes the pattern of oscillatory events in the LFPs recorded along the somato-dendritic axis of CA1. The cognition-dependent changes of this pattern of neural activity are relatively constrained in WT mice compared to KO mice, which exhibit abnormally weak changes during the cognitive challenge caused by changing the location of the shock zone and exaggerated patterns of change when the shock zone is turned off. Such pathophysiology might explain how dysregulated translation leads to intellectual disability in FXS. These findings demonstrate major functional abnormalities after the loss of FMRP in the dynamics of neural oscillations and that these impairments would be difficult to detect by steady-state measurements with the subject at rest or in steady conditions. PMID:26792400

  17. AdS5 solutions from M5-branes on Riemann surface and D6-branes sources

    Energy Technology Data Exchange (ETDEWEB)

    Bah, Ibrahima [Department of Physics and Astronomy, University of Southern California,Los Angeles, CA 90089 (United States); Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France)

    2015-09-24

    We describe the gravity duals of four-dimensional N=1 superconformal field theories obtained by wrapping M5-branes on a punctured Riemann surface. The internal geometry, normal to the AdS{sub 5} factor, generically preserves two U(1)s, with generators (J{sup +},J{sup −}), that are fibered over the Riemann surface. The metric is governed by a single potential that satisfies a version of the Monge-Ampère equation. The spectrum of N=1 punctures is given by the set of supersymmetric sources of the potential that are localized on the Riemann surface and lead to regular metrics near a puncture. We use this system to study a class of punctures where the geometry near the sources corresponds to M-theory description of D6-branes. These carry a natural (p,q) label associated to the circle dual to the killing vector pJ{sup +}+qJ{sup −} which shrinks near the source. In the generic case the world volume of the D6-branes is AdS{sub 5}×S{sup 2} and they locally preserve N=2 supersymmetry. When p=−q, the shrinking circle is dual to a flavor U(1). The metric in this case is non-degenerate only when there are co-dimension one sources obtained by smearing M5-branes that wrap the AdS{sub 5} factor and the circle dual the superconformal R-symmetry. The D6-branes are extended along the AdS{sub 5} and on cups that end on the co-dimension one branes. In the special case when the shrinking circle is dual to the R-symmetry, the D6-branes are extended along the AdS{sub 5} and wrap an auxiliary Riemann surface with an arbitrary genus. When the Riemann surface is compact with constant curvature, the system is governed by a Monge-Ampère equation.

  18. Changes in hippocampal theta rhythm and their correlations with speed during different phases of voluntary wheel running in rats.

    Science.gov (United States)

    Li, J-Y; Kuo, T B J; Hsieh, I-T; Yang, C C H

    2012-06-28

    Hippocampal theta rhythm (4-12 Hz) can be observed during locomotor behavior, but findings on the relationship between locomotion speed and theta frequency are inconsistent if not contradictory. The inconsistency may be because of the difficulties that previous analyses and protocols have had excluding the effects of behavior training. We recorded the first or second voluntary wheel running each day, and assumed that theta frequency and activity are correlated with speed in different running phases. By simultaneously recording electroencephalography, physical activity, and wheel running speed, this experiment explored the theta oscillations during spontaneous running of the 12-h dark period. The recording was completely wireless and allowed the animal to run freely while being recorded in the wheel. Theta frequency and theta power of middle frequency were elevated before running and theta frequency, theta power of middle frequency, physical activity, and running speed maintained persistently high levels during running. The slopes of the theta frequency and theta activity (4-9.5 Hz) during the initial running were different compared to the same values during subsequent running. During the initial running, the running speed was positively correlated with theta frequency and with theta power of middle frequency. Over the 12-h dark period, the running speed did not positively correlate with theta frequency but was significantly correlated with theta power of middle frequency. Thus, theta frequency was associated with running speed only at the initiation of running. Furthermore, theta power of middle frequency was associated with speed and with physical activity during running when chronological order was not taken into consideration. Copyright © 2012 IBRO. Published by Elsevier Ltd. All rights reserved.

  19. TVEDIM, 2-D Homogeneous and Inhomogeneous Neutron Diffusion for X-Y, R-Z, R-Theta Geometry

    International Nuclear Information System (INIS)

    Kristiansen, G.K.

    1987-01-01

    1 - Nature of physical problem solved: The two-dimensional neutron diffusion equation (x-y, r-z, or r-theta geometry is solved, either in the inhomogeneous (source calculation) or the homogeneous form (K eff calculation or absorber adjustment). The boundary conditions specify each group current as a linear homogeneous function of the group fluxes (gamma matrix concept). For each material, the fission matrix is assumed to by dyadic. 2 - Method of solution: Finite difference formulation (5 point scheme, mesh corner variant) is used. Solution technique: multi-line SOR. Eigenvalue estimate by neutron balance

  20. Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme

    International Nuclear Information System (INIS)

    Doliwa, A.; Grinevich, P.; Nieszporski, M.; Santini, P. M.

    2007-01-01

    We present the sublattice approach, a procedure to generate, from a given integrable lattice, a sublattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point equation and its sublattice, the self-adjoint 5-point scheme on the star of the square lattice, which are relevant in the theory of the integrable discrete geometries and in the theory of discrete holomorphic and harmonic functions (in this last context, the discrete Moutard equation is called discrete Cauchy-Riemann equation). Therefore an integrable, at one energy, discretization of elliptic two-dimensional operators is considered. We use the sublattice point of view to derive, from the Darboux transformations and superposition formulas of the discrete Moutard equation, the Darboux transformations and superposition formulas of the self-adjoint 5-point scheme. We also construct, from algebro-geometric solutions of the discrete Moutard equation, algebro-geometric solutions of the self-adjoint 5-point scheme. In particular, we show that the corresponding restrictions on the finite-gap data are of the same type as those for the fixed energy problem for the two-dimensional Schroedinger operator. We finally use these solutions to construct explicit examples of discrete holomorphic and harmonic functions, as well as examples of quadrilateral surfaces in R 3

  1. Search for the Theta+ pentaquark in the reactions gammap-->[overline K]0K+n and gammap-->[overline K]0K0p

    Energy Technology Data Exchange (ETDEWEB)

    Raffaella De Vita; Marco Battaglieri; V. Kubarovsky; Nathan Baltzell; Matthew Bellis; John Goett; Lei Guo; Gordon Mutchler; Paul Stoler; Maurizio Ungaro; Dennis Weygand; Moscov Amaryan; Pawel Ambrozewicz; Marco Anghinolfi; Gegham Asryan; Harutyun AVAKIAN; Harutyun Avakian; Hovhannes Baghdasaryan; Nathan Baillie; Jacques Ball; Vitaly Baturin; Ivan Bedlinski; Ivan Bedlinskiy; Nawal Benmouna; Barry Berman; Angela Biselli; Sergey Boyarinov; Sylvain Bouchigny; Robert Bradford; Derek Branford; William Briscoe; William Brooks; Stephen Bueltmann; Volker Burkert; Cornel Butuceanu; John Calarco; Sharon Careccia; Daniel Carman; Shifeng Chen; Eric Clinton; Philip Cole; Patrick Collins; Philip Coltharp; Donald Crabb; Hall Crannell; Volker Crede; John Cummings; D. Dale; Raffaella De Vita; Enzo De Sanctis; Pavel Degtiarenko; Alexandre Deur; Kahanawita Dharmawardane; Chaden Djalali; Gail Dodge; Joseph Donnelly; David Doughty; Michael Dugger; Oleksandr Dzyubak; Hovanes Egiyan; Kim Egiyan; Lamiaa Elfassi; Latifa Elouadrhiri; Paul Eugenio; Gleb Fedotov; Herbert Funsten; Marianna Gabrielyan; Liping Gan; Michel Garcon; Ashot Gasparian; Gagik Gavalian; Gerard Gilfoyle; Kevin Giovanetti; Francois-Xavier Girod; Oleksandr Glamazdin; John Goetz; Evgueni Golovatch; Atilla Gonenc; Christopher Gordon; Ralf Gothe; Keith Griffioen; Michel Guidal; Nevzat Guler; Harutyun Gyurjyan; Cynthia Hadjidakis; Kawtar Hafidi; Hayk Hakobyan; Rafael Hakobyan; John Hardie; F. Hersman; Kenneth Hicks; Ishaq Hleiqawi; Maurik Holtrop; Charles Hyde-Wright; Yordanka Ilieva; David Ireland; Boris Ishkhanov; Eugeny Isupov; Mark Ito; D. Jenkins; Hyon-Suk Jo; Kyungseon Joo; Henry Juengst; James Kellie; Mahbubul Khandaker; Wooyoung Kim; Andreas Klein; Franz Klein; Alexei Klimenko; Mikhail Kossov; Laird Kramer; Joachim Kuhn; Sebastian Kuhn; Sergey Kuleshov; Jeff Lachniet; Jean Laget; Jorn Langheinrich; Dave Lawrence; Tsung-shung Lee; Ji Li; K. Livingston; Haiyun Lu; Marion MacCormick; Nikolai Markov; Bryan McKinnon; Bernhard Mecking; Joseph Melone; Mac Mestayer; Curtis Meyer; Tsutomu Mibe; Konstantin Mikhaylov; Ralph Minehart; Marco Mirazita; R. Miskimen; Vasiliy Mochalov; Viktor Mokeev; Ludyvine Morand; Steven Morrow; Maryam Moteabbed; Pawel Nadel-Turonski; Itaru Nakagawa; Rakhsha Nasseripour; Silvia Niccolai; Gabriel Niculescu; Maria-Ioana Niculescu; Bogdan Niczyporuk; Megh Niroula; Rustam Niyazov; Mina Nozar; Mikhail Osipenko; Alexander Ostrovidov; Kijun Park; Evgueni Pasyuk; Craig Paterson; Joshua Pierce; Nikolay Pivnyuk; Dinko Pocanic; Oleg Pogorelko; Sergey Pozdnyakov; John Price; Yelena Prok; Dan Protopopescu; Brian Raue; Gregory Riccardi; Giovanni Ricco; Marco Ripani; Barry Ritchie; Federico Ronchetti; Guenther Rosner; Patrizia Rossi; Franck Sabatie; Carlos Salgado; Joseph Santoro; Vladimir Sapunenko; Reinhard Schumacher; Vladimir Serov; Youri Sharabian; Nikolay Shvedunov; Elton Smith; Lee Smith; Daniel Sober; Aleksey Stavinskiy; Samuel Stepanyan; Stepan Stepanyan; Burnham Stokes; Igor Strakovski; Steffen Strauch; Mauro Taiuti; David Tedeschi; Aram Teymurazyan; Ulrike Thoma; Avtandil Tkabladze; Svyatoslav Tkachenko; Luminita Todor; Clarisse Tur; Michael Vineyard; Alexander Vlassov; Daniel Watts; Lawrence Weinstein; M. Williams; Elliott Wolin; Michael Wood; Amrit Yegneswaran; Lorenzo Zana; Jixie Zhang; Bo Zhao; Zhiwen Zhao

    2006-11-16

    The exclusive reactions {gamma}p {yields} {bar K}{sup 0} K{sup +} n and {gamma}p {yields} {bar K}{sup 0} K{sup 0} p have been studied in the photon energy range 1.6--3.8 GeV, searching for evidence of the exotic baryon {Theta}{sup +}(1540) in the decays {Theta}{sup +} {yields} nK{sup +} and {Theta}{sup +} {yields} pK{sup 0}. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. The integrated luminosity was about 70 pb{sup -1}. The reactions have been isolated by detecting the K{sup +} and proton directly, the neutral kaon via its decay to K{sub S} {yields} {pi}{sup +}{pi}{sup -} and the neutron or neutral kaon via the missing mass technique. The mass and width of known hyperons such as {Sigma}{sup +}, {Sigma}{sup -} and {Lambda}(1116) were used as a check of the mass determination accuracy and experimental resolution. Approximately 100,000 {Lambda}*(1520)'s and 150,000 {phi}'s were observed in the {bar K}{sup 0} K{sup +} n and {bar K}{sup 0} K{sup 0} p final state respectively. No evidence for the {Theta}{sup +} pentaquark was found in the nK{sup +} or pK{sub S} invariant mass spectra. Upper limits were set on the production cross section of the reaction {gamma}p {yields} {Theta}{sup +} {bar K}{sup 0} as functions of center-of-mass angle, nK{sup +} and pK{sub S} masses. Combining the results of the two reactions, the 95% C.L. upper limit on the total cross section for a resonance peaked at 1540 MeV was found to be 0.7 nb. Within most of the available theoretical models, this corresponds to an upper limit on the {Theta}{sup +} width, {Gamma}{sub {Theta}{sup +}}, ranging between 0.01 and 7 MeV.

  2. Note on asymptotic series expansions for the derivative of the Hurwitz zeta function and related functions

    International Nuclear Information System (INIS)

    Rudaz, S.

    1990-01-01

    Asymptotic series for the Hurwitz zeta function, its derivative, and related functions (including the Riemann zeta function of odd integer argument) are derived as an illustration of a simple, direct method of broad applicability, inspired by the calculus of finite differences

  3. Algebraic functions

    CERN Document Server

    Bliss, Gilbert Ames

    1933-01-01

    This book, immediately striking for its conciseness, is one of the most remarkable works ever produced on the subject of algebraic functions and their integrals. The distinguishing feature of the book is its third chapter, on rational functions, which gives an extremely brief and clear account of the theory of divisors.... A very readable account is given of the topology of Riemann surfaces and of the general properties of abelian integrals. Abel's theorem is presented, with some simple applications. The inversion problem is studied for the cases of genus zero and genus unity. The chapter on t

  4. Interhemispheric Plasticity following Intermittent Theta Burst Stimulation in Chronic Poststroke Aphasia

    Directory of Open Access Journals (Sweden)

    Joseph C. Griffis

    2016-01-01

    Full Text Available The effects of noninvasive neurostimulation on brain structure and function in chronic poststroke aphasia are poorly understood. We investigated the effects of intermittent theta burst stimulation (iTBS applied to residual language-responsive cortex in chronic patients using functional and anatomical MRI data acquired before and after iTBS. Lateralization index (LI analyses, along with comparisons of inferior frontal gyrus (IFG activation and connectivity during covert verb generation, were used to assess changes in cortical language function. Voxel-based morphometry (VBM was used to assess effects on regional grey matter (GM. LI analyses revealed a leftward shift in IFG activity after treatment. While left IFG activation increased, right IFG activation decreased. Changes in right to left IFG connectivity during covert verb generation also decreased after iTBS. Behavioral correlations revealed a negative relationship between changes in right IFG activation and improvements in fluency. While anatomical analyses did not reveal statistically significant changes in grey matter volume, the fMRI results provide evidence for changes in right and left IFG function after iTBS. The negative relationship between post-iTBS changes in right IFG activity during covert verb generation and improvements in fluency suggests that iTBS applied to residual left-hemispheric language areas may reduce contralateral responses related to language production and facilitate recruitment of residual language areas after stroke.

  5. Interhemispheric Plasticity following Intermittent Theta Burst Stimulation in Chronic Poststroke Aphasia.

    Science.gov (United States)

    Griffis, Joseph C; Nenert, Rodolphe; Allendorfer, Jane B; Szaflarski, Jerzy P

    2016-01-01

    The effects of noninvasive neurostimulation on brain structure and function in chronic poststroke aphasia are poorly understood. We investigated the effects of intermittent theta burst stimulation (iTBS) applied to residual language-responsive cortex in chronic patients using functional and anatomical MRI data acquired before and after iTBS. Lateralization index (LI) analyses, along with comparisons of inferior frontal gyrus (IFG) activation and connectivity during covert verb generation, were used to assess changes in cortical language function. Voxel-based morphometry (VBM) was used to assess effects on regional grey matter (GM). LI analyses revealed a leftward shift in IFG activity after treatment. While left IFG activation increased, right IFG activation decreased. Changes in right to left IFG connectivity during covert verb generation also decreased after iTBS. Behavioral correlations revealed a negative relationship between changes in right IFG activation and improvements in fluency. While anatomical analyses did not reveal statistically significant changes in grey matter volume, the fMRI results provide evidence for changes in right and left IFG function after iTBS. The negative relationship between post-iTBS changes in right IFG activity during covert verb generation and improvements in fluency suggests that iTBS applied to residual left-hemispheric language areas may reduce contralateral responses related to language production and facilitate recruitment of residual language areas after stroke.

  6. Theta-rhythmic drive between medial septum and hippocampus in slow-wave sleep and microarousal: a Granger causality analysis.

    Science.gov (United States)

    Kang, D; Ding, M; Topchiy, I; Shifflett, L; Kocsis, B

    2015-11-01

    Medial septum (MS) plays a critical role in controlling the electrical activity of the hippocampus (HIPP). In particular, theta-rhythmic burst firing of MS neurons is thought to drive lasting HIPP theta oscillations in rats during waking motor activity and REM sleep. Less is known about MS-HIPP interactions in nontheta states such as non-REM sleep, in which HIPP theta oscillations are absent but theta-rhythmic burst firing in subsets of MS neurons is preserved. The present study used Granger causality (GC) to examine the interaction patterns between MS and HIPP in slow-wave sleep (SWS, a nontheta state) and during its short interruptions called microarousals (a transient theta state). We found that during SWS, while GC revealed a unidirectional MS→HIPP influence over a wide frequency band (2-12 Hz, maximum: ∼8 Hz), there was no theta peak in the hippocampal power spectra, indicating a lack of theta activity in HIPP. In contrast, during microarousals, theta peaks were seen in both MS and HIPP power spectra and were accompanied by bidirectional GC with MS→HIPP and HIPP→MS theta drives being of equal magnitude. Thus GC in a nontheta state (SWS) vs. a theta state (microarousal) primarily differed in the level of HIPP→MS. The present findings suggest a modification of our understanding of the role of MS as the theta generator in two regards. First, a MS→HIPP theta drive does not necessarily induce theta field oscillations in the hippocampus, as found in SWS. Second, HIPP theta oscillations entail bidirectional theta-rhythmic interactions between MS and HIPP. Copyright © 2015 the American Physiological Society.

  7. Adaptive spacetime method using Riemann jump conditions for coupled atomistic-continuum dynamics

    International Nuclear Information System (INIS)

    Kraczek, B.; Miller, S.T.; Haber, R.B.; Johnson, D.D.

    2010-01-01

    We combine the Spacetime Discontinuous Galerkin (SDG) method for elastodynamics with the mathematically consistent Atomistic Discontinuous Galerkin (ADG) method in a new scheme that concurrently couples continuum and atomistic models of dynamic response in solids. The formulation couples non-overlapping continuum and atomistic models across sharp interfaces by weakly enforcing jump conditions, for both momentum balance and kinematic compatibility, using Riemann values to preserve the characteristic structure of the underlying hyperbolic system. Momentum balances to within machine-precision accuracy over every element, on each atom, and over the coupled system, with small, controllable energy dissipation in the continuum region that ensures numerical stability. When implemented on suitable unstructured spacetime grids, the continuum SDG model offers linear computational complexity in the number of elements and powerful adaptive analysis capabilities that readily bridge between atomic and continuum scales in both space and time. A special trace operator for the atomic velocities and an associated atomistic traction field enter the jump conditions at the coupling interface. The trace operator depends on parameters that specify, at the scale of the atomic spacing, the position of the coupling interface relative to the atoms. In a key finding, we demonstrate that optimizing these parameters suppresses spurious reflections at the coupling interface without the use of non-physical damping or special boundary conditions. We formulate the implicit SDG-ADG coupling scheme in up to three spatial dimensions, and describe an efficient iterative solution scheme that outperforms common explicit schemes, such as the Velocity Verlet integrator. Numerical examples, in 1dxtime and employing both linear and nonlinear potentials, demonstrate the performance of the SDG-ADG method and show how adaptive spacetime meshing reconciles disparate time steps and resolves atomic-scale signals in

  8. Riemann solvers for multi-component gas mixtures with temperature dependent heat capacities; Solveurs de riemann pour des melanges de gaz parfaits avec capacites calorifiques dependant de la temperature

    Energy Technology Data Exchange (ETDEWEB)

    Beccantini, A

    2001-07-01

    This thesis represents a contribution to the development of upwind splitting schemes for the Euler equations for ideal gaseous mixtures and their investigation in computing multidimensional flows in irregular geometries. In the preliminary part we develop and investigate the parameterization of the shock and rarefaction curves in the phase space. Then, we apply them to perform some field-by-field decompositions of the Riemann problem: the entropy-respecting one, the one which supposes that genuinely-non-linear (GNL) waves are both shocks (shock-shock one) and the one which supposes that GNL waves are both rarefactions (rarefaction-rarefaction one). We emphasize that their analysis is fundamental in Riemann solvers developing: the simpler the field-by-field decomposition, the simpler the Riemann solver based on it. As the specific heat capacities of the gases depend on the temperature, the shock-shock field-by-field decomposition is the easiest to perform. Then, in the second part of the thesis, we develop an upwind splitting scheme based on such decomposition. Afterwards, we investigate its robustness, precision and CPU-time consumption, with respect to some of the most popular upwind splitting schemes for polytropic/non-polytropic ideal gases. 1-D test-cases show that this scheme is both precise (exact capturing of stationary shock and stationary contact) and robust in dealing with strong shock and rarefaction waves. Multidimensional test-cases show that it suffers from some of the typical deficiencies which affect the upwind splitting schemes capable of exact capturing stationary contact discontinuities i.e the developing of non-physical instabilities in computing strong shock waves. In the final part, we use the high-order multidimensional solver here developed to compute fully-developed detonation flows. (author)

  9. Experimental study of CF4 conical theta pinch plasma expanding into vacuum

    International Nuclear Information System (INIS)

    Pedrow, P.D.; Nasiruddin, A.M.

    1989-01-01

    Langmuir probe, photodiode, and optical multichannel analyzer (OMA) measurements have been made on a pulsed CF 4 conical theta pinch plasma. A cloud of CF 4 gas was puffed into a conical theta pinch coil, converted to plasma, and propelled into the vacuum region ahead of the expanding gas cloud. At a position 67 cm away from the conical theta pinch coil, the plasma arrived in separate packets that were about 20 μs in duration. The average drift velocity of these packets corresponded to an energy of about 3 eV. The OMA measurements showed that the second packet contained neutral atomic fluorine as well as charged particles

  10. The electric dipole moment of the deuteron from the QCD {theta}-term

    Energy Technology Data Exchange (ETDEWEB)

    Bsaisou, J.; Liebig, S. [Forschungszentrum Juelich, Institut fuer Kernphysik and Juelich Center for Hadron Physics, Juelich (Germany); Hanhart, C.; Nogga, A.; Wirzba, A. [Forschungszentrum Juelich, Institut fuer Kernphysik and Juelich Center for Hadron Physics, Juelich (Germany); Forschungszentrum Juelich, Institute for Advanced Simulation, Juelich (Germany); Forschungszentrum Juelich, JARA - Forces And Matter Experiments, Juelich (Germany); Meissner, U.G. [Forschungszentrum Juelich, Institut fuer Kernphysik and Juelich Center for Hadron Physics, Juelich (Germany); Forschungszentrum Juelich, Institute for Advanced Simulation, Juelich (Germany); Forschungszentrum Juelich, JARA - Forces And Matter Experiments, Juelich (Germany); Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik, Bonn (Germany); Universitaet Bonn, Bethe Center for Theoretical Physics, Bonn (Germany)

    2013-03-15

    The two-nucleon contributions to the electric dipole moment (EDM) of the deuteron, induced by the QCD {theta}-term, are calculated in the framework of effective field theory up-to-and-including next-to-next-to-leading order. In particular we find for the difference of the deuteron EDM and the sum of proton and neutron EDM induced by the QCD {theta}-term a value of (- 5.4 {+-}3.9) anti {theta} x 10{sup -} {sup 4} e fm. The by far dominant uncertainty comes from the CP- and isospin-violating {pi}NN coupling constant. (orig.)

  11. Frontal and parietal theta burst TMS impairs working memory for visual-spatial conjunctions.

    Science.gov (United States)

    Morgan, Helen M; Jackson, Margaret C; van Koningsbruggen, Martijn G; Shapiro, Kimron L; Linden, David E J

    2013-03-01

    In tasks that selectively probe visual or spatial working memory (WM) frontal and posterior cortical areas show a segregation, with dorsal areas preferentially involved in spatial (e.g. location) WM and ventral areas in visual (e.g. object identity) WM. In a previous fMRI study [1], we showed that right parietal cortex (PC) was more active during WM for orientation, whereas left inferior frontal gyrus (IFG) was more active during colour WM. During WM for colour-orientation conjunctions, activity in these areas was intermediate to the level of activity for the single task preferred and non-preferred information. To examine whether these specialised areas play a critical role in coordinating visual and spatial WM to perform a conjunction task, we used theta burst transcranial magnetic stimulation (TMS) to induce a functional deficit. Compared to sham stimulation, TMS to right PC or left IFG selectively impaired WM for conjunctions but not single features. This is consistent with findings from visual search paradigms, in which frontal and parietal TMS selectively affects search for conjunctions compared to single features, and with combined TMS and functional imaging work suggesting that parietal and frontal regions are functionally coupled in tasks requiring integration of visual and spatial information. Our results thus elucidate mechanisms by which the brain coordinates spatially segregated processing streams and have implications beyond the field of working memory. Copyright © 2013 Elsevier Inc. All rights reserved.

  12. The relationship between hippocampal EEG theta activity and locomotor behaviour in freely moving rats: effects of vigabatrin.

    Science.gov (United States)

    Bouwman, B M; van Lier, H; Nitert, H E J; Drinkenburg, W H I M; Coenen, A M L; van Rijn, C M

    2005-01-30

    The relationship between hippocampal electroencephalogram (EEG) theta activity and locomotor speed in both spontaneous and forced walking conditions was studied in rats after vigabatrin injection (500 mg/kg i.p.). Vigabatrin increased the percentage of time that rats spent being immobile. During spontaneous walking in the open field, the speed of locomotion was increased by vigabatrin, while theta peak frequency was decreased. Vigabatrin also reduced the theta peak frequency during forced (speed controlled) walking. There was only a weak positive correlation (r=0.22) between theta peak frequency and locomotor speed for the saline condition. Furthermore, vigabatrin abolishes the weak relationship between speed of locomotion and theta peak frequency. Vigabatrin and saline did not differ in the slope of the regression line, but showed different offset points at the theta peak frequency axis. Thus, other factors than speed of locomotion seem to be involved in determination of the theta peak frequency.

  13. Measurement of the ion temperature in a diffuse theta pinch

    International Nuclear Information System (INIS)

    Kudo, Koichi; Watanabe, Yukio; Ogi, Sukeomi; Sumikawa, Toshio; Akazaki, Masanori

    1979-01-01

    The Doppler broadening of helium ion spectra was observed, and the ion temperature of theta pinch plasma was obtained. The apparatus for the measurement consists of a spectroscope, a photomultiplier and an oscilloscope. The time variation of initial plasma density was obtained. The doppler broadening of the spectra was observed in case of the plasma density of 2 x 10 13 /cm 3 and 3 x 10 12 /cm 3 . The analyses of the spectra gave the ion temperature. The double temperature distribution was seen. The temperature of the low temperature part was 5 to 9 electron-volt, and that of the high temperature part several hundred electron-volt. The high temperature is caused by the thermalization of particles accelerated by the magnetic piston. The decay of high temperature ions is due to the charge exchange with the neutral particles. The time of the highest temperature corresponds to the time at which the luminescent layer reaches to the central axis. (Kato, T.)

  14. ''Theta gun,'' a multistage, coaxial, magnetic induction projectile accelerator

    International Nuclear Information System (INIS)

    Burgess, T.J.; Duggin, B.W.; Cowan, M. Jr.

    1985-11-01

    We experimentally and theoretically studied a multistage coaxial magnetic induction projectile accelerator. We call this system a ''theta gun'' to differentiate it from other coaxial accelerator concepts such as the mass driver. We conclude that this system can theoretically attain railgun performance only for large caliber or very high injection velocity and, even then, only for long coil geometry. Our experiments with a three-stage, capactor bank-driven accelerator are described. The experiments are modeled with a 1-1/2 dimensional equivalent circuit-hydrodynamics code which is also described. We derive an expression for the conditions of coaxial accelerator-railgun ''velocity breakeven'' in the absence of ohmic and hydrodynamic effects. This, in conjunction with an expression for the magnetic coupling coefficient, defines a set of geometric relations which the coaxial system must simultaneously satisfy. Conclusions concerning both the existence and configuration of a breakeven coaxial system follow from this requirement. The relative advantages and disadvantages of the coaxial induction projectile accelerator, previously cited in the literature, are critiqued from the viewpoint of our analysis and experimental results. We find that the advantages vis-a-vis the railgun have been overstated. 13 refs., 17 figs

  15. Continuous theta-burst stimulation modulates tactile synchronization.

    Science.gov (United States)

    Lee, Kevin Gh; Jacobs, Mark F; Asmussen, Michael J; Zapallow, Christopher M; Tommerdahl, Mark; Nelson, Aimee J

    2013-08-23

    Temporal order judgement (TOJ) is the ability to detect the order of occurrence of two sequentially delivered stimuli. Previous research has shown that TOJ in the presence of synchronized periodic conditioning stimuli impairs TOJ performance, and this phenomenon is suggested to be mediated by GABAergic interneurons that cause perceptual binding across the two skin sites. Application of continuous theta-burst repetitive TMS (cTBS) over primary somatosensory cortex (SI) alters temporal and spatial tactile perception. The purpose of this study was to examine TOJ perception in the presence and absence of synchronized periodic conditioning stimuli before and after cTBS applied over left-hemisphere SI. A TOJ task was administered on the right index and middle finger (D2 and D3) in two separate sessions in the presence and absence of conditioning stimuli (a background low amplitude sinusoidal vibration). CTBS reduced the impact of the conditioning stimuli on TOJ performance for up to 18 minutes following stimulation while sham cTBS did not affect TOJ performance. In contrast, the TOJ task performed in the absence of synchronized conditioning stimulation was unaltered following cTBS. We conclude that cTBS suppresses inhibitory networks in SI that mediate perceptual binding during TOJ synchronization. CTBS offers one method to suppress cortical excitability in the cortex and potentially benefit clinical populations with altered inhibitory cortical circuits. Additionally, TOJ measures with conditioning stimuli may provide an avenue to assess sensory processing in neurologically impaired patient populations.

  16. Bilateral theta-burst TMS to influence global gestalt perception.

    Directory of Open Access Journals (Sweden)

    Bernd Ritzinger

    Full Text Available While early and higher visual areas along the ventral visual pathway in the inferotemporal cortex are critical for the recognition of individual objects, the neural representation of human perception of complex global visual scenes remains under debate. Stroke patients with a selective deficit in the perception of a complex global Gestalt with intact recognition of individual objects - a deficit termed simultanagnosia - greatly helped to study this question. Interestingly, simultanagnosia typically results from bilateral lesions of the temporo-parietal junction (TPJ. The present study aimed to verify the relevance of this area for human global Gestalt perception. We applied continuous theta-burst TMS either unilaterally (left or right or bilateral simultaneously over TPJ. Healthy subjects were presented with hierarchically organized visual stimuli that allowed parametrical degrading of the object at the global level. Identification of the global Gestalt was significantly modulated only for the bilateral TPJ stimulation condition. Our results strengthen the view that global Gestalt perception in the human brain involves TPJ and is co-dependent on both hemispheres.

  17. Developmental differences in beta and theta power during sentence processing

    Directory of Open Access Journals (Sweden)

    Julie M. Schneider

    2016-06-01

    Full Text Available Although very young children process ongoing language quickly and effortlessly, research indicates that they continue to improve and mature in their language skills through adolescence. This prolonged development may be related to differing engagement of semantic and syntactic processes. This study used event related potentials and time frequency analysis of EEG to identify developmental differences in neural engagement as children (ages 10–12 and adults performed an auditory verb agreement grammaticality judgment task. Adults and children revealed very few differences in comprehending grammatically correct sentences. When identifying grammatical errors, however, adults displayed widely distributed beta and theta power decreases that were significantly less pronounced in children. Adults also demonstrated a significant P600 effect, while children exhibited an apparent N400 effect. Thus, when identifying subtle grammatical errors in real time, adults display greater neural activation that is traditionally associated with syntactic processing whereas children exhibit greater activity more commonly associated with semantic processing. These findings support previous claims that the cognitive and neural underpinnings of syntactic processing are still developing in adolescence, and add to them by more clearly identifying developmental changes in the neural oscillations underlying grammatical processing.

  18. Liner of a thermonuclear pulse THETA-pinch reactor

    International Nuclear Information System (INIS)

    Baranov, G.A.; Izotov, E.N.; Karasev, B.G.; Komin, A.V.; Krivosheev, M.V.; Levashov, A.D.

    1975-01-01

    Some possible constructive solutions to the problem of fabrication of the theta-pinch reactor liner by the method of centrifugal casting in a casting mould are considered. A scheme for liner manufacturing is presented, which includes the following elements: 1) a casting mould of dielectric material presenting a hollow cylinder of 4 m in diam., 3 m in length and 12 t in weight, which rotates at 8 rps in the reactor chamber; 2) a system for heat protection of the casting mould; the volume heat of the mould is suggested to remove by gaseous helium flowing under pressure along axial cooling channels of 5 mm in diam.; the channels are evenly distributed throughout the thickness of the mould shell; 3) a system for preparation and supply of a liquid metal to the casting mould, the metal is being supplied into the casting mould from its both ends at a rate of 1.7 t of the melt per second; 4) a system for rotation of the mould, which comprises two gas turbines mounted on both ends of the mould and two main stop-radial slip supports with gas lubrication

  19. Results from TRX-2 slow field-reversed-theta-pinch

    International Nuclear Information System (INIS)

    Slough, J.T.; Harding, D.; Hoffman, A.L.

    1984-01-01

    FRCs have been successfully generated in the TRX-2 slow risetime theta pinch. Initial studies indicate that the flux trapping through field reversal is about as good (''50%) as on TRX-1, although the quarter cycle time of the main coil was increased from 3 to 10 μsec. Formation studies have been started using the programmed formation techniques developed on TRX-1. The plasma dynamics are very similar to those exhibited in the faster rise TRX-1 experiments. The formation phase shows the same high degree of symmetry and reproducibility that was observed in TRX-1. Equilibrium behaviour of the FRCs formed is very similar to that observed on TRX-1, as long as impurity content is kept low. T/sub e/ + T/sub i/ temperatures of 400 to 500 eV are obtained and confirmed by impurity line broadening and decay rates. Flux and particle lifetimes ≅ 100 μsec have been observed and show the same strong scaling with x/sub s/ that was observed on TRX-1

  20. Effects of intermittent theta burst stimulation on spasticity after stroke.

    Science.gov (United States)

    Kim, Dae Hyun; Shin, Ji Cheol; Jung, Seungsoo; Jung, Tae-Min; Kim, Deog Young

    2015-07-08

    Spasticity is a common cause of long-term disability in poststroke hemiplegic patients. We investigated whether intermittent theta burst stimulation (iTBS) could reduce upper-limb spasticity after a stroke. Fifteen hemiplegic stroke patients were recruited for a double-blind sham-controlled cross-over design study. A single session of iTBS or sham stimulation was delivered on the motor hotspot of the affected flexor carpi radialis muscle in a random and counterbalanced order with a 1-week interval. Modified Ashworth scale (MAS), modified Tardieu scale (MTS), H-wave/M-wave amplitude ratio, peak torque (PT), peak torque angle (PTA), work of affected wrist flexor, and rectified integrated electromyographic activity of the flexor carpi radialis muscle were measured before, immediately after, 30 min after, and 1 week after iTBS or sham stimulation. Repeated-measures analysis of variance showed a significant interaction between time and intervention for the MAS, MTS, PT, PTA, and rectified integrated electromyographic activity (PiTBS compared with sham stimulation. However, the H-wave/M-wave amplitude ratio and work were not affected. MAS and MTS significantly improved for at least 30 min after iTBS, but the other parameters only improved immediately after iTBS (PiTBS on the affected hemisphere may help to reduce poststroke spasticity transiently.

  1. Modulation of EEG Theta Band Signal Complexity by Music Therapy

    Science.gov (United States)

    Bhattacharya, Joydeep; Lee, Eun-Jeong

    The primary goal of this study was to investigate the impact of monochord (MC) sounds, a type of archaic sounds used in music therapy, on the neural complexity of EEG signals obtained from patients undergoing chemotherapy. The secondary goal was to compare the EEG signal complexity values for monochords with those for progressive muscle relaxation (PMR), an alternative therapy for relaxation. Forty cancer patients were randomly allocated to one of the two relaxation groups, MC and PMR, over a period of six months; continuous EEG signals were recorded during the first and last sessions. EEG signals were analyzed by applying signal mode complexity, a measure of complexity of neuronal oscillations. Across sessions, both groups showed a modulation of complexity of beta-2 band (20-29Hz) at midfrontal regions, but only MC group showed a modulation of complexity of theta band (3.5-7.5Hz) at posterior regions. Therefore, the neuronal complexity patterns showed different changes in EEG frequency band specific complexity resulting in two different types of interventions. Moreover, the different neural responses to listening to monochords and PMR were observed after regular relaxation interventions over a short time span.

  2. Rational Functions with a General Distribution of Poles on the Real Line Orthogonal with Respect to Varying Exponential Weights: I

    International Nuclear Information System (INIS)

    McLaughlin, K. T.-R.; Vartanian, A. H.; Zhou, X.

    2008-01-01

    Orthogonal rational functions are characterized in terms of a family of matrix Riemann-Hilbert problems on R, and a related family of energy minimisation problems is presented. Existence, uniqueness, and regularity properties of the equilibrium measures which solve the energy minimisation problems are established. These measures are used to derive a family of 'model' matrix Riemann-Hilbert problems which are amenable to asymptotic analysis via the Deift-Zhou non-linear steepest-descent method

  3. On a Nonlocal Ostrovsky-Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability

    Directory of Open Access Journals (Sweden)

    Jolanta Golenia

    2010-01-01

    Full Text Available Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible Poisson structures and a Lax type representation for the special case N=3 are constructed.

  4. Production of $\\Theta^{+}$ (1540) and $\\Xi$ pentaquark states in proton- proton interactions

    CERN Document Server

    Bleicher, M; Liu, F M; Pierog, T; Werner, K; 10.1016/j.physletb.2004.05.010

    2004-01-01

    The production of strange pentaquark states (e.g., Theta baryons and Xi /sup --/states) in hadronic interactions within a Gribov-Regge approach is explored. In this approach the Theta /sup +/(1540) and the Xi are produced by disintegration of remnants formed by the exchange of pomerons between the two protons. We predict the rapidity and transverse momentum distributions as well as the 4 pi multiplicity of the Theta /sup +/, Xi /sup --/ , Xi /sup -/, Xi /sup 0/ and Xi /sup +/ for square root s=17 GeV (SPS) and 200 GeV (RHIC). For both energies more than 10/sup -3/ Theta /sup +/ and more than 10 /sup -5/ Xi per pp event should be observed by the present experiments.

  5. Validation Study of CODES Dragonfly Network Model with Theta Cray XC System

    Energy Technology Data Exchange (ETDEWEB)

    Mubarak, Misbah [Argonne National Lab. (ANL), Argonne, IL (United States); Ross, Robert B. [Argonne National Lab. (ANL), Argonne, IL (United States)

    2017-05-31

    This technical report describes the experiments performed to validate the MPI performance measurements reported by the CODES dragonfly network simulation with the Theta Cray XC system at the Argonne Leadership Computing Facility (ALCF).

  6. A Precision Measurement of sin$^{2}\\theta$$_{w}$ from Semileptonic Neutrino Scattering

    CERN Document Server

    Wotschack, Jorg

    1987-01-01

    There is considerable interest in measuring the electroweak mixing parameter sin$^{2}\\Theta$$_{w}$, of the Glashow-Salam-Weinberg theory $^{1}$ as precisely as possible: first, its value may be predicted by models of Grand Unification;$^{2}$ second, precise measurements of sin$^{2}\\Theta$$_{w}$ from different processes would test the validity of electroweak radiative corrections. $^{3,$}$. Different methods have been used to determine sin$^{2}\\Theta$$_{w}$, over a large range of $Q^{2}$ values. FIGURE 1 gives a compilation of sin$^{2}\\Theta$$_{w}$ with remarkable agreement between the results. At present, it is most precisely determined in semileptonic neutrino-nucleon scattering from the ratio of neutral current (NC) to charged current (CC) cross and in proton-antiproton collisions from the W boson mass. $^{10,11}$.

  7. TAO/TRITON, RAMA, and PIRATA Buoys, Quarterly, 1992-present, Sigma-Theta

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — This dataset has quarterly Sigma-Theta (Potential Density Anomaly) data from the TAO/TRITON (Pacific Ocean, https://www.pmel.noaa.gov/gtmba/ ), RAMA (Indian Ocean,...

  8. The electric dipole moment of the nucleon from simulations at imaginary vacuum angle theta

    Energy Technology Data Exchange (ETDEWEB)

    Aoki, S. [RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton (United States)]|[Tsukuba Univ. (Japan). Graduate School of Pure and Applied Sciences; Horsley, R.; Zanotti, J. [Edinburgh Univ. (United Kingdom). School of Physics; Izubuchi, T. [RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton (United States)]|[Kanazawa Univ. (Japan). Inst. for Theoretical Physics; Nakamura, Y.; Pleiter, D.; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Division. Dept. of Mathematical Sciences

    2008-07-15

    We compute the electric dipole moment of proton and neutron from lattice QCD simulations with N{sub f}=2 flavors of dynamical quarks at imaginary vacuum angle {theta}. The calculation proceeds via the CP odd form factor F{sub 3}. A novel feature of our calculation is that we use partially twisted boundary conditions to extract F{sub 3} at zero momentum transfer. As a byproduct, we test the QCD vacuum at nonvanishing {theta}. (orig.)

  9. The Effects of Theta and Gamma tACS on Working Memory and Electrophysiology

    Directory of Open Access Journals (Sweden)

    Anja Pahor

    2018-01-01

    Full Text Available A single blind sham-controlled study was conducted to explore the effects of theta and gamma transcranial alternating current stimulation (tACS on offline performance on working memory tasks. In order to systematically investigate how specific parameters of tACS affect working memory, we manipulated the frequency of stimulation (theta frequency vs. gamma frequency, the type of task (n-back vs. change detection task and the content of the tasks (verbal vs. figural stimuli. A repeated measures design was used that consisted of three sessions: theta tACS, gamma tACS and sham tACS. In total, four experiments were conducted which differed only with respect to placement of tACS electrodes (bilateral frontal, bilateral parietal, left fronto-parietal and right-fronto parietal. Healthy female students (N = 72 were randomly assigned to one of these groups, hence we were able to assess the efficacy of theta and gamma tACS applied over different brain areas, contrasted against sham stimulation. The pre-post/sham resting electroencephalogram (EEG analysis showed that theta tACS significantly affected theta amplitude, whereas gamma tACS had no significant effect on EEG amplitude in any of the frequency bands of interest. Gamma tACS did not significantly affect working memory performance compared to sham, and theta tACS led to inconsistent changes in performance on the n-back tasks. Active theta tACS significantly affected P3 amplitude and latency during performance on the n-back tasks in the bilateral parietal and right-fronto parietal protocols.

  10. Theta rhythm-like bidirectional cycling dynamics of living neuronal networks in vitro.

    Science.gov (United States)

    Gladkov, Arseniy; Grinchuk, Oleg; Pigareva, Yana; Mukhina, Irina; Kazantsev, Victor; Pimashkin, Alexey

    2018-01-01

    The phenomena of synchronization, rhythmogenesis and coherence observed in brain networks are believed to be a dynamic substrate for cognitive functions such as learning and memory. However, researchers are still debating whether the rhythmic activity emerges from the network morphology that developed during neurogenesis or as a result of neuronal dynamics achieved under certain conditions. In the present study, we observed self-organized spiking activity that converged to long, complex and rhythmically repeated superbursts in neural networks formed by mature hippocampal cultures with a high cellular density. The superburst lasted for tens of seconds and consisted of hundreds of short (50-100 ms) small bursts with a high spiking rate of 139.0 ± 78.6 Hz that is associated with high-frequency oscillations in the hippocampus. In turn, the bursting frequency represents a theta rhythm (11.2 ± 1.5 Hz). The distribution of spikes within the bursts was non-random, representing a set of well-defined spatio-temporal base patterns or motifs. The long superburst was classified into two types. Each type was associated with a unique direction of spike propagation and, hence, was encoded by a binary sequence with random switching between the two "functional" states. The precisely structured bidirectional rhythmic activity that developed in self-organizing cultured networks was quite similar to the activity observed in the in vivo experiments.

  11. Theta rhythm-like bidirectional cycling dynamics of living neuronal networks in vitro.

    Directory of Open Access Journals (Sweden)

    Arseniy Gladkov

    Full Text Available The phenomena of synchronization, rhythmogenesis and coherence observed in brain networks are believed to be a dynamic substrate for cognitive functions such as learning and memory. However, researchers are still debating whether the rhythmic activity emerges from the network morphology that developed during neurogenesis or as a result of neuronal dynamics achieved under certain conditions. In the present study, we observed self-organized spiking activity that converged to long, complex and rhythmically repeated superbursts in neural networks formed by mature hippocampal cultures with a high cellular density. The superburst lasted for tens of seconds and consisted of hundreds of short (50-100 ms small bursts with a high spiking rate of 139.0 ± 78.6 Hz that is associated with high-frequency oscillations in the hippocampus. In turn, the bursting frequency represents a theta rhythm (11.2 ± 1.5 Hz. The distribution of spikes within the bursts was non-random, representing a set of well-defined spatio-temporal base patterns or motifs. The long superburst was classified into two types. Each type was associated with a unique direction of spike propagation and, hence, was encoded by a binary sequence with random switching between the two "functional" states. The precisely structured bidirectional rhythmic activity that developed in self-organizing cultured networks was quite similar to the activity observed in the in vivo experiments.

  12. Numerical simulation of a theta-pinch: two-dimensional hybrid model

    International Nuclear Information System (INIS)

    Zenum, C.S.S.

    1987-01-01

    A numerical code based on a 2D-hybrid model, were the electrons are considered as a fluid of zero mass and the ions as discrete particles, was elaborated. The magnetic field responsable by ion acceleration was obtained from equation of motion of the electrons and Maxwell equations. The ions are randomly distributed in a space phase of five dimensions (Vr, Vo, Vz, r, z), according to the Maxwellian. The equation of motion is solved for each ion, and the distribution functions of ion is obtained by the technique of particle into the box. The resistivity was classically and phenomenologically treated. The model was applied to theta-pinch to study: the plasma physical behaviour during the phase of implosion; the effect of reflected ions by magnetic piston; and the effect of magnetic field line reconnection 3D graphics of magnetic field, electric field current density, particle, and pressure densities, electron temperature, ion temperature is presented space phase of ion velocity in function of the position is also shown. The obtained results allow to characterized the obtained phenomena which occur during the phase of implosion. (M.C.K.) [pt

  13. Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo

    Science.gov (United States)

    Bui-Thanh, T.; Girolami, M.

    2014-11-01

    We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint

  14. Chemotherapy disrupts learning, neurogenesis and theta activity in the adult brain.

    Science.gov (United States)

    Nokia, Miriam S; Anderson, Megan L; Shors, Tracey J

    2012-12-01

    Chemotherapy, especially if prolonged, disrupts attention, working memory and speed of processing in humans. Most cancer drugs that cross the blood-brain barrier also decrease adult neurogenesis. Because new neurons are generated in the hippocampus, this decrease may contribute to the deficits in working memory and related thought processes. The neurophysiological mechanisms that underlie these deficits are generally unknown. A possible mediator is hippocampal oscillatory activity within the theta range (3-12 Hz). Theta activity predicts and promotes efficient learning in healthy animals and humans. Here, we hypothesised that chemotherapy disrupts learning via decreases in hippocampal adult neurogenesis and theta activity. Temozolomide was administered to adult male Sprague-Dawley rats in a cyclic manner for several weeks. Treatment was followed by training with different types of eyeblink classical conditioning, a form of associative learning. Chemotherapy reduced both neurogenesis and endogenous theta activity, as well as disrupted learning and related theta-band responses to the conditioned stimulus. The detrimental effects of temozolomide only occurred after several weeks of treatment, and only on a task that requires the association of events across a temporal gap and not during training with temporally overlapping stimuli. Chemotherapy did not disrupt the memory for previously learned associations, a memory independent of (new neurons in) the hippocampus. In conclusion, prolonged systemic chemotherapy is associated with a decrease in hippocampal adult neurogenesis and theta activity that may explain the selective deficits in processes of learning that describe the 'chemobrain'. © 2012 Federation of European Neuroscience Societies and Blackwell Publishing Ltd.

  15. Theta Neurofeedback Effects on Motor Memory Consolidation and Performance Accuracy: An Apparent Paradox?

    Science.gov (United States)

    Reiner, Miriam; Lev, Dror D; Rosen, Amit

    2018-05-15

    Previous studies have shown that theta neurofeedback enhances motor memory consolidation on an easy-to-learn finger-tapping task. However, the simplicity of the finger-tapping task precludes evaluating the putative effects of elevated theta on performance accuracy. Mastering a motor sequence is classically assumed to entail faster performance with fewer errors. The speed-accuracy tradeoff (SAT) principle states that as action speed increases, motor performance accuracy decreases. The current study investigated whether theta neurofeedback could improve both performance speed and performance accuracy, or would only enhance performance speed at the cost of reduced accuracy. A more complex task was used to study the effects of parietal elevated theta on 45 healthy volunteers The findings confirmed previous results on the effects of theta neurofeedback on memory consolidation. In contrast to the two control groups, in the theta-neurofeedback group the speed-accuracy tradeoff was reversed. The speed-accuracy tradeoff patterns only stabilized after a night's sleep implying enhancement in terms of both speed and accuracy. Copyright © 2017 IBRO. Published by Elsevier Ltd. All rights reserved.

  16. Palmitic acid mediates hypothalamic insulin resistance by altering PKC-theta subcellular localization in rodents.

    Science.gov (United States)

    Benoit, Stephen C; Kemp, Christopher J; Elias, Carol F; Abplanalp, William; Herman, James P; Migrenne, Stephanie; Lefevre, Anne-Laure; Cruciani-Guglielmacci, Céline; Magnan, Christophe; Yu, Fang; Niswender, Kevin; Irani, Boman G; Holland, William L; Clegg, Deborah J

    2009-09-01

    Insulin signaling can be modulated by several isoforms of PKC in peripheral tissues. Here, we assessed whether one specific isoform, PKC-theta, was expressed in critical CNS regions that regulate energy balance and whether it mediated the deleterious effects of diets high in fat, specifically palmitic acid, on hypothalamic insulin activity in rats and mice. Using a combination of in situ hybridization and immunohistochemistry, we found that PKC-theta was expressed in discrete neuronal populations of the arcuate nucleus, specifically the neuropeptide Y/agouti-related protein neurons and the dorsal medial nucleus in the hypothalamus. CNS exposure to palmitic acid via direct infusion or by oral gavage increased the localization of PKC-theta to cell membranes in the hypothalamus, which was associated with impaired hypothalamic insulin and leptin signaling. This finding was specific for palmitic acid, as the monounsaturated fatty acid, oleic acid, neither increased membrane localization of PKC-theta nor induced insulin resistance. Finally, arcuate-specific knockdown of PKC-theta attenuated diet-induced obesity and improved insulin signaling. These results suggest that many of the deleterious effects of high-fat diets, specifically those enriched with palmitic acid, are CNS mediated via PKC-theta activation, resulting in reduced insulin activity.

  17. Distributed Attention Is Implemented through Theta-Rhythmic Gamma Modulation.

    Science.gov (United States)

    Landau, Ayelet Nina; Schreyer, Helene Marianne; van Pelt, Stan; Fries, Pascal

    2015-08-31

    When subjects monitor a single location, visual target detection depends on the pre-target phase of an ∼8 Hz brain rhythm. When multiple locations are monitored, performance decrements suggest a division of the 8 Hz rhythm over the number of locations, indicating that different locations are sequentially sampled. Indeed, when subjects monitor two locations, performance benefits alternate at a 4 Hz rhythm. These performance alternations were revealed after a reset of attention to one location. Although resets are common and important events for attention, it is unknown whether, in the absence of resets, ongoing attention samples stimuli in alternation. Here, we examined whether spatially specific attentional sampling can be revealed by ongoing pre-target brain rhythms. Visually induced gamma-band activity plays a role in spatial attention. Therefore, we hypothesized that performance on two simultaneously monitored stimuli can be predicted by a 4 Hz modulation of gamma-band activity. Brain rhythms were assessed with magnetoencephalography (MEG) while subjects monitored bilateral grating stimuli for a unilateral target event. The corresponding contralateral gamma-band responses were subtracted from each other to isolate spatially selective, target-related fluctuations. The resulting lateralized gamma-band activity (LGA) showed opposite pre-target 4 Hz phases for detected versus missed targets. The 4 Hz phase of pre-target LGA accounted for a 14.5% modulation in performance. These findings suggest that spatial attention is a theta-rhythmic sampling process that is continuously ongoing, with each sampling cycle being implemented through gamma-band synchrony. Copyright © 2015 Elsevier Ltd. All rights reserved.

  18. (Anti-) selfdual Riemann curvature tensor in four spacelike compactified dimensions, O5 isometry group and chiral fermion zero modes

    International Nuclear Information System (INIS)

    Minkowski, P.

    1986-01-01

    The metric and contorsion tensors are constructed which yield a combined Riemann curvature tensor of the form Rsup(+-)sub(μνsigmatau)=(1/2a 2 )(gsub(μsigma)gsub(νtau) - gsub(μtau)gsub(νsigma)+-√g epsilonsub(μνsigmatau)). The metric with euclidean signature (++++) describes a sphere S 4 with radius a, i.e. admits the isometry group O5. For selfdual (antiselfdual) curvature tensor the contorsion tensor is given by the antiselfdual (selfdual) instanton configuration with respect to the spin gauge group SU2sub(R) (SU2sub(L)). The selfdual (antiselfdual) Riemann tensor admits two covariantly constant right-handed (left-handed) spin 1/2 fermion zero modes, one J=1/2 and one J=3/2 right-handed (left-handed) multiplet corresponding to L=1, transforming as a pseudoreal representation of O4 (SU2sub(R(L))). The hermitean Dirac equation retains only the two constant chiral modes. (orig.)

  19. La notion husserlienne de multiplicité : au-delà de Cantor et Riemann

    Directory of Open Access Journals (Sweden)

    Carlo Ierna

    2012-04-01

    Full Text Available En raison du rôle changeant qu’il joue dans les différents ouvrages de Husserl, le concept de Mannigfaltigkeit afait l’objet de nombreuses interprétations. La présence de ce terme a notamment induit en erreur plusieurs commentateurs, qui ont cru en déterminer l’origine dans les années de Halle, à l’époque où Husserl, ami et collègue de Cantor, rédigeait la Philosophie de l’arithmétique. Mais force est de constater qu’à cette époque Husserl s’était déjà ouvertement éloigné de la définition cantorienne de Mannigfaltigkeit en s’approchant plutôt de Riemann, comme le montrent les nombreuses études et leçons qui lui sont consacrées. La Mannigfaltigkeitslehre de Husserl semble donc plus proche de la topologie que de la théorie des ensembles de Cantor. Ainsi, dans les Prolégomènes, Husserl introduit l’idée d’une Mannigfaltigkeitslehre pure en tant qu’entreprise méta-théorique dont le but est d’étudier les relations entre théories, à savoir la manière par laquelle une théorie est dérivée ou fondée à partir d’une autre. Dès lors, lorsque Husserl affirme que le meilleur exemple d’une telle théorie pure des multiplicités se trouve dans les mathématiques, cela risque donc de prêter à confusion. En effet, la théorie pure des théories ne saurait être simplement identifiée aux mathématiques qui relèvent de la topologie, mais considérée en tant que mathesis universalis. Bien qu’une telle position ne fût sans doute pas entièrement claire en 1900-01, Husserl ne tardera pas à relier explicitement théorie des multiplicités et mathesis universalis.En ce sens, la mathesis universalis, théorie des théories en général, est une discipline formelle, apriori et analytique qui a pour but l’analyse des catégories sémantiques suprêmes et des catégories d’objets qui leur sont corrélées. Dans cet article j’essayerai de comprendre le développement de la notion de

  20. Activation of GABAergic pathway by hypocretin in the median raphe nucleus (MRN) mediates stress-induced theta rhythm in rats.

    Science.gov (United States)

    Hsiao, Yi-Tse; Jou, Shuo-Bin; Yi, Pei-Lu; Chang, Fang-Chia

    2012-07-15

    The frequency of electroencephalograms (EEGs) is predominant in theta rhythm during stress (e.g., footshock) in rats. Median raphe nucleus (MRN) desynchronizes hippocampal theta waves via activation of GABAergic neurons in the medial septum-diagonal band of Broca (MS-DBB), a theta rhythm pacemaker. Increased hypocretin mediates stress responses in addition to the maintenance of wakefulness. Hypocretin receptors are abundant in the MRN, suggesting a possible role of hypocretin in modulating stress-induced theta rhythm. Our results indicated that the intensity of theta waves was enhanced by footshock and that a hypocretin receptor antagonist (TCS1102) suppressed the footshock-induced theta waves. Administration of hypocretin-1 (1 and 10 μg) and hypocretin-2 (10 μg) directly into the MRN simulated the effect of footshock and significantly increased theta waves. Co-administration of GABA(A) receptor antagonist, bicuculline, into the MRN blocked the increase of theta waves induced by hypocretins or footshock. These results suggested that stress enhances the release of hypocretins, activates GABAergic neurons in the MRN, blocks the ability of MRN to desynchronize theta waves, and subsequently increases the intensity of theta rhythm. Copyright © 2012 Elsevier B.V. All rights reserved.

  1. Optogenetic activation of septal cholinergic neurons suppresses sharp wave ripples and enhances theta oscillations in the hippocampus.

    Science.gov (United States)

    Vandecasteele, Marie; Varga, Viktor; Berényi, Antal; Papp, Edit; Barthó, Péter; Venance, Laurent; Freund, Tamás F; Buzsáki, György

    2014-09-16

    Theta oscillations in the limbic system depend on the integrity of the medial septum. The different populations of medial septal neurons (cholinergic and GABAergic) are assumed to affect different aspects of theta oscillations. Using optogenetic stimulation of cholinergic neurons in ChAT-Cre mice, we investigated their effects on hippocampal local field potentials in both anesthetized and behaving mice. Cholinergic stimulation completely blocked sharp wave ripples and strongly suppressed the power of both slow oscillations (0.5-2 Hz in anesthetized, 0.5-4 Hz in behaving animals) and supratheta (6-10 Hz in anesthetized, 10-25 Hz in behaving animals) bands. The same stimulation robustly increased both the power and coherence of theta oscillations (2-6 Hz) in urethane-anesthetized mice. In behaving mice, cholinergic stimulation was less effective in the theta (4-10 Hz) band yet it also increased the ratio of theta/slow oscillation and theta coherence. The effects on gamma oscillations largely mirrored those of theta. These findings show that medial septal cholinergic activation can both enhance theta rhythm and suppress peri-theta frequency bands, allowing theta oscillations to dominate.

  2. Upsilon NU: Our chapter in Sigma Theta Tau Internacional Upsilon NU: nuestro capítulo en Sigma Theta Tau International

    Directory of Open Access Journals (Sweden)

    GARZÓN ALARCÓN NELLY

    2008-07-01

    Full Text Available ALa Sociedad de Honor de Enfermería, Sigma Theta Tau Internacional, es una organización que nace y vive para desarrollar el conocimiento y la ciencia de enfermería como fundamentos del liderazgo y la búsqueda de la excelencia en el cuidado de la persona, la familia y la comunidad.

  3. Long lasting effects of daily theta burst rTMS sessions in the human amblyopic cortex.

    Science.gov (United States)

    Clavagnier, Simon; Thompson, Benjamin; Hess, Robert F

    2013-11-01

    It has been reported that a single session of 1 Hz or 10 Hz repetitive transcranial magnetic stimulation (rTMS) of the visual cortex can temporarily improve contrast sensitivity in adults with amblyopia. More recently, continuous theta burst stimulation (cTBS) of the visual cortex has been found to improve contrast sensitivity in observers with normal vision. The aims of this study were to assess whether cTBS of the visual cortex could improve contrast sensitivity in adults with amblyopia and whether repeated sessions of cTBS would lead to more pronounced and/or longer lasting effects. cTBS was delivered to the visual cortex while patients viewed a high contrast stimulus with their non-amblyopic eye. This manipulation was designed to bias the effects of cTBS toward inputs from the amblyopic eye. Contrast sensitivity was measured before and after stimulation. The effects of one cTBS session were measured in five patients and the effects of five consecutive daily sessions were measured in four patients. Three patients were available for follow-up at varying intervals after the final session. cTBS improved amblyopic eye contrast sensitivity to high spatial frequencies (P enduring visual function improvements in adults with amblyopia. Copyright © 2013 Elsevier Inc. All rights reserved.

  4. The effects of theta-burst stimulation on vigilance in humans

    Directory of Open Access Journals (Sweden)

    Armand eMensen

    2014-06-01

    Full Text Available Repetitive transcranial magnetic stimulation has become a popular tool to modulate neuronal networks and associated brain functions in both clinical and basic research. Yet few studies have examined the potential effects of cortical stimulation on general levels of vigilance. In this exploratory study, we used theta-burst protocols, both continuous (cTBS and intermittent (iTBS patterns, to examine whether inhibition or excitation of the left dorso-lateral prefrontal cortex (dlPFC was able to induce reliable and acute changes to vigilance measures, compared to the left dorso-lateral associative visual cortex (dlAVC as a control site in line with previous work. Partially sleep restricted participants underwent four separate sessions in a single day, in a between subjects design for TBS stimulation type and within subjects for locaton, each consisting of maintenance of wakefulness test, a sleep latency test, and a psychomotor vigilance task. TBS significantly affected measures of sleep consolidation, namely latency to sleep stage 2 and sleep efficiency, but had no effects on sleep drive or psychomotor vigilance levels for either TBS type or location. Contrary to our initial hypothesis of the dlAVC as a control site, stimulation to this region resulted in the largest differential effects between stimulation types. Moreover, the effect of TBS was found to be consistent throughout the day. These data may provide the basis for further investigation into therapeutic applications of TBS in sleep disorders.

  5. Theta-Gamma Coupling and Working Memory in Alzheimer’s Dementia and Mild Cognitive Impairment

    Directory of Open Access Journals (Sweden)

    Michelle S. Goodman

    2018-04-01

    Full Text Available Working memory deficits are common among individuals with Alzheimer’s dementia (AD or mild cognitive impairment (MCI. Yet, little is known about the mechanisms underlying these deficits. Theta-gamma coupling—the modulation of high-frequency gamma oscillations by low-frequency theta oscillations—is a neurophysiologic process underlying working memory. We assessed the relationship between theta-gamma coupling and working memory deficits in AD and MCI. We hypothesized that: (1 individuals with AD would display the most significant working memory impairments followed by MCI and finally healthy control (HC participants; and (2 there would be a significant association between working memory performance and theta-gamma coupling across all participants. Ninety-eight participants completed the N-back working memory task during an electroencephalography (EEG recording: 33 with AD (mean ± SD age: 76.5 ± 6.2, 34 with MCI (mean ± SD age: 74.8 ± 5.9 and 31 HCs (mean ± SD age: 73.5 ± 5.2. AD participants performed significantly worse than control and MCI participants on the 1- and 2-back conditions. Regarding theta-gamma coupling, AD participants demonstrated the lowest level of coupling followed by the MCI and finally control participants on the 2-back condition. Finally, a linear regression analysis demonstrated that theta-gamma coupling (β = 0.69, p < 0.001 was the most significant predictor of 2-back performance. Our results provide evidence for a relationship between altered theta-gamma coupling and working memory deficits in individuals with AD and MCI. They also provide insight into a potential mechanism underlying working memory impairments in these individuals.

  6. Different types of theta rhythmicity are induced by social and fearful stimuli in a network associated with social memory.

    Science.gov (United States)

    Tendler, Alex; Wagner, Shlomo

    2015-02-16

    Rhythmic activity in the theta range is thought to promote neuronal communication between brain regions. In this study, we performed chronic telemetric recordings in socially behaving rats to monitor electrophysiological activity in limbic brain regions linked to social behavior. Social encounters were associated with increased rhythmicity in the high theta range (7-10 Hz) that was proportional to the stimulus degree of novelty. This modulation of theta rhythmicity, which was specific for social stimuli, appeared to reflect a brain-state of social arousal. In contrast, the same network responded to a fearful stimulus by enhancement of rhythmicity in the low theta range (3-7 Hz). Moreover, theta rhythmicity showed different pattern of coherence between the distinct brain regions in response to social and fearful stimuli. We suggest that the two types of stimuli induce distinct arousal states that elicit different patterns of theta rhythmicity, which cause the same brain areas to communicate in different modes.

  7. Phase precession through acceleration of local theta rhythm: a biophysical model for the interaction between place cells and local inhibitory neurons.

    Science.gov (United States)

    Castro, Luísa; Aguiar, Paulo

    2012-08-01

    Phase precession is one of the most well known examples within the temporal coding hypothesis. Here we present a biophysical spiking model for phase precession in hippocampal CA1 which focuses on the interaction between place cells and local inhibitory interneurons. The model's functional block is composed of a place cell (PC) connected with a local inhibitory cell (IC) which is modulated by the population theta rhythm. Both cells receive excitatory inputs from the entorhinal cortex (EC). These inputs are both theta modulated and space modulated. The dynamics of the two neuron types are described by integrate-and-fire models with conductance synapses, and the EC inputs are described using non-homogeneous Poisson processes. Phase precession in our model is caused by increased drive to specific PC/IC pairs when the animal is in their place field. The excitation increases the IC's firing rate, and this modulates the PC's firing rate such that both cells precess relative to theta. Our model implies that phase coding in place cells may not be independent from rate coding. The absence of restrictive connectivity constraints in this model predicts the generation of phase precession in any network with similar architecture and subject to a clocking rhythm, independently of the involvement in spatial tasks.

  8. Reward Expectancy Strengthens CA1 Theta and Beta Band Synchronization and Hippocampal-Ventral Striatal Coupling.

    Science.gov (United States)

    Lansink, Carien S; Meijer, Guido T; Lankelma, Jan V; Vinck, Martin A; Jackson, Jadin C; Pennartz, Cyriel M A

    2016-10-12

    The use of information from the hippocampal memory system in motivated behavior depends on its communication with the ventral striatum. When an animal encounters cues that signal subsequent reward, its reward expectancy is raised. It is unknown, however, how this process affects hippocampal dynamics and their influence on target structures, such as ventral striatum. We show that, in rats, reward-predictive cues result in enhanced hippocampal theta and beta band rhythmic activity during subsequent action, compared with uncued goal-directed navigation. The beta band component, also labeled theta's harmonic, involves selective hippocampal CA1 cell groups showing frequency doubling of firing periodicity relative to theta rhythmicity and it partitions the theta cycle into segments showing clear versus poor spike timing organization. We found that theta phase precession occurred over a wider range than previously reported. This was apparent from spikes emitted near the peak of the theta cycle exhibiting large "phase precessing jumps" relative to spikes in foregoing cycles. Neither this phenomenon nor the regular manifestation of theta phase precession was affected by reward expectancy. Ventral striatal neuronal firing phase-locked not only to hippocampal theta, but also to beta band activity. Both hippocampus and ventral striatum showed increased synchronization between neuronal firing and local field potential activity during cued compared with uncued goal approaches. These results suggest that cue-triggered reward expectancy intensifies hippocampal output to target structures, such as the ventral striatum, by which the hippocampus may gain prioritized access to systems modulating motivated behaviors. Here we show that temporally discrete cues raising reward expectancy enhance both theta and beta band activity in the hippocampus once goal-directed navigation has been initiated. These rhythmic activities are associated with increased synchronization of neuronal firing

  9. Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers

    Science.gov (United States)

    Balsara, Dinshaw S.; Dumbser, Michael

    2015-10-01

    Several advances have been reported in the recent literature on divergence-free finite volume schemes for Magnetohydrodynamics (MHD). Almost all of these advances are restricted to structured meshes. To retain full geometric versatility, however, it is also very important to make analogous advances in divergence-free schemes for MHD on unstructured meshes. Such schemes utilize a staggered Yee-type mesh, where all hydrodynamic quantities (mass, momentum and energy density) are cell-centered, while the magnetic fields are face-centered and the electric fields, which are so useful for the time update of the magnetic field, are centered at the edges. Three important advances are brought together in this paper in order to make it possible to have high order accurate finite volume schemes for the MHD equations on unstructured meshes. First, it is shown that a divergence-free WENO reconstruction of the magnetic field can be developed for unstructured meshes in two and three space dimensions using a classical cell-centered WENO algorithm, without the need to do a WENO reconstruction for the magnetic field on the faces. This is achieved via a novel constrained L2-projection operator that is used in each time step as a postprocessor of the cell-centered WENO reconstruction so that the magnetic field becomes locally and globally divergence free. Second, it is shown that recently-developed genuinely multidimensional Riemann solvers (called MuSIC Riemann solvers) can be used on unstructured meshes to obtain a multidimensionally upwinded representation of the electric field at each edge. Third, the above two innovations work well together with a high order accurate one-step ADER time stepping strategy, which requires the divergence-free nonlinear WENO reconstruction procedure to be carried out only once per time step. The resulting divergence-free ADER-WENO schemes with MuSIC Riemann solvers give us an efficient and easily-implemented strategy for divergence-free MHD on

  10. Theta oscillations at encoding mediate the context-dependent nature of human episodic memory.

    Science.gov (United States)

    Staudigl, Tobias; Hanslmayr, Simon

    2013-06-17

    Human episodic memory is highly context dependent. Therefore, retrieval benefits when a memory is recalled in the same context compared to a different context. This implies that items and contexts are bound together during encoding, such that the reinstatement of the initial context at test improves retrieval. Animal studies suggest that theta oscillations and theta-to-gamma cross-frequency coupling modulate such item-context binding, but direct evidence from humans is scarce. We investigated this issue by manipulating the overlap of contextual features between encoding and retrieval. Participants studied words superimposed on movie clips and were later tested by presenting the word with either the same or a different movie. The results show that memory performance and the oscillatory correlates of memory formation crucially depend on the overlap of the context between encoding and test. When the context matched, high theta power during encoding was related to successful recognition, whereas the opposite pattern emerged in the context-mismatch condition. In addition, cross-frequency coupling analysis revealed a context-dependent theta-to-gamma memory effect specifically in the left hippocampus. These results reveal for the first time that context-dependent episodic memory effects are mediated by theta oscillatory activity. Copyright © 2013 Elsevier Ltd. All rights reserved.

  11. Theta Phase Synchronization Is the Glue that Binds Human Associative Memory.

    Science.gov (United States)

    Clouter, Andrew; Shapiro, Kimron L; Hanslmayr, Simon

    2017-10-23

    Episodic memories are information-rich, often multisensory events that rely on binding different elements [1]. The elements that will constitute a memory episode are processed in specialized but distinct brain modules. The binding of these elements is most likely mediated by fast-acting long-term potentiation (LTP), which relies on the precise timing of neural activity [2]. Theta oscillations in the hippocampus orchestrate such timing as demonstrated by animal studies in vitro [3, 4] and in vivo [5, 6], suggesting a causal role of theta activity for the formation of complex memory episodes, but direct evidence from humans is missing. Here, we show that human episodic memory formation depends on phase synchrony between different sensory cortices at the theta frequency. By modulating the luminance of visual stimuli and the amplitude of auditory stimuli, we directly manipulated the degree of phase synchrony between visual and auditory cortices. Memory for sound-movie associations was significantly better when the stimuli were presented in phase compared to out of phase. This effect was specific to theta (4 Hz) and did not occur in slower (1.7 Hz) or faster (10.5 Hz) frequencies. These findings provide the first direct evidence that episodic memory formation in humans relies on a theta-specific synchronization mechanism. Copyright © 2017 Elsevier Ltd. All rights reserved.

  12. Search for $\\Theta^{++}$ Pentaquarks in the Exclusive Reaction $\\gamma p\\to K^+K^-p$

    Energy Technology Data Exchange (ETDEWEB)

    V. Kubarovsky; Marco Battaglieri; Raffaella De Vita; John Goett; Lei Guo; Gordon Mutchler; Paul Stoler; Dennis Weygand; Pawel Ambrozewicz; Marco Anghinolfi; Gegham Asryan; Harutyun AVAKIAN; Harutyun Avakian; H. Bagdasaryan; Nathan Baillie; Jacques Ball; Nathan Baltzell; V. Batourine; Ivan Bedlinski; Ivan Bedlinskiy; Matthew Bellis; Nawal Benmouna; Barry Berman; Angela Biselli; Sylvain Bouchigny; Sergey Boyarinov; Robert Bradford; Derek Branford; William Briscoe; William Brooks; Stephen Bueltmann; Volker Burkert; Cornel Butuceanu; John Calarco; Sharon Careccia; Daniel Carman; Shifeng Chen; Eric Clinton; Philip Cole; Patrick Collins; Philip Coltharp; Donald Crabb; Hall Crannell; Volker Crede; John Cummings; Rita De Masi; Daniel Dale; Enzo De Sanctis; Pavel Degtiarenko; Alexandre Deur; Kahanawita Dharmawardane; Chaden Djalali; Gail Dodge; Joseph Donnelly; David Doughty; Michael Dugger; Oleksandr Dzyubak; Hovanes Egiyan; Kim Egiyan; Latifa Elouadrhiri; Paul Eugenio; Gleb Fedotov; Herbert Funsten; Marianna Gabrielyan; Liping Gan; Michel Garcon; Ashot Gasparian; Gagik Gavalian; Gerard Gilfoyle; Kevin Giovanetti; Francois-Xavier Girod; Oleksandr Glamazdin; John Goetz; Evgueni Golovatch; Atilla Gonenc; Christopher Gordon; Ralf Gothe; Keith Griffioen; Michel Guidal; Nevzat Guler; Vardan Gyurjyan; Cynthia Hadjidakis; Kawtar Hafidi; Rafael Hakobyan; John Hardie; F. Hersman; Kenneth Hicks; Ishaq Hleiqawi; Maurik Holtrop; Charles Hyde-Wright; Yordanka Ilieva; David Ireland; Boris Ishkhanov; Eugeny Isupov; Mark Ito; David Jenkins; Hyon-Suk Jo; Kyungseon Joo; Henry Juengst; James Kellie; Mahbubul Khandaker; Wooyoung Kim; Franz Klein; Friedrich Klein; Alexei Klimenko; Mikhail Kossov; Laird Kramer; Joachim Kuhn; Sebastian Kuhn; Sergey Kuleshov; Jeff Lachniet; Jean Laget; Jorn Langheinrich; David Lawrence; Tsung-shung Lee; Ji Li; Kenneth Livingston; Hai-jiang Lu; Marion MacCormick; Nikolai Markov; Bryan McKinnon; Bernhard Mecking; Joseph Melone; Mac Mestayer; Curtis Meyer; Tsutomu Mibe; Konstantin Mikhaylov; Ralph Minehart; Marco Mirazita; Rory Miskimen; Vasiliy Mochalov; Viktor Mokeev; Ludyvine Morand; Steven Morrow; Maryam Moteabbed; Pawel Nadel-Turonski; Itaru Nakagawa; Rakhsha Nasseripour; Silvia Niccolai; Gabriel Niculescu; Maria-Ioana Niculescu; Bogdan Niczyporuk; Megh Niroula; Rustam Niyazov; Mina Nozar; Mikhail Osipenko; Alexander Ostrovidov; Kijun Park; Evgueni Pasyuk; Craig Paterson; Joshua Pierce; Nikolay Pivnyuk; Dinko Pocanic; Oleg Pogorelko; Sergey Pozdnyakov; John Price; Yelena Prok; Dan Protopopescu; Brian Raue; Gregory Riccardi; Giovanni Ricco; Marco Ripani; Barry Ritchie; Federico Ronchetti; Guenther Rosner; Patrizia Rossi; Franck Sabatie; Carlos Salgado; Joseph Santoro; Vladimir Sapunenko; Reinhard Schumacher; Vladimir Serov; Youri Sharabian; Nikolay Shvedunov; Elton Smith; Lee Smith; Daniel Sober; Aleksey Stavinskiy; Samuel Stepanyan; Stepan Stepanyan; Burnham Stokes; Igor Strakovski; Steffen Strauch; Mauro Taiuti; David Tedeschi; Aram Teymurazyan; Ulrike Thoma; Avtandil Tkabladze; Svyatoslav Tkachenko; Luminita Todor; Clarisse Tur; Maurizio Ungaro; Michael Vineyard; Alexander Vlassov; Lawrence Weinstein; Michael Williams; Elliott Wolin; Michael Wood; Amrit Yegneswaran; Lorenzo Zana; Jixie Zhang; Bo Zhao

    2006-04-28

    The reaction {gamma}p {yields} K{sup +}K{sup -}p was studied at Jefferson Lab with photon energies from 1.8 to 3.8 GeV using a tagged photon beam. The goal was to search for a {Theta}{sup ++} pentaquark, a narrow doubly charged baryon state having strangeness S = +1 and isospin I = 1, in the pK{sup +} invariant mass spectrum. No statistically significant evidence of a {Theta}{sup ++} was found. Upper limits on the total and differential production cross section for the reaction {gamma}p {yields} K{sup -}{Theta}{sup ++} were obtained in the mass range from 1.5 to 2.0 GeV/c{sup 2}, with an upper limit of about 0.15 nb, 95% C.L. for a narrow resonance with a mass M{sub {Theta}{sup ++}} = 1.54 GeV/c{sup 2}. This result places a very stringent upper limit on the {Theta}{sup ++} width.

  13. The Coupling between Gamma and Theta Oscillation and Visuotactile Integration Process

    Directory of Open Access Journals (Sweden)

    Noriaki Kanayama

    2011-10-01

    Full Text Available Some researches revealed the relationship between multisensory integration and EEG oscillations. Previous studies revealed that the visuotactile integration process could be explained by gamma and theta band oscillation. In addition, recent studies have showed the possibility that a coupling between oscillations at the different frequency bands plays an important role on the multisensory integration system. This study aimed to investigate whether the gamma and theta oscillations show the coupling during the visuotactile integration. Using congruency effect paradigm only for left hand, we measured scalp EEG during simultaneous presentation of “spatially congruent” or “spatially incongruent” visuotactile stimuli. In Experiment 1, the proportion of the spatially congruent trials (80% vs 20% was changed across the experimental blocks. The results showed that the relationship between gamma power and theta phase at the parietal area was modulated by the proportion. In Experiment 2, the saliency of the vibration stimulus (0dB vs −20dB was changed across trials. The results showed that the relationship between gamma power and theta phase was immune to the saliency. These results suggest that multisensory integration process has a plasticity, which is modulated by the proportion of congruent trial, and the process could be explained by the coupling between gamma/theta oscillations.

  14. Hippocampal Theta-Gamma Coupling Reflects State-Dependent Information Processing in Decision Making.

    Science.gov (United States)

    Amemiya, Seiichiro; Redish, A David

    2018-03-20

    During decision making, hippocampal activity encodes information sometimes about present and sometimes about potential future plans. The mechanisms underlying this transition remain unknown. Building on the evidence that gamma oscillations at different frequencies (low gamma [LG], 30-55 Hz; high gamma [HG], 60-90 Hz; and epsilon, 100-140 Hz) reflect inputs from different circuits, we identified how changes in those frequencies reflect different information-processing states. Using a unique noradrenergic manipulation by clonidine, which shifted both neural representations and gamma states, we found that future representations depended on gamma components. These changes were identifiable on each cycle of theta as asymmetries in the theta cycle, which arose from changes within the ratio of LG and HG power and the underlying phases of those gamma rhythms within the theta cycle. These changes in asymmetry of the theta cycle reflected changes in representations of present and future on each theta cycle. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.

  15. Effective action and β-functions for the heterotic string

    International Nuclear Information System (INIS)

    Foakes, A.P.; Mohammedi, N.; Ross, D.A.

    1988-01-01

    The results of the calculation of the metric β-function for the heterotic string sigma model up to three loops are presented and it is shown that although this β-function is non vanishing it is compatible with an O((α') 2 ) effective action in which there are no terms cubic in the Riemann tensor or gauge field strength. (orig.)

  16. Extension problem for generalized multi-monogenic functions in Clifford analysis

    International Nuclear Information System (INIS)

    Tran Quyet Thang.

    1992-10-01

    The main purpose of this paper is to extend some properties of multi-monogenic functions, which is a generalization of monogenic functions in higher dimensions, for a class of functions satisfying Vekua-type generalized Cauchy-Riemann equations in Clifford Analysis. It is proved that the Hartogs theorem is valid for these functions. (author). 7 refs

  17. Theta coupling between V4 and prefrontal cortex predicts visual short-term memory performance.

    Science.gov (United States)

    Liebe, Stefanie; Hoerzer, Gregor M; Logothetis, Nikos K; Rainer, Gregor

    2012-01-29

    Short-term memory requires communication between multiple brain regions that collectively mediate the encoding and maintenance of sensory information. It has been suggested that oscillatory synchronization underlies intercortical communication. Yet, whether and how distant cortical areas cooperate during visual memory remains elusive. We examined neural interactions between visual area V4 and the lateral prefrontal cortex using simultaneous local field potential (LFP) recordings and single-unit activity (SUA) in monkeys performing a visual short-term memory task. During the memory period, we observed enhanced between-area phase synchronization in theta frequencies (3-9 Hz) of LFPs together with elevated phase locking of SUA to theta oscillations across regions. In addition, we found that the strength of intercortical locking was predictive of the animals' behavioral performance. This suggests that theta-band synchronization coordinates action potential communication between V4 and prefrontal cortex that may contribute to the maintenance of visual short-term memories.

  18. Episodic sequence memory is supported by a theta-gamma phase code.

    Science.gov (United States)

    Heusser, Andrew C; Poeppel, David; Ezzyat, Youssef; Davachi, Lila

    2016-10-01

    The meaning we derive from our experiences is not a simple static extraction of the elements but is largely based on the order in which those elements occur. Models propose that sequence encoding is supported by interactions between high- and low-frequency oscillations, such that elements within an experience are represented by neural cell assemblies firing at higher frequencies (gamma) and sequential order is encoded by the specific timing of firing with respect to a lower frequency oscillation (theta). During episodic sequence memory formation in humans, we provide evidence that items in different sequence positions exhibit greater gamma power along distinct phases of a theta oscillation. Furthermore, this segregation is related to successful temporal order memory. Our results provide compelling evidence that memory for order, a core component of an episodic memory, capitalizes on the ubiquitous physiological mechanism of theta-gamma phase-amplitude coupling.

  19. Cueing vocabulary during sleep increases theta activity during later recognition testing.

    Science.gov (United States)

    Schreiner, Thomas; Göldi, Maurice; Rasch, Björn

    2015-11-01

    Neural oscillations in the theta band have repeatedly been implicated in successful memory encoding and retrieval. Several recent studies have shown that memory retrieval can be facilitated by reactivating memories during their consolidation during sleep. However, it is still unknown whether reactivation during sleep also enhances subsequent retrieval-related neural oscillations. We have recently demonstrated that foreign vocabulary cues presented during sleep improve later recall of the associated translations. Here, we examined the effect of cueing foreign vocabulary during sleep on oscillatory activity during subsequent recognition testing after sleep. We show that those words that were replayed during sleep after learning (cued words) elicited stronger centroparietal theta activity during recognition as compared to noncued words. The reactivation-induced increase in theta oscillations during later recognition testing might reflect a strengthening of individual memory traces and the integration of the newly learned words into the mental lexicon by cueing during sleep. © 2015 Society for Psychophysiological Research.

  20. Efficient analytical implementation of the DOT Riemann solver for the de Saint Venant-Exner morphodynamic model

    Science.gov (United States)

    Carraro, F.; Valiani, A.; Caleffi, V.

    2018-03-01

    Within the framework of the de Saint Venant equations coupled with the Exner equation for morphodynamic evolution, this work presents a new efficient implementation of the Dumbser-Osher-Toro (DOT) scheme for non-conservative problems. The DOT path-conservative scheme is a robust upwind method based on a complete Riemann solver, but it has the drawback of requiring expensive numerical computations. Indeed, to compute the non-linear time evolution in each time step, the DOT scheme requires numerical computation of the flux matrix eigenstructure (the totality of eigenvalues and eigenvectors) several times at each cell edge. In this work, an analytical and compact formulation of the eigenstructure for the de Saint Venant-Exner (dSVE) model is introduced and tested in terms of numerical efficiency and stability. Using the original DOT and PRICE-C (a very efficient FORCE-type method) as reference methods, we present a convergence analysis (error against CPU time) to study the performance of the DOT method with our new analytical implementation of eigenstructure calculations (A-DOT). In particular, the numerical performance of the three methods is tested in three test cases: a movable bed Riemann problem with analytical solution; a problem with smooth analytical solution; a test in which the water flow is characterised by subcritical and supercritical regions. For a given target error, the A-DOT method is always the most efficient choice. Finally, two experimental data sets and different transport formulae are considered to test the A-DOT model in more practical case studies.

  1. A Data-Driven Approach to Responder Subgroup Identification after Paired Continuous Theta Burst Stimulation

    Directory of Open Access Journals (Sweden)

    Tonio Heidegger

    2017-08-01

    Full Text Available Background: Modulation of cortical excitability by transcranial magnetic stimulation (TMS is used for investigating human brain functions. A common observation is the high variability of long-term depression (LTD-like changes in human (motor cortex excitability. This study aimed at analyzing the response subgroup distribution after paired continuous theta burst stimulation (cTBS as a basis for subject selection.Methods: The effects of paired cTBS using 80% active motor threshold (AMT in 31 healthy volunteers were assessed at the primary motor cortex (M1 corresponding to the representation of the first dorsal interosseous (FDI muscle of the left hand, before and up to 50 min after plasticity induction. The changes in motor evoked potentials (MEPs were analyzed using machine-learning derived methods implemented as Gaussian mixture modeling (GMM and computed ABC analysis.Results: The probability density distribution of the MEP changes from baseline was tri-modal, showing a clear separation at 80.9%. Subjects displaying at least this degree of LTD-like changes were n = 6 responders. By contrast, n = 7 subjects displayed a paradox response with increase in MEP. Reassessment using ABC analysis as alternative approach led to the same n = 6 subjects as a distinct category.Conclusion: Depressive effects of paired cTBS using 80% AMT endure at least 50 min, however, only in a small subgroup of healthy subjects. Hence, plasticity induction by paired cTBS might not reflect a general mechanism in human motor cortex excitability. A mathematically supported criterion is proposed to select responders for enrolment in assessments of human brain functional networks using virtual brain lesions.

  2. Differential impact of continuous theta-burst stimulation over left and right DLPFC on planning.

    Science.gov (United States)

    Kaller, Christoph P; Heinze, Katharina; Frenkel, Annekathrein; Läppchen, Claus H; Unterrainer, Josef M; Weiller, Cornelius; Lange, Rüdiger; Rahm, Benjamin

    2013-01-01

    Most neuroimaging studies on planning report bilateral activations of the dorsolateral prefrontal cortex (dlPFC). Recently, these concurrent activations of left and right dlPFC have been shown to double dissociate with different cognitive demands imposed by the planning task: Higher demands on the extraction of task-relevant information led to stronger activation in left dlPFC, whereas higher demands on the integration of interdependent information into a coherent action sequence entailed stronger activation of right dlPFC. Here, we used continuous theta-burst stimulation (cTBS) to investigate the supposed causal structure-function mapping underlying this double dissociation. Two groups of healthy subjects (left-lateralized stimulation, n = 26; right-lateralized stimulation, n = 26) were tested within-subject on a variant of the Tower of London task following either real cTBS over dlPFC or sham stimulation over posterior parietal cortex. Results revealed that, irrespective of specific task demands, cTBS over left and right dlPFC was associated with a global decrease and increase, respectively, in initial planning times compared to sham stimulation. Moreover, no interaction between task demands and stimulation type (real vs. sham) and/or stimulation side (left vs. right hemisphere) were found. Together, against expectations from previous neuroimaging data, lateralized cTBS did not lead to planning-parameter specific changes in performance, but instead revealed a global asymmetric pattern of faster versus slower task processing after left versus right cTBS. This global asymmetry in the absence of any task-parameter specific impact of cTBS suggests that different levels of information processing may span colocalized, but independent axes of functional lateralization in the dlPFC. Copyright © 2011 Wiley Periodicals, Inc.

  3. Effects of intermittent theta burst stimulation on cerebral blood flow and cerebral vasomotor reactivity.

    Science.gov (United States)

    Pichiorri, Floriana; Vicenzini, Edoardo; Gilio, Francesca; Giacomelli, Elena; Frasca, Vittorio; Cambieri, Chiara; Ceccanti, Marco; Di Piero, Vittorio; Inghilleri, Maurizio

    2012-08-01

    To determine whether intermittent theta burst stimulation influences cerebral hemodynamics, we investigated changes induced by intermittent theta burst stimulation on the middle cerebral artery cerebral blood flow velocity and vasomotor reactivity to carbon dioxide (CO(2)) in healthy participants. The middle cerebral artery flow velocity and vasomotor reactivity were monitored by continuous transcranial Doppler sonography. Changes in cortical excitability were tested by transcranial magnetic stimulation. In 11 healthy participants, before and immediately after delivering intermittent theta burst stimulation, we tested cortical excitability measured by the resting motor threshold and motor evoked potential amplitude over the stimulated hemisphere and vasomotor reactivity to CO(2) bilaterally. The blood flow velocity was monitored in both middle cerebral arteries throughout the experimental session. In a separate session, we tested the effects of sham stimulation under the same experimental conditions. Whereas the resting motor threshold remained unchanged before and after stimulation, motor evoked potential amplitudes increased significantly (P = .04). During and after stimulation, middle cerebral artery blood flow velocities also remained bilaterally unchanged, whereas vasomotor reactivity to CO(2) increased bilaterally (P = .04). The sham stimulation left all variables unchanged. The expected intermittent theta burst stimulation-induced changes in cortical excitability were not accompanied by changes in cerebral blood flow velocities; however, the bilateral increased vasomotor reactivity suggests that intermittent theta burst stimulation influences the cerebral microcirculation, possibly involving subcortical structures. These findings provide useful information on hemodynamic phenomena accompanying intermittent theta burst stimulation, which should be considered in research aimed at developing this noninvasive, low-intensity stimulation technique for safe

  4. Characterizing the roles of alpha and theta oscillations in multisensory attention.

    Science.gov (United States)

    Keller, Arielle S; Payne, Lisa; Sekuler, Robert

    2017-05-01

    Cortical alpha oscillations (8-13Hz) appear to play a role in suppressing distractions when just one sensory modality is being attended, but do they also contribute when attention is distributed over multiple sensory modalities? For an answer, we examined cortical oscillations in human subjects who were dividing attention between auditory and visual sequences. In Experiment 1, subjects performed an oddball task with auditory, visual, or simultaneous audiovisual sequences in separate blocks, while the electroencephalogram was recorded using high-density scalp electrodes. Alpha oscillations were present continuously over posterior regions while subjects were attending to auditory sequences. This supports the idea that the brain suppresses processing of visual input in order to advantage auditory processing. During a divided-attention audiovisual condition, an oddball (a rare, unusual stimulus) occurred in either the auditory or the visual domain, requiring that attention be divided between the two modalities. Fronto-central theta band (4-7Hz) activity was strongest in this audiovisual condition, when subjects monitored auditory and visual sequences simultaneously. Theta oscillations have been associated with both attention and with short-term memory. Experiment 2 sought to distinguish these possible roles of fronto-central theta activity during multisensory divided attention. Using a modified version of the oddball task from Experiment 1, Experiment 2 showed that differences in theta power among conditions were independent of short-term memory load. Ruling out theta's association with short-term memory, we conclude that fronto-central theta activity is likely a marker of multisensory divided attention. Copyright © 2017 Elsevier Ltd. All rights reserved.

  5. Multifractal Detrended Fluctuation Analysis of alpha and theta EEG rhythms with musical stimuli

    International Nuclear Information System (INIS)

    Maity, Akash Kumar; Pratihar, Ruchira; Mitra, Anubrato; Dey, Subham; Agrawal, Vishal; Sanyal, Shankha; Banerjee, Archi; Sengupta, Ranjan; Ghosh, Dipak

    2015-01-01

    Highlights: • EEG was done to record the brain electrical activity of 10 subjects in response to simple acoustical tanpura stimuli. • Empirical Mode Decomposition (EMD) technique used to make the EEG signal free from blink and other muscular artifacts. • Multifractal Detrended Fluctuation Analysis (MFDFA) performed to assess the complexity of extracted alpha and theta brain rhythms. • The findings show spectral width i.e. complexity of alpha and theta rhythms increase in all the seven frontal locations studied, under the effect of musical stimuli. - Abstract: Electroencephalography (EEG) was performed on 10 participants using a simple acoustical stimuli i.e. a tanpura drone. The tanpura drone is free from any semantic content and is used with a hypothesis that it provides a specific resting environment for the listeners. The EEG data was extracted for all the frontal electrodes viz. F3, F4, F7, F8, Fp1, Fp2 and Fz. Empirical Mode Decomposition (EMD) was applied on the acquired raw EEG signal to make it free from blink as well as other muscular artifacts. Wavelet Transform (WT) technique was used to segregate alpha and theta waves from the denoised EEG signal. Non-linear analysis in the form of Multifractal Detrended Fluctuation Analysis (MFDFA) was carried out on the extracted alpha and theta time series data to study the variation of their complexity. It was found that in all the frontal electrodes alpha as well as theta complexity increases as is evident from the increase of multifractal spectral width. This study is entirely new and gives interesting data regarding neural activation of the alpha and theta brain rhythms while listening to simple acoustical stimuli. The importance of this study lies in the context of emotion quantification using multifractal spectral width as a parameter as well as in the field of cognitive music therapy. The results are discussed in detail.

  6. Double Chooz and non Asian efforts towards {theta}{sub 13}

    Energy Technology Data Exchange (ETDEWEB)

    Lasserre, Thierry [CEA/Saclay and Laboratoire Astroparticle and Cosmologie Institut de Recherche des Lois Fondamentales de l' Univers Service de Physique des Particules 91191 Gif-s-Yvette (France)], E-mail: thierry.lasserre@cea.fr

    2008-11-01

    Neutrino oscillation physics is entering a precision measurement area. The smallness of the {theta}{sub 13} neutrino mixing angle is still enigmatic and should be resolved. Double Chooz will use two identical detectors near the Chooz nuclear power station to search for a non vanishing {theta}{sub 13}, and hopefully open the way to experiments aspiring to discover CP violation in the leptonic sector. The Angra project aims to prevail over the Double Chooz experiment if the third neutrino oscillation channel is not discovered in the forthcoming years.

  7. Transient loss of plasma from a theta pinch having an initially reversed magnetic field

    International Nuclear Information System (INIS)

    Heidrich, J.E.

    1981-01-01

    The results of an experimental study of the transient loss of plasma from a 25-cm-long theta pinch initially containing a reversed trapped magnetic field are presented. The plasma, amenable to MHD analyses, was a doubly ionized helium plasma characterized by an ion density N/sub i/ = 2 x 10 16 cm -3 and an ion temperature T/sub i/ = 15 eV at midcoil and by N/sub i/ = 0.5 x 10 16 cm -3 and T/sub i/ = 6 eV at a position 2.5 cm beyond the end of the theta coil

  8. Why don't you like me? : Midfrontal theta power in response to unexpected peer rejection feedback

    NARCIS (Netherlands)

    van der Molen, M.J.W.; Dekkers, L.M.S.; Westenberg, P.M.; van der Veen, F.M.; van der Molen, M.W.

    2017-01-01

    Social connectedness theory posits that the brain processes social rejection as a threat to survival. Recent electrophysiological evidence suggests that midfrontal theta (4–8 Hz) oscillations in the EEG provide a window on the processing of social rejection. Here we examined midfrontal theta

  9. Fractional derivative of the Hurwitz ζ-function and chaotic decay to zero

    Directory of Open Access Journals (Sweden)

    C. Cattani

    2016-01-01

    Full Text Available In this paper the fractional order derivative of a Dirichlet series, Hurwitz zeta function and Riemann zeta function is explicitly computed using the Caputo fractional derivative in the Ortigueira sense. It is observed that the obtained results are a natural generalization of the integer order derivative. Some interesting properties of the fractional derivative of the Riemann zeta function are also investigated to show that there is a chaotic decay to zero (in the Gaussian plane and a promising expression as a complex power series.

  10. Theta phase precession and phase selectivity: a cognitive device description of neural coding

    Science.gov (United States)

    Zalay, Osbert C.; Bardakjian, Berj L.

    2009-06-01

    Information in neural systems is carried by way of phase and rate codes. Neuronal signals are processed through transformative biophysical mechanisms at the cellular and network levels. Neural coding transformations can be represented mathematically in a device called the cognitive rhythm generator (CRG). Incoming signals to the CRG are parsed through a bank of neuronal modes that orchestrate proportional, integrative and derivative transformations associated with neural coding. Mode outputs are then mixed through static nonlinearities to encode (spatio) temporal phase relationships. The static nonlinear outputs feed and modulate a ring device (limit cycle) encoding output dynamics. Small coupled CRG networks were created to investigate coding functionality associated with neuronal phase preference and theta precession in the hippocampus. Phase selectivity was found to be dependent on mode shape and polarity, while phase precession was a product of modal mixing (i.e. changes in the relative contribution or amplitude of mode outputs resulted in shifting phase preference). Nonlinear system identification was implemented to help validate the model and explain response characteristics associated with modal mixing; in particular, principal dynamic modes experimentally derived from a hippocampal neuron were inserted into a CRG and the neuron's dynamic response was successfully cloned. From our results, small CRG networks possessing disynaptic feedforward inhibition in combination with feedforward excitation exhibited frequency-dependent inhibitory-to-excitatory and excitatory-to-inhibitory transitions that were similar to transitions seen in a single CRG with quadratic modal mixing. This suggests nonlinear modal mixing to be a coding manifestation of the effect of network connectivity in shaping system dynamic behavior. We hypothesize that circuits containing disynaptic feedforward inhibition in the nervous system may be candidates for interpreting upstream rate codes to

  11. Posterior versus frontal theta activity indexes approach motivation during affective autobiographical memories.

    Science.gov (United States)

    Walden, K; Pornpattananangkul, N; Curlee, A; McAdams, D P; Nusslock, R

    2015-03-01

    Research has recently identified a promising neurophysiological marker of approach motivation involving posterior versus frontal (Pz - Fz) electroencephalographic (EEG) theta activity PFTA; Wacker, Chavanon, & Stemmler (Journal of Personality and Social Psychology 91:171-187, 2006). Preliminary evidence indicated that PFTA is modulated by dopaminergic activity, thought to underlie appetitive tendencies, and that it indexes self-reported behavioral activation system (BAS) sensitivity. To date, research has largely relied on resting indices of PFTA and has yet to examine the relationship between PFTA and specific approach-related affective states generated by emotionally salient laboratory tasks. Accordingly, the present study evaluated PFTA both at rest and during an ecologically valid autobiographical memory task in which participants recalled personal life experiences involving a goal-striving, an anxious apprehension, a low-point (i.e., difficult), and a neutral memory while EEG data were recorded. In line with prediction, elevated PFTA was observed during both goal-striving and anxious apprehension autobiographical memories. PFTA was particularly elevated during anxious apprehension memories coded as being high on approach-related tendencies. Elevated PFTA during anxious apprehension is consistent with a growing literature indicating that anxious apprehension is associated with elevated approach- and reward-related brain function. Lastly, elevated resting PFTA was positively correlated with self-reported trait anger, a negatively valenced emotion characterized by approach-related tendencies. These results have implications for (a) enhancing our understanding of the neurophysiology of approach-related emotions, (b) establishing PFTA as an index of appetitive motivational states, and (c) clarifying our understanding of the neurophysiology and approach-related tendencies associated with both anxious apprehension and anger.

  12. Intermittent theta-burst transcranial magnetic stimulation for treatment of Parkinson disease.

    Science.gov (United States)

    Benninger, D H; Berman, B D; Houdayer, E; Pal, N; Luckenbaugh, D A; Schneider, L; Miranda, S; Hallett, M

    2011-02-15

    To investigate the safety and efficacy of intermittent theta-burst stimulation (iTBS) in the treatment of motor symptoms in Parkinson disease (PD). Progression of PD is characterized by the emergence of motor deficits, which eventually respond less to dopaminergic therapy and pose a therapeutic challenge. Repetitive transcranial magnetic stimulation (rTMS) has shown promising results in improving gait, a major cause of disability, and may provide a therapeutic alternative. iTBS is a novel type of rTMS that may be more efficacious than conventional rTMS. In this randomized, double-blind, sham-controlled study, we investigated safety and efficacy of iTBS of the motor and dorsolateral prefrontal cortices in 8 sessions over 2 weeks (evidence Class I). Assessment of safety and clinical efficacy over a 1-month period included timed tests of gait and bradykinesia, Unified Parkinson's Disease Rating Scale (UPDRS), and additional clinical, neuropsychological, and neurophysiologic measures. We investigated 26 patients with mild to moderate PD: 13 received iTBS and 13 sham stimulation. We found beneficial effects of iTBS on mood, but no improvement of gait, bradykinesia, UPDRS, and other measures. EEG/EMG monitoring recorded no pathologic increase of cortical excitability or epileptic activity. Few reported discomfort or pain and one experienced tinnitus during real stimulation. iTBS of the motor and prefrontal cortices appears safe and improves mood, but failed to improve motor performance and functional status in PD. This study provides Class I evidence that iTBS was not effective for gait, upper extremity bradykinesia, or other motor symptoms in PD.

  13. Facilitation of speech repetition accuracy by theta burst stimulation of the left posterior inferior frontal gyrus.

    Science.gov (United States)

    Restle, Julia; Murakami, Takenobu; Ziemann, Ulf

    2012-07-01

    The posterior part of the inferior frontal gyrus (pIFG) in the left hemisphere is thought to form part of the putative human mirror neuron system and is assigned a key role in mapping sensory perception onto motor action. Accordingly, the pIFG is involved in motor imitation of the observed actions of others but it is not known to what extent speech repetition of auditory-presented sentences is also a function of the pIFG. Here we applied fMRI-guided facilitating intermittent theta burst transcranial magnetic stimulation (iTBS), or depressant continuous TBS (cTBS), or intermediate TBS (imTBS) over the left pIFG of healthy subjects and compared speech repetition accuracy of foreign Japanese sentences before and after TBS. We found that repetition accuracy improved after iTBS and, to a lesser extent, after imTBS, but remained unchanged after cTBS. In a control experiment, iTBS was applied over the left middle occipital gyrus (MOG), a region not involved in sensorimotor processing of auditory-presented speech. Repetition accuracy remained unchanged after iTBS of MOG. We argue that the stimulation type and stimulation site specific facilitating effect of iTBS over left pIFG on speech repetition accuracy indicates a causal role of the human left-hemispheric pIFG in the translation of phonological perception to motor articulatory output for repetition of speech. This effect may prove useful in rehabilitation strategies that combine repetitive speech training with iTBS of the left pIFG in speech disorders, such as aphasia after cerebral stroke. Copyright © 2012 Elsevier Ltd. All rights reserved.

  14. Bilateral theta-burst magnetic stimulation influence on event-related brain potentials.

    Science.gov (United States)

    Pinto, Nuno; Duarte, Marta; Gonçalves, Helena; Silva, Ricardo; Gama, Jorge; Pato, Maria Vaz

    2018-01-01

    Theta-burst stimulation (TBS) can be a non-invasive technique to modulate cognitive functions, with promising therapeutic potential, but with some contradictory results. Event related potentials are used as a marker of brain deterioration and can be used to evaluate TBS-related cognitive performance, but its use remains scant. This study aimed to study bilateral inhibitory and excitatory TBS effects upon neurocognitive performance of young healthy volunteers, using the auditory P300' results. Using a double-blind sham-controlled study, 51 healthy volunteers were randomly assigned to five different groups, two submitted to either excitatory (iTBS) or inhibitory (cTBS) stimulation over the left dorsolateral pre-frontal cortex (DLPFC), two other actively stimulated the right DLPFC and finally a sham stimulation group. An oddball based auditory P300 was performed just before a single session of iTBS, cTBS or sham stimulation and repeated immediately after. P300 mean latency comparison between the pre- and post-TBS stimulation stages revealed significantly faster post stimulation latencies only when iTBS was performed on the left hemisphere (p = 0.003). Right and left hemisphere cTBS significantly delayed P300 latency (right p = 0.026; left p = 0.000). Multiple comparisons for N200 showed slower latencies after iTBS over the right hemisphere. No significant difference was found in amplitude variation. TBS appears to effectively influence neural networking involved in P300 formation, but effects seem distinct for iTBS vs cTBS and for the right or the left hemisphere. P300 evoked potentials can be an effective and practical tool to evaluate transcranial magnetic stimulation related outcomes.

  15. Enhanced Constraints on theta13 from A Three-Flavor Oscillation Analysis of Reactor Antineutrinos at KamLAND

    Energy Technology Data Exchange (ETDEWEB)

    The KamLAND Collaboration; Gando, A.; Gando, Y.; Ichimura, K.; Ikeda, H.; Inoue, K.; Kibe, Y.; Kishimoto, Y.; Koga, M.; Minekawa, Y.; Mitsui, T.; Morikawa, T.; Nagai, N.; Nakajima, K.; Nakamura, K.; Narita, K.; Shimizu, I.; Shimizu, Y.; Shirai, J.; Suekane, F.; Suzuki, A.; Takahashi, H.; Takahashi, N.; Takemoto, Y.; Tamae, K.; Watanabe, H.; Xu, B. D.; Yabumoto, H.; Yoshida, H.; Yoshida, S.; Enomoto, S.; Kozlov, A.; Murayama, H.; Grant, C.; Keefer, G.; Piepke, A.; Banks, T. I.; Bloxham, T.; Detwiler, J. A.; Freedman, S. J.; Fujikawa, B. K.; Han, K.; Kadel, R.; O' Donnell, T.; Steiner, H. M.; Dwyer, D. A.; McKeown, R. D.; Zhang, C.; Berger, B. E.; Lane, C. E.; Maricic, J.; Miletic, T.; Batygov, M.; Learned, J. G.; Matsuno, S.; Sakai, M.; Horton-Smith, G. A.; Downum, K. E.; Gratta, G.; Efremenko, Y.; Perevozchikov, O.; Karwowski, H. J.; Markoff, D. M.; Tornow, W.; Heeger, K. M.; Decowski, M. P.

    2010-09-24

    We present new constraints on the neutrino oscillation parameters {Delta}m{sub 21}{sup 2}, {theta}{sub 12}, and {theta}{sub 13} from a three-flavor analysis of solar and KamLAND data. The KamLAND data set includes data acquired following a radiopurity upgrade and amounts to a total exposure of 3.49 x 10{sup 32} target-proton-year. Under the assumption of CPT invariance, a two-flavor analysis ({theta}{sub 13} = 0) of the KamLAND and solar data yields the best-fit values tan{sup 2} {theta}{sub 12} = 0.444{sub -0.030}{sup +0.036} and {Delta}m{sub 21}{sup 2} = 7.50{sub -0.20}{sup +0.19} x 10{sup -5} eV{sup 2}; a three-flavor analysis with {theta}{sub 13} as a free parameter yields the best-fit values tan{sup 2} {theta}{sub 12} = 0.452{sub -0.033}{sup +0.035}, {Delta}m{sub 21}{sup 2} = 7.50{sub -0.20}{sup +0.19} x 10{sup -5}eV{sup 2}, and sin{sup 2} {theta}{sub 13} = 0.020{sub -0.016}{sup +0.016}. This {theta}{sub 13} interval is consistent with other recent work combining the CHOOZ, atmospheric and long-baseline accelerator experiments. We also present a new global {theta}{sub 13} analysis, incorporating the CHOOZ, atmospheric and accelerator data, which indicates sin{sup 2} {theta}{sub 13} = 0.017{sub -0.009}{sup +0.010}, a nonzero value at the 93% C.L. This finding will be further tested by upcoming accelerator and reactor experiments.

  16. Plasma resistivity in a slow rising current theta-pinch device

    International Nuclear Information System (INIS)

    Kayama, Milton Eiji; Dobrowolsky, Marcelo Shubert; Honda, Roberto Yzumi; Aramaki, Emilia Akemi; Algatti, Mauricio Antonio

    1998-01-01

    Anomalous behavior of plasma resistivity was observed in a Theta-pinch plasma. A comparative analysis was performed with a hybrid numerical code where the Chodura s resistivity algorithm is included. Good agreement was found in the radial plasma dynamic description. The experimental value of resistivity at null field point was found to be one order of magnitude greater than the theoretical prediction. (author)

  17. Theta oscillations orchestrate medial temporal lobe and neocortex in remembering autobiographical memories.

    Science.gov (United States)

    Fuentemilla, L; Barnes, G R; Düzel, E; Levine, B

    2014-01-15

    Remembering autobiographical events can be associated with detailed visual imagery. The medial temporal lobe (MTL), precuneus and prefrontal cortex are held to jointly enable such vivid retrieval, but how these regions are orchestrated remains unclear. An influential prediction from animal physiology is that neural oscillations in theta frequency may be important. In this experiment, participants prospectively collected audio recordings describing personal autobiographical episodes or semantic knowledge over 2 to 7 months. These were replayed as memory retrieval cues while recording brain activity with magnetoencephalography (MEG). We identified a peak of theta power within a left MTL region of interest during both autobiographical and General Semantic retrieval. This MTL region was selectively phase-synchronized with theta oscillations in precuneus and medial prefrontal cortex, and this synchrony was higher during autobiographical as compared to General Semantic knowledge retrieval. Higher synchrony also predicted more detailed visual imagery during retrieval. Thus, theta phase-synchrony orchestrates in humans the MTL with a distributed neocortical memory network when vividly remembering autobiographical experiences. © 2013.

  18. EEG theta and gamma responses to semantic violations in online sentence processing

    NARCIS (Netherlands)

    Hald, L.A.; Bastiaansen, M.C.M.; Hagoort, P.

    2006-01-01

    We explore the nature of the oscillatory dynamics in the EEG of subjects reading sentences that contain a semantic violation. More specifically, we examine whether increases in theta (≈3–7 Hz) and gamma (around 40 Hz) band power occur in response to sentences that were either semantically correct or

  19. Complementary theta resonance filtering by two spatially segregated mechanisms in CA1 hippocampal pyramidal neurons.

    Science.gov (United States)

    Hu, Hua; Vervaeke, Koen; Graham, Lyle J; Storm, Johan F

    2009-11-18

    Synaptic input to a neuron may undergo various filtering steps, both locally and during transmission to the soma. Using simultaneous whole-cell recordings from soma and apical dendrites from rat CA1 hippocampal pyramidal cells, and biophysically detailed modeling, we found two complementary resonance (bandpass) filters of subthreshold voltage signals. Both filters favor signals in the theta (3-12 Hz) frequency range, but have opposite location, direction, and voltage dependencies: (1) dendritic H-resonance, caused by h/HCN-channels, filters signals propagating from soma to dendrite when the membrane potential is close to rest; and (2) somatic M-resonance, caused by M/Kv7/KCNQ and persistent Na(+) (NaP) channels, filters signals propagating from dendrite to soma when the membrane potential approaches spike threshold. Hippocampal pyramidal cells participate in theta network oscillations during behavior, and we suggest that that these dual, polarized theta resonance mechanisms may convey voltage-dependent tuning of theta-mediated neural coding in the entorhinal/hippocampal system during locomotion, spatial navigation, memory, and sleep.

  20. Energy- and particle-confinement properties of an end-plugged, linear, theta pinch

    International Nuclear Information System (INIS)

    Commisso, R.J.; Bartsch, R.R.; Ekdahl, C.A.; McKenna, K.F.; Siemon, R.E.

    1979-01-01

    Experiments show that axial confinement of plasma in a straight theta-pinch solenoid is improved by placing solid lithium deuteride plugs at the ends. The energy confinement is increased nearly threefold in agreement with theoretical estimates which assume classical electron thermal conduction and no convective losses. The confinement of deuterium ions is explained by classical Coulomb collisions in the ablated lithium deuteride plasma