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.).

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

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

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.

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.

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.)

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

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.

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.

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

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.

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

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

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.

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

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.

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)

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.

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 ...

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

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

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.)

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.).

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.

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, ...

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...

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

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.)

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,...

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.)

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)

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)

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...

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.

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.

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

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.)

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.

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.)

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

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.

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.

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.

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

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) .

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...

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

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

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.

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

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 ...

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...

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)

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

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

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

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.

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.

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...

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)

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

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)

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

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.

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.

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.

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.

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.

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.)

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.

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.

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.

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.

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.

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)

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.

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

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)

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.

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

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

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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.

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

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.)

A Riemann problem with small viscosity and dispersion

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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.

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

Oscillatory frontal theta responses are increased upon bisensory stimulation.

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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.

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

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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.

Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

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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.

Collisionless analogs of Riemann S ellipsoids with halo

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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

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

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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

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

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

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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.

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.)

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

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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.

On genus-two solutions for the ILW equation

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Tutiya, Y.

2018-02-01

The existence of theta function solutions of genus two for the intermediate long-wave equation is established. A numerical example is also presented. The method basically goes along with Krichever's construction of theta function solutions for soliton equations, such as the Kronecker product equation. This idea leads us to a question whether a Riemann surface exists which allows a peculiar abelian integral of the third kind. The answer is affirmative at least for genus-two curves.

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

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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

Theta series, wall-crossing and quantum dilogarithm identities

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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...

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

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.)

The Neumann Type Systems and Algebro-Geometric Solutions of a System of Coupled Integrable Equations

International Nuclear Information System (INIS)

Chen Jinbing; Qiao Zhijun

2011-01-01

A system of (1+1)-dimensional coupled integrable equations is decomposed into a pair of new Neumann type systems that separate the spatial and temporal variables for this system over a symplectic submanifold. Then, the Neumann type flows associated with the coupled integrable equations are integrated on the complex tour of a Riemann surface. Finally, the algebro-geometric solutions expressed by Riemann theta functions of the system of coupled integrable equations are obtained by means of the Jacobi inversion.

Theta power is reduced in healthy cognitive aging.

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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.

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

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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.)

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

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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.

Long-term plasticity is proportional to theta-activity.

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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.

Ice cream and orbifold Riemann-Roch

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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.

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.

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...

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.

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.

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

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)

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)

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

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....

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.

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.

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

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

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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.

Supertori are algebraic curves

International Nuclear Information System (INIS)

Rabin, J.M.; Freund, P.G.O.; Chicago Univ., IL; Chicago Univ., IL

1988-01-01

Super Riemann surfaces of genus 1, with arbitrary spin structures, are shown to be the sets of zeroes of certain polynomial equations in projective superspace. We conjecture that the same is true for arbitrary genus. Properties of superelliptic functions and super theta functions are discussed. The boundary of the genus 1 super moduli space is determined. (orig.)

The path-integral formulation of supersymmetric string theory

International Nuclear Information System (INIS)

Verlinde, H.L.

1988-01-01

The loop corrections to superstring scattering amplitudes are studied. An explicit construction of the partition and correlation functions of all the string fields on an arbitrary ordinary Riemann surface is given in terms of theta-functions. The amplitudes of the space-time supersymmetry current are studied. These are shown to contain unphysical singularities. 94 refs.; 4 figs

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

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

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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.

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

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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.

{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.

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

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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.

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

Submaximal Riemann-Roch expected curves and symplectic packing.

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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.

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

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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.

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

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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.

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)

Seiberg-Witten curves and double-elliptic integrable systems

International Nuclear Information System (INIS)

Aminov, G.; Braden, H.W.; Mironov, A.; Morozov, A.; Zotov, A.

2015-01-01

An old conjecture claims that commuting Hamiltonians of the double-elliptic integrable system are constructed from the theta-functions associated with Riemann surfaces from the Seiberg-Witten family, with moduli treated as dynamical variables and the Seiberg-Witten differential providing the pre-symplectic structure. We describe a number of theta-constant equations needed to prove this conjecture for the N-particle system. These equations provide an alternative method to derive the Seiberg-Witten prepotential and we illustrate this by calculating the perturbative contribution. We provide evidence that the solutions to the commutativity equations are exhausted by the double-elliptic system and its degenerations (Calogero and Ruijsenaars systems). Further, the theta-function identities that lie behind the Poisson commutativity of the three-particle Hamiltonians are proven.

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,.

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

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.

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.)

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.

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

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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.

PKC-theta in regulatory and effector T-cell functions

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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.

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

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.

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

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.)

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.

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.

Asymptotic Behavior of Periodic Wave Solution to the Hirota—Satsuma Equation

International Nuclear Information System (INIS)

Wu Yong-Qi

2011-01-01

The one- and two-periodic wave solutions for the Hirota—Satsuma (HS) equation are presented by using the Hirota derivative and Riemann theta function. The rigorous proofs on asymptotic behaviors of these two solutions are given such that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure. (general)

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.

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

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.

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)

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.

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

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)

The two loop superstring vacuum amplitude and canonical divisors

International Nuclear Information System (INIS)

Parkes, A.

1989-01-01

I use the prescription of placing the picture changing operators at the zeroes of some holomorphic one-form and calculate the two loop superstring vacuum amplitude in the language of theta functions. It vanishes pointwise on moduli space after the use of Fay's trisecant identity and generalised Riemann identities. I briefly discuss the higher genus case. (orig.)

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

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

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

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.

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 $\\sigma>1$).

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

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.

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 $\\beta$-$\\theta$-$R_0$

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.

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

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…

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

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.

Exact quantization conditions, toric Calabi-Yau and non-perturbative topological string

Energy Technology Data Exchange (ETDEWEB)

Sun, Kaiwen [Department of Mathematics, University of Science and Technology of China,96 Jinzhai Road, Hefei, Anhui 230026 (China); Wang, Xin; Huang, Min-xin [Interdisciplinary Center for Theoretical Study,Department of Modern Physics, University of Science and Technology of China,96 Jinzhai Road, Hefei, Anhui 230026 (China)

2017-01-16

We establish the precise relation between the Nekrasov-Shatashvili (NS) quantization scheme and Grassi-Hatsuda-Mariño conjecture for the mirror curve of arbitrary toric Calabi-Yau threefold. For a mirror curve of genus g, the NS quantization scheme leads to g quantization conditions for the corresponding integrable system. The exact NS quantization conditions enjoy a self S-duality with respect to Planck constant ℏ and can be derived from the Lockhart-Vafa partition function of non-perturbative topological string. Based on a recent observation on the correspondence between spectral theory and topological string, another quantization scheme was proposed by Grassi-Hatsuda-Mariño, in which there is a single quantization condition and the spectra are encoded in the vanishing of a quantum Riemann theta function. We demonstrate that there actually exist at least g nonequivalent quantum Riemann theta functions and the intersections of their theta divisors coincide with the spectra determined by the exact NS quantization conditions. This highly nontrivial coincidence between the two quantization schemes requires infinite constraints among the refined Gopakumar-Vafa invariants. The equivalence for mirror curves of genus one has been verified for some local del Pezzo surfaces. In this paper, we generalize the correspondence to higher genus, and analyze in detail the resolved ℂ{sup 3}/ℤ{sub 5} orbifold and several SU(N) geometries. We also give a proof for some models at ℏ=2π/k.

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

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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...

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.

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.

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.

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.

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

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)

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

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.

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.

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.

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.

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.).

[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

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.

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

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.)

On a conjecture of Chen-Guo-Wang

OpenAIRE

Ning, Bo; Zheng, Yu

2015-01-01

Towards confirming Sun's conjecture on the strict log-concavity of combinatorial sequence involving the n$th$ Bernoulli number, Chen, Guo and Wang proposed a conjecture about the log-concavity of the function $\\theta(x)=\\sqrt[x]{2\\zeta(x)\\Gamma(x+1)}$ for $x\\in (6,\\infty)$, where $\\zeta(x)$ is the Riemann zeta function and $\\Gamma(x)$ is the Gamma function. In this paper, we first prove this conjecture along the spirit of Zhu's previous work. Second, we extend Chen et al.'s conjecture in the ...

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

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.

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.

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...

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)

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 $0.10-0.15$.

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

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.

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.

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

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.)

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.

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

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.

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...

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

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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.

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.

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.

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)

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.

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.

Riemann type algebraic structures and their differential-algebraic integrability analysis

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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.

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.

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

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.).

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

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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.

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

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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.

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...

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.

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

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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.

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.

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.)

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.

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.

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

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)

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)

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.

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.

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.

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

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.

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.

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

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.

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.)

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.

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.

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

Generalized Bilinear Differential Operators, Binary Bell Polynomials, and Exact Periodic Wave Solution of Boiti-Leon-Manna-Pempinelli Equation

Directory of Open Access Journals (Sweden)

Huanhe Dong

2014-01-01

Full Text Available We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized Dp-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value of p is 5.

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

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....

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.

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

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.

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.

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)

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

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)

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

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)

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

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.

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)

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.)

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)

On the numerical evaluation of algebro-geometric solutions to integrable equations

International Nuclear Information System (INIS)

Kalla, C; Klein, C

2012-01-01

Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated with real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis not related to automorphisms of the curve, we study symplectic transformations to an adapted basis and give explicit formulae for M-curves. As examples we discuss solutions of the Davey–Stewartson and the multi-component nonlinear Schrödinger equations

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.

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)

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.)

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

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)

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.

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

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.

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)

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.

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.

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.)

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…

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.

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.

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.

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.

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.

Search for {theta}(1540){sup +} in the exclusive proton-induced reaction p+C(N){yields}{theta}{sup +} anti K{sup 0}+C(N) at the energy of 70 GeV

Energy Technology Data Exchange (ETDEWEB)

Antipov, Yu.M.; Artamonov, A.V.; Batarin, V.A.; Eroshin, O.V. [Inst. for High Energy Physics, Protvino (Russian Federation); Kolgamov, V.Z. [Inst. of Theoretical and Experimental Physics, Moscow (RU)] [and others

2004-09-01

A search for narrow {theta}(1540){sup +}, a candidate for pentaquark baryon with positive strangeness, has been performed in an exclusive proton-induced reaction p+C(N){yields}{theta}{sup +} anti K{sup 0}+C(N) on carbon nuclei or quasifree nucleons at E{sub beam}=70 GeV ({radical}(s)=11.5 GeV) studying nK{sup +}, pK{sub S}{sup 0} and pK{sub L}{sup 0} decay channels of {theta}(1540){sup +} in four different final states of the {theta}{sup +} anti K{sup 0} system. In order to assess the quality of the identification of the final states with neutron or K {sup 0} {sub L}, we reconstructed {lambda}(1520){yields}nK{sup 0}{sub S} and {phi}{yields}K{sup 0}{sub L}K{sup 0}{sub S} decays in the calibration reactions p+C(N){yields}{lambda}(1520)K{sup +}+C(N) and p+C(N){yields}p{phi}+C(N). We found no evidence for narrow pentaquark peak in any of the studied final states and decay channels. Assuming that the production characteristics of the {theta}{sup +} anti K{sup 0} system are not drastically different from those of the {lambda}(1520)K{sup +} and p{phi} systems, we established upper limits on the cross-section ratios {sigma}({theta}{sup +} anti K{sup 0})/{sigma}({lambda}(1520)K{sup +})< 0.02 and {sigma}({theta}{sup +} anti K{sup 0})/{sigma}(p{phi})< 0.15 at 90% CL and a preliminary upper limit for the forward hemisphere cross-section {sigma}({theta}{sup +} anti K{sup 0})< 30 nb/nucleon. (orig.)

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)

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

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

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.

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)

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.

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.

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}.

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.

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.

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

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

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.

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

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.

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

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.

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.

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. $^{10,11}$.

Projective and superconformal structures on surfaces

International Nuclear Information System (INIS)

Harvey, W.J.

1990-01-01

Much attention has recently been given to the study of super Riemann surfaces. Detailed accounts of these objects and their infinitesimal deformation theory are referenced where they are fitted into the framework of complex supermanifolds, superconformal structures and graded sheaves. One difficulty, which seems even more of a barrier than in the case of classical deformations of Riemann surface structure, is the lack of a good global description of super-moduli spaces. In this note, we outline an approach which places the theory in the classical setting of projective structures on variable Riemann surfaces. We explain how to construct a distribution (family of vector subspaces) inside the holomorphic cotangent space to the moduli space M g of Riemann surfaces with genus g and furnished with a level-4 homology structure, such that the corresponding rank-(2g-2) complex vector bundle models the soul deformations of a family of super-Riemann surfaces. The keystone in this construction is the existence of holomorphic sections for the space of non-singular odd theta characteristics on C g the universal curve over M g . (author)

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.

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

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.

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.)

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.

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)

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)

Dimers and the Critical Ising Model on lattices of genus >1

International Nuclear Information System (INIS)

Costa-Santos, Ruben; McCoy, B.M.

2002-01-01

We study the partition function of both Close-Packed Dimers and the Critical Ising Model on a square lattice embedded on a genus two surface. Using numerical and analytical methods we show that the determinants of the Kasteleyn adjacency matrices have a dependence on the boundary conditions that, for large lattice size, can be expressed in terms of genus two theta functions. The period matrix characterizing the continuum limit of the lattice is computed using a discrete holomorphic structure. These results relate in a direct way the lattice combinatorics with conformal field theory, providing new insight to the lattice regularization of conformal field theories on higher genus Riemann surfaces

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.)

Theta Phase Synchronization Is the Glue that Binds Human Associative Memory.

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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.

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.

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.

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

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.

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.

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

Theta coordinated error-driven learning in the hippocampus.

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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.

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.

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.)

Fractional derivative of the Hurwitz ζ-function and chaotic decay to zero

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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.

Isomonodromic tau-functions from Liouville conformal blocks

International Nuclear Information System (INIS)

Iorgov, N.; Lisovyy, O.

2014-01-01

The goal of this note is to show that the Riemann-Hilbert problem to find multivalued analytic functions with SL(2,C)-valued monodromy on Riemann surfaces of genus zero with n punctures can be solved by taking suitable linear combinations of the conformal blocks of Liouville theory at c=1. This implies a similar representation for the isomonodromic tau-function. In the case n=4 we thereby get a proof of the relation between tau-functions and conformal blocks discovered in O. Gamayun, N. Iorgov, and O. Lisovyy (2012). We briefly discuss a possible application of our results to the study of relations between certain N=2 supersymmetric gauge theories and conformal field theory.

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.

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.

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.

Search for $\\Theta^{++}$ Pentaquarks in the Exclusive Reaction $\\gamma p\\to K^+K^-p$

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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.

Task-related modulation of anterior theta and posterior alpha EEG reflects top-down preparation

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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.

Delta-gamma-theta Hedging of Crude Oil Asian Options

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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.

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.

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.

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

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

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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.

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...

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

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.

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 .

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.

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....

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.

Bernoulli numbers and zeta functions

CERN Document Server

Arakawa, Tsuneo; Kaneko, Masanobu

2014-01-01

Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of ...

Why don't you like me? Midfrontal theta power in response to unexpected peer rejection feedback.

Science.gov (United States)

van der Molen, M J W; Dekkers, L M S; Westenberg, P M; van der Veen, F M; van der Molen, M W

2017-02-01

Social connectedness theory posits that the brain processes social rejection as a threat to survival. Recent electrophysiological evidence suggests that midfrontal theta (4-8Hz) oscillations in the EEG provide a window on the processing of social rejection. Here we examined midfrontal theta dynamics (power and inter-trial phase synchrony) during the processing of social evaluative feedback. We employed the Social Judgment paradigm in which 56 undergraduate women (mean age=19.67 years) were asked to communicate their expectancies about being liked vs. disliked by unknown peers. Expectancies were followed by feedback indicating social acceptance vs. rejection. Results revealed a significant increase in EEG theta power to unexpected social rejection feedback. This EEG theta response could be source-localized to brain regions typically reported during activation of the saliency network (i.e., dorsal anterior cingulate cortex, insula, inferior frontal gyrus, frontal pole, and the supplementary motor area). Theta phase dynamics mimicked the behavior of the time-domain averaged feedback-related negativity (FRN) by showing stronger phase synchrony for feedback that was unexpected vs. expected. Theta phase, however, differed from the FRN by also displaying stronger phase synchrony in response to rejection vs. acceptance feedback. Together, this study highlights distinct roles for midfrontal theta power and phase synchrony in response to social evaluative feedback. Our findings contribute to the literature by showing that midfrontal theta oscillatory power is sensitive to social rejection but only when peer rejection is unexpected, and this theta response is governed by a widely distributed neural network implicated in saliency detection and conflict monitoring. Copyright © 2016 Elsevier Inc. All rights reserved.

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.

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.

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.

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

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.

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…

Computational study of hippocampal-septal theta rhythm changes due to β-amyloid-altered ionic channels.

Directory of Open Access Journals (Sweden)

Xin Zou

Full Text Available Electroencephagraphy (EEG of many dementia patients has been characterized by an increase in low frequency field potential oscillations. One of the characteristics of early stage Alzheimer's disease (AD is an increase in theta band power (4-7 Hz. However, the mechanism(s underlying the changes in theta oscillations are still unclear. To address this issue, we investigate the theta band power changes associated with β-Amyloid (Aβ peptide (one of the main markers of AD using a computational model, and by mediating the toxicity of hippocampal pyramidal neurons. We use an established biophysical hippocampal CA1-medial septum network model to evaluate four ionic channels in pyramidal neurons, which were demonstrated to be affected by Aβ. They are the L-type Ca²⁺ channel, delayed rectifying K⁺ channel, A-type fast-inactivating K⁺ channel and large-conductance Ca²⁺-activated K⁺ channel. Our simulation results demonstrate that only the Aβ inhibited A-type fast-inactivating K⁺ channel can induce an increase in hippocampo-septal theta band power, while the other channels do not affect theta rhythm. We further deduce that this increased theta band power is due to enhanced synchrony of the pyramidal neurons. Our research may elucidate potential biomarkers and therapeutics for AD. Further investigation will be helpful for better understanding of AD-induced theta rhythm abnormalities and associated cognitive deficits.

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.

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

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)

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.

1-loop partition function in AdS{sub 3}/CFT{sub 2}

Energy Technology Data Exchange (ETDEWEB)

Chen, Bin [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Collaborative Innovation Center of Quantum Matter,5 Yiheyuan Rd, Beijing 100871 (China); Center for High Energy Physics, Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Wu, Jie-qiang [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University,5 Yiheyuan Rd, Beijing 100871 (China)

2015-12-16

The 1-loop partition function of the handlebody solutions in the AdS{sub 3} gravity have been derived some years ago using the heat kernel techniques and the method of images. In the semiclassical limit, such partition function should correspond to the order O(c{sup 0}) part in the partition function of dual conformal field theory(CFT) on the boundary Riemann surface. The higher genus partition function could be computed by the multi-point functions in the Riemann sphere via sewing prescription. In the large central charge limit, the CFT is effectively free in the sense that to the leading order of c the multi-point function is further simplified to be a summation over the products of two-point functions of single-particle states. Correspondingly in the bulk, the graviton is freely propagating without interaction. Furthermore the product of the two-point functions may define the links, each of which is in one-to-one correspondence with the conjugacy class of the Schottky group of the Riemann surface. Moreover, the value of a link is determined by the multiplier of the element in the conjugacy class. This allows us to reproduce exactly the gravitational 1-loop partition function. The proof can be generalized to the higher spin gravity and its dual CFT.

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.

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.

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 ...

Vanishing of the vacuum amplitude of heterotic string compactified on a tensor product of N=2 superconformal models

International Nuclear Information System (INIS)

Kei Ito.

1988-07-01

The vacuum amplitude of heterotic string compactified on a tensor product of nine copies of c=1, N=2 superconformal models is shown to vanish due to a generalized Riemann's theta identity associated with the 12x12 matrix identity t BB=6 2 I 12 , identity B ij =-5(i=j), 1(i≠j). (author). 4 refs

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.

Fronto-parietal and fronto-temporal theta phase synchronization for visual and auditory-verbal working memory.

Science.gov (United States)

Kawasaki, Masahiro; Kitajo, Keiichi; Yamaguchi, Yoko

2014-01-01

In humans, theta phase (4-8 Hz) synchronization observed on electroencephalography (EEG) plays an important role in the manipulation of mental representations during working memory (WM) tasks; fronto-temporal synchronization is involved in auditory-verbal WM tasks and fronto-parietal synchronization is involved in visual WM tasks. However, whether or not theta phase synchronization is able to select the to-be-manipulated modalities is uncertain. To address the issue, we recorded EEG data from subjects who were performing auditory-verbal and visual WM tasks; we compared the theta synchronizations when subjects performed either auditory-verbal or visual manipulations in separate WM tasks, or performed both two manipulations in the same WM task. The auditory-verbal WM task required subjects to calculate numbers presented by an auditory-verbal stimulus, whereas the visual WM task required subjects to move a spatial location in a mental representation in response to a visual stimulus. The dual WM task required subjects to manipulate auditory-verbal, visual, or both auditory-verbal and visual representations while maintaining auditory-verbal and visual representations. Our time-frequency EEG analyses revealed significant fronto-temporal theta phase synchronization during auditory-verbal manipulation in both auditory-verbal and auditory-verbal/visual WM tasks, but not during visual manipulation tasks. Similarly, we observed significant fronto-parietal theta phase synchronization during visual manipulation tasks, but not during auditory-verbal manipulation tasks. Moreover, we observed significant synchronization in both the fronto-temporal and fronto-parietal theta signals during simultaneous auditory-verbal/visual manipulations. These findings suggest that theta synchronization seems to flexibly connect the brain areas that manipulate WM.

Fronto-parietal and fronto-temporal theta phase synchronization for visual and auditory-verbal working memory

Directory of Open Access Journals (Sweden)

Masahiro eKawasaki

2014-03-01

Full Text Available In humans, theta phase (4–8 Hz synchronization observed on electroencephalography (EEG plays an important role in the manipulation of mental representations during working memory (WM tasks; fronto-temporal synchronization is involved in auditory-verbal WM tasks and fronto-parietal synchronization is involved in visual WM tasks. However, whether or not theta phase synchronization is able to select the to-be-manipulated modalities is uncertain. To address the issue, we recorded EEG data from subjects who were performing auditory-verbal and visual WM tasks; we compared the theta synchronizations when subjects performed either auditory-verbal or visual manipulations in separate WM tasks, or performed both two manipulations in the same WM task. The auditory-verbal WM task required subjects to calculate numbers presented by an auditory-verbal stimulus, whereas the visual WM task required subjects to move a spatial location in a mental representation in response to a visual stimulus. The dual WM task required subjects to manipulate auditory-verbal, visual, or both auditory-verbal and visual representations while maintaining auditory-verbal and visual representations. Our time-frequency EEG analyses revealed significant fronto-temporal theta phase synchronization during auditory-verbal manipulation in both auditory-verbal and auditory-verbal/visual WM tasks, but not during visual manipulation tasks. Similarly, we observed significant fronto-parietal theta phase synchronization during visual manipulation tasks, but not during auditory-verbal manipulation tasks. Moreover, we observed significant synchronization in both the fronto-temporal and fronto-parietal theta signals during simultaneous auditory-verbal/visual manipulations. These findings suggest that theta synchronization seems to flexibly connect the brain areas that manipulate WM.

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

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.

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.

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

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.

Increase in short-term memory capacity induced by down-regulating individual theta frequency via transcranial alternating current stimulation.

Science.gov (United States)

Vosskuhl, Johannes; Huster, René J; Herrmann, Christoph S

2015-01-01

Working memory (WM) and short-term memory (STM) supposedly rely on the phase-amplitude coupling (PAC) of neural oscillations in the theta and gamma frequency ranges. The ratio between the individually dominant gamma and theta frequencies is believed to determine an individual's memory capacity. The aim of this study was to establish a causal relationship between the gamma/theta ratio and WM/STM capacity by means of transcranial alternating current stimulation (tACS). To achieve this, tACS was delivered at a frequency below the individual theta frequency. Thereby the individual ratio of gamma to theta frequencies was changed, resulting in an increase of STM capacity. Healthy human participants (N = 33) were allocated to two groups, one receiving verum tACS, the other underwent a sham control protocol. The electroencephalogram (EEG) was measured before stimulation and analyzed with regard to the properties of PAC between theta and gamma frequencies to determine individual stimulation frequencies. After stimulation, EEG was recorded again in order to find after-effects of tACS in the oscillatory features of the EEG. Measures of STM and WM were obtained before, during and after stimulation. Frequency spectra and behavioral data were compared between groups and different measurement phases. The tACS- but not the sham stimulated group showed an increase in STM capacity during stimulation. WM was not affected in either groups. An increase in task-related theta amplitude after stimulation was observed only for the tACS group. These augmented theta amplitudes indicated that the manipulation of individual theta frequencies was successful and caused the increase in STM capacity.

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

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.

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

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

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.

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.

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

A Randomized Trial of Comparing the Efficacy of Two Neurofeedback Protocols for Treatment of Clinical and Cognitive Symptoms of ADHD: Theta Suppression/Beta Enhancement and Theta Suppression/Alpha Enhancement

Directory of Open Access Journals (Sweden)

Arash Mohagheghi

2017-01-01

Full Text Available Introduction. Neurofeedback (NF is an adjuvant or alternative therapy for children with Attention Deficit Hyperactivity Disorder (ADHD. This study intended to compare the efficacy of two different NF protocols on clinical and cognitive symptoms of ADHD. Materials and Methods. In this clinical trial, sixty children with ADHD aged 7 to 10 years old were randomly grouped to receive two different NF treatments (theta suppression/beta enhancement protocol and theta suppression/alpha enhancement protocol. Clinical and cognitive assessments were conducted prior to and following the treatment and also after an eight-week follow-up. Results. Both protocols alleviated the symptoms of ADHD in general (p<0.001, hyperactivity (p<0.001, inattention (p<0.001, and omission errors (p<0.001; however, they did not affect the oppositional and impulsive scales nor commission errors. These effects were maintained after an eight-week intervention-free period. The only significant difference between the two NF protocols was that high-frequency alpha enhancement protocol performed better in suppressing omission errors (p<0.001. Conclusion. The two NF protocols with theta suppression/beta enhancement and theta suppression/alpha enhancement have considerable and comparable effect on clinical symptoms of ADHD. Alpha enhancement protocol was more effective in suppressing omission errors.

Increase in short-term memory capacity induced by down-regulating individual theta frequency via transcranial alternating current stimulation

Directory of Open Access Journals (Sweden)

Johannes eVosskuhl

2015-05-01

Full Text Available Working memory (WM and short-term memory (STM supposedly rely on the phase-amplitude coupling of neural oscillations in the theta and gamma frequency ranges. The ratio between the individually dominant gamma and theta frequencies is believed to determine an individual’s memory capacity. The aim of this study was to establish a causal relationship between the gamma/theta ratio and WM/STM capacity by means of transcranial alternating current stimulation (tACS. To achieve this, tACS was delivered at a frequency below the individual theta frequency. Thereby the individual ratio of gamma to theta frequencies was changed, resulting in an increase of STM capacity. Healthy human participants (N=33 were allocated to two groups, one receiving verum tACS, the other underwent a sham control protocol. The electroencephalogram (EEG was measured before stimulation and analyzed with regard to the properties of phase-amplitude coupling between theta and gamma frequencies to determine individual stimulation frequencies. After stimulation, EEG was recorded again in order to find after-effects of tACS in the oscillatory features of the EEG. Measures of STM and WM were obtained before, during and after stimulation. Frequency spectra and behavioral data were compared between groups and different measurement phases. The tACS- but not the sham stimulated group showed an increase in STM capacity during stimulation. WM was not affected in either groups. An increase in task-related theta amplitude after stimulation was observed only for the tACS group. These augmented theta amplitudes indicated that the manipulation of individual theta frequencies was successful and caused the increase in STM capacity.

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.

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.)

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…

Functional geometric method for solving free boundary problems for harmonic functions

Energy Technology Data Exchange (ETDEWEB)

Demidov, Aleksander S [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

2010-01-01

A survey is given of results and approaches for a broad spectrum of free boundary problems for harmonic functions of two variables. The main results are obtained by the functional geometric method. The core of these methods is an interrelated analysis of the functional and geometric characteristics of the problems under consideration and of the corresponding non-linear Riemann-Hilbert problems. An extensive list of open questions is presented. Bibliography: 124 titles.

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

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.

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.

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

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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.

High precision measurement of sin2theta/sub W/ in semi-leptonic neutrino interactions

International Nuclear Information System (INIS)

Guyot, C.

1985-01-01

The experiment has provided what is presently the most accurate measurement of sin 2 theta/sub W/. The errors are still too large for a significant test of the standard model and the measured value is in agreement with the measured values of M/sub W/ and M/sub Z/. On the other hand, this result can constrain the Grand Unified models. The standard SU(5) model predicts sin 2 theta/sub W//sup MS/ = 0.214 +/- 0.004 (the error comes from the uncertainty on Lambda/sub MS/), in very good agreement with the measured value. While this model has big problems with the proton lifetime, it could be saved by its supersymmetric extension. In the minimal SU(5) SUSY model (with 2 Higgs supermultiplets) sin 2 theta/sub W//sup MS/ = 0.233 +/- 0.004, [12] in bad agreement with the measured value. The addition of other Higgs supermultiplets increases the value of sin 2 theta/sub W/. Unless some unexpected large contribution from higher-twist terms occurs, the present measurement can already bring a significant constraint on Grand Unified models

Different types of theta rhythmicity are induced by social and fearful stimuli in a network associated with social memory.

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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.

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

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

Selective Entrainment of Theta Oscillations in the Dorsal Stream Causally Enhances Auditory Working Memory Performance.

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Albouy, Philippe; Weiss, Aurélien; Baillet, Sylvain; Zatorre, Robert J

2017-04-05

The implication of the dorsal stream in manipulating auditory information in working memory has been recently established. However, the oscillatory dynamics within this network and its causal relationship with behavior remain undefined. Using simultaneous MEG/EEG, we show that theta oscillations in the dorsal stream predict participants' manipulation abilities during memory retention in a task requiring the comparison of two patterns differing in temporal order. We investigated the causal relationship between brain oscillations and behavior by applying theta-rhythmic TMS combined with EEG over the MEG-identified target (left intraparietal sulcus) during the silent interval between the two stimuli. Rhythmic TMS entrained theta oscillation and boosted participants' accuracy. TMS-induced oscillatory entrainment scaled with behavioral enhancement, and both gains varied with participants' baseline abilities. These effects were not seen for a melody-comparison control task and were not observed for arrhythmic TMS. These data establish theta activity in the dorsal stream as causally related to memory manipulation. VIDEO ABSTRACT. Copyright © 2017 Elsevier Inc. All rights reserved.

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

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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.

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

Science.gov (United States)

Owolabi, Kolade M.

2018-03-01

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

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

The analyzing power Asub(y)(theta) for the elastic scattering of 12 MeV neutrons from deuterons

International Nuclear Information System (INIS)

Tornow, W.; Lisowski, P.W.; Byrd, R.C.; Walter, R.L.

1978-01-01

The analyzing power Asub(y)(theta) was obtained at 10 0 intervals between 30 0 (lab) to 120 0 (lab) for 2 H(n, n) 2 H at 12.0 MeV. The polarized neutron beam employed in the measurement was obtained by using neutrons emitted at 0 0 from the polarization transfer reaction 2 H(d(pol), n(pol)) 3 He. The accuracy in the Asub(y)(theta) values that was achieved ranged from +- 0.006 to +- 0.013. Comparison of the data to Asub(y)(theta) results obtained at 12 MeV for the charge symmetric reaction 2 H(p, p) 2 H shows that the two Asub(y)(theta) distributions are equal to within the above accuracy. (Auth.)

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

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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.

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

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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.

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

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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.

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

Temporal correlation between auditory neurons and the hippocampal theta rhythm induced by novel stimulations in awake guinea pigs.

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Liberman, Tamara; Velluti, Ricardo A; Pedemonte, Marisa

2009-11-17

The hippocampal theta rhythm is associated with the processing of sensory systems such as touch, smell, vision and hearing, as well as with motor activity, the modulation of autonomic processes such as cardiac rhythm, and learning and memory processes. The discovery of temporal correlation (phase locking) between the theta rhythm and both visual and auditory neuronal activity has led us to postulate the participation of such rhythm in the temporal processing of sensory information. In addition, changes in attention can modify both the theta rhythm and the auditory and visual sensory activity. The present report tested the hypothesis that the temporal correlation between auditory neuronal discharges in the inferior colliculus central nucleus (ICc) and the hippocampal theta rhythm could be enhanced by changes in sensory stimulation. We presented chronically implanted guinea pigs with auditory stimuli that varied over time, and recorded the auditory response during wakefulness. It was observed that the stimulation shifts were capable of producing the temporal phase correlations between the theta rhythm and the ICc unit firing, and they differed depending on the stimulus change performed. Such correlations disappeared approximately 6 s after the change presentation. Furthermore, the power of the hippocampal theta rhythm increased in half of the cases presented with a stimulation change. Based on these data, we propose that the degree of correlation between the unitary activity and the hippocampal theta rhythm varies with--and therefore may signal--stimulus novelty.

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

Behavioural Inhibition System (BIS) sensitivity differentiates EEG theta responses during goal conflict in a continuous monitoring task.

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Moore, Roger A; Mills, Matthew; Marshman, Paul; Corr, Philip J

2012-08-01

Previous research has revealed that EEG theta oscillations are affected during goal conflict processing. This is consistent with the behavioural inhibition system (BIS) theory of anxiety (Gray & McNaughton, 2000). However, studies have not attempted to relate these BIS-related theta effects to BIS personality measures. Confirmation of such an association would provide further support for BIS theory, especially as it relates to trait differences. EEG was measured (32 electrodes) from extreme groups (low/high trait BIS) engaged in a target detection task. Goal conflicts were introduced throughout the task. Results show that the two groups did not differ in behavioural performance. The major EEG result was that a stepwise discriminant analysis indicated discrimination by 6 variables derived from coherence and power, with 5 of the 6 in the theta range as predicted by BIS theory and one in the beta range. Also, across the whole sample, EEG theta coherence increased at a variety of regions during primary goal conflict and showed a general increase during response execution; EEG theta power, in contrast, was primarily reactive to response execution. This is the first study to reveal a three-way relationship between the induction of goal conflict, the induction of theta power and coherence, and differentiation by psychometrically-defined low/high BIS status. Copyright © 2012 Elsevier B.V. All rights reserved.

Ih tunes theta/gamma oscillations and cross-frequency coupling in an in silico CA3 model.

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Samuel A Neymotin

Full Text Available Ih channels are uniquely positioned to act as neuromodulatory control points for tuning hippocampal theta (4-12 Hz and gamma (25 Hz oscillations, oscillations which are thought to have importance for organization of information flow. contributes to neuronal membrane resonance and resting membrane potential, and is modulated by second messengers. We investigated oscillatory control using a multiscale computer model of hippocampal CA3, where each cell class (pyramidal, basket, and oriens-lacunosum moleculare cells, contained type-appropriate isoforms of . Our model demonstrated that modulation of pyramidal and basket allows tuning theta and gamma oscillation frequency and amplitude. Pyramidal also controlled cross-frequency coupling (CFC and allowed shifting gamma generation towards particular phases of the theta cycle, effected via 's ability to set pyramidal excitability. Our model predicts that in vivo neuromodulatory control of allows flexibly controlling CFC and the timing of gamma discharges at particular theta phases.

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)

Upsilon NU: Our chapter in Sigma Theta Tau Internacional Upsilon NU: nuestro capítulo en Sigma Theta Tau International

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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.

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.

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.

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

Reduction in LFP cross-frequency coupling between theta and gamma rhythms associated with impaired STP and LTP in a rat model of brain ischemia

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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.

Study of CP(N-1) theta-vacua by cluster simulation of SU(N) quantum spin ladders.

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Beard, B B; Pepe, M; Riederer, S; Wiese, U-J

2005-01-14

D-theory provides an alternative lattice regularization of the 2D CP(N-1) quantum field theory in which continuous classical fields emerge from the dimensional reduction of discrete SU(N) quantum spins. Spin ladders consisting of n transversely coupled spin chains lead to a CP(N-1) model with a vacuum angle theta=npi. In D-theory no sign problem arises and an efficient cluster algorithm is used to investigate theta-vacuum effects. At theta=pi there is a first order phase transition with spontaneous breaking of charge conjugation symmetry for CP(N-1) models with N>2.

Index of alpha/theta ratio of the electroencephalogram: a new marker for Alzheimer’s disease

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Magali eSchmidt

2013-10-01

Full Text Available Objective: We evaluated quantitative EEG measures to determine a screening index to discriminate AD patients from normal individuals. Methods: Two groups of individuals older than 50 years, comprising a control group of 57 normal volunteers and a study group of 50 patients with probable AD, were compared. EEG recordings were obtained from subjects in a wake state with eyes closed at rest for 30 min. Logistic regression analysis was conducted. Results: Spectral potentials of the alpha and theta bands were computed for all electrodes and the alpha/theta ratio calculated. Logistic regression of alpha/theta of the mean potential of the C3 and O1 electrodes was carried out. A formula was calculated to aid the diagnosis of AD yielding 76.4 % sensitivity and 84.6 specificity for AD with an area under the ROC curve of 0.92. Conclusions: Logistic regression of alpha/theta of the spectrum of the mean potential of EEG represents a good marker discriminating AD patients from normal controls.

Complementary theta resonance filtering by two spatially segregated mechanisms in CA1 hippocampal pyramidal neurons.

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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.

(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.)

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.

Frontal theta EEG dynamics in a real-world air traffic control task.

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Shou, Guofa; Ding, Lei

2013-01-01

Mental workload and time-on-task effect are two major factors expediting fatigue progress, which leads to performance decline and/or failure in real-world tasks. In the present study, electroencephalography (EEG) is applied to study mental fatigue development during an air traffic control (ATC) task. Specifically, the frontal theta EEG dynamics are firstly dissolved into a unique frontal independent component (IC) through a novel time-frequency independent component analysis (tfICA) method. Then the temporal fluctuations of the identified frontal ICs every minute are compared to workload (reflected by number of clicks per minute) and time-on-task effect by correlational analysis and linear regression analysis. It is observed that the frontal theta activity significantly increase with workload augment and time-on-task. The present study demonstrates that the frontal theta EEG activity identified by tfICA method is a sensitive and reliable metric to assess mental workload and time-on-task effect in a real-world task, i.e., ATC task, at the resolution of minute(s).

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

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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.

Scalar field Green functions on causal sets

International Nuclear Information System (INIS)

Nomaan Ahmed, S; Surya, Sumati; Dowker, Fay

2017-01-01

We examine the validity and scope of Johnston’s models for scalar field retarded Green functions on causal sets in 2 and 4 dimensions. As in the continuum, the massive Green function can be obtained from the massless one, and hence the key task in causal set theory is to first identify the massless Green function. We propose that the 2d model provides a Green function for the massive scalar field on causal sets approximated by any topologically trivial 2-dimensional spacetime. We explicitly demonstrate that this is indeed the case in a Riemann normal neighbourhood. In 4d the model can again be used to provide a Green function for the massive scalar field in a Riemann normal neighbourhood which we compare to Bunch and Parker’s continuum Green function. We find that the same prescription can also be used for de Sitter spacetime and the conformally flat patch of anti-de Sitter spacetime. Our analysis then allows us to suggest a generalisation of Johnston’s model for the Green function for a causal set approximated by 3-dimensional flat spacetime. (paper)

Entorhinal-CA3 Dual-Input Control of Spike Timing in the Hippocampus by Theta-Gamma Coupling.

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Fernández-Ruiz, Antonio; Oliva, Azahara; Nagy, Gergő A; Maurer, Andrew P; Berényi, Antal; Buzsáki, György

2017-03-08

Theta-gamma phase coupling and spike timing within theta oscillations are prominent features of the hippocampus and are often related to navigation and memory. However, the mechanisms that give rise to these relationships are not well understood. Using high spatial resolution electrophysiology, we investigated the influence of CA3 and entorhinal inputs on the timing of CA1 neurons. The theta-phase preference and excitatory strength of the afferent CA3 and entorhinal inputs effectively timed the principal neuron activity, as well as regulated distinct CA1 interneuron populations in multiple tasks and behavioral states. Feedback potentiation of distal dendritic inhibition by CA1 place cells attenuated the excitatory entorhinal input at place field entry, coupled with feedback depression of proximal dendritic and perisomatic inhibition, allowing the CA3 input to gain control toward the exit. Thus, upstream inputs interact with local mechanisms to determine theta-phase timing of hippocampal neurons to support memory and spatial navigation. Copyright © 2017 Elsevier Inc. All rights reserved.

Exponential mean-square stability of two classes of theta Milstein methods for stochastic delay differential equations

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Rouz, Omid Farkhondeh; Ahmadian, Davood; Milev, Mariyan

2017-12-01

This paper establishes exponential mean square stability of two classes of theta Milstein methods, namely split-step theta Milstein (SSTM) method and stochastic theta Milstein (STM) method, for stochastic differential delay equations (SDDEs). We consider the SDDEs problem under a coupled monotone condition on drift and diffusion coefficients, as well as a necessary linear growth condition on the last term of theta Milstein method. It is proved that the SSTM method with θ ∈ [0, ½] can recover the exponential mean square stability of the exact solution with some restrictive conditions on stepsize, but for θ ∈ (½, 1], we proved that the stability results hold for any stepsize. Then, based on the stability results of SSTM method, we examine the exponential mean square stability of the STM method and obtain the similar stability results to that of the SSTM method. In the numerical section the figures show thevalidity of our claims.

Associative-memory representations emerge as shared spatial patterns of theta activity spanning the primate temporal cortex.

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Nakahara, Kiyoshi; Adachi, Ken; Kawasaki, Keisuke; Matsuo, Takeshi; Sawahata, Hirohito; Majima, Kei; Takeda, Masaki; Sugiyama, Sayaka; Nakata, Ryota; Iijima, Atsuhiko; Tanigawa, Hisashi; Suzuki, Takafumi; Kamitani, Yukiyasu; Hasegawa, Isao

2016-06-10

Highly localized neuronal spikes in primate temporal cortex can encode associative memory; however, whether memory formation involves area-wide reorganization of ensemble activity, which often accompanies rhythmicity, or just local microcircuit-level plasticity, remains elusive. Using high-density electrocorticography, we capture local-field potentials spanning the monkey temporal lobes, and show that the visual pair-association (PA) memory is encoded in spatial patterns of theta activity in areas TE, 36, and, partially, in the parahippocampal cortex, but not in the entorhinal cortex. The theta patterns elicited by learned paired associates are distinct between pairs, but similar within pairs. This pattern similarity, emerging through novel PA learning, allows a machine-learning decoder trained on theta patterns elicited by a particular visual item to correctly predict the identity of those elicited by its paired associate. Our results suggest that the formation and sharing of widespread cortical theta patterns via learning-induced reorganization are involved in the mechanisms of associative memory representation.

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

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.

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)

On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

International Nuclear Information System (INIS)

Manakov, S V; Santini, P M

2008-01-01

We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking

On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

Energy Technology Data Exchange (ETDEWEB)

Manakov, S V [Landau Institute for Theoretical Physics, Moscow (Russian Federation); Santini, P M [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Piazz.le Aldo Moro 2, I-00185 Rome (Italy)

2008-02-08

We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking.

Sustained frontal midline theta enhancements during effortful listening track working memory demands.

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Wisniewski, Matthew G; Iyer, Nandini; Thompson, Eric R; Simpson, Brian D

2017-11-27

Recent studies demonstrate that frontal midline theta power (4-8 Hz) enhancements in the electroencephalogram (EEG) relate to effortful listening. It has been proposed that these enhancements reflect working memory demands. Here, the need to retain auditory information in working memory was manipulated in a 2-interval 2-alternative forced-choice delayed pitch discrimination task ("Which interval contained the higher pitch?"). On each trial, two square wave stimuli differing in pitch at an individual's ∼70.7% correct threshold were separated by a 3-second ISI. In a 'Roving' condition, the lowest pitch stimulus was randomly selected on each trial (uniform distribution from 840 to 1160 Hz). In a 'Fixed' condition, the lowest pitch was always 979 Hz. Critically, the 'Fixed' condition allowed one to know the correct response immediately following the first stimulus (e.g., if the first stimulus is 979 Hz, the second must be higher). In contrast, the 'Roving' condition required retention of the first tone for comparison to the second. Frontal midline theta enhancements during the ISI were only observed for the 'Roving' condition. Alpha (8-13 Hz) enhancements were apparent during the ISI, but did not differ significantly between conditions. Since conditions were matched for accuracy at threshold, results suggest that frontal midline theta enhancements will not always accompany difficult listening. Mixed results in the literature regarding frontal midline theta enhancements may be related to differences between tasks in regards to working memory demands. Alpha enhancements may reflect task general effortful listening processes. Copyright © 2017 Elsevier B.V. All rights reserved.

Spin structures on algebraic curves and their applications in string theories

International Nuclear Information System (INIS)

Ferrari, F.

1990-01-01

The free fields on a Riemann surface carrying spin structures live on an unramified r-covering of the surface itself. When the surface is represented as an algebraic curve related to the vanishing of the Weierstrass polynomial, its r-coverings are algebraic curves as well. We construct explicitly the Weierstrass polynomial associated to the r-coverings of an algebraic curve. Using standard techniques of algebraic geometry it is then possible to solve the inverse Jacobi problem for the odd spin structures. As an application we derive the partition functions of bosonic string theories in many examples, including two general curves of genus three and four. The partition functions are explicitly expressed in terms of branch points apart from a factor which is essentially a theta constant. 53 refs., 4 figs. (Author)

Frontal theta accounts for individual differences in the cost of conflict on decision making.

Science.gov (United States)

Pinner, John F L; Cavanagh, James F

2017-10-01

Cognitive conflict is often experienced as a difficult, frustrating, and aversive state. Recent studies have indicated that conflict acts as an implicit cost during learning, valuation, and the instantiation of cognitive control. Here we investigated if an implicit manipulation of conflict also influences explicit decision making to risk. Participants were required to perform a Balloon Analogue Risk Task wherein the virtual balloon was inflated by performing a flankers task. By varying the percent of incongruent flanker trials between balloons, we hypothesized that participants would pump the balloon fewer times in conditions of higher conflict and that frontal midline theta would account for significant variance in this relationship. Across two studies, we demonstrate that conflict did not elicit reliable behavioral changes in this task across participants. However, individual differences in frontal theta power accounted for significant variance by predicting diminished balloon pumps. Thus, while conflict costs may act as investments to some individuals (invigorating behavior), it is aversive to others (diminishing behavior), and frontal midline theta power accounts for these varying behavioral tendencies between individuals. These findings demonstrate how frontal midline theta is not only a candidate mechanism for implementing cognitive control, but it is sensitive to the inherent costs therein. Copyright © 2017 Elsevier B.V. All rights reserved.

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

Intrahemispheric theta rhythm desynchronization impairs working memory.

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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.

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.)

Two-point correlation function for Dirichlet L-functions

Science.gov (United States)

Bogomolny, E.; Keating, J. P.

2013-03-01

The two-point correlation function for the zeros of Dirichlet L-functions at a height E on the critical line is calculated heuristically using a generalization of the Hardy-Littlewood conjecture for pairs of primes in arithmetic progression. The result matches the conjectured random-matrix form in the limit as E → ∞ and, importantly, includes finite-E corrections. These finite-E corrections differ from those in the case of the Riemann zeta-function, obtained in Bogomolny and Keating (1996 Phys. Rev. Lett. 77 1472), by certain finite products of primes which divide the modulus of the primitive character used to construct the L-function in question.

Two-point correlation function for Dirichlet L-functions

International Nuclear Information System (INIS)

Bogomolny, E; Keating, J P

2013-01-01

The two-point correlation function for the zeros of Dirichlet L-functions at a height E on the critical line is calculated heuristically using a generalization of the Hardy–Littlewood conjecture for pairs of primes in arithmetic progression. The result matches the conjectured random-matrix form in the limit as E → ∞ and, importantly, includes finite-E corrections. These finite-E corrections differ from those in the case of the Riemann zeta-function, obtained in Bogomolny and Keating (1996 Phys. Rev. Lett. 77 1472), by certain finite products of primes which divide the modulus of the primitive character used to construct the L-function in question. (paper)

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.

Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers

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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

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.

Oscillatory theta activity during memory formation and its impact on overnight consolidation: a missing link?

Science.gov (United States)

Heib, Dominik P J; Hoedlmoser, Kerstin; Anderer, Peter; Gruber, Georg; Zeitlhofer, Josef; Schabus, Manuel

2015-08-01

Sleep has been shown to promote memory consolidation driven by certain oscillatory patterns, such as sleep spindles. However, sleep does not consolidate all newly encoded information uniformly but rather "selects" certain memories for consolidation. It is assumed that such selection depends on salience tags attached to the new memories before sleep. However, little is known about the underlying neuronal processes reflecting presleep memory tagging. The current study sought to address the question of whether event-related changes in spectral theta power (theta ERSP) during presleep memory formation could reflect memory tagging that influences subsequent consolidation during sleep. Twenty-four participants memorized 160 word pairs before sleep; in a separate laboratory visit, they performed a nonlearning control task. Memory performance was tested twice, directly before and after 8 hr of sleep. Results indicate that participants who improved their memory performance overnight displayed stronger theta ERSP during the memory task in comparison with the control task. They also displayed stronger memory task-related increases in fast sleep spindle activity. Furthermore, presleep theta activity was directly linked to fast sleep spindle activity, indicating that processes during memory formation might indeed reflect memory tagging that influences subsequent consolidation during sleep. Interestingly, our results further indicate that the suggested relation between sleep spindles and overnight performance change is not as direct as once believed. Rather, it appears to be mediated by processes beginning during presleep memory formation. We conclude that theta ERSP during presleep memory formation reflects cortico-hippocampal interactions that lead to a better long-term accessibility by tagging memories for sleep spindle-related reprocessing.

Theta synchronization between medial prefrontal cortex and cerebellum is associated with adaptive performance of associative learning behavior

Science.gov (United States)

Chen, Hao; Wang, Yi-jie; Yang, Li; Sui, Jian-feng; Hu, Zhi-an; Hu, Bo

2016-01-01

Associative learning is thought to require coordinated activities among distributed brain regions. For example, to direct behavior appropriately, the medial prefrontal cortex (mPFC) must encode and maintain sensory information and then interact with the cerebellum during trace eyeblink conditioning (TEBC), a commonly-used associative learning model. However, the mechanisms by which these two distant areas interact remain elusive. By simultaneously recording local field potential (LFP) signals from the mPFC and the cerebellum in guinea pigs undergoing TEBC, we found that theta-frequency (5.0–12.0 Hz) oscillations in the mPFC and the cerebellum became strongly synchronized following presentation of auditory conditioned stimulus. Intriguingly, the conditioned eyeblink response (CR) with adaptive timing occurred preferentially in the trials where mPFC-cerebellum theta coherence was stronger. Moreover, both the mPFC-cerebellum theta coherence and the adaptive CR performance were impaired after the disruption of endogenous orexins in the cerebellum. Finally, association of the mPFC -cerebellum theta coherence with adaptive CR performance was time-limited occurring in the early stage of associative learning. These findings suggest that the mPFC and the cerebellum may act together to contribute to the adaptive performance of associative learning behavior by means of theta synchronization. PMID:26879632

A Comparison of Frontal Theta Activity During Shooting among Biathletes and Cross-Country Skiers before and after Vigorous Exercise.

Directory of Open Access Journals (Sweden)

Harri Luchsinger

Full Text Available Previous studies using electroencephalography (EEG to monitor brain activity have linked higher frontal theta activity to more focused attention and superior performance in goal-directed precision tasks. In biathlon, shooting performance requires focused attention after high-intensity cross-country skiing.To compare biathletes (serving as experts and cross-country skiers (novices and examine the effect of vigorous exercise on frontal theta activity during shooting.EEG frontal theta (4-7 Hz activity was compared between nine biathletes and eight cross-country skiers at comparable skiing performance levels who fired 100 shots on a 5-m indoor shooting range in quiescent condition followed by 20 shots after each of five 6-min high-intensity roller skiing sessions in the skating technique on a treadmill.Biathletes hit 80±14% and 81±10% before and after the roller skiing sessions, respectively. For the cross-country skiers these values were significantly lower than for the biathletes and amounted to 39±13% and 44±11% (p<0.01. Biathletes had on average 6% higher frontal theta activity during shooting as compared to cross-country skiers (F1,15 = 4.82, p = 0.044, but no significant effect of vigorous exercise on frontal theta activity in either of the two groups were found (F1,15 = 0.14, p = 0.72.Biathletes had significantly higher frontal theta activity than cross-country skiers during shooting, indicating higher focused attention in biathletes. Vigorous exercise did not decrease shooting performance or frontal theta activity during shooting in biathletes and cross-country skiers.

Change in hippocampal theta oscillation associated with multiple lever presses in a bimanual two-lever choice task for robot control in rats.

Directory of Open Access Journals (Sweden)

Norifumi Tanaka

Full Text Available Hippocampal theta oscillations have been implicated in working memory and attentional process, which might be useful for the brain-machine interface (BMI. To further elucidate the properties of the hippocampal theta oscillations that can be used in BMI, we investigated hippocampal theta oscillations during a two-lever choice task. During the task body-restrained rats were trained with a food reward to move an e-puck robot towards them by pressing the correct lever, ipsilateral to the robot several times, using the ipsilateral forelimb. The robot carried food and moved along a semicircle track set in front of the rat. We demonstrated that the power of hippocampal theta oscillations gradually increased during a 6-s preparatory period before the start of multiple lever pressing, irrespective of whether the correct lever choice or forelimb side were used. In addition, there was a significant difference in the theta power after the first choice, between correct and incorrect trials. During the correct trials the theta power was highest during the first lever-releasing period, whereas in the incorrect trials it occurred during the second correct lever-pressing period. We also analyzed the hippocampal theta oscillations at the termination of multiple lever pressing during the correct trials. Irrespective of whether the correct forelimb side was used, the power of hippocampal theta oscillations gradually decreased with the termination of multiple lever pressing. The frequency of theta oscillation also demonstrated an increase and decrease, before and after multiple lever pressing, respectively. There was a transient increase in frequency after the first lever press during the incorrect trials, while no such increase was observed during the correct trials. These results suggested that hippocampal theta oscillations reflect some aspects of preparatory and cognitive neural activities during the robot controlling task, which could be used for BMI.

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

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

Hippocampal theta activity is selectively associated with contingency detection but not discrimination in rabbit discrimination-reversal eyeblink conditioning.

Science.gov (United States)

Nokia, Miriam S; Wikgren, Jan

2010-04-01

The relative power of the hippocampal theta-band ( approximately 6 Hz) activity (theta ratio) is thought to reflect a distinct neural state and has been shown to affect learning rate in classical eyeblink conditioning in rabbits. We sought to determine if the theta ratio is mostly related to the detection of the contingency between the stimuli used in conditioning or also to the learning of more complex inhibitory associations when a highly demanding delay discrimination-reversal eyeblink conditioning paradigm is used. A high hippocampal theta ratio was not only associated with a fast increase in conditioned responding in general but also correlated with slow emergence of discriminative responding due to sustained responding to the conditioned stimulus not paired with an unconditioned stimulus. The results indicate that the neural state reflected by the hippocampal theta ratio is specifically linked to forming associations between stimuli rather than to the learning of inhibitory associations needed for successful discrimination. This is in line with the view that the hippocampus is responsible for contingency detection in the early phase of learning in eyeblink conditioning. (c) 2009 Wiley-Liss, Inc.

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...

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

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.

White paper report on using nuclear reactors to search for a value of theta13

Energy Technology Data Exchange (ETDEWEB)

Anderson, K.; Anjos, J.C.; Ayres, D.; Beacom, J.; Bediaga, I.; de Bellefon, A.; Berger, B.E.; Bilenky, S.; Blucher, E.; Bolton, T.; Buck, C.; Bugg, W.; Busenitz, J.; Choubey, S.; Conrad, J.; Cribier, M.; Dadoun, O.; Dalnoki-Veress, F.; Decowski, M.; de Gouvea, Andre; Demutrh, D.; Dessages-Ardellier, F.; Efremenko, Y.; von Feilitzsch, F.; Finley, D.; Formaggio, J.A.; Freedman, S.J.; Fujikawa, B.K.; Garbini, M.; Giusti, P.; Goger-Neff, M.; Goodman, M.; Gray, F.; Grieb, C.; Grudzinski, J.J.; Guarino, V.J.; Hartmann, F.; Hagner, C.; Heeger, K.M.; Hofmann, W.; Horton-Smith, G.; Huber, P.; Inzhechik, L.; Jochum, J.; Jostlein, H.; Kadel, R.; Kamyshkov, Y.; Kaplan, D.; Kasper, P.; de Kerret, H.; Kersten, J.; Klein, J.; Knopfle, K.T.; Kopeikin, V.; Kozlov, Yu.; Kryn, D.; Kuchler, V.; Kuze, M.; Lachenmaier, T.; Lasserre, T.; Laughton, C.; Lendvai, C.; Li, J.; Lindner, M.; Link, J.; Longo, M.; Lu, Y.S.; Luk, K.B.; Ma, Y.Q.; Martemyanov, V.P.; Mauger, C.; Manghetti, H.; McKeown, R.; Mention, G.; Meyer, J.P.; Mikaelyan, L.; Minakata, H.; Naples, D.; Nunokawa, H.; Oberauer, L.; Obolensky, M.; Parke, S.; Petcov, S.T.; Peres, O.L.G.; Potzel, W.; Pilcher, J.; Plunkett, R.; Raffelt, G.; Rapidis, P.; Reyna, D.; Roe, B.; Rolinec, M.; Sakamoto, Y.; Sartorelli, G.; Schonert, S.; Schwertz, T.; Selvi, M.; Shaevitz, M.; Shellard, R.; Shrock, R.; Sidwell, R.; Sims, J.; Sinev, V.; Stanton, N.; Stancu, I.; Stefanski, R.; Seukane, F.; Sugiyama, H.; Sukhotin, S.; Sumiyoshi, T.; Svoboda, R.; Talaga, R.; Tamura, N.; Tanimoto, M.; Thron, J.; von Toerne, E.; Vignaud, D.; Wagner, C.; Wang, Y.F.; Wang, Z.; Winter, W.; Wong, H.; Yakushev, E.; Yang, C.G.; Yasuda, O.

2004-02-26

There has been superb progress in understanding the neutrino sector of elementary particle physics in the past few years. It is now widely recognized that the possibility exists for a rich program of measuring CP violation and matter effects in future accelerator {nu} experiments, which has led to intense efforts to consider new programs at neutrino superbeams, off-axis detectors, neutrino factories and beta beams. However, the possibility of measuring CP violation can be fulfilled only if the value of the neutrino mixing parameter {theta}{sub 13} is such that sin{sup 2} (2{theta}{sub 13}) greater than or equal to on the order of 0.01. The authors of this white paper are an International Working Group of physicists who believe that a timely new experiment at a nuclear reactor sensitive to the neutrino mixing parameter {theta}{sub 13} in this range has a great opportunity for an exciting discovery, a non-zero value to {theta}{sub 13}. This would be a compelling next step of this program. We are studying possible new reactor experiments at a variety of sites around the world, and we have collaborated to prepare this document to advocate this idea and describe some of the issues that are involved.

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.

Theta band activity in response to emotional expressions and its relationship with gamma band activity as revealed by MEG and advanced beamformer source imaging

Directory of Open Access Journals (Sweden)

Qian eLuo

2014-02-01

Full Text Available Neuronal oscillations in the theta and gamma bands have been shown to be important for cognition. Here we examined the temporal and spatial relationship between the two frequency bands in emotional processing using Magnetoencephalography and an advanced dynamic beamformer source imaging method called Synthetic Aperture Magnetometry. We found that areas including the amygdala, visual and frontal cortex showed significant event-related synchronization (ERS in both bands, suggesting a functional association of neuronal oscillations in the same areas in the two bands. However, while the temporal profile in both bands was similar in the amygdala, the peak in gamma band power was much earlier within both visual and frontal areas. Our results do not support a traditional view that the localizations of lower and higher frequencies are spatially distinct. Instead, they suggest that in emotional processing, neuronal oscillations in the gamma and theta bands may reflect, at least in visual and frontal cortex either different but related functional processes or, perhaps more probably, different computational components of the same functional process.

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,...

Integral approximants for functions of higher monodromic dimension

Energy Technology Data Exchange (ETDEWEB)

Baker, G.A. Jr.

1987-01-01

In addition to the description of multiform, locally analytic functions as covering a many sheeted version of the complex plane, Riemann also introduced the notion of considering them as describing a space whose ''monodromic'' dimension is the number of linearly independent coverings by the monogenic analytic function at each point of the complex plane. I suggest that this latter concept is natural for integral approximants (sub-class of Hermite-Pade approximants) and discuss results for both ''horizontal'' and ''diagonal'' sequences of approximants. Some theorems are now available in both cases and make clear the natural domain of convergence of the horizontal sequences is a disk centered on the origin and that of the diagonal sequences is a suitably cut complex-plane together with its identically cut pendant Riemann sheets. Some numerical examples have also been computed.

Fronto-parietal and fronto-temporal theta phase synchronization for visual and auditory-verbal working memory

OpenAIRE

Masahiro eKawasaki; Masahiro eKawasaki; Masahiro eKawasaki; Keiichi eKitajo; Keiichi eKitajo; Yoko eYamaguchi

2014-01-01

In humans, theta phase (4–8 Hz) synchronization observed on electroencephalography (EEG) plays an important role in the manipulation of mental representations during working memory (WM) tasks; fronto-temporal synchronization is involved in auditory-verbal WM tasks and fronto-parietal synchronization is involved in visual WM tasks. However, whether or not theta phase synchronization is able to select the to-be-manipulated modalities is uncertain. To address the issue, we recorded EEG data from...

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

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).

Measuring $\\theta_{13}$ via Muon Neutrino to Electron Neutrino Oscillations in the MINOS Experiment

Energy Technology Data Exchange (ETDEWEB)

Toner, Ruth B. [Univ. of Cambridge (United Kingdom). Pembroke College

2011-01-01

One of the primary goals in neutrino physics at the present moment is to make a measurement of the neutrino oscillation parameter $\\theta_{13}$. This parameter, in addition to being unknown, could potentially allow for the introduction of CP violation into the lepton sector. The MINOS long-baseline neutrino oscillation experiment has the ability to make a measurement of this parameter, by looking for the oscillation of muon neutrinos to electron neutrinos between a Near and Far Detector over a distance of 735 km. This thesis discusses the development of an analysis framework to search for this oscillation mode. Two major improvements to pre-existing analysis techniques have been implemented by the author. First, a novel particle ID technique based on strip topology, known as the Library Event Matching (LEM) method, is optimized for use in MINOS. Second, a multiple bin likelihood method is developed to fit the data. These two improvements, when combined, increase MINOS' sensitivity to $\\sin^2(2\\theta_{13})$ by 27\\% over previous analyses. This thesis sees a small excess over background in the Far Detector. A Frequentist interpretation of the data rules out $\\theta_{13}=0$ at 91\\%. A Bayesian interpretation of the data is also presented, placing the most stringent upper boundary on the oscillation parameter to date, at $\\sin^2(2\\theta_{13})<0.09(0.015)$ for the Normal (Inverted) Hierarchy and $\\delta_{CP}=0$.

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

Discrete coupled derivative nonlinear Schroedinger equations and their quasi-periodic solutions

International Nuclear Information System (INIS)

Geng Xianguo; Su Ting

2007-01-01

A hierarchy of nonlinear differential-difference equations associated with a discrete isospectral problem is proposed, in which a typical differential-difference equation is a discrete coupled derivative nonlinear Schroedinger equation. With the help of the nonlinearization of the Lax pairs, the hierarchy of nonlinear differential-difference equations is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows, from which quasi-periodic solutions for these differential-difference equations are obtained resorting to the Riemann-theta functions. Moreover, a (2+1)-dimensional discrete coupled derivative nonlinear Schroedinger equation is proposed and its quasi-periodic solutions are derived

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...

Operating point considerations for the Reference Theta-Pinch Reactor (RTPR)

International Nuclear Information System (INIS)

Krakowski, R.A.; Miller, R.L.; Hagenson, R.L.

1976-01-01

Aspects of the continuing engineering design-point reassessment and optimization of the Reference Theta-Pinch Reactor (RTPR) are discussed. An updated interim design point which achieves a favorable energy balance and involves relaxed technological requirements, which nonetheless satisfy more rigorous physics and engineering constraints, is presented

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

Optical design and performance of F-Theta lenses for high-power and high-precision applications

Science.gov (United States)

Yurevich, V. I.; Grimm, V. A.; Afonyushkin, A. A.; Yudin, K. V.; Gorny, S. G.

2015-09-01

F-Theta lenses are widely used in remote laser processing. Nowadays, a large variety of scanning systems utilizing these devices are commercially available. In this paper, we demonstrate that all practical issues lose their triviality in designing high-performance F-Theta scanning systems. Laser power scaling requires attention to thermally-induced phenomena and ghost reflections. This requirement considerably complicates optimization of the optical configuration of the system and primary aberration correction, even during preliminary design. Obtaining high positioning accuracy requires taking into consideration all probable reasons for processing field distortion. We briefly describe the key engineering relationships and invariants as well as the typical design of a scanner lens and the main field-flattening techniques. Specific emphasis is directed to consideration of the fundamental nonlinearity of two-mirror scanners. To the best of our knowledge, this issue has not been yet studied. We also demonstrate the benefits of our F-Theta lens optimization technique, which uses a plurality of entrance pupils. The problems of eliminating focused ghost reflections and the effects of thermally-induced processes in high-power F-Theta lenses are considered. A set of multi-path 3D processing and laser cutting experiments were conducted and are presented herein to demonstrate the impact of laser beam degradation on the process performance. A selection of our non-standard optical designs is presented.

High-Field Nb3Sn Cos-theta Dipole with Stress Management

Energy Technology Data Exchange (ETDEWEB)

Novitski, Igor [Fermilab; Carmichael, Justin [Fermilab; Kashikhin, Vadim V. [Fermilab; Zlobin, Alexander V. [Fermilab

2017-01-01

Cost-effective superconducting dipole magnets with operating fields up to 16 T are being considered for the LHC en-ergy upgrade (HE-LHC) and a Future Circular Collider (FCC). To demonstrate feasibility of 15 T accelerator quality dipole mag-nets, FNAL as a part of the US-MDP is developing a single-aper-ture Nb3Sn dipole demonstrator based on a 4-layer graded cos-theta coil with 60 mm aperture and cold iron yoke. In parallel, to explore the limit of the Nb3Sn accelerator magnet technology, op-timize magnet design and performance parameters, and reduce magnet cost, magnet design studies are also being performed to push the nominal bore field to 16 T in a 60-mm aperture cos-theta dipole. Results of these studies are reported and discussed in this paper.

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

Robust fractional order differentiators using generalized modulating functions method

KAUST Repository

Liu, Dayan

2015-02-01

This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

Robust fractional order differentiators using generalized modulating functions method

KAUST Repository

Liu, Dayan; Laleg-Kirati, Taous-Meriem

2015-01-01

This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

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

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

Cortico-pontine theta carrier frequency phase shift across sleep/wake states following monoaminergic lesion in rat.

Science.gov (United States)

Kalauzi, Aleksandar; Spasic, Sladjana; Petrovic, Jelena; Ciric, Jelena; Saponjic, Jelena

2012-06-01

This study was aimed to explore the sleep/wake states related cortico-pontine theta carrier frequency phase shift following a systemically induced chemical axotomy of the monoaminergic afferents within a brain of the freely moving rats. Our experiments were performed in 14 adult, male Sprague Dawley rats, chronically implanted for sleep recording. We recorded sleep during baseline condition, following sham injection (saline i.p. 1 ml/kg), and every week for 5 weeks following injection of the systemic neurotoxins (DSP-4 or PCA; 1 ml/kg, i.p.) for chemical axotomy of the locus coeruleus (LC) and dorsal raphe (DR) axon terminals. After sleep/wake states identification, FFT analysis was performed on 5 s epochs. Theta carrier frequency phase shift (∆Φ) was calculated for each epoch by averaging theta Fourier component phase shifts, and the ∆Φ values were plotted for each rat in control condition and 28 days following the monoaminergic lesions, as a time for permanently established DR or LC chemical axotomy. Calculated group averages have shown that ∆Φ increased between pons and cortex significantly in all sleep/wake states (Wake, NREM and REM) following the monoaminergic lesions, with respect to controls. Monoaminergic lesions established the pontine leading role in the brain theta oscillations during all sleep/wake states.

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

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)

Increased coherence among striatal regions in the theta range during attentive wakefulness

Directory of Open Access Journals (Sweden)

G. Lepski

2012-08-01

Full Text Available The striatum, the largest component of the basal ganglia, is usually subdivided into associative, motor and limbic components. However, the electrophysiological interactions between these three subsystems during behavior remain largely unknown. We hypothesized that the striatum might be particularly active during exploratory behavior, which is presumably associated with increased attention. We investigated the modulation of local field potentials (LFPs in the striatum during attentive wakefulness in freely moving rats. To this end, we implanted microelectrodes into different parts of the striatum of Wistar rats, as well as into the motor, associative and limbic cortices. We then used electromyograms to identify motor activity and analyzed the instantaneous frequency, power spectra and partial directed coherence during exploratory behavior. We observed fine modulation in the theta frequency range of striatal LFPs in 92.5 ± 2.5% of all epochs of exploratory behavior. Concomitantly, the theta power spectrum increased in all striatal channels (P 0.7 between the primary motor cortex and the rostral part of the caudatoputamen nucleus, as well as among all striatal channels (P < 0.001. Conclusively, we observed a pattern of strong theta band activation in the entire striatum during attentive wakefulness, as well as a strong coherence between the motor cortex and the entire striatum. We suggest that this activation reflects the integration of motor, cognitive and limbic systems during attentive wakefulness.

Functional substrate for memory function differences between patients with left and right mesial temporal lobe epilepsy associated with hippocampal sclerosis.

Science.gov (United States)

Jin, Seung-Hyun; Chung, Chun Kee

2015-10-01

Little is known about the functional substrate for memory function differences in patients with left or right mesial temporal lobe epilepsy (mTLE) associated with hippocampal sclerosis (HS) from an electrophysiological perspective. To characterize these differences, we hypothesized that hippocampal theta connectivity in the resting-state might be different between patients with left and right mTLE with HS and be correlated with memory performance. Resting-state hippocampal theta connectivity, identified via whole-brain magnetoencephalography, was evaluated. Connectivity and memory function in 41 patients with mTLE with HS (left mTLE=22; right mTLE=19) were compared with those in 46 age-matched healthy controls and 28 patients with focal cortical dysplasia (FCD) but without HS. Connectivity between the right hippocampus and the left middle frontal gyrus was significantly stronger in patients with right mTLE than in patients with left mTLE. Moreover, this connectivity was positively correlated with delayed verbal recall and recognition scores in patients with mTLE. Patients with left mTLE had greater delayed recall impairment than patients with right mTLE and FCD. Similarly, delayed recognition performance was worse in patients with left mTLE than in patients with right mTLE and FCD. No significant differences in memory function between patients with right mTLE and FCD were detected. Patients with right mTLE showed significantly stronger hippocampal theta connectivity between the right hippocampus and left middle frontal gyrus than patients with FCD and left mTLE. Our results suggest that right hippocampal-left middle frontal theta connectivity could be a functional substrate that can account for differences in memory function between patients with left and right mTLE. This functional substrate might be related to different compensatory mechanisms against the structural hippocampal lesions in left and right mTLE groups. Given the positive correlation between

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

Validation Study of CODES Dragonfly Network Model with Theta Cray XC System