Garczynski, V.
1993-01-01
The Courant-Snyder invariants become Lyapunov functions when the β-functions admit non-zero lower, and finite upper bounds. The long-term stability of motion then follows. This alternative criterion for the long-term stability of motion can be generalized to the nonlinear case. A single particle subjected to an arbitrary static magnetic field is considered in some detail, as an example
Symmetries and Invariants of the Time-dependent Oscillator Equation and the Envelope Equation
Qin, Hong
2005-01-01
Single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant* is fundamentally the result of the corresponding symmetry admitted by the oscillator equation with time-dependent frequency.** A careful analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. The symmetries of the envelope equation enable a fast algorithm for finding matched solutions without using the conventional iterative shooting method.
Symmetries and invariants of the oscillator and envelope equations with time-dependent frequency
Hong Qin
2006-05-01
Full Text Available The single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant, a fundamental concept in accelerator physics, is fundamentally a result of the corresponding symmetry admitted by the harmonic oscillator equation with linear time-dependent frequency. It is demonstrated that the Lie algebra of the symmetry group for the oscillator equation with time-dependent frequency is eight dimensional, and is composed of four independent subalgebras. A detailed analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. As an application to accelerator physics, the symmetries of the envelope equation enable a fast numerical algorithm for finding matched solutions without using the conventional iterative Newton’s method, where the envelope equation needs to be numerically integrated once for every iteration, and the Jacobi matrix needs to be calculated for the envelope perturbation.
From tracking code to analysis generalised Courant-Snyder theory for any accelerator model
Forest, Etienne
2016-01-01
This book illustrates a theory well suited to tracking codes, which the author has developed over the years. Tracking codes now play a central role in the design and operation of particle accelerators. The theory is fully explained step by step with equations and actual codes that the reader can compile and run with freely available compilers. In this book, the author pursues a detailed approach based on finite “s”-maps, since this is more natural as long as tracking codes remain at the center of accelerator design. The hierarchical nature of software imposes a hierarchy that puts map-based perturbation theory above any other methods. This is not a personal choice: it follows logically from tracking codes overloaded with a truncated power series algebra package. After defining abstractly and briefly what a tracking code is, the author illustrates most of the accelerator perturbation theory using an actual code: PTC. This book may seem like a manual for PTC; however, the reader is encouraged to explore...
Yan, Y.T.
1991-01-01
The transverse motion of charged particles in a circular accelerator can be well represented by a one-turn high-order Taylor map. For particles without energy deviation, the one-turn Taylor map is a 4-dimensional polynomials of four variables. The four variables are the transverse canonical coordinates and their conjugate momenta. To include the energy deviation (off-momentum) effects, the map has to be parameterized with a smallness factor representing the off-momentum and so the Taylor map becomes a 4-dimensional polynomials of five variables. It is for this type of parameterized Taylor map that a mehtod is presented for converting it into a parameterized Dragt-Finn factorization map. Parameterized nonlinear normal form and parameterized kick factorization can thus be obtained with suitable modification of the existing technique
Steven M. Lund
2009-11-01
Full Text Available Self-consistent Vlasov-Poisson simulations of beams with high space-charge intensity often require specification of initial phase-space distributions that reflect properties of a beam that is well adapted to the transport channel—both in terms of low-order rms (envelope properties as well as the higher-order phase-space structure. Here, we first review broad classes of kinetic distributions commonly in use as initial Vlasov distributions in simulations of unbunched or weakly bunched beams with intense space-charge fields including the following: the Kapchinskij-Vladimirskij (KV equilibrium, continuous-focusing equilibria with specific detailed examples, and various nonequilibrium distributions, such as the semi-Gaussian distribution and distributions formed from specified functions of linear-field Courant-Snyder invariants. Important practical details necessary to specify these distributions in terms of standard accelerator inputs are presented in a unified format. Building on this presentation, a new class of approximate initial kinetic distributions are constructed using transformations that preserve linear focusing, single-particle Courant-Snyder invariants to map initial continuous-focusing equilibrium distributions to a form more appropriate for noncontinuous focusing channels. Self-consistent particle-in-cell simulations are employed to show that the approximate initial distributions generated in this manner are better adapted to the focusing channels for beams with high space-charge intensity. This improved capability enables simulations that more precisely probe intrinsic stability properties and machine performance.
Electron Model of Linear-Field FFAG
Koscielniak, Shane R
2005-01-01
A fixed-field alternating-gradient accelerator (FFAG) that employs only linear-field elements ushers in a new regime in accelerator design and dynamics. The linear-field machine has the ability to compact an unprecedented range in momenta within a small component aperture. With a tune variation which results from the natural chromaticity, the beam crosses many strong, uncorrec-table, betatron resonances during acceleration. Further, relativistic particles in this machine exhibit a quasi-parabolic time-of-flight that cannot be addressed with a fixed-frequency rf system. This leads to a new concept of bucketless acceleration within a rotation manifold. With a large energy jump per cell, there is possibly strong synchro-betatron coupling. A few-MeV electron model has been proposed to demonstrate the feasibility of these untested acceleration features and to investigate them at length under a wide range of operating conditions. This paper presents a lattice optimized for a 1.3 GHz rf, initial technology choices f...
Optics modules for circular accelerator design
Brown, K.L.; Servranckx, R.V.
1986-05-01
The first-order differential equations of motion for a single particle in a closed circular machine are solved, introducing the concepts of phase shift, beta functions, and the Courant-Snyder invariant. The transfer matrix between two points in the machine is derived as a function of the phase shift and the parameters contained in the Courant-Snyder invariant. Typical optical modules used in circular machine designs are introduced and related to their characteristic transfer matrix elements, the phase shift through them, and the Courant-Snyder-Twiss parameters. The systematics of some elementary phase ellipse matching problems between optical modules are discussed. Second-order optical modules are discussed, including how they are used to provide the momentum bandwidth needed for the design of a typical circular machine
Radjavi, Heydar
2003-01-01
This broad survey spans a wealth of studies on invariant subspaces, focusing on operators on separable Hilbert space. Largely self-contained, it requires only a working knowledge of measure theory, complex analysis, and elementary functional analysis. Subjects include normal operators, analytic functions of operators, shift operators, examples of invariant subspace lattices, compact operators, and the existence of invariant and hyperinvariant subspaces. Additional chapters cover certain results on von Neumann algebras, transitive operator algebras, algebras associated with invariant subspaces,
Group quantization on configuration space: Gauge symmetries and linear fields
Navarro, M.; Aldaya, V.; Calixto, M.
1997-01-01
A new, configuration-space picture of a formalism of group quantization, the GAQ formalism, is presented in the context of a previous algebraic generalization. This presentation serves to make a comprehensive discussion in which other extensions of the formalism, principally to incorporate gauge symmetries, are developed as well. Both images are combined in order to analyze, in a systematic manner and with complete generality, the case of linear fields (Abelian current groups). To illustrate these developments we particularize them for several fields and, in particular, we carry out the quantization of the Abelian Chern endash Simons models over an arbitrary closed surface in detail. copyright 1997 American Institute of Physics
Mackrodt, C.; Reeh, H.
1997-01-01
General summational invariants, i.e., conservation laws acting additively on asymptotic particle states, are investigated within a classical framework for point particles with nontrivial scattering. copyright 1997 American Institute of Physics
Olver, Peter J [School of Mathematics, University of Minnesota, Minneapolis, MN 55455 (United States)], E-mail: olver@math.umn.edu
2008-08-29
Given a Lie group acting on a manifold, our aim is to analyze the evolution of differential invariants under invariant submanifold flows. The constructions are based on the equivariant method of moving frames and the induced invariant variational bicomplex. Applications to integrable soliton dynamics, and to the evolution of differential invariant signatures, used in equivalence problems and object recognition and symmetry detection in images, are discussed.
Construction of local and non-local conservation laws for non-linear field equations
Vladimirov, V.S.; Volovich, I.V.
1984-08-01
A method of constructing conserved currents for non-linear field equations is presented. More explicitly for non-linear equations, which can be derived from compatibility conditions of some linear system with a parameter, a procedure of obtaining explicit expressions for local and non-local currents is developed. Some examples such as the classical Heisenberg spin chain and supersymmetric Yang-Mills theory are considered. (author)
Rotationally invariant correlation filtering
Schils, G.F.; Sweeney, D.W.
1985-01-01
A method is presented for analyzing and designing optical correlation filters that have tailored rotational invariance properties. The concept of a correlation of an image with a rotation of itself is introduced. A unified theory of rotation-invariant filtering is then formulated. The unified approach describes matched filters (with no rotation invariance) and circular-harmonic filters (with full rotation invariance) as special cases. The continuum of intermediate cases is described in terms of a cyclic convolution operation over angle. The angular filtering approach allows an exact choice for the continuous trade-off between loss of the correlation energy (or specificity regarding the image) and the amount of rotational invariance desired
Computational invariant theory
Derksen, Harm
2015-01-01
This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be ...
Rotation Invariance Neural Network
Li, Shiyuan
2017-01-01
Rotation invariance and translation invariance have great values in image recognition tasks. In this paper, we bring a new architecture in convolutional neural network (CNN) named cyclic convolutional layer to achieve rotation invariance in 2-D symbol recognition. We can also get the position and orientation of the 2-D symbol by the network to achieve detection purpose for multiple non-overlap target. Last but not least, this architecture can achieve one-shot learning in some cases using thos...
Lorentz invariance with an invariant energy scale.
Magueijo, João; Smolin, Lee
2002-05-13
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.
Moriyasu, K.
1978-01-01
A pedagogical approach to gauge invariance is presented which is based on the analogy between gauge transformations and relativity. By using the concept of an internal space, purely geometrical arguments are used to teach the physical ideas behind gauge invariance. Many of the results are applicable to general gauge theories
Measurement invariance versus selection invariance: Is fair selection possible?
Borsboom, D.; Romeijn, J.W.; Wicherts, J.M.
2008-01-01
This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement
Measurement invariance versus selection invariance : Is fair selection possible?
Borsboom, Denny; Romeijn, Jan-Willem; Wicherts, Jelte M.
This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement
Invariance Signatures: Characterizing contours by their departures from invariance
Squire, David; Caelli, Terry M.
1997-01-01
In this paper, a new invariant feature of two-dimensional contours is reported: the Invariance Signature. The Invariance Signature is a measure of the degree to which a contour is invariant under a variety of transformations, derived from the theory of Lie transformation groups. It is shown that the Invariance Signature is itself invariant under shift, rotation and scaling of the contour. Since it is derived from local properties of the contour, it is well-suited to a neural network implement...
Infinite sets of conservation laws for linear and non-linear field equations
Niederle, J.
1984-01-01
The work was motivated by a desire to understand group theoretically the existence of an infinite set of conservation laws for non-interacting fields and to carry over these conservation laws to the case of interacting fields. The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of its space-time symmetry group was established. It is shown that in the case of the Korteweg-de Vries (KdV) equation to each symmetry of the corresponding linear equation delta sub(o)uxxx=u sub() determined by an element of the enveloping algebra of the space translation algebra, there corresponds a symmetry of the full KdV equation
Morozov, Albert D; Dragunov, Timothy N; Malysheva, Olga V
1999-01-01
This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. The authors have created a special Windows 95 application called WInSet, which allows one to visualize the invariant sets. A WInSet installation disk is enclosed with the book.The book consists of two parts. Part I contains a description of WInSet and a list of the built-in invariant sets which can be plotted using the program. This part is intended for a wide audience with interests ranging from dynamical
Cosmological disformal invariance
Domènech, Guillem; Sasaki, Misao [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Naruko, Atsushi, E-mail: guillem.domenech@yukawa.kyoto-u.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)
2015-10-01
The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a disformal transformation is made.
Algorithms in invariant theory
Sturmfels, Bernd
2008-01-01
J. Kung and G.-C. Rota, in their 1984 paper, write: "Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics". The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems.
Coordinate-invariant regularization
Halpern, M.B.
1987-01-01
A general phase-space framework for coordinate-invariant regularization is given. The development is geometric, with all regularization contained in regularized DeWitt Superstructures on field deformations. Parallel development of invariant coordinate-space regularization is obtained by regularized functional integration of the momenta. As representative examples of the general formulation, the regularized general non-linear sigma model and regularized quantum gravity are discussed. copyright 1987 Academic Press, Inc
Moller-Nielsen, Thomas [University of Oxford (United Kingdom)
2014-07-01
Physicists and philosophers have long claimed that the symmetries of our physical theories - roughly speaking, those transformations which map solutions of the theory into solutions - can provide us with genuine insight into what the world is really like. According to this 'Invariance Principle', only those quantities which are invariant under a theory's symmetries should be taken to be physically real, while those quantities which vary under its symmetries should not. Physicists and philosophers, however, are generally divided (or, indeed, silent) when it comes to explaining how such a principle is to be justified. In this paper, I spell out some of the problems inherent in other theorists' attempts to justify this principle, and sketch my own proposed general schema for explaining how - and when - the Invariance Principle can indeed be used as a legitimate tool of metaphysical inference.
Perez-Nadal, Guillem [Universidad de Buenos Aires, Buenos Aires (Argentina)
2017-07-15
We consider a non-relativistic free scalar field theory with a type of anisotropic scale invariance in which the number of coordinates ''scaling like time'' is generically greater than one. We propose the Cartesian product of two curved spaces, the metric of each space being parameterized by the other space, as a notion of curved background to which the theory can be extended. We study this type of geometries, and find a family of extensions of the theory to curved backgrounds in which the anisotropic scale invariance is promoted to a local, Weyl-type symmetry. (orig.)
Qin, Hong; Chung, Moses; Davidson, Ronald C.
2009-01-01
In an uncoupled lattice, the Kapchinskij-Vladimirskij (KV) distribution function first analyzed in 1959 is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high- intensity beams including self-fields in a self-consistent manner. The KV solution is generalized here to high-intensity beams in a coupled transverse lattice using the recently developed generalized Courant-Snyder invariant for coupled transverse dynamics. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space, determined by the generalized matrix envelope equation.
Hermiticity and gauge invariance
Treder, H.J.
1987-01-01
In the Theory of Hermitian Relativity (HRT) the postulates of hermiticity and gauge invariance are formulated in different ways, due to a different understanding of the idea of hermiticity. However all hermitian systems of equations have to satisfy Einstein's weak system of equations being equivalent to Einstein-Schroedinger equations. (author)
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.
Invariant differential operators
Dobrev, Vladimir K
2016-01-01
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory.
Invariant differential operators
Dobrev, Vladimir K
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory.
Bramson, B.D.
1978-01-01
An isolated system in general relativity makes a transition between stationary states. It is shown that the spin vectors of the system, long before and long after the emission of radiation, are supertranslation invariant and, hence, independent of the choice of Minkowski observation space. (author)
Invariants of generalized Lie algebras
Agrawala, V.K.
1981-01-01
Invariants and invariant multilinear forms are defined for generalized Lie algebras with arbitrary grading and commutation factor. Explicit constructions of invariants and vector operators are given by contracting invariant forms with basic elements of the generalized Lie algebra. The use of the matrix of a linear map between graded vector spaces is emphasized. With the help of this matrix, the concept of graded trace of a linear operator is introduced, which is a rich source of multilinear forms of degree zero. To illustrate the use of invariants, a characteristic identity similar to that of Green is derived and a few Racah coefficients are evaluated in terms of invariants
Properties of invariant modelling and invariant glueing of vector fields
Petukhov, V.R.
1987-01-01
Invariant modelling and invariant glueing of both continuous (rates and accelerations) and descrete vector fields, gradient and divergence cases are considered. The following appendices are discussed: vector fields in crystals, crystal disclinations, topological charges and their fields
Status of time reversal invariance
Henley, E.M.
1989-01-01
Time Reversal Invariance is introduced, and theories for its violation are reviewed. The present experimental and theoretical status of Time Reversal Invariance and tests thereof will be presented. Possible future tests will be discussed. 30 refs., 2 figs., 1 tab
Analytic invariants of boundary links
Garoufalidis, Stavros; Levine, Jerome
2001-01-01
Using basic topology and linear algebra, we define a plethora of invariants of boundary links whose values are power series with noncommuting variables. These turn out to be useful and elementary reformulations of an invariant originally defined by M. Farber.
Moment invariants for particle beams
Lysenko, W.P.; Overley, M.S.
1988-01-01
The rms emittance is a certain function of second moments in 2-D phase space. It is preserved for linear uncoupled (1-D) motion. In this paper, the authors present new functions of moments that are invariants for coupled motion. These invariants were computed symbolically using a computer algebra system. Possible applications for these invariants are discussed. Also, approximate moment invariants for nonlinear motion are presented
Reducing Lookups for Invariant Checking
Thomsen, Jakob Grauenkjær; Clausen, Christian; Andersen, Kristoffer Just
2013-01-01
This paper helps reduce the cost of invariant checking in cases where access to data is expensive. Assume that a set of variables satisfy a given invariant and a request is received to update a subset of them. We reduce the set of variables to inspect, in order to verify that the invariant is still...
Conformal invariance in supergravity
Bergshoeff, E.A.
1983-01-01
In this thesis the author explains the role of conformal invariance in supergravity. He presents the complete structure of extended conformal supergravity for N <= 4. The outline of this work is as follows. In chapter 2 he briefly summarizes the essential properties of supersymmetry and supergravity and indicates the use of conformal invariance in supergravity. The idea that the introduction of additional symmetry transformations can make clear the structure of a field theory is not reserved to supergravity only. By means of some simple examples it is shown in chapter 3 how one can always introduce additional gauge transformations in a theory of massive vector fields. Moreover it is shown how the gauge invariant formulation sometimes explains the quantum mechanical properties of the theory. In chapter 4 the author defines the conformal transformations and summarizes their main properties. He explains how these conformal transformations can be used to analyse the structure of gravity. The supersymmetric extension of these results is discussed in chapter 5. Here he describes as an example how N=1 supergravity can be reformulated in a conformally-invariant way. He also shows that beyond N=1 the gauge fields of the superconformal symmetries do not constitute an off-shell field representation of extended conformal supergravity. Therefore, in chapter 6, a systematic method to construct the off-shell formulation of all extended conformal supergravity theories with N <= 4 is developed. As an example he uses this method to construct N=1 conformal supergravity. Finally, in chapter 7 N=4 conformal supergravity is discussed. (Auth.)
Flusser, Jan; Kautský, J.; Šroubek, Filip
2010-01-01
Roč. 86, č. 1 (2010), s. 72-86 ISSN 0920-5691 R&D Projects: GA MŠk 1M0572; GA ČR GA102/08/1593 Institutional research plan: CEZ:AV0Z10750506 Keywords : Implicit invariants * Orthogonal polynomials * Polynomial image deformation Subject RIV: BD - Theory of Information Impact factor: 4.930, year: 2010 http://library.utia.cas.cz/separaty/2009/ZOI/flusser-0329394.pdf
Suk, Tomáš; Flusser, Jan
2004-01-01
Roč. 26, č. 10 (2004), s. 1364-1367 ISSN 0162-8828 R&D Projects: GA ČR GA201/03/0675 Institutional research plan: CEZ:AV0Z1075907 Keywords : projective transform * moment invariants * object recognition Subject RIV: JD - Computer Applications, Robotics Impact factor: 4.352, year: 2004 http://library.utia.cas.cz/prace/20040112.pdf
Method of chronokinemetrical invariants
Vladimirov, Yu.S.; Shelkovenko, A.Eh.
1976-01-01
A particular case of a general dyadic method - the method of chronokinemetric invariants is formulated. The time-like dyad vector is calibrated in a chronometric way, and the space-like vector - in a kinemetric way. Expressions are written for the main physical-geometrical values of the dyadic method and for differential operators. The method developed may be useful for predetermining the reference system of a single observer, and also for studying problems connected with emission and absorption of gravitational and electromagnetic waves [ru
Viability, invariance and applications
Carja, Ovidiu; Vrabie, Ioan I
2007-01-01
The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.The book includes the most important necessary and sufficient conditions for viability starting with Nagumo's Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In th...
Donaldson invariants in algebraic geometry
Goettsche, L.
2000-01-01
In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)
Remarks on the E-invariant and the Casson invariant
Seade, J.
1991-08-01
In this work a framed manifold means a pair (M,F) consisting of a closed C ∞ , stably parallelizable manifold M, together with a trivialization F of its stable tangent bundle. The purpose of this work is to understand and determine in higher dimensions the invariant h(M,F) appearing in connection with the Adams e-invariants. 28 refs
Invariant and Absolute Invariant Means of Double Sequences
Abdullah Alotaibi
2012-01-01
Full Text Available We examine some properties of the invariant mean, define the concepts of strong σ-convergence and absolute σ-convergence for double sequences, and determine the associated sublinear functionals. We also define the absolute invariant mean through which the space of absolutely σ-convergent double sequences is characterized.
Kauffman, L.; Saleur, H.
1991-01-01
Various aspects of knot theory are discussed when fermionic degrees of freedom are taken into account in the braid group representations and in the state models. It is discussed how the R matrix for the Alexander polynomial arises from the Fox differential calculus, and how it is related to the quantum group U q gl(1,1). New families of solutions of the Yang Baxter equation obtained from ''linear'' representations of the braid group and exterior algebra are investigated. State models associated with U q sl(n,m), and in the case n=m=1 a state model for the multivariable Alexander polynomial are studied. Invariants of links in solid handlebodies are considered and it is shown how the non trivial topology lifts the boson fermion degeneracy is present in S 3 . (author) 36 refs
Wulan, Hasi
2017-01-01
This monograph summarizes the recent major achievements in Möbius invariant QK spaces. First introduced by Hasi Wulan and his collaborators, the theory of QK spaces has developed immensely in the last two decades, and the topics covered in this book will be helpful to graduate students and new researchers interested in the field. Featuring a wide range of subjects, including an overview of QK spaces, QK-Teichmüller spaces, K-Carleson measures and analysis of weight functions, this book serves as an important resource for analysts interested in this area of complex analysis. Notes, numerous exercises, and a comprehensive up-to-date bibliography provide an accessible entry to anyone with a standard graduate background in real and complex analysis.
Permutationally invariant state reconstruction
Moroder, Tobias; Hyllus, Philipp; Tóth, Géza
2012-01-01
Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large-scale opti...... optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations easily allow reconstruction of a state of 20 qubits in a few minutes on a standard computer.......-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum...
A linear-field plasma jet for generating a brush-shaped laminar plume at atmospheric pressure
Li, Xuechen; Jia, Pengying, E-mail: plasmalab@126.com [College of Physics Science and Technology, Hebei University, Baoding 071002 (China); Key Laboratory of Photo-Electronics Information Materials of Hebei Province, Baoding 071002 (China); Li, Jiyuan; Chu, Jingdi; Zhang, Panpan [College of Physics Science and Technology, Hebei University, Baoding 071002 (China)
2016-06-15
A linear-field plasma jet composed of line-to-plate electrodes is used to generate a large-scale brush-shaped plasma plume with flowing argon used as working gas. Through electrical measurement and fast photography, it is found that the plasma plume bridges the two electrodes for the discharge in the positive voltage half-cycle, which behaves like fast moving plasma bullets directed from the anode to the cathode. Compared with the positive discharge, the negative discharge only develops inside the nozzle and propagates much slower. Results also indicate that the gas temperature of the plume is close to room temperature, which is promising for biomedical application.
Finite type invariants and fatgraphs
Andersen, Jørgen Ellegaard; Bene, Alex; Meilhan, Jean-Baptiste Odet Thierry
2010-01-01
–Murakami–Ohtsuki of the link invariant of Andersen–Mattes–Reshetikhin computed relative to choices determined by the fatgraph G; this provides a basic connection between 2d geometry and 3d quantum topology. For each fixed G, this invariant is shown to be universal for homology cylinders, i.e., G establishes an isomorphism...
Novel topological invariants and anomalies
Hirayama, M.; Sugimasa, N.
1987-01-01
It is shown that novel topological invariants are associated with a class of Dirac operators. Trace formulas which are similar to but different from Callias's formula are derived. Implications of these topological invariants to anomalies in quantum field theory are discussed. A new class of anomalies are calculated for two models: one is two dimensional and the other four dimensional
Hidden scale invariance of metals
Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.
2015-01-01
Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general “hidden” scale invariance...... of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Grüneisen parameter, are in good agreement with experimental values for the 16 elements where reliable data were...... available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant...
Physical Invariants of Intelligence
Zak, Michail
2010-01-01
A program of research is dedicated to development of a mathematical formalism that could provide, among other things, means by which living systems could be distinguished from non-living ones. A major issue that arises in this research is the following question: What invariants of mathematical models of the physics of systems are (1) characteristic of the behaviors of intelligent living systems and (2) do not depend on specific features of material compositions heretofore considered to be characteristic of life? This research at earlier stages has been reported, albeit from different perspectives, in numerous previous NASA Tech Briefs articles. To recapitulate: One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Mathematical models of motor dynamics are used to simulate the observable physical behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. At the time of reporting the information for this article, the focus of this research was upon the following aspects of the formalism: Intelligence is considered to be a means by which a living system preserves itself and improves its ability to survive and is further considered to manifest itself in feedback from the mental dynamics to the motor dynamics. Because of the feedback from the mental dynamics, the motor dynamics attains quantum-like properties: The trajectory of the physical aspect of the system in the space of dynamical variables splits into a family of different trajectories, and each of those trajectories can be chosen with a probability prescribed by the mental dynamics. From a slightly different perspective
Cohomological invariants in Galois cohomology
Garibaldi, Skip; Serre, Jean Pierre
2003-01-01
This volume is concerned with algebraic invariants, such as the Stiefel-Whitney classes of quadratic forms (with values in Galois cohomology mod 2) and the trace form of �tale algebras (with values in the Witt ring). The invariants are analogues for Galois cohomology of the characteristic classes of topology. Historically, one of the first examples of cohomological invariants of the type considered here was the Hasse-Witt invariant of quadratic forms. The first part classifies such invariants in several cases. A principal tool is the notion of versal torsor, which is an analogue of the universal bundle in topology. The second part gives Rost's determination of the invariants of G-torsors with values in H^3(\\mathbb{Q}/\\mathbb{Z}(2)), when G is a semisimple, simply connected, linear group. This part gives detailed proofs of the existence and basic properties of the Rost invariant. This is the first time that most of this material appears in print.
Mass generation within conformal invariant theories
Flato, M.; Guenin, M.
1981-01-01
The massless Yang-Mills theory is strongly conformally invariant and renormalizable; however, when masses are introduced the theory becomes nonrenormalizable and weakly conformally invariant. Conditions which recover strong conformal invariance are discussed in the letter. (author)
Test of charge conjugation invariance
Nefkens, B.M.K.; Prakhov, S.; Gaardestig, A.; Clajus, M.; Marusic, A.; McDonald, S.; Phaisangittisakul, N.; Price, J.W.; Starostin, A.; Tippens, W.B.; Allgower, C.E.; Spinka, H.; Bekrenev, V.; Koulbardis, A.; Kozlenko, N.; Kruglov, S.; Lopatin, I.; Briscoe, W.J.; Shafi, A.; Comfort, J.R.
2005-01-01
We report on the first determination of upper limits on the branching ratio (BR) of η decay to π 0 π 0 γ and to π 0 π 0 π 0 γ. Both decay modes are strictly forbidden by charge conjugation (C) invariance. Using the Crystal Ball multiphoton detector, we obtained BR(η→π 0 π 0 γ) -4 at the 90% confidence level, in support of C invariance of isoscalar electromagnetic interactions of the light quarks. We have also measured BR(η→π 0 π 0 π 0 γ) -5 at the 90% confidence level, in support of C invariance of isovector electromagnetic interactions
Relating measurement invariance, cross-level invariance, and multilevel reliability
Jak, S.; Jorgensen, T.D.
2017-01-01
Data often have a nested, multilevel structure, for example when data are collected from children in classrooms. This kind of data complicate the evaluation of reliability and measurement invariance, because several properties can be evaluated at both the individual level and the cluster level, as well as across levels. For example, cross-level invariance implies equal factor loadings across levels, which is needed to give latent variables at the two levels a similar interpretation. Reliabili...
Invariant and semi-invariant probabilistic normed spaces
Ghaemi, M.B. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: mghaemi@iust.ac.ir; Lafuerza-Guillen, B. [Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, Almeria E-04120 (Spain)], E-mail: blafuerz@ual.es; Saiedinezhad, S. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: ssaiedinezhad@yahoo.com
2009-10-15
Probabilistic metric spaces were introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger . We introduce the concept of semi-invariance among the PN spaces. In this paper we will find a sufficient condition for some PN spaces to be semi-invariant. We will show that PN spaces are normal spaces. Urysohn's lemma, and Tietze extension theorem for them are proved.
The Dynamical Invariant of Open Quantum System
Wu, S. L.; Zhang, X. Y.; Yi, X. X.
2015-01-01
The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the dynamical invariant for the closed quantum system, the evolution of the dynamical invariant for the open quantum system is no longer unitary, and the eigenvalues of it are time-dependent. Since any hermitian operator fulfilling dynamical invariant condition ...
On density of the Vassiliev invariants
Røgen, Peter
1999-01-01
The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots......The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots...
Invariant measures in brain dynamics
Boyarsky, Abraham; Gora, Pawel
2006-01-01
This note concerns brain activity at the level of neural ensembles and uses ideas from ergodic dynamical systems to model and characterize chaotic patterns among these ensembles during conscious mental activity. Central to our model is the definition of a space of neural ensembles and the assumption of discrete time ensemble dynamics. We argue that continuous invariant measures draw the attention of deeper brain processes, engendering emergent properties such as consciousness. Invariant measures supported on a finite set of ensembles reflect periodic behavior, whereas the existence of continuous invariant measures reflect the dynamics of nonrepeating ensemble patterns that elicit the interest of deeper mental processes. We shall consider two different ways to achieve continuous invariant measures on the space of neural ensembles: (1) via quantum jitters, and (2) via sensory input accompanied by inner thought processes which engender a 'folding' property on the space of ensembles
The invariant theory of matrices
Concini, Corrado De
2017-01-01
This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of m\\times m matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving the first fundamental theorem that describes a set of generators in the ring of invariants, and the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case...
Object recognition by implicit invariants
Flusser, Jan; Kautsky, J.; Šroubek, Filip
2007-01-01
Roč. 2007, č. 4673 (2007), s. 856-863 ISSN 0302-9743. [Computer Analysis of Images and Patterns. Vienna, 27.08.2007-29.08.2007] R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : Invariants * implicit invariants * moments * orthogonal polynomials * nonlinear object deformation Subject RIV: JD - Computer Applications, Robotics Impact factor: 0.402, year: 2005 http:// staff .utia.cas.cz/sroubekf/papers/CAIP_07.pdf
Classification of simple current invariants
Gato-Rivera, Beatriz
1992-01-01
We summarize recent work on the classification of modular invariant partition functions that can be obtained with simple currents in theories with a center (Z_p)^k with p prime. New empirical results for other centers are also presented. Our observation that the total number of invariants is monodromy-independent for (Z_p)^k appears to be true in general as well. (Talk presented in the parallel session on string theory of the Lepton-Photon/EPS Conference, Geneva, 1991.)
Affine invariants of convex polygons.
Flusser, Jan
2002-01-01
In this correspondence, we prove that the affine invariants, for image registration and object recognition, proposed recently by Yang and Cohen (see ibid., vol.8, no.7, p.934-46, July 1999) are algebraically dependent. We show how to select an independent and complete set of the invariants. The use of this new set leads to a significant reduction of the computing complexity without decreasing the discrimination power.
Identification of invariant measures of interacting systems
Chen Jinwen
2004-01-01
In this paper we provide an approach for identifying certain mixture representations of some invariant measures of interacting stochastic systems. This is related to the problem of ergodicity of certain extremal invariant measures that are translation invariant. Corresponding to these, results concerning the existence of invariant measures and certain weak convergence of the systems are also provided
Link invariants from finite Coxeter racks
Nelson, Sam; Wieghard, Ryan
2008-01-01
We study Coxeter racks over $\\mathbb{Z}_n$ and the knot and link invariants they define. We exploit the module structure of these racks to enhance the rack counting invariants and give examples showing that these enhanced invariants are stronger than the unenhanced rack counting invariants.
Nonlocal, yet translation invariant, constraints for rotationally invariant slave bosons
Ayral, Thomas; Kotliar, Gabriel
The rotationally-invariant slave boson (RISB) method is a lightweight framework allowing to study the low-energy properties of complex multiorbital problems currently out of the reach of more comprehensive, yet more computationally demanding methods such as dynamical mean field theory. In the original formulation of this formalism, the slave-boson constraints can be made nonlocal by enlarging the unit cell and viewing the quantum states enclosed in this new unit cell as molecular levels. In this work, we extend RISB to constraints which are nonlocal while preserving translation invariance. We apply this extension to the Hubbard model.
Invariant probabilities of transition functions
Zaharopol, Radu
2014-01-01
The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of t...
Invariants of triangular Lie algebras
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-01-01
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated
Dark coupling and gauge invariance
Gavela, M.B.; Honorez, L. Lopez; Mena, O.; Rigolin, S.
2010-01-01
We study a coupled dark energy-dark matter model in which the energy-momentum exchange is proportional to the Hubble expansion rate. The inclusion of its perturbation is required by gauge invariance. We derive the linear perturbation equations for the gauge invariant energy density contrast and velocity of the coupled fluids, and we determine the initial conditions. The latter turn out to be adiabatic for dark energy, when assuming adiabatic initial conditions for all the standard fluids. We perform a full Monte Carlo Markov Chain likelihood analysis of the model, using WMAP 7-year data
Numeric invariants from multidimensional persistence
Skryzalin, Jacek [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Carlsson, Gunnar [Stanford Univ., Stanford, CA (United States)
2017-05-19
In this paper, we analyze the space of multidimensional persistence modules from the perspectives of algebraic geometry. We first build a moduli space of a certain subclass of easily analyzed multidimensional persistence modules, which we construct specifically to capture much of the information which can be gained by using multidimensional persistence over one-dimensional persistence. We argue that the global sections of this space provide interesting numeric invariants when evaluated against our subclass of multidimensional persistence modules. Lastly, we extend these global sections to the space of all multidimensional persistence modules and discuss how the resulting numeric invariants might be used to study data.
Dark Coupling and Gauge Invariance
Gavela, M B; Mena, O; Rigolin, S
2010-01-01
We study a coupled dark energy-dark matter model in which the energy-momentum exchange is proportional to the Hubble expansion rate. The inclusion of its perturbation is required by gauge invariance. We derive the linear perturbation equations for the gauge invariant energy density contrast and velocity of the coupled fluids, and we determine the initial conditions. The latter turn out to be adiabatic for dark energy, when assuming adiabatic initial conditions for all the standard fluids. We perform a full Monte Carlo Markov Chain likelihood analysis of the model, using WMAP 7-year data.
Relating measurement invariance, cross-level invariance, and multilevel reliability
Jak, S.; Jorgensen, T.D.
2017-01-01
Data often have a nested, multilevel structure, for example when data are collected from children in classrooms. This kind of data complicate the evaluation of reliability and measurement invariance, because several properties can be evaluated at both the individual level and the cluster level, as
Dattoli, G.; Torre, A.
1991-12-01
The theory of partial and ordinary differential equations is reformulated within the context of a unifying formalism, which combines the algebric ordering procedure with the matrix image technique. The problems of the invariant forms, associated with ordinary differential equations, is approached within the framework of the same formalism, thus dispalying interesting relations with the Courant-Snyder invariant, introduced in the analysis of the motion of a charged particle along a transport channel, and with the Lewis-Riesenfeld invariant, introduced in the analysis of the evolution of a quantum harmonic oscillator with time-dependent frequency. Particular attention is devoted to the paraxial propagation of an electromagnetic wave through a non homogeneous medium and to the paraxial motion of a charged particle beam in a circular accelerator.
Entendue invariance in speckle fields
Medina, F.F.; Garcia-Sucerquia, J.; Henao, R.; Trivi, M.
2000-04-01
Experimental evidence is shown that confirms the Entendue invariance in speckle fields. Because of this condition, the coherence patch of the speckle field can be significantly greater than the mean size of the speckles, as is shown by double exposure speckle interferometry. (author)
Geometric Invariants and Object Recognition.
1992-08-01
University of Chicago Press. Maybank , S.J. [1992], "The Projection of Two Non-coplanar Conics", in Geometric Invariance in Machine Vision, eds. J.L...J.L. Mundy and A. Zisserman, MIT Press, Cambridge, MA. Mundy, J.L., Kapur, .. , Maybank , S.J., and Quan, L. [1992a] "Geometric Inter- pretation of
On renormalization-invariant masses
Fleming, H.; Furuya, K.
1978-02-01
It is shown that spontaneous generation of renormalization invariant mass is possible in infra-red stable theories with more than one coupling constant. If relations among the coupling constants are permitted the effect can be made compatible with pertubation theory
Gauge invariance of string fields
Banks, T.; Peskin, M.E.
1985-10-01
Some work done to understand the appearance of gauge bosons and gravitons in string theories is reported. An action has been constructed for free (bosonic) string field theory which is invariant under an infinite set of gauge transformations which include Yang-Mills transformations and general coordinate transformations as special cases. 15 refs., 1 tab
Continuous Integrated Invariant Inference, Phase I
National Aeronautics and Space Administration — The proposed project will develop a new technique for invariant inference and embed this and other current invariant inference and checking techniques in an...
Gauge-invariant cosmological density perturbations
Sasaki, Misao.
1986-06-01
Gauge-invariant formulation of cosmological density perturbation theory is reviewed with special emphasis on its geometrical aspects. Then the gauge-invariant measure of the magnitude of a given perturbation is presented. (author)
Constructing Invariant Fairness Measures for Surfaces
Gravesen, Jens; Ungstrup, Michael
1998-01-01
of the size of this vector field is used as the fairness measure on the family.Six basic 3rd order invariants satisfying two quadratic equations are defined. They form a complete set in the sense that any invariant 3rd order function can be written as a function of the six basic invariants together...
Gauge invariance and holographic renormalization
Keun-Young Kim
2015-10-01
Full Text Available We study the gauge invariance of physical observables in holographic theories under the local diffeomorphism. We find that gauge invariance is intimately related to the holographic renormalization: the local counter terms defined in the boundary cancel most of gauge dependences of the on-shell action as well as the divergences. There is a mismatch in the degrees of freedom between the bulk theory and the boundary one. We resolve this problem by noticing that there is a residual gauge symmetry (RGS. By extending the RGS such that it satisfies infalling boundary condition at the horizon, we can understand the problem in the context of general holographic embedding of a global symmetry at the boundary into the local gauge symmetry in the bulk.
Gauge invariant fractional electromagnetic fields
Lazo, Matheus Jatkoske
2011-01-01
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. -- Highlights: → We propose a fractional Lagrangian formulation for fractional Maxwell's fields. → We obtain gauge invariant fractional electromagnetic fields. → Our generalized fractional Maxwell's field is spatially symmetrical. → We discuss the non-causality of the theory.
Gauge invariant fractional electromagnetic fields
Lazo, Matheus Jatkoske, E-mail: matheuslazo@furg.br [Instituto de Matematica, Estatistica e Fisica - FURG, Rio Grande, RS (Brazil)
2011-09-26
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. -- Highlights: → We propose a fractional Lagrangian formulation for fractional Maxwell's fields. → We obtain gauge invariant fractional electromagnetic fields. → Our generalized fractional Maxwell's field is spatially symmetrical. → We discuss the non-causality of the theory.
Invariance for Single Curved Manifold
Castro, Pedro Machado Manhaes de
2012-01-01
Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Testing CPT invariance with neutrinos
Ohlsson, Tommy
2003-01-01
We investigate possible tests of CPT invariance on the level of event rates at neutrino factories. We do not assume any specific model, but phenomenological differences in the neutrino-antineutrino masses and mixing angles in a Lorentz invariance preserving context, which could be induced by physics beyond the Standard Model. We especially focus on the muon neutrino and antineutrino disappearance channels in order to obtain constraints on the neutrino-antineutrino mass and mixing angle differences. In a typical neutrino factory setup simulation, we find, for example, that vertical bar m 3 - m-bar 3 vertical bar $1.9 · 10 -4 eV and vertical bar ≡ 23 - ≡-bar 23 vertical bar < or approx. 2 deg
Invariance for Single Curved Manifold
Castro, Pedro Machado Manhaes de
2012-08-01
Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Wetterich, C.
2018-06-01
We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.
Molecular invariants: atomic group valence
Mundim, K.C.; Giambiagi, M.; Giambiagi, M.S. de.
1988-01-01
Molecular invariants may be deduced in a very compact way through Grassman algebra. In this work, a generalized valence is defined for an atomic group; it reduces to the Known expressions for the case of an atom in a molecule. It is the same of the correlations between the fluctions of the atomic charges qc and qd (C belongs to the group and D does not) around their average values. Numerical results agree with chemical expectation. (author) [pt
Holographic multiverse and conformal invariance
Garriga, Jaume [Departament de Física Fonamental i Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, 08193 Barcelona (Spain); Vilenkin, Alexander, E-mail: jaume.garriga@ub.edu, E-mail: vilenkin@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, 212 College Ave., Medford, MA 02155 (United States)
2009-11-01
We consider a holographic description of the inflationary multiverse, according to which the wave function of the universe is interpreted as the generating functional for a lower dimensional Euclidean theory. We analyze a simple model where transitions between inflationary vacua occur through bubble nucleation, and the inflating part of spacetime consists of de Sitter regions separated by thin bubble walls. In this model, we present some evidence that the dual theory is conformally invariant in the UV.
Holographic multiverse and conformal invariance
Garriga, Jaume; Vilenkin, Alexander
2009-01-01
We consider a holographic description of the inflationary multiverse, according to which the wave function of the universe is interpreted as the generating functional for a lower dimensional Euclidean theory. We analyze a simple model where transitions between inflationary vacua occur through bubble nucleation, and the inflating part of spacetime consists of de Sitter regions separated by thin bubble walls. In this model, we present some evidence that the dual theory is conformally invariant in the UV
Random SU(2) invariant tensors
Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei
2018-04-01
SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n = 4. In this paper, we show that for n > 4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.
Example 1 (Word Problem): This is taken from Em- peror's New Mind ... is as follows. We are given a set of equalities of words .... pictures without proper definitions, and without being ... a polynomial, or in other words it could be a collection of.
Dynamical topological invariant after a quantum quench
Yang, Chao; Li, Linhu; Chen, Shu
2018-02-01
We show how to define a dynamical topological invariant for one-dimensional two-band topological systems after a quantum quench. By analyzing general two-band models of topological insulators, we demonstrate that the reduced momentum-time manifold can be viewed as a series of submanifolds S2, and thus we are able to define a dynamical topological invariant on each of the spheres. We also unveil the intrinsic relation between the dynamical topological invariant and the difference in the topological invariant of the initial and final static Hamiltonian. By considering some concrete examples, we illustrate the calculation of the dynamical topological invariant and its geometrical meaning explicitly.
Cartan invariants and event horizon detection
Brooks, D.; Chavy-Waddy, P. C.; Coley, A. A.; Forget, A.; Gregoris, D.; MacCallum, M. A. H.; McNutt, D. D.
2018-04-01
We show that it is possible to locate the event horizon of a black hole (in arbitrary dimensions) by the zeros of certain Cartan invariants. This approach accounts for the recent results on the detection of stationary horizons using scalar polynomial curvature invariants, and improves upon them since the proposed method is computationally less expensive. As an application, we produce Cartan invariants that locate the event horizons for various exact four-dimensional and five-dimensional stationary, asymptotically flat (or (anti) de Sitter), black hole solutions and compare the Cartan invariants with the corresponding scalar curvature invariants that detect the event horizon.
Translationally invariant and non-translationally invariant empirical effective interactions
Golin, M.; Zamick, L.
1975-01-01
In this work empirical deficiencies of the core-renormalized realistic effective interactions are examined and simple corrective potentials are sought. The inability of the current realistic interactions to account for the energies of isobaric analog states is noted, likewise they are unable to reproduce the changes in the single-particle energies, as one goes from one closed shell to another. It is noted that the Schiffer interaction gives better results for these gross properties and this is attributed to a combination of several facts. First, to the inclusion of long range terms in the Schiffer potential, then to the presence of relative p-state terms (l=1), in addition to the usual relative s-state terms (l=0). The strange shape of the above interaction is further attributed to the fact that it is translationally invariant whereas the theory of core-polarization yields non-translationally invariant potentials. Consequently, as a correction to the monopole deficiencies of the realistic interactions the term Vsub(mon)=ar 2 (1)r 2 (2)+r 2 (1)+β[r 4 (1)r 2 (2)r 4 (2) ] is proposed. (Auth.)
Conformal invariance in harmonic superspace
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1987-01-01
In the present paper we show how the N = 2 superconformal group is realised in harmonic superspace and examine conformal invariance of N = 2 off-shell theories. We believe that the example of N = O self-dual Yang-Mills equations can serve as an instructive introduction to the subject of harmonic superspace and this is examined. The rigid N = 2 conformal supersymmetry and its local version, i.e. N = 2 conformal supergravity is also discussed. The paper is a contribution to the book commemorating the sixtieth birthday of E.S. Fradkin. (author)
Gauge invariant fractional electromagnetic fields
Lazo, Matheus Jatkoske
2011-09-01
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators.
Invariant metrics for Hamiltonian systems
Rangarajan, G.; Dragt, A.J.; Neri, F.
1991-05-01
In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs
Admissible invariant distributions on reductive
Harish-Chandra; Paul J Sally, Jr
1999-01-01
Harish-Chandra presented these lectures on admissible invariant distributions for p-adic groups at the Institute for Advanced Study in the early 1970s. He published a short sketch of this material as his famous "Queen's Notes". This book, which was prepared and edited by DeBacker and Sally, presents a faithful rendering of Harish-Chandra's original lecture notes. The main purpose of Harish-Chandra's lectures was to show that the character of an irreducible admissible representation of a connected reductive p-adic group G is represented by a locally summable function on G. A key ingredient in this proof is the study of the Fourier transforms of distributions on \\mathfrak g, the Lie algebra of G. In particular, Harish-Chandra shows that if the support of a G-invariant distribution on \\mathfrak g is compactly generated, then its Fourier transform has an asymptotic expansion about any semisimple point of \\mathfrak g. Harish-Chandra's remarkable theorem on the local summability of characters for p-adic groups was ...
Scale-invariant gravity: geometrodynamics
Anderson, Edward; Barbour, Julian; Foster, Brendan; Murchadha, Niall O
2003-01-01
We present a scale-invariant theory, conformal gravity, which closely resembles the geometrodynamical formulation of general relativity (GR). While previous attempts to create scale-invariant theories of gravity have been based on Weyl's idea of a compensating field, our direct approach dispenses with this and is built by extension of the method of best matching w.r.t. scaling developed in the parallel particle dynamics paper by one of the authors. In spatially compact GR, there is an infinity of degrees of freedom that describe the shape of 3-space which interact with a single volume degree of freedom. In conformal gravity, the shape degrees of freedom remain, but the volume is no longer a dynamical variable. Further theories and formulations related to GR and conformal gravity are presented. Conformal gravity is successfully coupled to scalars and the gauge fields of nature. It should describe the solar system observations as well as GR does, but its cosmology and quantization will be completely different
Synthesizing Modular Invariants for Synchronous Code
Pierre-Loic Garoche
2014-12-01
Full Text Available In this paper, we explore different techniques to synthesize modular invariants for synchronous code encoded as Horn clauses. Modular invariants are a set of formulas that characterizes the validity of predicates. They are very useful for different aspects of analysis, synthesis, testing and program transformation. We describe two techniques to generate modular invariants for code written in the synchronous dataflow language Lustre. The first technique directly encodes the synchronous code in a modular fashion. While in the second technique, we synthesize modular invariants starting from a monolithic invariant. Both techniques, take advantage of analysis techniques based on property-directed reachability. We also describe a technique to minimize the synthesized invariants.
Link invariants for flows in higher dimensions
Garcia-Compean, Hugo; Santos-Silva, Roberto
2010-01-01
Linking numbers in higher dimensions and their generalization including gauge fields are studied in the context of BF theories. The linking numbers associated with n-manifolds with smooth flows generated by divergence-free p-vector fields, endowed with an invariant flow measure, are computed in the context of quantum field theory. They constitute invariants of smooth dynamical systems (for nonsingular flows) and generalize previous proposals of invariants. In particular, they generalize Arnold's asymptotic Hopf invariant from three to higher dimensions. This invariant is generalized by coupling with a non-Abelian gauge flat connection with nontrivial holonomy. The computation of the asymptotic Jones-Witten invariants for flows is naturally extended to dimension n=2p+1. Finally, we give a possible interpretation and implementation of these issues in the context of 11-dimensional supergravity and string theory.
Recent progress in invariant pattern recognition
Arsenault, Henri H.; Chang, S.; Gagne, Philippe; Gualdron Gonzalez, Oscar
1996-12-01
We present some recent results in invariant pattern recognition, including methods that are invariant under two or more distortions of position, orientation and scale. There are now a few methods that yield good results under changes of both rotation and scale. Some new methods are introduced. These include locally adaptive nonlinear matched filters, scale-adapted wavelet transforms and invariant filters for disjoint noise. Methods using neural networks will also be discussed, including an optical method that allows simultaneous classification of multiple targets.
Modular invariance, chiral anomalies and contact terms
Kutasov, D.
1988-03-01
The chiral anomaly in heterotic strings with full and partial modular invariance in D=2n+2 dimensions is calculated. The boundary terms which were present in previous calculations are shown to be cancelled in the modular invariant case by contact terms, which can be obtained by an appropriate analytic continuation. The relation to the low energy field theory is explained. In theories with partial modular invariance, an expression for the anomaly is obtained and shown to be non zero in general. (author)
Wilson loop invariants from WN conformal blocks
Oleg Alekseev
2015-12-01
Full Text Available Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern–Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for WN conformal blocks with one component in the fundamental representation and another component in a rectangular representation of SU(N, which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of WN algebra.
A functional LMO invariant for Lagrangian cobordisms
Cheptea, Dorin; Habiro, Kazuo; Massuyeau, Gwénaël
2008-01-01
Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le–Murakami–Ohtsuki invariant of homology three-spheres to a functor from the category of Lagrangian cobordisms to a certain category...... of Jacobi diagrams. We prove some properties of this functorial LMO invariant, including its universality among rational finite-type invariants of Lagrangian cobordisms. Finally, we apply the LMO functor to the study of homology cylinders from the point of view of their finite-type invariants....
Energy principle with global invariants
Bhattacharjee, A.; Dewar, R.L.
1981-04-01
A variational principle is proposed for constructing equilibria with minimum energy in a toroidal plasma. The total energy is minimized subject to global invariants which act as constraints during relaxation of the plasma. These global integrals of motion are preserved exactly for all idea motions and approximately for a wide class of resistive motions. We assume, specifically, that relaxation of the plasma is dominated by a tearing mode of single helicity. Equilibria with realistic current density and pressure profiles may be constructed in this theory, which is also used here to study current penetration in tokamaks. The second variation of the free energy functional is computed. It is shown that if the second variation of any equilibrium constructed in this theory is positive, the equilibrium satisfies the necessary and sufficient conditions for ideal stability
Scale-invariant extended inflation
Holman, R.; Kolb, E.W.; Vadas, S.L.; Wang, Y.
1991-01-01
We propose a model of extended inflation which makes use of the nonlinear realization of scale invariance involving the dilaton coupled to an inflaton field whose potential admits a metastable ground state. The resulting theory resembles the Jordan-Brans-Dicke version of extended inflation. However, quantum effects, in the form of the conformal anomaly, generate a mass for the dilaton, thus allowing our model to evade the problems of the original version of extended inflation. We show that extended inflation can occur for a wide range of inflaton potentials with no fine-tuning of dimensionless parameters required. Furthermore, we also find that it is quite natural for the extended-inflation period to be followed by an epoch of slow-rollover inflation as the dilaton settles down to the minimum of its induced potential
Conformal invariance from nonconformal gravity
Meissner, Krzysztof A.; Nicolai, Hermann
2009-01-01
We discuss the conditions under which classically conformally invariant models in four dimensions can arise out of nonconformal (Einstein) gravity. As an 'existence proof' that this is indeed possible we show how to derive N=4 super Yang-Mills theory with any compact gauge group G from nonconformal gauged N=4 supergravity as a special flat space limit. We stress the role that the anticipated UV finiteness of the (so far unknown) underlying theory of quantum gravity would have to play in such a scheme, as well as the fact that the masses of elementary particles would have to arise via quantum gravitational effects which mimic the conformal anomalies of standard (flat space) UV divergent quantum field theory.
Modular invariance and stochastic quantization
Ordonez, C.R.; Rubin, M.A.; Zwanziger, D.
1989-01-01
In Polyakov path integrals and covariant closed-string field theory, integration over Teichmueller parameters must be restricted by hand to a single modular region. This problem has an analog in Yang-Mills gauge theory---namely, the Gribov problem, which can be resolved by the method of stochastic gauge fixing. This method is here employed to quantize a simple modular-invariant system: the Polyakov point particle. In the limit of a large gauge-fixing force, it is shown that suitable choices for the functional form of the gauge-fixing force can lead to a restriction of Teichmueller integration to a single modular region. Modifications which arise when applying stochastic quantization to a system in which the volume of the orbits of the gauge group depends on a dynamical variable, such as a Teichmueller parameter, are pointed out, and the extension to Polyakov strings and covariant closed-string field theory is discussed
Elementary introduction to conformal invariance
Grandati, Y.
1992-01-01
These notes constitute an elementary introduction to the concept of conformal invariance and its applications to the study of bidimensional critical phenomena. The aim is to give an access as pedestrian as possible to this vast subject. After a brief account of the general properties of conformal transformation in D dimensions, we study more specifically the case D = 2. The center of the discussion is then the consequences of the action of this symmetry group on bidimensional field theories, and in particular the links between the representations of the Virasoro algebra and the structure of the correlation functions of conformal field theories. Finally after showing how the Ising model reduces to a Majorana fermionic field theory, we see how the general formalism previously discussed can be applied to the Ising case at the critical point. (orig.)
Negation switching invariant signed graphs
Deepa Sinha
2014-04-01
Full Text Available A signed graph (or, $sigraph$ in short is a graph G in which each edge x carries a value $\\sigma(x \\in \\{-, +\\}$ called its sign. Given a sigraph S, the negation $\\eta(S$ of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs $S_{1}$ and $S_{2}$ on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus' or `-' (`minus' to vertices of $S_{1}$ such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains $S_{2}$. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and $\\eta (S$ are signed isomorphic.
Translational invariance in bag model
Megahed, F.
1981-10-01
In this thesis, the effect of restoring the translational invariance to an approximation to the MIT bag model on the calculation of deep inelastic structure functions is investigated. In chapter one, the model and its major problems are reviewed and Dirac's method of quantisation is outlined. This method is used in chapter two to quantise a two-dimensional complex scalar bag and formal expressions for the form factor and the structure functions are obtained. In chapter three, the expression for the structure function away from the Bjorken limit is studied. The corrections to the L 0 - approximation to the structure function is calculated in chapter four and it is shown to be large. Finally, in chapter five, a bag-like model for kinematic corrections to structure functions is introduced and agreement with data between 2 and 6 (GeV/C) 2 is obtained. (author)
Chirality invariance and 'chiral' fields
Ziino, G.
1978-01-01
The new field model derived in the present paper actually gives a definite answer to three fundamental questions concerning elementary-particle physics: 1) The phenomenological dualism between parity and chirality invariance: it would be only an apparent display of a general 'duality' principle underlying the intrinsic nature itself of (spin 1/2) fermions and expressed by the anticommutativity property between scalar and pseudoscalar charges. 2) The real physical meaning of V - A current structure: it would exclusively be connected to the one (just pointed out) of chiral fields themselves. 3) The unjustified apparent oddness shown by Nature in weak interactions, for the fact of picking out only one of the two (left- and right-handed) fermion 'chiral' projections: the key to such a 'mystery' would just be provided by the consequences of the dual and partial character of the two fermion-antifermion field bases. (Auth.)
Correction of dispersion and the betatron functions in the CEBAF accelerator
Lebedev, V.A.; Bickley, M.; Schaffner, S.; Zeijts, J. van; Krafft, G.A.; Watson, C.
1996-01-01
During the commissioning of the CEBAF accelerator, correction of dispersion and momentum compaction, and, to a lesser extent, transverse transfer matrices were essential for robust operation. With changing machine conditions, repeated correction was found necessary. To speed the diagnostic process the authors developed a method which allows one to rapidly track the machine optics. The method is based on measuring the propagation of 30 Hz modulated betatron oscillations downstream of a point of perturbation. Compared to the usual methods of dispersion or difference orbit measurement, synchronous detection of the beam displacement, as measured by beam position monitors, offers significantly improved speed and accuracy of the measurements. The beam optics of the accelerator was altered to decrease lattice sensitivity at critical points and to simplify control of the betatron function match. The calculation of the Courant-Snyder invariant from signals of each pair of nearby beam position monitors has allowed one to perform on-line measurement and correction of the lattice properties
Steinmann, O [Bielefeld Univ. (F.R. Germany). Fakultaet fuer Physik
1975-01-01
Massive quantum electrodynamics of the electron is formulated as an LSZ theory of the electromagnetic field F(..mu nu..) and the electron-positron fields PSI. The interaction is introduced with the help of mathematically well defined subsidiary conditions. These are: 1) gauge invariance of the first kind, assumed to be generated by a conserved current j(..mu..); 2) the homogeneous Maxwell equations and a massive version of the inhomogeneous Maxwell equations; 3) a minimality condition concerning the high momentum behaviour of the theory. The inhomogeneous Maxwell equation is a linear differential equation connecting Fsub(..mu nu..) with the current Jsub(..mu..). No Lagrangian, no non-linear field equations, and no explicit expression of Jsub(..mu..) in terms of PSI, anti-PSI are needed. It is shown in perturbation theory that the proposed conditions fix the physically relevant (i.e. observable) quantities of the theory uniquely.
Spontaneously broken abelian gauge invariant supersymmetric model
Mainland, G.B.; Tanaka, K.
A model is presented that is invariant under an Abelian gauge transformation and a modified supersymmetry transformation. This model is broken spontaneously, and the interplay between symmetry breaking, Goldstone particles, and mass breaking is studied. In the present model, spontaneously breaking the Abelian symmetry of the vacuum restores the invariance of the vacuum under a modified supersymmetry transformation. (U.S.)
Scale invariant Volkov–Akulov supergravity
S. Ferrara
2015-10-01
Full Text Available A scale invariant goldstino theory coupled to supergravity is obtained as a standard supergravity dual of a rigidly scale-invariant higher-curvature supergravity with a nilpotent chiral scalar curvature. The bosonic part of this theory describes a massless scalaron and a massive axion in a de Sitter Universe.
Pattern recognition: invariants in 3D
Proriol, J.
1992-01-01
In e + e - events, the jets have a spherical 3D symmetry. A set of invariants are defined for 3D objects with a spherical symmetry. These new invariants are used to tag the number of jets in e + e - events. (K.A.) 3 refs
Triality invariance in the N=2 superstring
Castellani, Leonardo; Grassi, Pietro Antonio; Sommovigo, Luca
2009-01-01
We prove the discrete triality invariance of the N=2 NSR superstring moving in a D=2+2 target space. We find that triality holds also in the Siegel-Berkovits formulation of the selfdual superstring. A supersymmetric generalization of Cayley's hyperdeterminant, based on a quartic invariant of the SL(2|1) 3 superalgebra, is presented.
Triality invariance in the N=2 superstring
Castellani, Leonardo [Dipartimento di Scienze e Tecnologie Avanzate and INFN Gruppo collegato di Alessandria, Universita del Piemonte Orientale, Via Teresa Michel 11, 15121 Alessandria (Italy)], E-mail: leonardo.castellani@mfn.unipmn.it; Grassi, Pietro Antonio [Dipartimento di Scienze e Tecnologie Avanzate and INFN Gruppo collegato di Alessandria, Universita del Piemonte Orientale, Via Teresa Michel 11, 15121 Alessandria (Italy)], E-mail: pietro.grassi@mfn.unipmn.it; Sommovigo, Luca [Dipartimento di Scienze e Tecnologie Avanzate and INFN Gruppo collegato di Alessandria, Universita del Piemonte Orientale, Via Teresa Michel 11, 15121 Alessandria (Italy)], E-mail: luca.sommovigo@mfn.unipmn.it
2009-07-20
We prove the discrete triality invariance of the N=2 NSR superstring moving in a D=2+2 target space. We find that triality holds also in the Siegel-Berkovits formulation of the selfdual superstring. A supersymmetric generalization of Cayley's hyperdeterminant, based on a quartic invariant of the SL(2|1){sup 3} superalgebra, is presented.
Borromean surgery formula for the Casson invariant
Meilhan, Jean-Baptiste Odet Thierry
2008-01-01
It is known that every oriented integral homology 3-sphere can be obtained from S3 by a finite sequence of Borromean surgeries. We give an explicit formula for the variation of the Casson invariant under such a surgery move. The formula involves simple classical invariants, namely the framing...
Invariant subsets under compact quantum group actions
Huang, Huichi
2012-01-01
We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact metrizable spaces with infinitely many points are not quantum homogeneous spaces.
Action priors for learning domain invariances
Rosman, Benjamin S
2015-04-01
Full Text Available behavioural invariances in the domain, by identifying actions to be prioritised in local contexts, invariant to task details. This information has the effect of greatly increasing the speed of solving new problems. We formalise this notion as action priors...
Quantum Hall Conductivity and Topological Invariants
Reyes, Andres
2001-04-01
A short survey of the theory of the Quantum Hall effect is given emphasizing topological aspects of the quantization of the conductivity and showing how topological invariants can be derived from the hamiltonian. We express these invariants in terms of Chern numbers and show in precise mathematical terms how this relates to the Kubo formula.
Conformal invariance and two-dimensional physics
Zuber, J.B.
1993-01-01
Actually, physicists and mathematicians are very interested in conformal invariance: geometric transformations which keep angles. This symmetry is very important for two-dimensional systems as phase transitions, string theory or node mathematics. In this article, the author presents the conformal invariance and explains its usefulness
Knot invariants derived from quandles and racks
Kamada, Seiichi
2002-01-01
The homology and cohomology of quandles and racks are used in knot theory: given a finite quandle and a cocycle, we can construct a knot invariant. This is a quick introductory survey to the invariants of knots derived from quandles and racks.
Synthesizing chaotic maps with prescribed invariant densities
Rogers, Alan; Shorten, Robert; Heffernan, Daniel M.
2004-01-01
The Inverse Frobenius-Perron Problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this Letter, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized
Scale invariant Volkov–Akulov supergravity
Ferrara, S., E-mail: sergio.ferrara@cern.ch [Th-Ph Department, CERN, CH-1211 Geneva 23 (Switzerland); INFN – Laboratori Nazionali di Frascati, Via Enrico Fermi 40, 00044 Frascati (Italy); Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1547 (United States); Porrati, M., E-mail: mp9@nyu.edu [Th-Ph Department, CERN, CH-1211 Geneva 23 (Switzerland); CCPP, Department of Physics, NYU, 4 Washington Pl., New York, NY 10003 (United States); Sagnotti, A., E-mail: sagnotti@sns.it [Th-Ph Department, CERN, CH-1211 Geneva 23 (Switzerland); Scuola Normale Superiore and INFN, Piazza dei Cavalieri 7, 56126 Pisa (Italy)
2015-10-07
A scale invariant goldstino theory coupled to supergravity is obtained as a standard supergravity dual of a rigidly scale-invariant higher-curvature supergravity with a nilpotent chiral scalar curvature. The bosonic part of this theory describes a massless scalaron and a massive axion in a de Sitter Universe.
Invariance group of the Finster metric function
Asanov, G.S.
1985-01-01
An invariance group of the Finsler metric function is introduced and studied that directly generalized the respective concept (a group of Euclidean rolations) of the Rieman geometry. A sequential description of the isotopic invariance of physical fields on the base of the Finsler geometry is possible in terms of this group
A test for ordinal measurement invariance
Ligtvoet, R.; Millsap, R.E.; Bolt, D.M.; van der Ark, L.A.; Wang, W.-C.
2015-01-01
One problem with the analysis of measurement invariance is the reliance of the analysis on having a parametric model that accurately describes the data. In this paper an ordinal version of the property of measurement invariance is proposed, which relies only on nonparametric restrictions. This
The usage of color invariance in SURF
Meng, Gang; Jiang, Zhiguo; Zhao, Danpei
2009-10-01
SURF (Scale Invariant Feature Transform) is a robust local invariant feature descriptor. However, SURF is mainly designed for gray images. In order to make use of the information provided by color (mainly RGB channels), this paper presents a novel colored local invariant feature descriptor, CISURF (Color Invariance based SURF). The proposed approach builds the descriptors in a color invariant space, which stems from Kubelka-Munk model and provides more valuable information than the gray space. Compared with the conventional SURF and SIFT descriptors, the experimental results show that descriptors created by CISURF is more robust to the circumstance changes such as the illumination direction, illumination intensity, and the viewpoints, and are more suitable for the deep space background objects.
BRDF invariant stereo using light transport constancy.
Wang, Liang; Yang, Ruigang; Davis, James E
2007-09-01
Nearly all existing methods for stereo reconstruction assume that scene reflectance is Lambertian and make use of brightness constancy as a matching invariant. We introduce a new invariant for stereo reconstruction called light transport constancy (LTC), which allows completely arbitrary scene reflectance (bidirectional reflectance distribution functions (BRDFs)). This invariant can be used to formulate a rank constraint on multiview stereo matching when the scene is observed by several lighting configurations in which only the lighting intensity varies. In addition, we show that this multiview constraint can be used with as few as two cameras and two lighting configurations. Unlike previous methods for BRDF invariant stereo, LTC does not require precisely configured or calibrated light sources or calibration objects in the scene. Importantly, the new constraint can be used to provide BRDF invariance to any existing stereo method whenever appropriate lighting variation is available.
Conformal invariance in hydrodynamic turbulence
Falkovich, Gregory
2007-01-01
This short survey is written by a physicist. It contains neither theorems nor precise definitions. Its main content is a description of the results of numerical solution of the equations of fluid mechanics in the regime of developed turbulence. Due to limitations of computers, the results are not very precise. Despite being neither exact nor rigorous, the findings may nevertheless be of interest for mathematicians. The main result is that the isolines of some scalar fields (vorticity, temperature) in two-dimensional turbulence belong to the class of conformally invariant curves called SLE (Scramm-Loewner evolution) curves. First, this enables one to predict and find a plethora of quantitative relations going far beyond what was known previously about turbulence. Second, it suggests relations between phenomena that seemed unrelated, like the Euler equation and critical percolation. Third, it shows that one is able to get exact analytic results in statistical hydrodynamics. In short, physicists have found something unexpected and hope that mathematicians can help to explain it.
Stereo Correspondence Using Moment Invariants
Premaratne, Prashan; Safaei, Farzad
Autonomous navigation is seen as a vital tool in harnessing the enormous potential of Unmanned Aerial Vehicles (UAV) and small robotic vehicles for both military and civilian use. Even though, laser based scanning solutions for Simultaneous Location And Mapping (SLAM) is considered as the most reliable for depth estimation, they are not feasible for use in UAV and land-based small vehicles due to their physical size and weight. Stereovision is considered as the best approach for any autonomous navigation solution as stereo rigs are considered to be lightweight and inexpensive. However, stereoscopy which estimates the depth information through pairs of stereo images can still be computationally expensive and unreliable. This is mainly due to some of the algorithms used in successful stereovision solutions require high computational requirements that cannot be met by small robotic vehicles. In our research, we implement a feature-based stereovision solution using moment invariants as a metric to find corresponding regions in image pairs that will reduce the computational complexity and improve the accuracy of the disparity measures that will be significant for the use in UAVs and in small robotic vehicles.
A scale invariance criterion for LES parametrizations
Urs Schaefer-Rolffs
2015-01-01
Full Text Available Turbulent kinetic energy cascades in fluid dynamical systems are usually characterized by scale invariance. However, representations of subgrid scales in large eddy simulations do not necessarily fulfill this constraint. So far, scale invariance has been considered in the context of isotropic, incompressible, and three-dimensional turbulence. In the present paper, the theory is extended to compressible flows that obey the hydrostatic approximation, as well as to corresponding subgrid-scale parametrizations. A criterion is presented to check if the symmetries of the governing equations are correctly translated into the equations used in numerical models. By applying scaling transformations to the model equations, relations between the scaling factors are obtained by demanding that the mathematical structure of the equations does not change.The criterion is validated by recovering the breakdown of scale invariance in the classical Smagorinsky model and confirming scale invariance for the Dynamic Smagorinsky Model. The criterion also shows that the compressible continuity equation is intrinsically scale-invariant. The criterion also proves that a scale-invariant turbulent kinetic energy equation or a scale-invariant equation of motion for a passive tracer is obtained only with a dynamic mixing length. For large-scale atmospheric flows governed by the hydrostatic balance the energy cascade is due to horizontal advection and the vertical length scale exhibits a scaling behaviour that is different from that derived for horizontal length scales.
Feedback-Driven Dynamic Invariant Discovery
Zhang, Lingming; Yang, Guowei; Rungta, Neha S.; Person, Suzette; Khurshid, Sarfraz
2014-01-01
Program invariants can help software developers identify program properties that must be preserved as the software evolves, however, formulating correct invariants can be challenging. In this work, we introduce iDiscovery, a technique which leverages symbolic execution to improve the quality of dynamically discovered invariants computed by Daikon. Candidate invariants generated by Daikon are synthesized into assertions and instrumented onto the program. The instrumented code is executed symbolically to generate new test cases that are fed back to Daikon to help further re ne the set of candidate invariants. This feedback loop is executed until a x-point is reached. To mitigate the cost of symbolic execution, we present optimizations to prune the symbolic state space and to reduce the complexity of the generated path conditions. We also leverage recent advances in constraint solution reuse techniques to avoid computing results for the same constraints across iterations. Experimental results show that iDiscovery converges to a set of higher quality invariants compared to the initial set of candidate invariants in a small number of iterations.
Topological excitations in U(1) -invariant theories
Savit, R.
1977-01-01
A class of U(1) -invariant theories in d dimensions is introduced on a lattice. These theories are labeled by a simplex number s, with 1 < or = s < d. The case with s = 1 is the X-Y model; and s = 2 gives compact photodynamics. An exact duality transformation is applied to show that the U(1) -invariant theory in d dimensions with simplex number s is the same as a similar theory in d dimensions but which is Z /sub infinity/-invariant and has simplex number s = d-s. This dual theory describes the topological excitations of the original theory. These excitations are of dimension s - 1
Inflation in a Scale Invariant Universe
Ferreira, Pedro G. [Oxford U.; Hill, Christopher T. [Fermilab; Noller, Johannes [Zurich U.; Ross, Graham G. [Oxford U., Theor. Phys.
2018-02-16
A scale-invariant universe can have a period of accelerated expansion at early times: inflation. We use a frame-invariant approach to calculate inflationary observables in a scale invariant theory of gravity involving two scalar fields - the spectral indices, the tensor to scalar ratio, the level of isocurvature modes and non-Gaussianity. We show that scale symmetry leads to an exact cancellation of isocurvature modes and that, in the scale-symmetry broken phase, this theory is well described by a single scalar field theory. We find the predictions of this theory strongly compatible with current observations.
Multiperiod Maximum Loss is time unit invariant.
Kovacevic, Raimund M; Breuer, Thomas
2016-01-01
Time unit invariance is introduced as an additional requirement for multiperiod risk measures: for a constant portfolio under an i.i.d. risk factor process, the multiperiod risk should equal the one period risk of the aggregated loss, for an appropriate choice of parameters and independent of the portfolio and its distribution. Multiperiod Maximum Loss over a sequence of Kullback-Leibler balls is time unit invariant. This is also the case for the entropic risk measure. On the other hand, multiperiod Value at Risk and multiperiod Expected Shortfall are not time unit invariant.
View synthesis using parallax invariance
Dornaika, Fadi
2001-06-01
View synthesis becomes a focus of attention of both the computer vision and computer graphics communities. It consists of creating novel images of a scene as it would appear from novel viewpoints. View synthesis can be used in a wide variety of applications such as video compression, graphics generation, virtual reality and entertainment. This paper addresses the following problem. Given a dense disparity map between two reference images, we would like to synthesize a novel view of the same scene associated with a novel viewpoint. Most of the existing work is relying on building a set of 3D meshes which are then projected onto the new image (the rendering process is performed using texture mapping). The advantages of our view synthesis approach are as follows. First, the novel view is specified by a rotation and a translation which are the most natural way to express the virtual location of the camera. Second, the approach is able to synthesize highly realistic images whose viewing position is significantly far away from the reference viewpoints. Third, the approach is able to handle the visibility problem during the synthesis process. Our developed framework has two main steps. The first step (analysis step) consists of computing the homography at infinity, the epipoles, and thus the parallax field associated with the reference images. The second step (synthesis step) consists of warping the reference image into a new one, which is based on the invariance of the computed parallax field. The analysis step is working directly on the reference views, and only need to be performed once. Examples of synthesizing novel views using either feature correspondences or dense disparity map have demonstrated the feasibility of the proposed approach.
Invariant metric for nonlinear symplectic maps
One popular method of treating Hamiltonian systems perturbatively is the Lie ... to be a symmetric, positive definite, bilinear form that is invariant under the action of ... we apply the above procedure to a FODO lattice (a common component of a.
Testing Lorentz invariance of dark matter
Blas, Diego; Sibiryakov, Sergey
2012-01-01
We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we represent through a dynamical timelike vector field. If DM does not obey Lorentz invariance, it couples to this vector field. We find that this coupling affects the inertial mass of small DM halos which no longer satisfy the equivalence principle. For large enough lumps of DM we identify a (chameleon) mechanism that restores the inertial mass to its standard value. As a consequence, the dynamics of gravitational clustering are modified. Two prominent effects are a scale dependent enhancement in the growth of large scale structure and a scale dependent bias between DM and baryon density perturbations. The comparison with the measured linear matter power spectrum in principle allows to bound the departure from Lorentz invariance of DM at the per cent level.
Testing Lorentz invariance of dark matter
Blas, Diego [Theory Group, Physics Department, CERN, CH-1211 Geneva 23 (Switzerland); Ivanov, Mikhail M.; Sibiryakov, Sergey, E-mail: diego.blas@cern.ch, E-mail: mm.ivanov@physics.msu.ru, E-mail: sibir@inr.ac.ru [Faculty of Physics, Moscow State University, Vorobjevy Gory, 119991 Moscow (Russian Federation)
2012-10-01
We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we represent through a dynamical timelike vector field. If DM does not obey Lorentz invariance, it couples to this vector field. We find that this coupling affects the inertial mass of small DM halos which no longer satisfy the equivalence principle. For large enough lumps of DM we identify a (chameleon) mechanism that restores the inertial mass to its standard value. As a consequence, the dynamics of gravitational clustering are modified. Two prominent effects are a scale dependent enhancement in the growth of large scale structure and a scale dependent bias between DM and baryon density perturbations. The comparison with the measured linear matter power spectrum in principle allows to bound the departure from Lorentz invariance of DM at the per cent level.
Spectral properties of supersymmetric shape invariant potentials
Keywords. Supersymmetry; shape invariant potential; spectral statistics. ... Pramana – J. Phys., Vol. 70, No. ... the fluctuation properties of different systems whose average behaviours are not the same. ... coefficient c defined as [15] c = ∑.
N = 2 coset compactifictions with nondiagonal invariants
Aldazabal, G.; Allekotte, I.; Font, A.
1992-01-01
In this paper, the authors consider four-dimensional string models obtained by tensoring N = 2 coset theories with nondiagonal modular invariants. The authors present results from a systematic analysis including moddings by discrete symmetries
Conformal invariance of extended spinning particle mechanics
Siegel, W.
1988-01-01
Recently a mechanics action has been considered with extended, local, one-dimensional supersymmetry. The authors show this action is conformally invariant in arbitrary spacetime dimensions, and derive the corresponding quantum mechanical restriction on the Lorentz representations it describes
Ermakov–Lewis invariants and Reid systems
Mancas, Stefan C., E-mail: stefan.mancas@erau.edu [Department of Mathematics, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la presa San José 2055, Col. Lomas 4a Sección, 78216 San Luis Potosí, S.L.P. (Mexico)
2014-06-13
Reid's mth-order generalized Ermakov systems of nonlinear coupling constant α are equivalent to an integrable Emden–Fowler equation. The standard Ermakov–Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m≥3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden–Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy. - Highlights: • Reid systems of order m are connected to Emden–Fowler equations. • General expressions for the Ermakov–Lewis invariants both for m=2 and m≥3 are obtained. • Parametric solutions of the Emden–Fowler equations related to Reid systems are obtained.
Modified dispersion relations, inflation, and scale invariance
Bianco, Stefano; Friedhoff, Victor Nicolai; Wilson-Ewing, Edward
2018-02-01
For a certain type of modified dispersion relations, the vacuum quantum state for very short wavelength cosmological perturbations is scale-invariant and it has been suggested that this may be the source of the scale-invariance observed in the temperature anisotropies in the cosmic microwave background. We point out that for this scenario to be possible, it is necessary to redshift these short wavelength modes to cosmological scales in such a way that the scale-invariance is not lost. This requires nontrivial background dynamics before the onset of standard radiation-dominated cosmology; we demonstrate that one possible solution is inflation with a sufficiently large Hubble rate, for this slow roll is not necessary. In addition, we also show that if the slow-roll condition is added to inflation with a large Hubble rate, then for any power law modified dispersion relation quantum vacuum fluctuations become nearly scale-invariant when they exit the Hubble radius.
Maxwell equations in conformal invariant electrodynamics
Fradkin, E.S.; AN SSSR, Novosibirsk. Inst. Avtomatiki i Ehlektrometrii); Kozhevnikov, A.A.; Palchik, M.Ya.; Pomeransky, A.A.
1983-01-01
We consider a conformal invariant formulation of quantum electrodynamics. Conformal invariance is achieved with a specific mathematical construction based on the indecomposable representations of the conformal group associated with the electromagnetic potential and current. As a corolary of this construction modified expressions for the 3-point Green functions are obtained which both contain transverse parts. They make it possible to formulate a conformal invariant skeleton perturbation theory. It is also shown that the Euclidean Maxwell equations in conformal electrodynamics are manifestations of its kinematical structure: in the case of the 3-point Green functions these equations follow (up to constants) from the conformal invariance while in the case of higher Green functions they are equivalent to the equality of the kernels of the partial wave expansions. This is the manifestation of the mathematical fast of a (partial) equivalence of the representations associated with the potential, current and the field tensor. (orig.)
Invariant Theory (IT) & Standard Monomial Theory (SMT)
2013-07-06
Jul 6, 2013 ... Why invariant theory? (continued). Now imagine algebraic calculations being made, with the two different sets of co-ordinates, about something of geometrical or physical interest concerning the configuration of points, ...
Anomalies and modular invariance in string theory
Schellekens, A.N.; Warner, N.P.
1986-01-01
All known anomaly cancellations of heterotic string theories are derived directly from one-loop modular invariance, and are shown to be related to a property of modular functions of weight 2. Using modular invariance infinite classes of anomaly free field theories are constructed in (8m+2) dimensions for any m. A generating function is obtained for the anomalies of string-related field theories in (8m+2) dimensions. (orig.)
Dynamical invariants for variable quadratic Hamiltonians
Suslov, Sergei K
2010-01-01
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.
Invariant relations in Boussinesq-type equations
Meletlidou, Efi; Pouget, Joeel; Maugin, Gerard; Aifantis, Elias
2004-01-01
A wide class of partial differential equations have at least three conservation laws that remain invariant for certain solutions of them and especially for solitary wave solutions. These conservation laws can be considered as the energy, pseudomomentum and mass integrals of these solutions. We investigate the invariant relation between the energy and the pseudomomentum for solitary waves in two Boussinesq-type equations that come from the theory of elasticity and lattice models
Computer calculation of Witten's 3-manifold invariant
Freed, D.S.; Gompf, R.E.
1991-01-01
Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant. (orig.)
Conformal (WEYL) invariance and Higgs mechanism
Zhao Shucheng.
1991-10-01
A massive Yang-Mills field theory with conformal invariance and gauge invariance is proposed. It involves gravitational and various gauge interactions, in which all the mass terms appear as a uniform form of interaction m(x) KΦ(x). When the conformal symmetry is broken spontaneously and gravitation is ignored, the Higgs field emerges naturally, where the imaginary mass μ can be described as a background curvature. (author). 7 refs
Notes on algebraic invariants for non-commutative dynamical systems
Longo, R [Rome Univ. (Italy). Istituto di Matematica
1979-11-01
We consider an algebraic invariant for non-commutative dynamical systems naturally arising as the spectrum of the modular operator associated to an invariant state, provided certain conditions of mixing type are present. This invariant turns out to be exactly the annihilator of the invariant T of Connes. Further comments are included, in particular on the type of certain algebras of local observables
Construction of time-dependent dynamical invariants: A new approach
Bertin, M. C.; Pimentel, B. M.; Ramirez, J. A.
2012-01-01
We propose a new way to obtain polynomial dynamical invariants of the classical and quantum time-dependent harmonic oscillator from the equations of motion. We also establish relations between linear and quadratic invariants, and discuss how the quadratic invariant can be related to the Ermakov invariant.
De Roover, K.; Timmerman, Marieke; De Leersnyder, J.; Mesquita, B.; Ceulemans, Eva
2014-01-01
The issue of measurement invariance is ubiquitous in the behavioral sciences nowadays as more and more studies yield multivariate multigroup data. When measurement invariance cannot be established across groups, this is often due to different loadings on only a few items. Within the multigroup CFA
Slow feature analysis: unsupervised learning of invariances.
Wiskott, Laurenz; Sejnowski, Terrence J
2002-04-01
Invariant features of temporally varying signals are useful for analysis and classification. Slow feature analysis (SFA) is a new method for learning invariant or slowly varying features from a vectorial input signal. It is based on a nonlinear expansion of the input signal and application of principal component analysis to this expanded signal and its time derivative. It is guaranteed to find the optimal solution within a family of functions directly and can learn to extract a large number of decorrelated features, which are ordered by their degree of invariance. SFA can be applied hierarchically to process high-dimensional input signals and extract complex features. SFA is applied first to complex cell tuning properties based on simple cell output, including disparity and motion. Then more complicated input-output functions are learned by repeated application of SFA. Finally, a hierarchical network of SFA modules is presented as a simple model of the visual system. The same unstructured network can learn translation, size, rotation, contrast, or, to a lesser degree, illumination invariance for one-dimensional objects, depending on only the training stimulus. Surprisingly, only a few training objects suffice to achieve good generalization to new objects. The generated representation is suitable for object recognition. Performance degrades if the network is trained to learn multiple invariances simultaneously.
Quantum implications of a scale invariant regularization
Ghilencea, D. M.
2018-04-01
We study scale invariance at the quantum level in a perturbative approach. For a scale-invariant classical theory, the scalar potential is computed at a three-loop level while keeping manifest this symmetry. Spontaneous scale symmetry breaking is transmitted at a quantum level to the visible sector (of ϕ ) by the associated Goldstone mode (dilaton σ ), which enables a scale-invariant regularization and whose vacuum expectation value ⟨σ ⟩ generates the subtraction scale (μ ). While the hidden (σ ) and visible sector (ϕ ) are classically decoupled in d =4 due to an enhanced Poincaré symmetry, they interact through (a series of) evanescent couplings ∝ɛ , dictated by the scale invariance of the action in d =4 -2 ɛ . At the quantum level, these couplings generate new corrections to the potential, as scale-invariant nonpolynomial effective operators ϕ2 n +4/σ2 n. These are comparable in size to "standard" loop corrections and are important for values of ϕ close to ⟨σ ⟩. For n =1 , 2, the beta functions of their coefficient are computed at three loops. In the IR limit, dilaton fluctuations decouple, the effective operators are suppressed by large ⟨σ ⟩, and the effective potential becomes that of a renormalizable theory with explicit scale symmetry breaking by the DR scheme (of μ =constant).
Knot invariants and higher representation theory
Webster, Ben
2018-01-01
The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for \\mathfrak{sl}_2 and \\mathfrak{sl}_3 and by Mazorchuk-Stroppel and Sussan for \\mathfrak{sl}_n. The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimensional algebras with an explicit diagrammatic presentation, generalizing the cyclotomic quotient of the KLR algebra. When the Lie algebra under consideration is \\mathfrak{sl}_n, the author shows that these categories agree with certain subcategories of parabolic category \\mathcal{O} for \\mathfrak{gl}_k.
Modular categories and 3-manifold invariants
Tureav, V.G.
1992-01-01
The aim of this paper is to give a concise introduction to the theory of knot invariants and 3-manifold invariants which generalize the Jones polynomial and which may be considered as a mathematical version of the Witten invariants. Such a theory was introduced by N. Reshetikhin and the author on the ground of the theory of quantum groups. here we use more general algebraic objects, specifically, ribbon and modular categories. Such categories in particular arise as the categories of representations of quantum groups. The notion of modular category, interesting in itself, is closely related to the notion of modular tensor category in the sense of G. Moore and N. Seiberg. For simplicity we restrict ourselves in this paper to the case of closed 3-manifolds
Spin foam diagrammatics and topological invariance
Girelli, Florian; Oeckl, Robert; Perez, Alejandro
2002-01-01
We provide a simple proof of the topological invariance of the Turaev-Viro model (corresponding to simplicial 3D pure Euclidean gravity with cosmological constant) by means of a novel diagrammatic formulation of the state sum models for quantum BF theories. Moreover, we prove the invariance under more general conditions allowing the state sum to be defined on arbitrary cellular decompositions of the underlying manifold. Invariance is governed by a set of identities corresponding to local gluing and rearrangement of cells in the complex. Due to the fully algebraic nature of these identities our results extend to a vast class of quantum groups. The techniques introduced here could be relevant for investigating the scaling properties of non-topological state sums, proposed as models of quantum gravity in 4D, under refinement of the cellular decomposition
Gromov-Witten invariants and localization
Morrison, David R.
2017-11-01
We give a pedagogical review of the computation of Gromov-Witten invariants via localization in 2D gauged linear sigma models. We explain the relationship between the two-sphere partition function of the theory and the Kähler potential on the conformal manifold. We show how the Kähler potential can be assembled from classical, perturbative, and non-perturbative contributions, and explain how the non-perturbative contributions are related to the Gromov-Witten invariants of the corresponding Calabi-Yau manifold. We then explain how localization enables efficient calculation of the two-sphere partition function and, ultimately, the Gromov-Witten invariants themselves. This is a contribution to the review issue ‘Localization techniques in quantum field theories’ (ed V Pestun and M Zabzine) which contains 17 chapters, available at [1].
Change of adiabatic invariant near the separatrix
Bulanov, S.V.
1995-10-01
The properties of particle motion in the vicinity of the separatrix in a phase plane are investigated. The change of adiabatic invariant value due to the separatrix crossing is evaluated as a function of a perturbation parameter magnitude and a phase of a particle for time dependent Hamiltonians. It is demonstrated that the change of adiabatic invariant value near the separatrix birth is much larger than that in the case of the separatrix crossing near the saddle point in a phase plane. The conditions of a stochastic regime to appear around the separatrix are found. The results are applied to study the longitudinal invariant behaviour of charged particles near singular lines of the magnetic field. (author). 22 refs, 9 figs
Differential invariants in nonclassical models of hydrodynamics
Bublik, Vasily V.
2017-10-01
In this paper, differential invariants are used to construct solutions for equations of the dynamics of a viscous heat-conducting gas and the dynamics of a viscous incompressible fluid modified by nanopowder inoculators. To describe the dynamics of a viscous heat-conducting gas, we use the complete system of Navier—Stokes equations with allowance for heat fluxes. Mathematical description of the dynamics of liquid metals under high-energy external influences (laser radiation or plasma flow) includes, in addition to the Navier—Stokes system of an incompressible viscous fluid, also heat fluxes and processes of nonequilibrium crystallization of a deformable fluid. Differentially invariant solutions are a generalization of partially invariant solutions, and their active study for various models of continuous medium mechanics is just beginning. Differentially invariant solutions can also be considered as solutions with differential constraints; therefore, when developing them, the approaches and methods developed by the science schools of academicians N. N. Yanenko and A. F. Sidorov will be actively used. In the construction of partially invariant and differentially invariant solutions, there are overdetermined systems of differential equations that require a compatibility analysis. The algorithms for reducing such systems to involution in a finite number of steps are described by Cartan, Finikov, Kuranishi, and other authors. However, the difficultly foreseeable volume of intermediate calculations complicates their practical application. Therefore, the methods of computer algebra are actively used here, which largely helps in solving this difficult problem. It is proposed to use the constructed exact solutions as tests for formulas, algorithms and their software implementations when developing and creating numerical methods and computational program complexes. This combination of effective numerical methods, capable of solving a wide class of problems, with
Fractal properties of critical invariant curves
Hunt, B.R.; Yorke, J.A.; Khanin, K.M.; Sinai, Y.G.
1996-01-01
We examine the dimension of the invariant measure for some singular circle homeomorphisms for a variety of rotation numbers, through both the thermodynamic formalism and numerical computation. The maps we consider include those induced by the action of the standard map on an invariant curve at the critical parameter value beyond which the curve is destroyed. Our results indicate that the dimension is universal for a given type of singularity and rotation number, and that among all rotation numbers, the golden mean produces the largest dimension
Spontaneously broken supersymmetry and Poincare invariance
Tata, X.R.; Sudarshan, E.C.G.; Schechter, J.M.
1982-12-01
It is argued that the spontaneous breakdown of global supersymmetry is consistent with unbroken Poincare invariance if and only if the supersymmetry algebra A = 0 is understood to mean the invariance of the dynamical variables phi under the transformations generated by the algebra, i.e. [A, phi] = 0 rather than as an operator equation. It is further argued that this weakening of the algebra does not alter any of the conclusions about supersymmetric quantum field theories that have been obtained using the original (stronger) form of the algebra
Perturbative string theory in BRST invariant formalism
Di Vecchia, P.; Hornfeck, K.; Frau, M.; Lerda, A.
1988-01-01
In this talk we present a constructive and very explicit way of calculating multiloop amplitudes in string theories. The main ingredients are the BRST invariant N String Vertex and the BRST invariant twisted propagator. This approach naturally leads to the Schottky parametrization of moduli space in terms of multipliers and fixed points of the g projective transformations which characterize a Riemann surface of genus g. The complete expression (including measure) of the multiloop corrections to the N String Vertex for the bosonic string is exhibited. (orig.)
Jet invariant mass in quantum chromodynamics
Clavelli, L.
1979-03-01
We give heuristic argument that a new class of observable related to the invariant mass of jets in e + e - annihilation is infrared finite to all orders of perturbation theory in Quantum Chromodynamics. We calculate the lowest order QCD predictions for the mass distribution as well as for the double differential cross section to produce back to back jets of invariant mass M 1 and M 2 . The resulting cross sections are quite different from that expected in simple hadronic fireball models and should provide experimentally accessible tests of QCD. (orig.) [de
Spontaneously broken supersymmetry and Poincare invariance
Tata, X.R.; Sudarshan, E.C.G.; Schechter, J.M.
1983-01-01
It is argued that the spontaneous breakdown of global supersymmetry is consistent with unbroken Poincare invariance if and only if the supersymmetry algebra 'A=0' is understood to mean the invariance of the dynamical variables phi under the transformations generated by the algebra, i.e. [A, phi]=0 rather than as an operator equation. It is further argued that this 'weakening' of the algrebra does not alter any of the conclusions about supersymmetry quantum field theories that have been obtained using the original (stronger) form of the algebra. (orig.)
Invariant measures on multimode quantum Gaussian states
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-12-01
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Invariant measures on multimode quantum Gaussian states
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-01-01
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Invariant measures on multimode quantum Gaussian states
Lupo, C. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Mancini, S. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia (Italy); De Pasquale, A. [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Facchi, P. [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Florio, G. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Piazza del Viminale 1, I-00184 Roma (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); Pascazio, S. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy)
2012-12-15
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
The decomposition of global conformal invariants
Alexakis, Spyros
2012-01-01
This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? Dese
Hidden invariance of the free classical particle
Garcia, S.
1994-01-01
A formalism describing the dynamics of classical and quantum systems from a group theoretical point of view is presented. We apply it to the simple example of the classical free particle. The Galileo group G is the symmetry group of the free equations of motion. Consideration of the free particle Lagrangian semi-invariance under G leads to a larger symmetry group, which is a central extension of the Galileo group by the real numbers. We study the dynamics associated with this group, and characterize quantities like Noether invariants and evolution equations in terms of group geometric objects. An extension of the Galileo group by U(1) leads to quantum mechanics
Quantized Hall conductance as a topological invariant
Niu, Q.; Thouless, Ds.J.; Wu, Y.S.
1984-10-01
Whenever the Fermi level lies in a gap (or mobility gap) the bulk Hall conductance can be expressed in a topologically invariant form showing the quantization explicitly. The new formulation generalizes the earlier result by TKNN to the situation where many body interaction and substrate disorder are also present. When applying to the fractional quantized Hall effect we draw the conclusion that there must be a symmetry breaking in the many body ground state. The possibility of writing the fractionally quantized Hall conductance as a topological invariant is also carefully discussed. 19 references
A Family of Invariant Stress Surfaces
Krenk, S.
A family of invariant stress surfaces with a cubic dependence on the deviatoric stress components is expressed as a linear combination of the second and third deviatori stress invariants. A simple geometric derivation demonstrates the convexity of the contours in the deviatoric plane. An explicit...... representation of the deviatoric contours in terms of a size and a shape parameter is given. The shape parameter effects a continuous transition from a triangle to a circle in the deviatoric plane. An explicit format in terms of the triaxial compresson and tension generators is derived, and the plane stress...
Invariant structures in gauge theories and confinement
Prokhorov, L.V.; Shabanov, S.V.
1991-01-01
The problem of finding all gauge invariants is considered in connection with the problem of confinement. Polylocal gauge tensors are introduced and studied. It is shown (both in physical and pure geometrical approaches) that the path-ordered exponent is the only fundamental bilocal gauge tensor, which means that any irreducible polylocal gauge tensor is built of P-exponents and local tensors (matter fields). The simplest invariant structures in electrodynamics, chromodynamics and a theory with the gauge group SU(2) are considered separately. 23 refs.; 2 figs
Nonlinear Lorentz-invariant theory of gravitation
Petry, W.
1976-01-01
A nonlinear Lorentz-invariant theory of gravitation and a Lorentz-invariant Hamiltonian for a particle with spin in the gravitational field are developed. The equations of motions are studied. The theory is applied to the three well known tests of General Relativity. In the special case of the red shift of spectral lines and of the deflection of light, the theory gives the same results as the General Theory of Relativity, whereas in the case of the perihelion of the Mercury, the theory gives 40,3'', in good agreement with experimental results of Dicke. (author)
Tests of CPT invariance at neutrino factories
Bilenky, Samoil M.; Freund, Martin; Lindner, Manfred; Ohlsson, Tommy; Winter, Walter
2002-01-01
We investigate possible tests of CPT invariance on the level of event rates at neutrino factories. We do not assume any specific model but phenomenological differences in the neutrino-antineutrino masses and mixing angles in a Lorentz invariance preserving context, such as could be induced by physics beyond the standard model. We especially focus on the muon neutrino and antineutrino disappearance channels in order to obtain constraints on the neutrino-antineutrino mass and mixing angle differences; we found, for example, that the sensitivity |m 3 -m(bar sign) 3 |(less-or-similar sign)1.9x10 -4 eV could be achieved
Reparametrization invariance and the Schroedinger equation
Tkach, V.I.; Pashnev, A.I.; Rosales, J.J.
1999-01-01
A time-dependent Schroedinger equation for systems invariant under the reparametrization of time is considered. We develop the two-stage procedure of construction such systems from a given initial ones, which are not invariant under the time reparametrization. One of the first-class constraints of the systems in such description becomes the time-dependent Schroedinger equation. The procedure is applicable in the supersymmetric theories as well. The n = 2 supersymmetric quantum mechanics is coupled to world-line supergravity, and the local supersymmetric action is constructed leading to the square root representation of the time-dependent Schroedinger equation
Invariant functionals in higher-spin theory
M.A. Vasiliev
2017-03-01
Full Text Available A new construction for gauge invariant functionals in the nonlinear higher-spin theory is proposed. Being supported by differential forms closed by virtue of the higher-spin equations, invariant functionals are associated with central elements of the higher-spin algebra. In the on-shell AdS4 higher-spin theory we identify a four-form conjectured to represent the generating functional for 3d boundary correlators and a two-form argued to support charges for black hole solutions. Two actions for 3d boundary conformal higher-spin theory are associated with the two parity-invariant higher-spin models in AdS4. The peculiarity of the spinorial formulation of the on-shell AdS3 higher-spin theory, where the invariant functional is supported by a two-form, is conjectured to be related to the holomorphic factorization at the boundary. The nonlinear part of the star-product function F⁎(B(x in the higher-spin equations is argued to lead to divergencies in the boundary limit representing singularities at coinciding boundary space–time points of the factors of B(x, which can be regularized by the point splitting. An interpretation of the RG flow in terms of proposed construction is briefly discussed.
Conformal branching rules and modular invariants
Walton, M.A.
1989-01-01
Using the outer automorphisms of the affine algebra SU(n), we show how the branching rules for the conformal subalgebra SU(pq) contains SU(p) x SU(q) may be simply calculated. We demonstrate that new modular invariant combinations of SU(n) characters are obtainable from the branching rules. (orig.)
Invariant of dynamical systems: A generalized entropy
Meson, A.M.; Vericat, F.
1996-01-01
In this work the concept of entropy of a dynamical system, as given by Kolmogorov, is generalized in the sense of Tsallis. It is shown that this entropy is an isomorphism invariant, being complete for Bernoulli schemes. copyright 1996 American Institute of Physics
Invariant metric for nonlinear symplectic maps
In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree (≥ 3). The homogeneous polynomials specify a nonlinear symplectic map which in turn represents a Hamiltonian system. By minimizing the norm constructed out of this metric as a function of system parameters, we ...
A Sim(2 invariant dimensional regularization
J. Alfaro
2017-09-01
Full Text Available We introduce a Sim(2 invariant dimensional regularization of loop integrals. Then we can compute the one loop quantum corrections to the photon self energy, electron self energy and vertex in the Electrodynamics sector of the Very Special Relativity Standard Model (VSRSM.
Translationally invariant self-consistent field theories
Shakin, C.M.; Weiss, M.S.
1977-01-01
We present a self-consistent field theory which is translationally invariant. The equations obtained go over to the usual Hartree-Fock equations in the limit of large particle number. In addition to deriving the dynamic equations for the self-consistent amplitudes we discuss the calculation of form factors and various other observables
Quantized gauge invariant periodic TDHF solutions
Kan, K.-K.; Griffin, J.J.; Lichtner, P.C.; Dworzecka, M.
1979-01-01
Time-dependent Hartree-Fock (TDHF) is used to study steady state large amplitude nuclear collective motions, such as vibration and rotation. As is well known the small amplitude TDHF leads to the RPA equation. The analysis of periodicity in TDHF is not trivial because TDHF is a nonlinear theory and it is not known under what circumstances a nonlinear theory can support periodic solutions. It is also unknown whether such periodic solution, if they exist, form a continuous or a discrete set. But, these properties may be important in obtaining the energy spectrum of the collective states from the TDHF description. The periodicity and Gauge Invariant Periodicity of solutions are investigated for that class of models whose TDHF solutions depend on time through two parameters. In such models TDHF supports a continuous family of periodic solutions, but only a discrete subset of these is gauge invariant. These discrete Gauge Invariant Periodic solutions obey the Bohr-Summerfeld quantization rule. The energy spectrum of the Gauge Invariant Periodic solutions is compared with the exact eigenergies in one specific example
Invariant Hilbert spaces of holomorphic functions
Faraut, J; Thomas, EGF
1999-01-01
A Hilbert space of holomorphic functions on a complex manifold Z, which is invariant under a group G of holomorphic automorphisms of Z, can be decomposed into irreducible subspaces by using Choquet theory. We give a geometric condition on Z and G which implies that this decomposition is multiplicity
Gauge invariance and fermion mass dimensions
Elias, V.
1979-05-01
Renormalization-group equation fermion mass dimensions are shown to be gauge dependent in gauge theories possessing non-vector couplings of gauge bosons to fermions. However, the ratios of running fermion masses are explicitly shown to be gauge invariant in the SU(5) and SU(2) x U(1) examples of such theories. (author)
Gauge invariance and fractional quantized Hall effect
Tao, R.; Wu, Y.S.
1984-01-01
It is shown that gauge invariance arguments imply the possibility of fractional quantized Hall effect; the Hall conductance is accurately quantized to a rational value. The ground state of a system showing the fractional quantized Hall effect must be degenerate; the non-degenerate ground state can only produce the integral quantized Hall effect. 12 references
Analytic stochastic regularization and gange invariance
Abdalla, E.; Gomes, M.; Lima-Santos, A.
1986-05-01
A proof that analytic stochastic regularization breaks gauge invariance is presented. This is done by an explicit one loop calculation of the vaccum polarization tensor in scalar electrodynamics, which turns out not to be transversal. The counterterm structure, Langevin equations and the construction of composite operators in the general framework of stochastic quantization, are also analysed. (Author) [pt
General relativity invariance and string field theory
Aref'eva, I.Ya.; Volovich, I.V.
1987-04-01
The general covariance principle in the string field theory is considered. The algebraic properties of the string Lie derivative are discussed. The string vielbein and spin connection are introduced and an action invariant under general co-ordinate transformation is proposed. (author). 18 refs
Size-change termination and transition invariants
Heizmann, Matthias; Jones, Neil; Podelski, Andreas
2010-01-01
Two directions of recent work on program termination use the concepts of size-change termination resp. transition invariants. The difference in the setting has as consequence the inherent incomparability of the analysis and verification methods that result from this work. Yet, in order...
Superfield approach to symmetry invariance in quantum ...
The Nakanishi–Lautrup auxiliary field B is required to .... In the language of the physical terms, the above HC is the assertion that the electric and magnetic fields (that are gauge and BRST invariant quantities) should remain independent of .... the 4D Lagrangian density (2.1) can be captured in the language of the superfield.
Invariant imbedding equations for linear scattering problems
Apresyan, L.
1988-01-01
A general form of the invariant imbedding equations is investigated for the linear problem of scattering by a bounded scattering volume. The conditions for the derivability of such equations are described. It is noted that the possibility of the explicit representation of these equations for a sphere and for a layer involves the separation of variables in the unperturbed wave equation
Loop quasi-invariant chunk detection
Moyen, Jean-Yves; Rubiano, Thomas; Seiller, Thomas
2017-01-01
Several techniques for analysis and transformations are used in compilers. Among them, the peeling of loops for hoisting quasi-invariants can be used to optimize generated code, or simply ease developers’ lives. In this paper, we introduce a new concept of dependency analysis borrowed from the fi...
Broken Scale Invariance and Anomalous Dimensions
Wilson, K. G.
1970-05-01
Mack and Kastrup have proposed that broken scale invariance is a symmetry of strong interactions. There is evidence from the Thirring model and perturbation theory that the dimensions of fields defined by scale transformations will be changed by the interaction from their canonical values. We review these ideas and their consequences for strong interactions.
Performance evaluation of local colour invariants
Burghouts, G.J.; Geusebroek, J.M.
2009-01-01
In this paper, we compare local colour descriptors to grey-value descriptors. We adopt the evaluation framework of Mikolayzcyk and Schmid. We modify the framework in several ways. We decompose the evaluation framework to the level of local grey-value invariants on which common region descriptors are
Quantum field theory and link invariants
Cotta-Ramusino, P.; Guadagnini, E.; Mintchev, M.; Martellini, M.
1990-01-01
A skein relation for the expectation values of Wilson line operators in three-dimensional SU(N) Chern-Simons gauge theory is derived at first order in the coupling constant. We use a variational method based on the properties of the three-dimensional field theory. The relationship between the above expectation values and the known link invariants is established. (orig.)
Gowdy phenomenology in scale-invariant variables
Andersson, Lars; Elst, Henk van; Uggla, Claes
2004-01-01
The dynamics of Gowdy vacuum spacetimes is considered in terms of Hubble-normalized scale-invariant variables, using the timelike area temporal gauge. The resulting state space formulation provides for a simple mechanism for the formation of 'false' and 'true spikes' in the approach to the singularity, and a geometrical formulation for the local attractor
Coloured Petri Nets and the Invariant Method
Jensen, Kurt
1981-01-01
processes to be described by a common subnet, without losing the ability to distinguish between them. Our generalization, called coloured Petri nets, is heavily influenced by predicate transition-nets introduced by H.J. Genrich and K. Lautenbach. Moreover our paper shows how the invariant-method, introduced...... for Petri nets by K. Lautenbach, can be generalized to coloured Petri nets....
Field transformations, collective coordinates and BRST invariance
Alfaro, J.; Damgaard, P.H.
1989-12-01
A very large class of general field transformations can be viewed as a field theory generalization of the method of collective coordinates. The introduction of new variables induces a gauge invariance in the transformed theory, and the freedom left in gauge fixing this new invariance can be used to find equivalent formulations of the same theory. First the Batalin-Fradkin-Vilkovisky formalism is applied to the Hamiltonian formulation of physical systems that can be described in terms of collective coordinates. We then show how this type of collective coordinate scheme can be generalized to field transformations, and discuss the War Identities of the associated BRST invariance. For Yang-Mills theory a connection to topological field theory and the background field method is explained in detail. In general the resulting BRST invariance we find hidden in any quantum field theory can be viewed as a consequence of our freedom in choosing a basis of coordinates φ(χ) in the action S[φ]. (orig.)
Automatic invariant detection in dynamic web applications
Groeneveld, F.; Mesbah, A.; Van Deursen, A.
2010-01-01
The complexity of modern web applications increases as client-side JavaScript and dynamic DOM programming are used to offer a more interactive web experience. In this paper, we focus on improving the dependability of such applications by automatically inferring invariants from the client-side and
Invariant properties between stroke features in handwriting
Teulings, H L; Schomaker, L R
A handwriting pattern is considered as a sequence of ballistic strokes. Replications of a pattern may be generated from a single, higher-level memory representation, acting as a motor program. Therefore, those stroke features which show the most invariant pattern are probably related to the
Foliated vector fields, the Godbillon-Vey invariant and the invariant I(F)
Banyaga, A.; Landa, Alain Musesa
2004-03-01
We prove that if the invariant I(F) constructed in 'An invariant of contact structures and transversally oriented foliations', Ann. Global Analysis and Geom. 14(1996) 427-441 (A. Banyaga), through the Lie algebra of infinitesimal automorphisms of transversally oriented foliations F is trivial, then the Godbillon-Vey invariant GV (F) of F is also trivial, but that the converse is not true. For codimension one foliations, the restrictions I τ , (F) of I(F) to the Lie subalgebra of vector fields tangent to the leaves is the Reeb class R(F) of F. We also prove that if there exists a foliated vector field which is everywhere transverse to a codimension one foliation, then the Reeb class R(F) is trivial, hence so is the GV(F) invariant. (author)
Kim eDe Roover
2014-06-01
Full Text Available The issue of measurement invariance is ubiquitous in the behavioral sciences nowadays as more and more studies yield multivariate multigroup data. When measurement invariance cannot be established across groups, this is often due to different loadings on only a few items. Within the multigroup CFA framework, methods have been proposed to trace such non-invariant items, but these methods have some disadvantages in that they require researchers to run a multitude of analyses and in that they imply assumptions that are often questionable. In this paper, we propose an alternative strategy which builds on clusterwise simultaneous component analysis (SCA. Clusterwise SCA, being an exploratory technique, assigns the groups under study to a few clusters based on differences and similarities in the covariance matrices, and thus based on the component structure of the items. Non-invariant items can then be traced by comparing the cluster-specific component loadings via congruence coefficients, which is far more parsimonious than comparing the component structure of all separate groups. In this paper we present a heuristic for this procedure. Afterwards, one can return to the multigroup CFA framework and check whether removing the non-invariant items or removing some of the equality restrictions for these items, yields satisfactory invariance test results. An empirical application concerning cross-cultural emotion data is used to demonstrate that this novel approach is useful and can co-exist with the traditional CFA approaches.
How to Find Invariants for Coloured Petri Nets
Jensen, Kurt
1981-01-01
This paper shows how invariants can be found for coloured Petri Nets. We define a set of transformation rules, which can be used to transform the incidence matrix, without changing the set of invariants....
Test of CPT and Lorentz invariance from muonium spectroscopy
Hughes, V. W.; Perdekamp, M. Grosse; Kawall, D.; Liu, W.; Jungmann, K.; Putlitz, G. zu
2001-01-01
Following a suggestion of Kostelecky et al. we have evaluated a test of CPT and Lorentz invariance from the microwave spectroscopy of muonium. Hamiltonian terms beyond the standard model violating CPT and Lorentz invariance would contribute frequency shifts $\\delta\
Quantifying Translation-Invariance in Convolutional Neural Networks
Kauderer-Abrams, Eric
2017-01-01
A fundamental problem in object recognition is the development of image representations that are invariant to common transformations such as translation, rotation, and small deformations. There are multiple hypotheses regarding the source of translation invariance in CNNs. One idea is that translation invariance is due to the increasing receptive field size of neurons in successive convolution layers. Another possibility is that invariance is due to the pooling operation. We develop a simple ...
A scale invariant covariance structure on jet space
Pedersen, Kim Steenstrup; Loog, Marco; Markussen, Bo
2005-01-01
This paper considers scale invariance of statistical image models. We study statistical scale invariance of the covariance structure of jet space under scale space blurring and derive the necessary structure and conditions of the jet covariance matrix in order for it to be scale invariant. As par...
BRS invariant stochastic quantization of Einstein gravity
Nakazawa, Naohito.
1989-11-01
We study stochastic quantization of gravity in terms of a BRS invariant canonical operator formalism. By introducing artificially canonical momentum variables for the original field variables, a canonical formulation of stochastic quantization is proposed in the sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. Then we show that there exists a nilpotent BRS symmetry in an enlarged phase space of the first-class constrained systems. The phase space is spanned by the dynamical variables, their canonical conjugate momentum variables, Faddeev-Popov ghost and anti-ghost. We apply the general BRS invariant formulation to stochastic quantization of gravity which is described as a second-class constrained system in terms of a pair of Langevin equations coupled with white noises. It is shown that the stochastic action of gravity includes explicitly the De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models. (author)
Mutation, Witten index, and quiver invariant
Kim, Heeyeon [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, N2L 2Y5, Ontario (Canada); Lee, Seung-Joo [Department of Physics, Robeson Hall, Virginia Tech,Blacksburg, VA 24061 (United States); Yi, Piljin [School of Physics, Korea Institute for Advanced Study,Seoul 130-722 (Korea, Republic of)
2015-07-20
We explore Seiberg-like dualities, or mutations, for N=4 quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed Fayet-Iliopoulos constants, at most two nodes can be mutated, one left and the other right, mapping a chamber of a quiver into a chamber of a mutated quiver. We delineate this complex pattern for triangle quivers and show how the Witten indices are preserved under such finely chosen mutations. On the other hand, the quiver invariants, or wall-crossing-safe part of supersymmetric spectra, mutate more straightforwardly, whereby a quiver is mapped to a quiver. The mutation rule that preserves the quiver invariant is different from the usual one, however, which we explore and confirm numerically.
Revisiting R-invariant direct gauge mediation
Chiang, Cheng-Wei [Center for Mathematics and Theoretical Physics andDepartment of Physics, National Central University,Taoyuan, Taiwan 32001, R.O.C. (China); Institute of Physics, Academia Sinica,Taipei, Taiwan 11529, R.O.C. (China); Physics Division, National Center for Theoretical Sciences,Hsinchu, Taiwan 30013, R.O.C. (China); Kavli IPMU (WPI), UTIAS, University of Tokyo,Kashiwa, Chiba 277-8583 (Japan); Harigaya, Keisuke [Department of Physics, University of California,Berkeley, California 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory,Berkeley, California 94720 (United States); ICRR, University of Tokyo,Kashiwa, Chiba 277-8582 (Japan); Ibe, Masahiro [Kavli IPMU (WPI), UTIAS, University of Tokyo,Kashiwa, Chiba 277-8583 (Japan); ICRR, University of Tokyo,Kashiwa, Chiba 277-8582 (Japan); Yanagida, Tsutomu T. [Kavli IPMU (WPI), UTIAS, University of Tokyo,Kashiwa, Chiba 277-8583 (Japan)
2016-03-21
We revisit a special model of gauge mediated supersymmetry breaking, the “R-invariant direct gauge mediation.” We pay particular attention to whether the model is consistent with the minimal model of the μ-term, i.e., a simple mass term of the Higgs doublets in the superpotential. Although the incompatibility is highlighted in view of the current experimental constraints on the superparticle masses and the observed Higgs boson mass, the minimal μ-term can be consistent with the R-invariant gauge mediation model via a careful choice of model parameters. We derive an upper limit on the gluino mass from the observed Higgs boson mass. We also discuss whether the model can explain the 3σ excess of the Z+jets+E{sub T}{sup miss} events reported by the ATLAS collaboration.
Mutation, Witten index, and quiver invariant
Kim, Heeyeon; Lee, Seung-Joo; Yi, Piljin
2015-01-01
We explore Seiberg-like dualities, or mutations, for N=4 quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed Fayet-Iliopoulos constants, at most two nodes can be mutated, one left and the other right, mapping a chamber of a quiver into a chamber of a mutated quiver. We delineate this complex pattern for triangle quivers and show how the Witten indices are preserved under such finely chosen mutations. On the other hand, the quiver invariants, or wall-crossing-safe part of supersymmetric spectra, mutate more straightforwardly, whereby a quiver is mapped to a quiver. The mutation rule that preserves the quiver invariant is different from the usual one, however, which we explore and confirm numerically.
Adiabatic invariance with first integrals of motion
Adib, Artur B.
2002-10-01
The construction of a microthermodynamic formalism for isolated systems based on the concept of adiabatic invariance is an old but seldom appreciated effort in the literature, dating back at least to P. Hertz [Ann. Phys. (Leipzig) 33, 225 (1910)]. An apparently independent extension of such formalism for systems bearing additional first integrals of motion was recently proposed by Hans H. Rugh [Phys. Rev. E 64, 055101 (2001)], establishing the concept of adiabatic invariance even in such singular cases. After some remarks in connection with the formalism pioneered by Hertz, it will be suggested that such an extension can incidentally explain the success of a dynamical method for computing the entropy of classical interacting fluids, at least in some potential applications where the presence of additional first integrals cannot be ignored.
Scale invariance from phase transitions to turbulence
Lesne, Annick
2012-01-01
During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos ...
Odor concentration invariance by chemical ratio coding
Naoshige Uchida
2008-08-01
Full Text Available Many animal species rely on chemical signals to extract ecologically important information from the environment. Yet in natural conditions chemical signals will frequently undergo concentration changes that produce differences in both level and pattern of activation of olfactory receptor neurons. Thus, a central problem in olfactory processing is how the system is able to recognize the same stimulus across different concentrations. To signal species identity for mate recognition, some insects use the ratio of two components in a binary chemical mixture to produce a code that is invariant to dilution. Here, using psychophysical methods, we show that rats also classify binary odor mixtures according to the molar ratios of their components, spontaneously generalizing over at least a tenfold concentration range. These results indicate that extracting chemical ratio information is not restricted to pheromone signaling and suggest a general solution for concentration-invariant odor recognition by the mammalian olfactory system.
The geometric Hopf invariant and surgery theory
Crabb, Michael
2017-01-01
Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .
Slow Invariant Manifolds in Chemically Reactive Systems
Paolucci, Samuel; Powers, Joseph M.
2006-11-01
The scientific design of practical gas phase combustion devices has come to rely on the use of mathematical models which include detailed chemical kinetics. Such models intrinsically admit a wide range of scales which renders their accurate numerical approximation difficult. Over the past decade, rational strategies, such as Intrinsic Low Dimensional Manifolds (ILDM) or Computational Singular Perturbations (CSP), for equilibrating fast time scale events have been successfully developed, though their computation can be challenging and their accuracy in most cases uncertain. Both are approximations to the preferable slow invariant manifold which best describes how the system evolves in the long time limit. Strategies for computing the slow invariant manifold are examined, and results are presented for practical combustion systems.
Hiding Lorentz invariance violation with MOND
Sanders, R. H.
2011-01-01
Horava-Lifshitz gravity is an attempt to construct a renormalizable theory of gravity by breaking the Lorentz invariance of the gravitational action at high energies. The underlying principle is that Lorentz invariance is an approximate symmetry and its violation by gravitational phenomena is somehow hidden to present limits of observational precision. Here I point out that a simple modification of the low-energy limit of Horava-Lifshitz gravity in its nonprojectable form can effectively camouflage the presence of a preferred frame in regions where the Newtonian gravitational field gradient is higher than cH 0 ; this modification results in the phenomenology of modified Newtonian dynamics (MOND) at lower accelerations. As a relativistic theory of MOND, this modified Horava-Lifshitz theory presents several advantages over its predecessors.
CP invariance: a point of view
Mohan, Gyan
1983-01-01
That the longlived component L of K 0 has both CP = +1 and CP = -1 modes of decay is often cited as evidence of violation of CP invariance. The careful ones find the compelling evidence to be the non-dilution of the regeneration interference pattern when the incident K 0 beam is mixed even substantially with anti-K 0 . However the two phenomena comprehensively imply that L has a CP = +1 component Lsub(+) and CP = -1 component Lsub(-) and that the longlived component of both K 0 and anti-K 0 are one and the same L. This does not demand abandoning CP invariance. It does imply that anti-K 0 is not the CP conjugate of K 0 . (author)
Improved test of Lorentz invariance in electrodynamics
Wolf, Peter; Bize, Sebastien; Clairon, Andre; Santarelli, Giorgio; Tobar, Michael E.; Luiten, Andre N.
2004-01-01
We report new results of a test of Lorentz invariance based on the comparison of a cryogenic sapphire microwave resonator and a hydrogen-maser. The experimental results are shown together with an extensive analysis of systematic effects. Previously, this experiment has set the most stringent constraint on Kennedy-Thorndike type violations of Lorentz invariance. In this work we present new data and interpret our results in the general Lorentz violating extension of the standard model of particle physics (SME). Within the photon sector of the SME, our experiment is sensitive to seven SME parameters. We marginally improve present limits on four of these, and by a factor seven to ten on the other three
Link invariant and $G_2$ web space
Sakamoto, Takuro; Yonezawa, Yasuyoshi
2017-01-01
In this paper, we reconstruct Kuperberg’s $G_2$ web space [5, 6]. We introduce a new web diagram (a trivalent graph with only double edges) and new relations between Kuperberg’s web diagrams and the new web diagram. Using the web diagrams, we give crossing formulas for the $R$-matrices associated to some irreducible representations of $U_q(G_2)$ and calculate $G_2$ quantum link invariants for generalized twist links.
Charge conjugation invariance of the spectator equations
Gross, F.
1999-01-01
In response to recent criticism, the authors show how to define the spectator equations for negative energies so that charge conjugation invariance is preserved. The result, which emerges naturally from the application of spectator principles to systems of particles with negative energies, is to replace all factors of the external energies W iota by √ W 2 iota , insuring that the amplitudes are independent of the sign of the energies W iota
O(3)-invariant tunneling in general relativity
Berezin, V.A.; Tkachev, I.I.; Kuzmin, V.A.; AN SSSR, Moscow. Inst. Yadernykh Issledovanij)
1987-12-01
We derived a general formula for the action for any O(3)-invariant tunneling processes in false vacuum decay in general relativity. The general classification of the bubble Euclidean trajectories is elaborated and explicit expressions for bounces for some processes like the vacuum creation of a double bubble, in particular in the vicinity of a black hole; the subbarrier creation of the Einstein-Rosen bridge, creation from nothing of two Minkowski worlds connected by a shell etc., are given. (orig.)
Remarks on Chern-Simons Invariants
Cattaneo, Alberto S.; Mnëv, Pavel
2010-02-01
The perturbative Chern-Simons theory is studied in a finite-dimensional version or assuming that the propagator satisfies certain properties (as is the case, e.g., with the propagator defined by Axelrod and Singer). It turns out that the effective BV action is a function on cohomology (with shifted degrees) that solves the quantum master equation and is defined modulo certain canonical transformations that can be characterized completely. Out of it one obtains invariants.
Generalized operator canonical formalism and gauge invariance
Fradkina, T.E.
1988-01-01
A direct proof is given in the functional representation of the invariance of the S-matrix constructed in the framework of the generalized operator canonical formalism. We find the traditional functional expression for the S-matrix (without point-splitting in the time factor) in the generalized phase space, as well as in the ghost configuration space. An explicit expression is obtained for the effective unitarizing Hamiltonian for gauge theories with constraints of arbitrary rank
Invariance algorithms for processing NDE signals
Mandayam, Shreekanth; Udpa, Lalita; Udpa, Satish S.; Lord, William
1996-11-01
Signals that are obtained in a variety of nondestructive evaluation (NDE) processes capture information not only about the characteristics of the flaw, but also reflect variations in the specimen's material properties. Such signal changes may be viewed as anomalies that could obscure defect related information. An example of this situation occurs during in-line inspection of gas transmission pipelines. The magnetic flux leakage (MFL) method is used to conduct noninvasive measurements of the integrity of the pipe-wall. The MFL signals contain information both about the permeability of the pipe-wall and the dimensions of the flaw. Similar operational effects can be found in other NDE processes. This paper presents algorithms to render NDE signals invariant to selected test parameters, while retaining defect related information. Wavelet transform based neural network techniques are employed to develop the invariance algorithms. The invariance transformation is shown to be a necessary pre-processing step for subsequent defect characterization and visualization schemes. Results demonstrating the successful application of the method are presented.
Permutation-invariant distance between atomic configurations
Ferré, Grégoire; Maillet, Jean-Bernard; Stoltz, Gabriel
2015-09-01
We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables us to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e., fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the root mean square distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e., their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity.
Permutation-invariant distance between atomic configurations
Ferré, Grégoire; Maillet, Jean-Bernard; Stoltz, Gabriel
2015-01-01
We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables us to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e., fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the root mean square distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e., their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity
On local invariants of singular symplectic forms
Domitrz, Wojciech
2017-04-01
We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a 2 n-dimensional manifold. In the C-analytic category this set consists of the Martinet hypersurface Σ2, the restriction of the singular symplectic form ω to TΣ2 and the kernel of ω n - 1 at the point p ∈Σ2. In the R-analytic and smooth categories this set contains one more invariant: the canonical orientation of Σ2. We find the conditions to determine the kernel of ω n - 1 at p by the other invariants. In dimension 4 we find sufficient conditions to determine the equivalence class of a singular symplectic form-germ with the structurally smooth Martinet hypersurface by the Martinet hypersurface and the restriction of the singular symplectic form to it. We also study the singular symplectic forms with singular Martinet hypersurfaces. We prove that the equivalence class of such singular symplectic form-germ is determined by the Martinet hypersurface, the canonical orientation of its regular part and the restriction of the singular symplectic form to its regular part if the Martinet hypersurface is a quasi-homogeneous hypersurface with an isolated singularity.
A Balanced Comparison of Object Invariances in Monkey IT Neurons.
Ratan Murty, N Apurva; Arun, Sripati P
2017-01-01
Our ability to recognize objects across variations in size, position, or rotation is based on invariant object representations in higher visual cortex. However, we know little about how these invariances are related. Are some invariances harder than others? Do some invariances arise faster than others? These comparisons can be made only upon equating image changes across transformations. Here, we targeted invariant neural representations in the monkey inferotemporal (IT) cortex using object images with balanced changes in size, position, and rotation. Across the recorded population, IT neurons generalized across size and position both stronger and faster than to rotations in the image plane as well as in depth. We obtained a similar ordering of invariances in deep neural networks but not in low-level visual representations. Thus, invariant neural representations dynamically evolve in a temporal order reflective of their underlying computational complexity.
Penfield, Randall D.; Myers, Nicholas D.; Wolfe, Edward W.
2008-01-01
Measurement invariance in the partial credit model (PCM) can be conceptualized in several different but compatible ways. In this article the authors distinguish between three forms of measurement invariance in the PCM: step invariance, item invariance, and threshold invariance. Approaches for modeling these three forms of invariance are proposed,…
Monomial codes seen as invariant subspaces
García-Planas María Isabel
2017-08-01
Full Text Available It is well known that cyclic codes are very useful because of their applications, since they are not computationally expensive and encoding can be easily implemented. The relationship between cyclic codes and invariant subspaces is also well known. In this paper a generalization of this relationship is presented between monomial codes over a finite field and hyperinvariant subspaces of n under an appropriate linear transformation. Using techniques of Linear Algebra it is possible to deduce certain properties for this particular type of codes, generalizing known results on cyclic codes.
Hidden Scale Invariance in Condensed Matter
Dyre, J. C.
2014-01-01
. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. Liquids and solids with isomorphs include most or all van der Waals bonded systems and metals, as well as weakly ionic or dipolar systems. On the other hand, systems with directional bonding...... (hydrogen bonds or covalent bonds) or strong Coulomb forces generally do not exhibit hidden scale invariance. The article reviews the theory behind this picture of condensed matter and the evidence for it coming from computer simulations and experiments...
The Invariance and the General CCT Theorems
Stancu, Alin
2010-01-01
The \\begin{it} Invariance Theorem \\end{it} of M. Gerstenhaber and S. D. Schack states that if $\\mathbb{A}$ is a diagram of algebras then the subdivision functor induces a natural isomorphism between the Yoneda cohomologies of the category $\\mathbb{A}$-$\\mathbf{mod}$ and its subdivided category $\\mathbb{A}'$-$\\mathbf{mod}$. In this paper we generalize this result and show that the subdivision functor is a full and faithful functor between two suitable derived categories of $\\mathbb{A}$-$\\mathb...
Origin of gauge invariance in string theory
Horowitz, G. T.; Strominger, A.
1986-01-01
A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.
On diffeomorphism invariance for lattice theories
Corichi, A.; Zapata, J.
1997-01-01
We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices one automatically takes care of the diffeomorphism constraint in the quantum theory. We use two systems in order to show that imposing the diffeomorphism constraint is imperative to obtain a physically acceptable quantum theory. First, we consider 2+1 gravity where an exact lattice formulation is available. Next, general theories of connections for compact gauge groups are treated, where the quantum theories are known - for both the continuum and the lattice - and can be compared. (orig.)
Gauge invariant actions for string models
Banks, T.
1986-06-01
String models of unified interactions are elegant sets of Feynman rules for the scattering of gravitons, gauge bosons, and a host of massive excitations. The purpose of these lectures is to describe the progress towards a nonperturbative formulation of the theory. Such a formulation should make the geometrical meaning of string theory manifest and explain the many ''miracles'' exhibited by the string Feynman rules. There are some new results on gauge invariant observables, on the cosmological constant, and on the symmetries of interacting string field theory. 49 refs
Testing Lorentz invariance in β decay
Sytema A.
2014-03-01
Experimentally we exploit the Gamow-Teller transition of polarized 20Na, where we can test the dependence of the β-decay rate on the spin orientation of 20Na. The polarization degree is measured using the β asymmetry, while the decay rate is measured by the γ yield. A change in the γ rate, when reversing the spin, implies Lorentz invariance violation. The decay rate should depend on sidereal time and the polarization direction relative to the rotation axis of the earth. The method of the measurement will be presented, together with the first results.
Modular invariance and covariant loop calculus
Petersen, J.L.; Roland, K.O.; Sidenius, J.R.
1988-01-01
The covariant loop calculus provides and efficient technique for computing explicit expressions for the density on moduli space corresponding to arbitrary (bosonic string) loop diagrams. Since modular invariance is not manifest, however, we carry out a detailed comparison with known explicit 2- and 3- loop results derived using analytic geometry (1 loop is known to be ok). We establish identity to 'high' order in some moduli and exactly in others. Agreement is found as a result of various non-trivial cancellations, in part related to number theory. We feel our results provide very strong support for the correctness of the covariant loop calculus approach. (orig.)
Scale invariants from Gaussian-Hermite moments
Yang, B.; Kostková, Jitka; Flusser, Jan; Suk, Tomáš
2017-01-01
Roč. 132, č. 1 (2017), s. 77-84 ISSN 0165-1684 R&D Projects: GA ČR GA15-16928S Institutional support: RVO:67985556 Keywords : Scale invariants * Gaussian–Hermite moments * Variable modulation * Normalization * Zernike moments Subject RIV: JD - Computer Applications, Robotics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 3.110, year: 2016 http://library.utia.cas.cz/separaty/2016/ZOI/flusser-0466031.pdf
Modular invariance and covariant loop calculus
Petersen, J.L.; Roland, K.O.; Sidenius, J.R.
1988-01-01
The covariant loop calculus provides an efficient technique for computing explicit expressions for the density on moduli space corresponding to arbitrary (bosonic string) loop diagrams. Since modular invariance is not manifest, however, we carry out a detailed comparison with known explicit two- and three-loop results derived using analytic geometry (one loop is known to be okay). We establish identity to 'high' order in some moduli and exactly in others. Agreement is found as a result of various nontrivial cancellations, in part related to number theory. We feel our results provide very strong support for the correctness of the covariant loop calculus approach. (orig.)
Structure of BRS-invariant local functionals
Brandt, F.
1993-01-01
For a large class of gauge theories a nilpotent BRS-operator s is constructed and its cohomology in the space of local functionals of the off-shell fields is shown to be isomorphic to the cohomology of s=s+d on functions f(C,T) of tensor fields T and of variables C which are constructed of the ghosts and the connection forms. The result allows general statements about the structure of invariant classical actions and anomaly cadidates whose BRS-variation vanishes off-shell. The assumptions under which the result holds are thoroughly discussed. (orig.)
Conformal invariance in quantum field theory
Grensing, G.
1978-01-01
We study the transformation law of interacting fields under the universal covering group of the conformal group. It is defined with respect to the representations of the discrete series. These representations are field representations in the sense that they act on finite component fields defined over Minkowski space. The conflict with Einstein causality is avoided as in the case of free fields with canonical dimension. Furthermore, we determine the conformal invariant two-point function of arbitrary spin. Our result coincides with that obtained by Ruehl. In particular, we investigate the two-point function of symmetric and traceless tensor fields and give the explicit form of the trace terms
The axion mass in modular invariant supergravity
Butter, Daniel; Gaillard, Mary K.
2005-01-01
When supersymmetry is broken by condensates with a single condensing gauge group, there is a nonanomalous R-symmetry that prevents the universal axion from acquiring a mass. It has been argued that, in the context of supergravity, higher dimension operators will break this symmetry and may generate an axion mass too large to allow the identification of the universal axion with the QCD axion. We show that such contributions to the axion mass are highly suppressed in a class of models where the effective Lagrangian for gaugino and matter condensation respects modular invariance (T-duality)
Invariant measures of mass migration processes
Fajfrová, Lucie; Gobron, T.; Saada, E.
2016-01-01
Roč. 21, č. 1 (2016), s. 1-52, č. článku 60. ISSN 1083-6489 R&D Projects: GA ČR GAP201/12/2613; GA ČR(CZ) GA16-15238S Institutional support: RVO:67985556 Keywords : interacting particle systems * product invariant measures * zero range process * target process * mass migration process * condensation Subject RIV: BA - General Mathematics Impact factor: 0.904, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/fajfrova-0464455.pdf
On the BRST invariance of field deformations
Alfaro, J.; Damgaard, P.H.; Latorre, J.I.; Montano, D.
1989-08-01
Topological quantum field theories are distinguished by a BRST symmetry corresponding to local field deformations. We investigate in this letter to what extent an arbitrary quantum field theory may be related to this BRST invariance. We demonstrate that at the expense of having to add extra variables (but without changing the physics) one may always extend to symmetry of an arbitrary action to include local field deformations. New avenues for gauge-fixing are then available. Examples are worked out for Yang-Mills theories. (orig.)
CPT non-invariance and weak interactions
Hsu, J.P.
1973-01-01
In this talk, I will describe a possible violation of CPT invariance in the domain of weak interactions. One can construct a model of weak interactions which, in order to be consistent with all experimental data, must violate CPT maximally. The model predicts many specific results for decay processes which could be tested in the planned neutral hyperon beam or neutrino beam at NAL. The motivations and the physical idea in the model are explained and the implications of the model are discussed. (U.S.)
Dijet invariant mass spectrum at CDF
Incagli, M.
1992-11-01
A summary of QCD results obtained using the dijet invariant mass spectrum dσ/dM jj is presented. The spectrum is compared with QCD Leader Order and with the recently published Next to Leading Order calculations. A limit on the scale of an eventual quark compositness can be set at Λ=1300 GeV. Limits on the production of new particles, decaying hadronically, are presented, too. Axigluons are ruled out in the mass range [240, 640] GeV, for a theory with N=10 strong interacting fermions, and in the two windows [260, 280] GeV and [450, 550] GeV, for N=20
Phenomenology of local scale invariance: from conformal invariance to dynamical scaling
Henkel, Malte
2002-01-01
Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent θ or a dynamical exponent z. For a given value of θ (or z), we construct local scale transformations, which can be viewed as scale transformations with a space-time-dependent dilatation factor. Two distinct types of local scale transformations are found. The first type may describe strongly anisotropic scaling of static systems with a given value of θ, whereas the second type may describe dynamical scaling with a dynamical exponent z. Local scale transformations act as a dynamical symmetry group of certain non-local free-field theories. Known special cases of local scale invariance are conformal invariance for θ=1 and Schroedinger invariance for θ=2. The hypothesis of local scale invariance implies that two-point functions of quasi primary operators satisfy certain linear fractional differential equations, which are constructed from commuting fractional derivatives. The explicit solution of these yields exact expressions for two-point correlators at equilibrium and for two-point response functions out of equilibrium. A particularly simple and general form is found for the two-time auto response function. These predictions are explicitly confirmed at the uniaxial Lifshitz points in the ANNNI and ANNNS models and in the aging behaviour of simple ferromagnets such as the kinetic Glauber-Ising model and the kinetic spherical model with a non-conserved order parameter undergoing either phase-ordering kinetics or non-equilibrium critical dynamics
Duality invariant class of exact string backgrounds
Klimcík, C
1994-01-01
We consider a class of $2+D$ - dimensional string backgrounds with a target space metric having a covariantly constant null Killing vector and flat `transverse' part. The corresponding sigma models are invariant under $D$ abelian isometries and are transformed by $O(D,D)$ duality into models belonging to the same class. The leading-order solutions of the conformal invariance equations (metric, antisymmetric tensor and dilaton), as well as the action of $O(D,D)$ duality transformations on them, are exact, i.e. are not modified by $\\a'$-corrections. This makes a discussion of different space-time representations of the same string solution (related by $O(D,D|Z)$ duality subgroup) rather explicit. We show that the $O(D,D)$ duality may connect curved $2+D$-dimensional backgrounds with solutions having flat metric but, in general, non-trivial antisymmetric tensor and dilaton. We discuss several particular examples including the $2+D=4$ - dimensional background that was recently interpreted in terms of a WZW model.
More modular invariant anomalous U(1) breaking
Gaillard, Mary K.; Giedt, Joel
2002-01-01
We consider the case of several scalar fields, charged under a number of U(1) factors, acquiring vacuum expectation values due to an anomalous U(1). We demonstrate how to make redefinitions at the superfield level in order to account for tree-level exchange of vector supermultiplets in the effective supergravity theory of the light fields in the supersymmetric vacuum phase. Our approach builds upon previous results that we obtained in a more elementary case. We find that the modular weights of light fields are typically shifted from their original values, allowing an interpretation in terms of the preservation of modular invariance in the effective theory. We address various subtleties in defining unitary gauge that are associated with the noncanonical Kaehler potential of modular invariant supergravity, the vacuum degeneracy, and the role of the dilaton field. We discuss the effective superpotential for the light fields and note how proton decay operators may be obtained when the heavy fields are integrated out of the theory at the tree-level. We also address how our formalism may be extended to describe the generalized Green-Schwarz mechanism for multiple anomalous U(1)'s that occur in four-dimensional Type I and Type IIB string constructions
Natural inflation with hidden scale invariance
Neil D. Barrie
2016-05-01
Full Text Available We propose a new class of natural inflation models based on a hidden scale invariance. In a very generic Wilsonian effective field theory with an arbitrary number of scalar fields, which exhibits scale invariance via the dilaton, the potential necessarily contains a flat direction in the classical limit. This flat direction is lifted by small quantum corrections and inflation is realised without need for an unnatural fine-tuning. In the conformal limit, the effective potential becomes linear in the inflaton field, yielding to specific predictions for the spectral index and the tensor-to-scalar ratio, being respectively: ns−1≈−0.025(N⋆60−1 and r≈0.0667(N⋆60−1, where N⋆≈30–65 is a number of efolds during observable inflation. This predictions are in reasonable agreement with cosmological measurements. Further improvement of the accuracy of these measurements may turn out to be critical in falsifying our scenario.
Perfect discretization of reparametrization invariant path integrals
Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian
2011-01-01
To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.
Perfect discretization of reparametrization invariant path integrals
Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian
2011-05-01
To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.
Conformal Invariance in the Long-Range Ising Model
Paulos, Miguel F; van Rees, Balt C; Zan, Bernardo
2016-01-01
We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.
Conformal invariance in the long-range Ising model
Miguel F. Paulos
2016-01-01
Full Text Available We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.
Rotation, scale, and translation invariant pattern recognition using feature extraction
Prevost, Donald; Doucet, Michel; Bergeron, Alain; Veilleux, Luc; Chevrette, Paul C.; Gingras, Denis J.
1997-03-01
A rotation, scale and translation invariant pattern recognition technique is proposed.It is based on Fourier- Mellin Descriptors (FMD). Each FMD is taken as an independent feature of the object, and a set of those features forms a signature. FMDs are naturally rotation invariant. Translation invariance is achieved through pre- processing. A proper normalization of the FMDs gives the scale invariance property. This approach offers the double advantage of providing invariant signatures of the objects, and a dramatic reduction of the amount of data to process. The compressed invariant feature signature is next presented to a multi-layered perceptron neural network. This final step provides some robustness to the classification of the signatures, enabling good recognition behavior under anamorphically scaled distortion. We also present an original feature extraction technique, adapted to optical calculation of the FMDs. A prototype optical set-up was built, and experimental results are presented.
On logarithmic extensions of local scale-invariance
Henkel, Malte
2013-01-01
Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may be generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is characterised by two independent scaling dimensions. Building on analogies with logarithmic conformal invariance and logarithmic Schrödinger-invariance, this work proposes a logarithmic extension of local scale-invariance, without time-translation-invariance. Carrying this out requires in general to replace both scaling dimensions of each scaling operator by Jordan cells. Co-variant two-point functions are derived for the most simple case of a two-dimensional logarithmic extension. Their form is compared to simulational data for autoresponse functions in several universality classes of non-equilibrium ageing phenomena
Conformal invariance in the long-range Ising model
Paulos, Miguel F. [CERN, Theory Group, Geneva (Switzerland); Rychkov, Slava, E-mail: slava.rychkov@lpt.ens.fr [CERN, Theory Group, Geneva (Switzerland); Laboratoire de Physique Théorique de l' École Normale Supérieure (LPTENS), Paris (France); Faculté de Physique, Université Pierre et Marie Curie (UPMC), Paris (France); Rees, Balt C. van [CERN, Theory Group, Geneva (Switzerland); Zan, Bernardo [Institute of Physics, Universiteit van Amsterdam, Amsterdam (Netherlands)
2016-01-15
We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.
Efficient and Invariant Convolutional Neural Networks for Dense Prediction
Gao, Hongyang; Ji, Shuiwang
2017-01-01
Convolutional neural networks have shown great success on feature extraction from raw input data such as images. Although convolutional neural networks are invariant to translations on the inputs, they are not invariant to other transformations, including rotation and flip. Recent attempts have been made to incorporate more invariance in image recognition applications, but they are not applicable to dense prediction tasks, such as image segmentation. In this paper, we propose a set of methods...
Real-time trajectory analysis using stacked invariance methods
Kitts, B.
1998-01-01
Invariance methods are used widely in pattern recognition as a preprocessing stage before algorithms such as neural networks are applied to the problem. A pattern recognition system has to be able to recognise objects invariant to scale, translation, and rotation. Presumably the human eye implements some of these preprocessing transforms in making sense of incoming stimuli, for example, placing signals onto a log scale. This paper surveys many of the commonly used invariance methods, and asse...
Dimuon Level-1 invariant mass in 2017 data
CMS Collaboration
2018-01-01
This document shows the Level-1 (L1) dimuon invariant mass with and without L1 muon track extrapolation to the collision vertex and how it compares with the offline reconstructed dimuon invariant mass. The plots are made with the data sample collected in 2017. The event selection, the matching algorithm and the results of the L1 dimuon invariant mass are described in the next pages.
Differential invariants for higher-rank tensors. A progress report
Tapial, V.
2004-07-01
We outline the construction of differential invariants for higher-rank tensors. In section 2 we outline the general method for the construction of differential invariants. A first result is that the simplest tensor differential invariant contains derivatives of the same order as the rank of the tensor. In section 3 we review the construction for the first-rank tensors (vectors) and second-rank tensors (metrics). In section 4 we outline the same construction for higher-rank tensors. (author)
On the hierarchy of partially invariant submodels of differential equations
Golovin, Sergey V [Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090 (Russian Federation)], E-mail: sergey@hydro.nsc.ru
2008-07-04
It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.
On the hierarchy of partially invariant submodels of differential equations
Golovin, Sergey V.
2008-07-01
It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.
On the hierarchy of partially invariant submodels of differential equations
Golovin, Sergey V
2008-01-01
It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given
Note on Weyl versus conformal invariance in field theory
Wu, Feng [Nanchang University, Department of Physics, Nanchang (China)
2017-12-15
It was argued recently that conformal invariance in flat spacetime implies Weyl invariance in a general curved background for unitary theories and possible anomalies in the Weyl variation of scalar operators are identified. We argue that generically unitarity alone is not sufficient for a conformal field theory to be Weyl invariant. Furthermore, we show explicitly that when a unitary conformal field theory couples to gravity in a Weyl-invariant way, each primary scalar operator that is either relevant or marginal in the unitary conformal field theory corresponds to a Weyl-covariant operator in the curved background. (orig.)
Algebraic groups and their birational invariants
Voskresenskiĭ, V E
2011-01-01
Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, R-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.
Gauge invariance and Weyl-polymer quantization
Strocchi, Franco
2016-01-01
The book gives an introduction to Weyl non-regular quantization suitable for the description of physically interesting quantum systems, where the traditional Dirac-Heisenberg quantization is not applicable. The latter implicitly assumes that the canonical variables describe observables, entailing necessarily the regularity of their exponentials (Weyl operators). However, in physically interesting cases -- typically in the presence of a gauge symmetry -- non-observable canonical variables are introduced for the description of the states, namely of the relevant representations of the observable algebra. In general, a gauge invariant ground state defines a non-regular representation of the gauge dependent Weyl operators, providing a mathematically consistent treatment of familiar quantum systems -- such as the electron in a periodic potential (Bloch electron), the Quantum Hall electron, or the quantum particle on a circle -- where the gauge transformations are, respectively, the lattice translations, the magne...
Blocks of finite groups and their invariants
Sambale, Benjamin
2014-01-01
Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods. In a powerful combination, these tools are applied to solve many special cases of famous open conjectures in the representation theory of finite groups. Most of the material is drawn from peer-reviewed journal articles, but there are also new previously unpublished results. In order to make the text self-contained, detailed proofs are given whenever possible. Several tables add to the text's usefulness as a reference. The book is aimed at experts in group theory or representation theory who may wish to make use of the presented ideas in their research.
Kahler stabilized, modular invariant heterotic string models
Gaillard, Mary K.; Gaillard, Mary K.; Nelson, Brent D.
2007-01-01
We review the theory and phenomenology of effective supergravity theories based on orbifold compactifications of the weakly-coupled heterotic string. In particular, we consider theories in which the four-dimensional theory displays target space modular invariance and where the dilatonic mode undergoes Kahler stabilization. A self-contained exposition of effective Lagrangian approaches to gaugino condensation and heterotic string theory is presented, leading to the development of the models of Bintruy, Gaillard and Wu. Various aspects of the phenomenology of this class of models are considered. These include issues of supersymmetry breaking and superpartner spectra, the role of anomalous U(1) factors, issues of flavor and R-parity conservation, collider signatures, axion physics, and early universe cosmology. For the vast majority of phenomenological considerations the theories reviewed here compare quite favorably to other string-derived models in the literature. Theoretical objections to the framework and directions for further research are identified and discussed
Invariant box-parameterization of neutrino oscillations
Weiler, Thomas J.; Wagner, DJ
1998-01-01
The model-independent 'box' parameterization of neutrino oscillations is examined. The invariant boxes are the classical amplitudes of the individual oscillating terms. Being observables, the boxes are independent of the choice of parameterization of the mixing matrix. Emphasis is placed on the relations among the box parameters due to mixing-matrix unitarity, and on the reduction of the number of boxes to the minimum basis set. Using the box algebra, we show that CP-violation may be inferred from measurements of neutrino flavor mixing even when the oscillatory factors have averaged. General analyses of neutrino oscillations among n≥3 flavors can readily determine the boxes, which can then be manipulated to yield magnitudes of mixing matrix elements
Joint survival probability via truncated invariant copula
Kim, Jeong-Hoon; Ma, Yong-Ki; Park, Chan Yeol
2016-01-01
Highlights: • We have studied an issue of dependence structure between default intensities. • We use a multivariate shot noise intensity process, where jumps occur simultaneously and their sizes are correlated. • We obtain the joint survival probability of the integrated intensities by using a copula. • We apply our theoretical result to pricing basket default swap spread. - Abstract: Given an intensity-based credit risk model, this paper studies dependence structure between default intensities. To model this structure, we use a multivariate shot noise intensity process, where jumps occur simultaneously and their sizes are correlated. Through very lengthy algebra, we obtain explicitly the joint survival probability of the integrated intensities by using the truncated invariant Farlie–Gumbel–Morgenstern copula with exponential marginal distributions. We also apply our theoretical result to pricing basket default swap spreads. This result can provide a useful guide for credit risk management.
Conformally invariant braneworld and the cosmological constant
Guendelman, E.I.
2004-01-01
A six-dimensional braneworld scenario based on a model describing the interaction of gravity, gauge fields and 3+1 branes in a conformally invariant way is described. The action of the model is defined using a measure of integration built of degrees of freedom independent of the metric. There is no need to fine tune any bulk cosmological constant or the tension of the two (in the scenario described here) parallel branes to obtain zero cosmological constant, the only solutions are those with zero 4D cosmological constant. The two extra dimensions are compactified in a 'football' fashion and the branes lie on the two opposite poles of the compact 'football-shaped' sphere
Invariant relationships deriving from classical scaling transformations
Bludman, Sidney; Kennedy, Dallas C.
2011-01-01
Because scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to evolutionary laws that prove useful, even if the transformations are not symmetries of the equations of motion. In the case of scaling, symmetry leads to a scaling evolutionary law, a first-order equation in terms of scale invariants, linearly relating kinematic and dynamic degrees of freedom. This scaling evolutionary law appears in dynamical and in static systems. Applied to dynamical central-force systems, the scaling evolutionary equation leads to generalized virial laws, which linearly connect the kinetic and potential energies. Applied to barotropic hydrostatic spheres, the scaling evolutionary equation linearly connects the gravitational and internal energy densities. This implies well-known properties of polytropes, describing degenerate stars and chemically homogeneous nondegenerate stellar cores.
Invariant mass distributions in cascade decays
Miller, D J; Raklev, A R
2006-01-01
We derive analytical expressions for the shape of the invariant mass distributions of massless Standard Model endproducts in cascade decays involving massive New Physics (NP) particles, D -> Cc -> Bbc -> Aabc, where the final NP particle A in the cascade is unobserved and where two of the particles a, b, c may be indistinguishable. Knowledge of these expressions can improve the determination of NP parameters at the LHC. The shape formulas are composite, but contain nothing more complicated than logarithms of simple expressions. We study the effects of cuts, final state radiation and detector effects on the distributions through Monte Carlo simulations, using a supersymmetric model as an example. We also consider how one can deal with the width of NP particles and with combinatorics from the misidentification of final state particles. The possible mismeasurements of NP masses through `feet' in the distributions are discussed. Finally, we demonstrate how the effects of different spin configurations can be inclu...
Invariant mass distributions in cascade decays
Miller, David J.; Osland, Per; Raklev, Are R.
2006-01-01
We derive analytical expressions for the shape of the invariant mass distributions of massless Standard Model endproducts in cascade decays involving massive New Physics (NP) particles, D→Cc→Bbc→Aabc, where the final NP particle A in the cascade is unobserved and where two of the particles a, b, c may be indistinguishable. Knowledge of these expressions can improve the determination of NP parameters at the LHC. The shape formulas are composite, but contain nothing more complicated than logarithms of simple expressions. We study the effects of cuts, final state radiation and detector effects on the distributions through Monte Carlo simulations, using a supersymmetric model as an example. We also consider how one can deal with the width of NP particles and with combinatorics from the misidentification of final state particles. The possible mismeasurements of NP masses through 'feet' in the distributions are discussed. Finally, we demonstrate how the effects of different spin configurations can be included in the distributions
Time-Scale Invariant Audio Data Embedding
Mansour Mohamed F
2003-01-01
Full Text Available We propose a novel algorithm for high-quality data embedding in audio. The algorithm is based on changing the relative length of the middle segment between two successive maximum and minimum peaks to embed data. Spline interpolation is used to change the lengths. To ensure smooth monotonic behavior between peaks, a hybrid orthogonal and nonorthogonal wavelet decomposition is used prior to data embedding. The possible data embedding rates are between 20 and 30 bps. However, for practical purposes, we use repetition codes, and the effective embedding data rate is around 5 bps. The algorithm is invariant after time-scale modification, time shift, and time cropping. It gives high-quality output and is robust to mp3 compression.
Invariant box parameterization of neutrino oscillations
Weiler, T.J.; Wagner, D.
1998-01-01
The model-independent 'box' parameterization of neutrino oscillations is examined. The invariant boxes are the classical amplitudes of the individual oscillating terms. Being observables, the boxes are independent of the choice of parameterization of the mixing matrix. Emphasis is placed on the relations among the box parameters due to mixing matrix unitarity, and on the reduction of the number of boxes to the minimum basis set. Using the box algebra, we show that CP-violation may be inferred from measurements of neutrino flavor mixing even when the oscillatory factors have averaged. General analyses of neutrino oscillations among n≥3 flavors can readily determine the boxes, which can then be manipulated to yield magnitudes of mixing matrix elements. copyright 1998 American Institute of Physics
Quantum critical phenomena and conformal invariance
Zhe Chang.
1995-05-01
We show that the Abelian bosonization of continuum limit of the 1D Hubbard model corresponds to the 2D explicitly conformal invariant Gaussian model at weak coupling limit. A universality argument is used to extend the equivalence to an entire segment of the critical line of the strongly correlated electron system. An integral equation satisfied by the mapping function between critical lines of the 1D Hubbard model and 2D Gaussian model is obtained and then solved in some limiting cases. By making use of the fact that the free Hubbard system reduces to four fermions and each of them is related to a c = 1/2 conformal field theory, we present exactly the partition function of the Hubbard model on a finite 1D lattice. (author). 16 refs
Gauge invariance and reciprocity in quantum mechanics
Leung, P. T.; Young, K.
2010-01-01
Reciprocity in wave propagation usually refers to the symmetry of the Green's function under the interchange of the source and the observer coordinates, but this condition is not gauge invariant in quantum mechanics, a problem that is particularly significant in the presence of a vector potential. Several possible alternative criteria are given and analyzed with reference to different examples with nonzero magnetic fields and/or vector potentials, including the case of a multiply connected spatial domain. It is shown that the appropriate reciprocity criterion allows for specific phase factors separable into functions of the source and observer coordinates and that this condition is robust with respect to the addition of any scalar potential. In the Aharonov-Bohm effect, reciprocity beyond monoenergetic experiments holds only because of subsidiary conditions satisfied in actual experiments: the test charge is in units of e and the flux is produced by a condensate of particles with charge 2e.
INVARIANTS OF GENERALIZED RAPOPORT-LEAS EQUATIONS
Elena N. Kushner
2018-01-01
Full Text Available For the generalized Rapoport-Leas equations, algebra of differential invariants is constructed with respect to point transformations, that is, transformations of independent and dependent variables. The finding of a general transformation of this type reduces to solving an extremely complicated functional equation. Therefore, following the approach of Sophus Lie, we restrict ourselves to the search for infinitesimal transformations which are generated by translations along the trajectories of vector fields. The problem of finding these vector fields reduces to the redefined system decision of linear differential equations with respect to their coefficients. The Rapoport-Leas equations arise in the study of nonlinear filtration processes in porous media, as well as in other areas of natural science: for example, these equations describe various physical phenomena: two-phase filtration in a porous medium, filtration of a polytropic gas, and propagation of heat at nuclear explosion. They are vital topic for research: in recent works of Bibikov, Lychagin, and others, the analysis of the symmetries of the generalized Rapoport-Leas equations has been carried out; finite-dimensional dynamics and conditions of attractors existence have been found. Since the generalized RapoportLeas equations are nonlinear partial differential equations of the second order with two independent variables; the methods of the geometric theory of differential equations are used to study them in this paper. According to this theory differential equations generate subvarieties in the space of jets. This makes it possible to use the apparatus of modern differential geometry to study differential equations. We introduce the concept of admissible transformations, that is, replacements of variables that do not derive equations outside the class of the Rapoport-Leas equations. Such transformations form a Lie group. For this Lie group there are differential invariants that separate
Conformally invariant processes in the plane
Lawler, G.F.
2004-01-01
These lectures will focus on recent rigorous work on continuum limits of planar lattice models from statistical physics at criticality. For an introduction, I would like to discuss the general problem of critical exponents and scaling limits for lattice models in equilibrium statistical mechanics. There are a number of models, [e.g., self-avoiding walk (polymers), percolation, loop-erased random walk (uniform spanning trees, domino tilings), Ising model, Potts model, nonintersecting simple random walks] that fall under this general framework. These lectures will consider the case d = 2. Mathematicians are now starting to understand rigorously the scaling limit of two-dimensional systems. For most of these models, the general strategy can be described as: Construct possible continuum limits for these models. Show that there are only a limited number of such limits that are conformally invariant. Prove that the lattice model approaches the continuum limit. We should think of the first step as being similar for all of these models. We will spend the next couple of lectures discussing the continuum limits. One example you should already know - the scaling limit of simple random walk is Brownian motion (which in two dimensions is conformally invariant). The important new ideas are restriction measures and stochastic Loewner evolution (SLE). The later lectures will discuss rigorous results about lattice models approaching the continuum limit - we will discuss nonintersecting random walks (which can be shown to be equivalent to problems about exceptional sets of Brownian paths), percolation on the triangular lattice, and the loop-erased random walk. As a rule, the methods used for the second step are particular to each model
BRST invariant mixed string vertex for the bosonic string
Clarizia, A.; Pezzella, F.
1987-09-01
We construct a BRST invariant (N+M)-string vertex including both open and closed string states. When we saturate it with N open string and M closed string physical states it reproduces their corresponding scattering amplitude. As a particular case we obtain BRST invariant vertex for the open-closed string transition. (orig.)
Kinetic theory in maximal-acceleration invariant phase space
Brandt, H.E.
1989-01-01
A vanishing directional derivative of a scalar field along particle trajectories in maximal acceleration invariant phase space is identical in form to the ordinary covariant Vlasov equation in curved spacetime in the presence of both gravitational and nongravitational forces. A natural foundation is thereby provided for a covariant kinetic theory of particles in maximal-acceleration invariant phase space. (orig.)
The relativistic invariant and the Galilean mass of bodies
Kapuscik, E.
1992-02-01
We generalize the concept of the Galilean mass to the relativistic case. In the case of inequality of Galilean and inertial masses we calculate the relativistic invariant being constant along the trajectory of the moving body. It enables us to define an invariant measure of inertia of bodies. 4 refs. (author)
Chronoprojective invariance of the five-dimensional Schroedinger formalism
Perrin, M.; Burdet, G.; Duval, C.
1984-10-01
Invariance properties of the five-dimensional Schroedinger formalism describing a quantum test particle in the Newton-Cartan theory of gravitation are studied. The geometry which underlies these invariance properties is presented as a reduction of the 0(5,2) conformal geometry various applications are given
Modular invariants and fusion rule automorphisms from Galois theory
Fuchs, J.; Gato-Rivera, B.; Schellekens, B.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica; Schweigert, C.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica
1994-05-01
We show that Galois theory of cyclotomic number fields provides a powerful tool to construct systematically integer-valued matrices commuting with the modular matrix S, as well as automorphisms of the fusion rules. Both of these prescriptions allow the construction of modular invariants and offer new insight in the structure of known exceptional invariants. (orig.)
Measurement Invariance: A Foundational Principle for Quantitative Theory Building
Nimon, Kim; Reio, Thomas G., Jr.
2011-01-01
This article describes why measurement invariance is a critical issue to quantitative theory building within the field of human resource development. Readers will learn what measurement invariance is and how to test for its presence using techniques that are accessible to applied researchers. Using data from a LibQUAL+[TM] study of user…
Projective invariants in a conformal finsler space - I
Mishra, C.K.; Singh, M.P.
1989-12-01
The projective invariants in a conformal Finsler space have been studied in regard to certain tensor and scalar which are invariant under projective transformation in a Finsler space. They have been the subject of further investigation by the present authors. (author). 8 refs
Heterotic superstring and curved, scale-invariant superspace
Kuusk, P.K.
1988-01-01
It is shown that the modified heterotic superstring [R. E. Kallosh, JETP Lett. 43, 456 (1986); Phys. Lett. 176B, 50 (1986)] demands a scale-invariant superspace for its existence. Explicit expressions are given for the connection, the torsion, and the curvature of an extended scale-invariant superspace with 506 bosonic and 16 fermionic coordinates
Invariants for the generalized Lotka-Volterra equations
Cairó, Laurent; Feix, Marc R.; Goedert, Joao
A generalisation of Lotka-Volterra System is given when self limiting terms are introduced in the model. We use a modification of the Carleman embedding method to find invariants for this system of equations. The position and stability of the equilibrium point and the regression of system under invariant conditions are studied.
N=2 supergravity in superspace: the invariant action
Gal'perin, A.S.; Sokachev, E.
1987-01-01
This paper continues the formulation of harmonic superspace supergravity. We write down the invariant action for the first off-shell version of the theory. The proof of the invariance relies on the existence of a new 'hybrid' basis in harmonic superspace in which semi-chirality combined with analyticity are manifest
The Scale Invariant Synchrotron Jet of Flat Spectrum Radio Quasars
2016-01-27
Jan 27, 2016 ... In this paper, the scale invariance of the synchrotron jet of Flat Spectrum Radio Quasars has been studied using a sample of combined sources from FKM04 and from SDSS DR3 catalogue. Since the research of scale invariance has been focused on sub-Eddington cases that can be fitted onto the ...
Galilean invariance and homogeneous anisotropic randomly stirred flows
Berera, Arjun; Hochberg, David
2005-01-01
The Ward-Takahashi identities for incompressible flow implied by Galilean invariance are derived for the randomly forced Navier-Stokes equation, in which both the mean and fluctuating velocity components are explicitly present. The consequences of the Galilean invariance for the vertex renormalization are drawn from this identity
Existence of a last invariant of conservative motion
Hall, L.S.
1982-01-01
A general theory of integrable systems in two dimensions is formulated and applied. (The theory also has applications to more dimensions). The constraints are found which admit to general integrability of the orbits for magnetic forces as well as for forces derivable from a potential. When a system admits a given invariant, the invariant is found. A number of examples including known and apparently previously unknown invariants are given. The theory of exact integrals of the motion also can be extended to the derivation of approximate invariants. The general theory admits a variational principle, among other approximation techniques, for the computation of a best approximate invariant. The problem of the general cubic potential with one symmetric coordinate, V = 1/2 Ax 2 + 1/2 By 2 + Cx 2 y + 1/3 Dy 3 (of which the well-studied Henon-Heiles potential is the special case for A = B and C = -D), is examined in detail
Strong coupling in a gauge invariant field theory
Johnson, K. [Physics Department, Massachusetts Institute of Technology, Cambridge, MA (United States)
1963-01-15
I would like to discuss some approximations which may be significant in the domain of strong coupling in a field system analogous to quantum electrodynamics. The motivation of this work is the idea that the strong couplings and elementary particle spectrum may be the consequence of the dynamics of a system whose underlying description is in terms of a set of Fermi fields gauge invariantly coupled to a single (''bare'') massless neutral vector field. The basis of this gauge invariance would of course be the exact conservation law of baryons or ''nucleonic charge''. It seems to me that a coupling scheme based on an invariance principle is most attractive if that invariance is an exact one. It would then be nice to try to account for the approximate invariance principles in the same way one would describe ''accidental degeneracies'' in any quantum system.
The holonomy expansion: Invariants and approximate supersymmetry
Jaffe, Arthur
2000-01-01
In this paper we give a new expansion, based on cyclicity of the trace, to study regularity properties of twisted expectations =Tr H (γU(θ)X(s)). Here X(s)=X 0 e -s 0 Q 2 X 1 e -s 1 Q 2 ...X k e -s k Q 2 is a product of operators X j , regularized by heat kernels e -s j Q 2 with s j >0. The twist groups γ(set-membership sign)Z 2 and U(θ)(set-membership sign)U(1) are commuting symmetries of Q 2 . The name ''holonomy expansion'' arises from picturing as a circular graph, with vertices in the graph representing the operators X j , in the order that they appear in the product, and the line-segment following X j representing the heat kernel e -s j Q 2 . The trace functional is cyclic, so the graph is circular. We generate our expansion by ''transporting'' a vertex X k around the circle, ending in its original position. We choose an X k that transforms under a one-dimensional representation of Z 2 xU(1). For θ in the complement of the discrete set γ sing (where the group Z 2 xU(1) acts trivially on X k ) we obtain an identity between the original expectation and some new expectations. We study an example from supersymmetric quantum mechanics, with a Dirac operator Q(λ) depending on a parameter λ and with a U(1) group of symmetries U(θ). We apply our expansion to invariants Z(λ;θ)=Z(Q(λ);θ) suggested by non-commutative geometry. These invariants are sums of expectations of the form above. We investigate this example as a first step toward developing an expansion to evaluate related invariants arising in supersymmetric quantum field theory. We establish differentiability of Z(λ; θ) in λ for λ(set-membership sign)(0,1] and show Z(λ; θ) is independent of λ. We wish to evaluate Z(λ; θ) at the endpoint λ=0, but Z(0; θ) is ill-defined. We regularize the endpoint, while preserving the U(θ)-symmetry, by replacing Q(λ) 2 with H(ε,λ)=Q(λ) 2 +ε 2 |z| 2 . The regularized function Z(ε, λ; θ) depends on all three variables ε, λ, θ; for fixed θ, it
Lorentz invariance violation in modified gravity
Brax, Philippe
2012-01-01
We consider an environmentally dependent violation of Lorentz invariance in scalar-tensor models of modified gravity where General Relativity is retrieved locally thanks to a screening mechanism. We find that fermions have a modified dispersion relation and would go faster than light in an anisotropic and space-dependent way along the scalar field lines of force. Phenomenologically, these models are tightly restricted by the amount of Cerenkov radiation emitted by the superluminal particles, a constraint which is only satisfied by chameleons. Measuring the speed of neutrinos emitted radially from the surface of the earth and observed on the other side of the earth would probe the scalar field profile of modified gravity models in dense environments. We argue that the test of the equivalence principle provided by the Lunar ranging experiment implies that a deviation from the speed of light, for natural values of the coupling scale between the scalar field and fermions, would be below detectable levels, unless gravity is modified by camouflaged chameleons where the field normalisation is environmentally dependent.
Magnetic monopoles, Galilean invariance, and Maxwell's equations
Crawford, F.S.
1992-01-01
Maxwell's equations have space reserved for magnetic monopoles. Whether or not they exist in our part of the universe, monopoles provide a useful didactic tool to help us recognize relations among Maxwell's equations less easily apparent in the approach followed by many introductory textbooks, wherein Coulomb's law, Biot and Savart's law, Ampere's law, Faraday's law, Maxwell's displacement current, etc., are introduced independently, ''as demanded by experiment.'' Instead a conceptual path that deduces all of Maxwell's equations from the near-minimal set of assumptions: (a) Inertial frames exist, in which Newton's laws hold, to a first approximation; (b) the laws of electrodynamics are Galilean invariant---i.e., they have the same form in every inertial frame, to a first approximation; (c) magnetic poles (as well as the usual electric charges) exist; (d) the complete Lorentz force on an electric charge is known; (e) the force on a monopole at rest is known; (f) the Coulomb-like field produced by a resting electric charge and by a resting monopole are known. Everything else is deduced. History is followed in the assumption that Newtonian mechanics have been discovered, but not special relativity. (Only particle velocities v much-lt c are considered.) This ends up with Maxwell's equations (Maxwell did not need special relativity, so why should we,) but facing Einstein's paradox, the solution of which is encapsulated in the Einstein velocity-addition formula
Magnocellular pathway for rotation invariant Neocognitron.
Ting, C H
1993-03-01
In the mammalian visual system, magnocellular pathway and parvocellular pathway cooperatively process visual information in parallel. The magnocellular pathway is more global and less particular about the details while the parvocellular pathway recognizes objects based on the local features. In many aspects, Neocognitron may be regarded as the artificial analogue of the parvocellular pathway. It is interesting then to model the magnocellular pathway. In order to achieve "rotation invariance" for Neocognitron, we propose a neural network model after the magnocellular pathway and expand its roles to include surmising the orientation of the input pattern prior to recognition. With the incorporation of the magnocellular pathway, a basic shift in the original paradigm has taken place. A pattern is now said to be recognized when and only when one of the winners of the magnocellular pathway is validified by the parvocellular pathway. We have implemented the magnocellular pathway coupled with Neocognitron parallel on transputers; our simulation programme is now able to recognize numerals in arbitrary orientation.
Implications of conformal invariance in momentum space
Bzowski, Adam; McFadden, Paul; Skenderis, Kostas
2014-03-01
We present a comprehensive analysis of the implications of conformal invariance for 3-point functions of the stress-energy tensor, conserved currents and scalar operators in general dimension and in momentum space. Our starting point is a novel and very effective decomposition of tensor correlators which reduces their computation to that of a number of scalar form factors. For example, the most general 3-point function of a conserved and traceless stress-energy tensor is determined by only five form factors. Dilatations and special conformal Ward identities then impose additional conditions on these form factors. The special conformal Ward identities become a set of first and second order differential equations, whose general solution is given in terms of integrals involving a product of three Bessel functions (`triple- K integrals'). All in all, the correlators are completely determined up to a number of constants, in agreement with well-known position space results. In odd dimensions 3-point functions are finite without renormalisation while in even dimensions non-trivial renormalisation in required. In this paper we restrict ourselves to odd dimensions. A comprehensive analysis of renormalisation will be discussed elsewhere. This paper contains two parts that can be read independently of each other. In the first part, we explain the method that leads to the solution for the correlators in terms of triple- K integrals while the second part contains a self-contained presentation of all results. Readers interested only in results may directly consult the second part of the paper.
AN ILLUMINATION INVARIANT TEXTURE BASED FACE RECOGNITION
K. Meena
2013-11-01
Full Text Available Automatic face recognition remains an interesting but challenging computer vision open problem. Poor illumination is considered as one of the major issue, since illumination changes cause large variation in the facial features. To resolve this, illumination normalization preprocessing techniques are employed in this paper to enhance the face recognition rate. The methods such as Histogram Equalization (HE, Gamma Intensity Correction (GIC, Normalization chain and Modified Homomorphic Filtering (MHF are used for preprocessing. Owing to great success, the texture features are commonly used for face recognition. But these features are severely affected by lighting changes. Hence texture based models Local Binary Pattern (LBP, Local Derivative Pattern (LDP, Local Texture Pattern (LTP and Local Tetra Patterns (LTrPs are experimented under different lighting conditions. In this paper, illumination invariant face recognition technique is developed based on the fusion of illumination preprocessing with local texture descriptors. The performance has been evaluated using YALE B and CMU-PIE databases containing more than 1500 images. The results demonstrate that MHF based normalization gives significant improvement in recognition rate for the face images with large illumination conditions.
ICECUBE NEUTRINOS AND LORENTZ INVARIANCE VIOLATION
Amelino-Camelia, Giovanni [Dipartimento di Fisica, Sapienza Università di Roma and INFN, Sez. Roma1, P.le A. Moro 2, I-00185 Roma (Italy); Guetta, D. [Osservatorio astronomico di Roma, v. Frascati 33, I-00040 Monte Porzio Catone (Italy); Piran, Tsvi [The Racah Institute for Physics, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2015-06-20
The IceCube neutrino telescope has found so far no evidence of gamma-ray burst (GRB) neutrinos. We here notice that these results assume the same travel times from source to telescope for neutrinos and photons, an assumption that is challenged by some much-studied pictures of spacetime quantization. We briefly review previous results suggesting that limits on quantum-spacetime effects obtained for photons might not be applicable to neutrinos, and we then observe that the outcome of GRB-neutrino searches could depend strongly on whether one allows for neutrinos to be affected by the minute effects of Lorentz invariance violation (LIV) predicted by some relevant quantum-spacetime models. We discuss some relevant issues using as an illustrative example three neutrinos that were detected by IceCube in good spatial coincidence with GRBs, but hours before the corresponding gamma rays. In general, this could happen if the earlier arrival reflects quantum-spacetime-induced LIV, but, as we stress, some consistency criteria must be enforced in order to properly test such a hypothesis. Our analysis sets the stage for future GRB-neutrino searches that could systematically test the possibility of quantum-spacetime-induced LIV.
Scale-invariant gravity: spacetime recovered
Kelleher, Bryan
2004-01-01
The configuration space of general relativity is superspace-the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace-the space of all Riemannian 3-metrics modulo diffeomorphisms and conformal transformations. Recently a manifestly three-dimensional theory was constructed with conformal superspace as the configuration space. Here a fully four-dimensional action is constructed so as to be invariant under conformal transformations of the 4-metric using general relativity as a guide. This action is then decomposed to a (3 + 1)-dimensional form and from this to its Jacobi form. The surprising thing is that the new theory turns out to be precisely the original three-dimensional theory. The physical data are identified and used to find the physical representation of the theory. In this representation the theory is extremely similar to general relativity. The clarity of the four-dimensional picture should prove very useful for comparing the theory with those aspects of general relativity which are usually treated in the four-dimensional framework
On a possible origin of modular invariance
Tahir Shah, K.
1991-06-01
We propose an information theoretic model of the space-time pre-geometry where the pre-geometry is considered as a ''coded state of matter and space-time'', distinctly different from the classical space-time or any known state of matter. Assuming that physical processes at Planck's dimensions are stochastic Markov processes and using information theoretic and algebro-geometric coding techniques, we show that modular invariance is a natural consequence of: 1. Shannon's channel capacity theorem. 2. Nature selects and uses only those error-correcting codes to transfer information between space-time entities which allow the value of propagation rate R reaching its critical value R C , the channel capacity. Next, using the strong converse theorem we show that a phase-transition occurs at (R C -R) 0. Furthermore, it is known that some symmetrically packed optimal codes lead to E 8 lattice while others to a 26-dimensional Lorentz lattice used in string theories. This suggests a precise connection between our model and string theories. (author). 26 refs
Lorentz invariance violation in modified gravity
Brax, Philippe, E-mail: philippe.brax@cea.fr [Institut de Physique Theorique, CEA, IPhT, CNRS, URA 2306, F-91191Gif/Yvette Cedex (France)
2012-06-06
We consider an environmentally dependent violation of Lorentz invariance in scalar-tensor models of modified gravity where General Relativity is retrieved locally thanks to a screening mechanism. We find that fermions have a modified dispersion relation and would go faster than light in an anisotropic and space-dependent way along the scalar field lines of force. Phenomenologically, these models are tightly restricted by the amount of Cerenkov radiation emitted by the superluminal particles, a constraint which is only satisfied by chameleons. Measuring the speed of neutrinos emitted radially from the surface of the earth and observed on the other side of the earth would probe the scalar field profile of modified gravity models in dense environments. We argue that the test of the equivalence principle provided by the Lunar ranging experiment implies that a deviation from the speed of light, for natural values of the coupling scale between the scalar field and fermions, would be below detectable levels, unless gravity is modified by camouflaged chameleons where the field normalisation is environmentally dependent.
Parity and time invariance violation in mercury
Ginges, J.S.M.; Dzuba, V.A.; Flambaum, V.V.; Kozlov, M.G.
2002-01-01
Full text: In a recent experiment, a stringent upper limit was placed on the atomic electric dipole moment (EDM) of 199 Hg corresponding to the best limit on an atomic EDM to date. This limit can be interpreted in terms of a limit on a parity-and time-invariance violating (P,T-odd) nuclear electric moment, the Schiff moment. This moment can arise in the nucleus due to an intrinsic EDM of an unpaired nucleon or a P,T-odd interaction between nucleons. In previous calculations the electrostatic potential of the Schiff moment was expressed in a singular form which must be treated carefully to avoid divergences in the electronic matrix elements. We have shown that the electric field distribution inside the nucleus arising from the Schiff moment is constant and directed along the nuclear spin. This allows us to express the Schiff moment in a form more convenient for numerical relativistic atomic calculations. We have calculated the atomic EDM induced in Hg due to the Schiff moment (for which no direct calculation has previously been performed) and have placed new limits on the fundamental P,T-odd parameters. These limits strongly constrain competing theories of CP-violation
Achieving Translationally Invariant Trapped Ion Rings
Urban, Erik; Li, Hao-Kun; Noel, Crystal; Hemmerling, Boerge; Zhang, Xiang; Haeffner, Hartmut
2017-04-01
We present the design and implementation of a novel surface ion trap design in a ring configuration. By eliminating the need for wire bonds through the use of electrical vias and using a rotationally invariant electrode configuration, we have realized a trap that is able to trap up to 20 ions in a ring geometry 45um in diameter, 400um above the trap surface. This large trapping height to ring diameter ratio allows for global addressing of the ring with both lasers and electric fields in the chamber, thereby increasing our ability to control the ring as a whole. Applying compensating electric fields, we measure very low tangential trap frequencies (less than 20kHz) corresponding to rotational barriers down to 4mK. This measurement is currently limited by the temperature of the ions but extrapolation indicates the barrier can be reduced much further with more advanced cooling techniques. Finally, we show that we are able to reduce this energy barrier sufficiently such that the ions are able to overcome it either through thermal motion or rotational motion and delocalize over the full extent of the ring. This work was funded by the Keck Foundation and the NSF.
Sprague, Briana N; Hyun, Jinshil; Molenaar, Peter C M
2017-01-01
Invariance of intelligence across age is often assumed but infrequently explicitly tested. Horn and McArdle (1992) tested measurement invariance of intelligence, providing adequate model fit but might not consider all relevant aspects such as sub-test differences. The goal of the current paper is to explore age-related invariance of the WAIS-R using an alternative model that allows direct tests of age on WAIS-R subtests. Cross-sectional data on 940 participants aged 16-75 from the WAIS-R normative values were used. Subtests examined were information, comprehension, similarities, vocabulary, picture completion, block design, picture arrangement, and object assembly. The two intelligence factors considered were fluid and crystallized intelligence. Self-reported ages were divided into young (16-22, n = 300), adult (29-39, n = 275), middle (40-60, n = 205), and older (61-75, n = 160) adult groups. Results suggested partial metric invariance holds. Although most of the subtests reflected fluid and crystalized intelligence similarly across different ages, invariance did not hold for block design on fluid intelligence and picture arrangement on crystallized intelligence for older adults. Additionally, there was evidence of a correlated residual between information and vocabulary for the young adults only. This partial metric invariance model yielded acceptable model fit compared to previously-proposed invariance models of Horn and McArdle (1992). Almost complete metric invariance holds for a two-factor model of intelligence. Most of the subtests were invariant across age groups, suggesting little evidence for age-related bias in the WAIS-R. However, we did find unique relationships between two subtests and intelligence. Future studies should examine age-related differences in subtests when testing measurement invariance in intelligence.
Berube, D.; Kroeger, H.; Lafrance, R.; Marleau, L.
1991-01-01
We discuss properties of a noncompact formulation of gauge theories with fermions on a momentum (k) lattice. (a) This formulation is suitable to build in Fourier acceleration in a direct way. (b) The numerical effort to compute the action (by fast Fourier transform) goes essentially like logV with the lattice volume V. (c) For the Yang-Mills theory we find that the action conserves gauge symmetry and chiral symmetry in a weak sense: On a finite lattice the action is invariant under infinitesimal transformations with compact support. Under finite transformations these symmetries are approximately conserved and they are restored on an infinite lattice and in the continuum limit. Moreover, these symmetries also hold on a finite lattice under finite transformations, if the classical fields, instead of being c-number valued, take values from a finite Galois field. (d) There is no fermion doubling. (e) For the φ 4 model we investigate the transition towards the continuum limit in lattice perturbation theory up to second order. We compute the two- and four-point functions and find local and Lorentz-invariant results. (f) In QED we compute a one-loop vacuum polarization and find in the continuum limit the standard result. (g) As a numerical application, we compute the propagator left-angle φ(k)φ(k')right-angle in the φ 4 model, investigate Euclidean invariance, and extract m R as well as Z R . Moreover we compute left-angle F μν (k)F μν (k')right-angle in the SU(2) model
A test of conformal invariance: Correlation functions on a disk
Badke, R.; Rittenberg, V.; Ruegg, H.
1985-06-01
Using conformal invariance one can derive the correlation functions of a disk from those in the half-plane. The correlation function in the half-plane is determined by the 'small' conformal invariance up to an unknown function of one variable. By measuring through the Monte Carlo method the correlation function for two different configurations, the unknown function can be eliminated and one obtains a test of conformal invariance. It is shown that the Ising and the three state Potts model pass the test for very small lattices. (orig.)
On a gauge invariant subtraction scheme for massive quantum electrodynamics
Abdalla, E.; Gomes, M.; Koeberle, R.
A momentum-space subtraction scheme for massive quantum electrodynamics is proposed which respects gauge invariance, in contrast to ordinary normal product techniques. As a consequence the dependence of Green functions on the ghost mass becomes very simple and formally gauge invariant normal products of degree up to four, when subtracted according to the proposed scheme, are automatically gauge invariant. As an aplication we discuss the proof of the Adler-Bardeen theorem. Zero mass limits can be taken for Green function after the integration over intermediate states has been carried out [pt
Weyl-Invariant Extension of the Metric-Affine Gravity
Vazirian, R.; Tanhayi, M. R.; Motahar, Z. A.
2015-01-01
Metric-affine geometry provides a nontrivial extension of the general relativity where the metric and connection are treated as the two independent fundamental quantities in constructing the spacetime (with nonvanishing torsion and nonmetricity). In this paper, we study the generic form of action in this formalism and then construct the Weyl-invariant version of this theory. It is shown that, in Weitzenböck space, the obtained Weyl-invariant action can cover the conformally invariant teleparallel action. Finally, the related field equations are obtained in the general case.
Invariant renormalization method for nonlinear realizations of dynamical symmetries
Kazakov, D.I.; Pervushin, V.N.; Pushkin, S.V.
1977-01-01
The structure of ultraviolet divergences is investigated for the field theoretical models with nonlinear realization of the arbitrary semisimple Lie group, with spontaneously broken symmetry of vacuum. An invariant formulation of the background field method of renormalization is proposed which gives the manifest invariant counterterms off mass shell. A simple algorithm for construction of counterterms is developed. It is based on invariants of the group of dynamical symmetry in terms of the Cartan forms. The results of one-loop and two-loop calculations are reported
Invariants for minimal conformal supergravity in six dimensions
Butter, Daniel [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Kuzenko, Sergei M. [School of Physics M013, The University of Western Australia,35 Stirling Highway, Crawley W.A. 6009 (Australia); Novak, Joseph; Theisen, Stefan [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,Am Mühlenberg 1, D-14476 Golm (Germany)
2016-12-15
We develop a new off-shell formulation for six-dimensional conformal supergravity obtained by gauging the 6D N=(1,0) superconformal algebra in superspace. This formulation is employed to construct two invariants for 6D N=(1,0) conformal supergravity, which contain C{sup 3} and C◻C terms at the component level. Using a conformal supercurrent analysis, we prove that these exhaust all such invariants in minimal conformal supergravity. Finally, we show how to construct the supersymmetric F◻F invariant in curved superspace.
Macdonald operators and homological invariants of the colored Hopf link
Awata, Hidetoshi; Kanno, Hiroaki
2011-01-01
Using a power sum (boson) realization for the Macdonald operators, we investigate the Gukov, Iqbal, Kozcaz and Vafa (GIKV) proposal for the homological invariants of the colored Hopf link, which include Khovanov-Rozansky homology as a special case. We prove the polynomiality of the invariants obtained by GIKV's proposal for arbitrary representations. We derive a closed formula of the invariants of the colored Hopf link for antisymmetric representations. We argue that a little amendment of GIKV's proposal is required to make all the coefficients of the polynomial non-negative integers. (paper)
Gauge invariance properties and singularity cancellations in a modified PQCD
Cabo-Montes de Oca, Alejandro; Cabo, Alejandro; Rigol, Marcos
2006-01-01
The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works, are investigated. The construction of the modified free propagators is generalized to include the dependence on the gauge parameter $\\alpha $. Further, a functional proof of the independence of the theory under the changes of the quantum and classical gauges is given. The singularities appearing in the perturbative expansion are eliminated by properly combining dimensional regularization with the Nakanishi infrared regularization for the invariant functions in the operator quantization of the $\\alpha$-dependent gauge theory. First-order evaluations of various quantities are presented, illustrating the gauge invariance-properties.
Verification of Java Programs using Symbolic Execution and Invariant Generation
Pasareanu, Corina; Visser, Willem
2004-01-01
Software verification is recognized as an important and difficult problem. We present a norel framework, based on symbolic execution, for the automated verification of software. The framework uses annotations in the form of method specifications an3 loop invariants. We present a novel iterative technique that uses invariant strengthening and approximation for discovering these loop invariants automatically. The technique handles different types of data (e.g. boolean and numeric constraints, dynamically allocated structures and arrays) and it allows for checking universally quantified formulas. Our framework is built on top of the Java PathFinder model checking toolset and it was used for the verification of several non-trivial Java programs.
Evolution of Brain Tumor and Stability of Geometric Invariants
K. Tawbe
2008-01-01
Full Text Available This paper presents a method to reconstruct and to calculate geometric invariants on brain tumors. The geometric invariants considered in the paper are the volume, the area, the discrete Gauss curvature, and the discrete mean curvature. The volume of a tumor is an important aspect that helps doctors to make a medical diagnosis. And as doctors seek a stable calculation, we propose to prove the stability of some invariants. Finally, we study the evolution of brain tumor as a function of time in two or three years depending on patients with MR images every three or six months.
Lagrangian model of conformal invariant interacting quantum field theory
Lukierski, J.
1976-01-01
A Lagrangian model of conformal invariant interacting quantum field theory is presented. The interacting Lagrangian and free Lagrangian are derived replacing the canonical field phi by the field operator PHIsub(d)sup(c) and introducing the conformal-invariant interaction Lagrangian. It is suggested that in the conformal-invariant QFT with the dimensionality αsub(B) obtained from the bootstrep equation, the normalization constant c of the propagator and the coupling parametery do not necessarily need to satisfy the relation xsub(B) = phi 2 c 3
Trojan Horse Particle Invariance: An Extensive Study
Pizzone, R. G.; Spitaleri, C.; Sergi, M. L.; Lamia, L.; Cognata, M. La; Spartá, R.; Tumino, A.; Bertulani, C. A.; Blokhintsev, L.; Burjan, V.; Kroha, V.; Mrazek, J.; Mukhamedzhanov, A. M.
2014-01-01
In the last decades, the Trojan Horse method (THM) has played a crucial role for the measurement of several particle (both neutron and charged one) induced cross sections for reactions of astrophysical interest. To better understand its cornerstones and its applications to physical cases, many tests were performed to verify all its properties and the possible future perspectives. The Trojan Horse nucleus invariance proves the relatively simple approach allowed by the pole approximation and sheds light in the involved reaction mechanisms. Here we shortly review the complete work for the binary 2 H(d,p) 3 H, 6 Li(d,α) 4 He, 6 Li(p,α) 3 He, 7 Li(p,α) 4 He reactions, by using the quasi free reactions after break-ups of different nuclides. Results are compared assuming the 6 Li and 3 He break-up in the case of the d(d,p)t, 6 Li(d,α) 4 He reactions and considering the 2 H and 3 He break-up for 6 Li(p,α) 3 He, 7 Li(p,α) 4 He reactions. These results, regardless of the Trojan Horse particle or the break-up scheme, confirms the applicability of the standard description of the THM and suggests the independence of binary indirect cross section on the chosen Trojan Horse nuclei for a whole spectra of different cases. This gives a strong basis for the understanding of the quasi-free mechanism which is the foundation on which the THM lies. (author)
The baryon asymmetry and CPT invariance in the early universe
Barshay, S.
1981-01-01
We discuss, and give a definite, simple phenomenological example, of the possibility that the baryon asymmetry is related to a failure of CPT invariance for a brief time interval at the origin of the universe. (orig.)
Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI
Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.
2015-01-01
Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085
A quantization scheme for scale-invariant pure gauge theories
Hortacsu, M.
1988-01-01
A scheme is suggested for the quantization of the recently proposed scale-invariant gauge theories in higher dimensions. The model is minimally coupled to a spinor field. Regularization algorithms are proposed. (orig.)
Galilean-Invariant Lattice-Boltzmann Models with H Theorem
Boghosian, Bruce
2003-01-01
The authors demonstrate that the requirement of Galilean invariance determines the choice of H function for a wide class of entropic lattice-Boltzmann models for the incompressible Navier-Stokes equations...
A new von Mises probabilistic formula for quartet invariants
Giacovazzo, C.; Camalli, M.; Spagna, R.
1989-01-01
Von Mises formulas for quartet invariants, even is useful in most cases of practical interest, suffer from some systematic errors. A new von Mises formula is suggested with better theoretical features. (orig.)
Statistical analysis of complex systems with nonclassical invariant measures
Fratalocchi, Andrea
2011-01-01
I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by employing a
Invariance properties of the Dirac equation with external electro ...
. Introduction. The objective of this short paper is to investigate the invariance properties of the Dirac equation with external electro-magnetic field. There exists a large number of literatures on the problem beginning almost from the formulation ...
Structural invariance of the Schroedinger equation and chronoprojective geometry
Burdet, G.; Perrin, M.
1983-07-01
We describe an extension of the chronoprojective geometry and show how its automorphisms are related to the invariance properties of the Schroedinger equation describing a quantum test particle in any Newton-Cartan structure
Testing measurement invariance of composites using partial least squares
Henseler, Jörg; Ringle, Christian M.; Sarstedt, Marko
2016-01-01
Purpose Research on international marketing usually involves comparing different groups of respondents. When using structural equation modeling (SEM), group comparisons can be misleading unless researchers establish the invariance of their measures. While methods have been proposed to analyze
Communication: Fitting potential energy surfaces with fundamental invariant neural network
Shao, Kejie; Chen, Jun; Zhao, Zhiqiang; Zhang, Dong H., E-mail: zhangdh@dicp.ac.cn [State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People’s Republic of China and University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China. (China)
2016-08-21
A more flexible neural network (NN) method using the fundamental invariants (FIs) as the input vector is proposed in the construction of potential energy surfaces for molecular systems involving identical atoms. Mathematically, FIs finitely generate the permutation invariant polynomial (PIP) ring. In combination with NN, fundamental invariant neural network (FI-NN) can approximate any function to arbitrary accuracy. Because FI-NN minimizes the size of input permutation invariant polynomials, it can efficiently reduce the evaluation time of potential energy, in particular for polyatomic systems. In this work, we provide the FIs for all possible molecular systems up to five atoms. Potential energy surfaces for OH{sub 3} and CH{sub 4} were constructed with FI-NN, with the accuracy confirmed by full-dimensional quantum dynamic scattering and bound state calculations.
Groups, generators, syzygies, and orbits in invariant theory
Popov, V L
2011-01-01
The history of invariant theory spans nearly a century and a half, with roots in certain problems from number theory, algebra, and geometry appearing in the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant theory was in fact subsumed by a general theory of algebraic groups. Written by one of the major leaders in the field, this book provides an excellent, comprehensive exposition of invariant theory. Its point of view is unique in that it combines both modern and classical approaches to the subject. The introductory chapter sets the historical stage for the subject, helping to make the book accessible to nonspecialists.
Webs on surfaces, rings of invariants, and clusters.
Fomin, Sergey; Pylyavskyy, Pavlo
2014-07-08
We construct and study cluster algebra structures in rings of invariants of the special linear group action on collections of 3D vectors, covectors, and matrices. The construction uses Kuperberg's calculus of webs on marked surfaces with boundary.
Invariant approach to CP in unbroken Δ(27
Gustavo C. Branco
2015-10-01
Full Text Available The invariant approach is a powerful method for studying CP violation for specific Lagrangians. The method is particularly useful for dealing with discrete family symmetries. We focus on the CP properties of unbroken Δ(27 invariant Lagrangians with Yukawa-like terms, which proves to be a rich framework, with distinct aspects of CP, making it an ideal group to investigate with the invariant approach. We classify Lagrangians depending on the number of fields transforming as irreducible triplet representations of Δ(27. For each case, we construct CP-odd weak basis invariants and use them to discuss the respective CP properties. We find that CP violation is sensitive to the number and type of Δ(27 representations.
The component structure of conformal supergravity invariants in six dimensions
Butter, Daniel [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); George and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University,College Station, TX 77843 (United States); Novak, Joseph [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Golm (Germany); Tartaglino-Mazzucchelli, Gabriele [Instituut voor Theoretische Fysica, KU Leuven,Celestijnenlaan 200D, B-3001 Leuven (Belgium)
2017-05-24
In the recent paper https://arxiv.org/abs/1606.02921, the two invariant actions for 6D N=(1,0) conformal supergravity were constructed in superspace, corresponding to the supersymmetrization of C{sup 3} and C◻C. In this paper, we provide the translation from superspace to the component formulation of superconformal tensor calculus, and we give the full component actions of these two invariants. As a second application, we build the component form for the supersymmetric F◻F action coupled to conformal supergravity. Exploiting the fact that the N=(2,0) Weyl multiplet has a consistent truncation to N=(1,0), we then verify that there is indeed only a single N=(2,0) conformal supergravity invariant and reconstruct most of its bosonic terms by uplifting a certain linear combination of N=(1,0) invariants.
Robust Image Hashing Using Radon Transform and Invariant Features
Y.L. Liu
2016-09-01
Full Text Available A robust image hashing method based on radon transform and invariant features is proposed for image authentication, image retrieval, and image detection. Specifically, an input image is firstly converted into a counterpart with a normalized size. Then the invariant centroid algorithm is applied to obtain the invariant feature point and the surrounding circular area, and the radon transform is employed to acquire the mapping coefficient matrix of the area. Finally, the hashing sequence is generated by combining the feature vectors and the invariant moments calculated from the coefficient matrix. Experimental results show that this method not only can resist against the normal image processing operations, but also some geometric distortions. Comparisons of receiver operating characteristic (ROC curve indicate that the proposed method outperforms some existing methods in classification between perceptual robustness and discrimination.
Inertial Spontaneous Symmetry Breaking and Quantum Scale Invariance
Ferreira, Pedro G. [Oxford U.; Hill, Christopher T. [Fermilab; Ross, Graham G. [Oxford U., Theor. Phys.
2018-01-23
Weyl invariant theories of scalars and gravity can generate all mass scales spontaneously, initiated by a dynamical process of "inertial spontaneous symmetry breaking" that does not involve a potential. This is dictated by the structure of the Weyl current, $K_\\mu$, and a cosmological phase during which the universe expands and the Einstein-Hilbert effective action is formed. Maintaining exact Weyl invariance in the renormalised quantum theory is straightforward when renormalisation conditions are referred back to the VEV's of fields in the action of the theory, which implies a conserved Weyl current. We do not require scale invariant regulators. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential.
Z3 - invariant effective theory of deconfining phase transition
So, Hiroto
1986-01-01
A Z 3 -invariant scalar model is proposed as an effective theory of deconfining phase transition of QCD. Coupling constants in the potential are determined by Monte Carlo methods. The structure of renormalization trajectories for coupling constants is investigated. (author)
Manifestly scale-invariant regularization and quantum effective operators
Ghilencea, D.M.
2016-01-01
Scale invariant theories are often used to address the hierarchy problem, however the regularization of their quantum corrections introduces a dimensionful coupling (dimensional regularization) or scale (Pauli-Villars, etc) which break this symmetry explicitly. We show how to avoid this problem and study the implications of a manifestly scale invariant regularization in (classical) scale invariant theories. We use a dilaton-dependent subtraction function $\\mu(\\sigma)$ which after spontaneous breaking of scale symmetry generates the usual DR subtraction scale $\\mu(\\langle\\sigma\\rangle)$. One consequence is that "evanescent" interactions generated by scale invariance of the action in $d=4-2\\epsilon$ (but vanishing in $d=4$), give rise to new, finite quantum corrections. We find a (finite) correction $\\Delta U(\\phi,\\sigma)$ to the one-loop scalar potential for $\\phi$ and $\\sigma$, beyond the Coleman-Weinberg term. $\\Delta U$ is due to an evanescent correction ($\\propto\\epsilon$) to the field-dependent masses (of...
Conformal invariant quantum field theory and composite field operators
Kurak, V.
1976-01-01
The present status of conformal invariance in quantum field theory is reviewed from a non group theoretical point of view. Composite field operators dimensions are computed in some simple models and related to conformal symmetry
On the hierarchy of partially invariant submodels of differential equations
Golovin, Sergey V.
2007-01-01
It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ...
A new formulation of non-relativistic diffeomorphism invariance
Banerjee, Rabin, E-mail: rabin@bose.res.in [S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake City, Kolkata-700 098 (India); Mitra, Arpita, E-mail: arpita12t@bose.res.in [S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake City, Kolkata-700 098 (India); Mukherjee, Pradip, E-mail: mukhpradip@gmail.com [Department of Physics, Barasat Government College, Barasat, West Bengal (India)
2014-10-07
We provide a new formulation of non-relativistic diffeomorphism invariance. It is generated by localising the usual global Galilean symmetry. The correspondence with the type of diffeomorphism invariant models currently in vogue in the theory of fractional quantum Hall effect has been discussed. Our construction is shown to open up a general approach of model building in theoretical condensed matter physics. Also, this formulation has the capacity of obtaining Newton–Cartan geometry from the gauge procedure.
Invariant object recognition based on the generalized discrete radon transform
Easley, Glenn R.; Colonna, Flavia
2004-04-01
We introduce a method for classifying objects based on special cases of the generalized discrete Radon transform. We adjust the transform and the corresponding ridgelet transform by means of circular shifting and a singular value decomposition (SVD) to obtain a translation, rotation and scaling invariant set of feature vectors. We then use a back-propagation neural network to classify the input feature vectors. We conclude with experimental results and compare these with other invariant recognition methods.
Modular invariant partition functions for toroidally compactified bosonic string
Ardalan, F.; Arfaei, H.
1988-06-01
We systematically find all the modular invariant partition functions for the toroidally compactified closed bosonic string defined on a subset of a simply laced simple Lie algebra lattice, or equivalently for the closed bosonic string moving on a group manifold with the WZW coefficient k=1. We examine the relation between modular invariance of partition function and the possibility of describing it by an even Lorentzian self dual lattice in our context. (author). 23 refs
Modular invariants from simple currents. An explicit proof
Schellekens, A.N.; Yankielowicz, S.
1989-01-01
In a previous paper an orbifold construction was used to demonstrate that the existence of primary fields with simple fusion rules in a conformal field theory implies the existence of non-diagonal modular invariant partition functions. Here we present a direct and explicit proof of modular invariance, which also covers a few cases that could not be obtained with the orbifold method. We also give a very simple general formula for the modular matrix M. (orig.)
Are the invariance principles really truly Lorentz covariant?
Arunasalam, V.
1994-02-01
It is shown that some sections of the invariance (or symmetry) principles such as the space reversal symmetry (or parity P) and time reversal symmetry T (of elementary particle and condensed matter physics, etc.) are not really truly Lorentz covariant. Indeed, I find that the Dirac-Wigner sense of Lorentz invariance is not in full compliance with the Einstein-Minkowski reguirements of the Lorentz covariance of all physical laws (i.e., the world space Mach principle)
Scale-Invariant Rotating Black Holes in Quadratic Gravity
Guido Cognola
2015-07-01
Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.
Rotation invariants from Gaussian-Hermite moments of color images
Yang, B.; Suk, Tomáš; Flusser, Jan; Shi, Z.; Chen, X.
2018-01-01
Roč. 143, č. 1 (2018), s. 282-291 ISSN 0165-1684 R&D Projects: GA ČR GA15-16928S Institutional support: RVO:67985556 Keywords : Color images * Object recognition * Rotation invariants * Gaussian–Hermite moments * Joint invariants Subject RIV: JD - Computer Applications, Robotics Impact factor: 3.110, year: 2016 http://library.utia.cas.cz/separaty/2017/ZOI/suk-0479748.pdf
On the construction of translationally invariant deformed wave functions
Guardiola, R.
1975-01-01
Translationally invariant nuclear wave functions are constructed from deformed harmonic oscillator shell-model wave functions, with an exact projection of angular momentum quantum numbers. It is shown that the computation of matrix elements with the translationally invariant wave functions is as simple as the standard calculation, and formulae are obtained for (i) the potential energy, (ii) the kinetic energy and rms radius, and (iii) the charge form factor. (Auth.)
Altered Perceptual Sensitivity to Kinematic Invariants in Parkinson's Disease
Dayan, Eran; Inzelberg, Rivka; Flash, Tamar
2012-01-01
Ample evidence exists for coupling between action and perception in neurologically healthy individuals, yet the precise nature of the internal representations shared between these domains remains unclear. One experimentally derived view is that the invariant properties and constraints characterizing movement generation are also manifested during motion perception. One prominent motor invariant is the "two-third power law," describing the strong relation between the kinematics of motion and th...
Rephasing-invariant CP violating parameters with Majorana neutrinos
Nieves, Jose F.; Pal, Palash B.
2001-06-01
We analyze the dependence of the squared amplitudes on the rephasing-invariant CP-violating parameters of the lepton sector, involving Majorana neutrinos, for various lepton- conserving and lepton-violating processes. We analyze the conditions under which the CP-violating effects in such processes vanish, in terms of the minimal set of rephasing invariants, giving special attention to the dependence on the extra CP-violating parameters that are due to the Majorana nature of the neutrinos. (author)
3D rotation invariants of Gaussian-Hermite moments
Yang, Bo; Flusser, Jan; Suk, Tomáš
2015-01-01
Roč. 54, č. 1 (2015), s. 18-26 ISSN 0167-8655 R&D Projects: GA ČR GAP103/11/1552 Institutional support: RVO:67985556 Keywords : Rotation invariants * Orthogonal moments * Gaussian–Hermite moments * 3D moment invariants Subject RIV: IN - Informatics, Computer Science Impact factor: 1.586, year: 2015 http://library.utia.cas.cz/separaty/2014/ZOI/yang-0438325.pdf
Translational invariance and the anisotropy of the cosmic microwave background
Carroll, Sean M.; Tseng, C.-Y.; Wise, Mark B.
2010-01-01
Primordial quantum fluctuations produced by inflation are conventionally assumed to be statistically homogeneous, a consequence of translational invariance. In this paper we quantify the potentially observable effects of a small violation of translational invariance during inflation, as characterized by the presence of a preferred point, line, or plane. We explore the imprint such a violation would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes lm a l ' m ' *> of the spherical-harmonic coefficients.
Translational invariance and the anisotropy of the cosmic microwave background
Carroll, Sean M.; Tseng, Chien-Yao; Wise, Mark B.
2010-04-01
Primordial quantum fluctuations produced by inflation are conventionally assumed to be statistically homogeneous, a consequence of translational invariance. In this paper we quantify the potentially observable effects of a small violation of translational invariance during inflation, as characterized by the presence of a preferred point, line, or plane. We explore the imprint such a violation would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes ⟨almal'm'*⟩ of the spherical-harmonic coefficients.
Algebraic invariant curves of plane polynomial differential systems
Tsygvintsev, Alexei
2001-01-01
We consider a plane polynomial vector field P(x,y) dx + Q(x,y) dy of degree m>1. With each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential ω = dx/P = dy/Q. The asymptotic estimate of the degree of an arbitrary algebraic invariant curve is found. In the smooth case this estimate has already been found by Cerveau and Lins Neto in a different way.
Invariance as a Tool for Ontology of Information
Marcin J. Schroeder
2016-03-01
Full Text Available Attempts to answer questions regarding the ontological status of information are frequently based on the assumption that information should be placed within an already existing framework of concepts of established ontological statuses related to science, in particular to physics. However, many concepts of physics have undetermined or questionable ontological foundations. We can look for a solution in the recognition of the fundamental role of invariance with respect to a change of reference frame and to other transformations as a criterion for objective existence. The importance of invariance (symmetry as a criterion for a primary ontological status can be identified in the methodology of physics from its beginnings in the work of Galileo, to modern classifications of elementary particles. Thus, the study of the invariance of the theoretical description of information is proposed as the first step towards ontology of information. With the exception of only a few works among publications which set the paradigm of information studies, the issues of invariance were neglected. Orthodox analysis of information lacks conceptual framework for the study of invariance. The present paper shows how invariance can be formalized for the definition of information and, accompanying it, mathematical formalism proposed by the author in his earlier publications.
Quantum tunneling, adiabatic invariance and black hole spectroscopy
Li, Guo-Ping; Zu, Xiao-Tao [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Pu, Jin [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); China West Normal University, College of Physics and Space Science, Nanchong (China); Jiang, Qing-Quan [China West Normal University, College of Physics and Space Science, Nanchong (China)
2017-05-15
In the tunneling framework, one of us, Jiang, together with Han has studied the black hole spectroscopy via adiabatic invariance, where the adiabatic invariant quantity has been intriguingly obtained by investigating the oscillating velocity of the black hole horizon. In this paper, we attempt to improve Jiang-Han's proposal in two ways. Firstly, we once again examine the fact that, in different types (Schwarzschild and Painleve) of coordinates as well as in different gravity frames, the adiabatic invariant I{sub adia} = circular integral p{sub i}dq{sub i} introduced by Jiang and Han is canonically invariant. Secondly, we attempt to confirm Jiang-Han's proposal reasonably in more general gravity frames (including Einstein's gravity, EGB gravity and HL gravity). Concurrently, for improving this proposal, we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable, but the horizon area is only an adiabatic invariant. In this sense, we emphasize the concept that the quantum of the black hole entropy is more natural than that of the horizon area. (orig.)
Neurons with two sites of synaptic integration learn invariant representations.
Körding, K P; König, P
2001-12-01
Neurons in mammalian cerebral cortex combine specific responses with respect to some stimulus features with invariant responses to other stimulus features. For example, in primary visual cortex, complex cells code for orientation of a contour but ignore its position to a certain degree. In higher areas, such as the inferotemporal cortex, translation-invariant, rotation-invariant, and even view point-invariant responses can be observed. Such properties are of obvious interest to artificial systems performing tasks like pattern recognition. It remains to be resolved how such response properties develop in biological systems. Here we present an unsupervised learning rule that addresses this problem. It is based on a neuron model with two sites of synaptic integration, allowing qualitatively different effects of input to basal and apical dendritic trees, respectively. Without supervision, the system learns to extract invariance properties using temporal or spatial continuity of stimuli. Furthermore, top-down information can be smoothly integrated in the same framework. Thus, this model lends a physiological implementation to approaches of unsupervised learning of invariant-response properties.
Quantum tunneling, adiabatic invariance and black hole spectroscopy
Li, Guo-Ping; Pu, Jin; Jiang, Qing-Quan; Zu, Xiao-Tao
2017-05-01
In the tunneling framework, one of us, Jiang, together with Han has studied the black hole spectroscopy via adiabatic invariance, where the adiabatic invariant quantity has been intriguingly obtained by investigating the oscillating velocity of the black hole horizon. In this paper, we attempt to improve Jiang-Han's proposal in two ways. Firstly, we once again examine the fact that, in different types (Schwarzschild and Painlevé) of coordinates as well as in different gravity frames, the adiabatic invariant I_adia = \\oint p_i dq_i introduced by Jiang and Han is canonically invariant. Secondly, we attempt to confirm Jiang-Han's proposal reasonably in more general gravity frames (including Einstein's gravity, EGB gravity and HL gravity). Concurrently, for improving this proposal, we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable, but the horizon area is only an adiabatic invariant. In this sense, we emphasize the concept that the quantum of the black hole entropy is more natural than that of the horizon area.
Wavelet-based moment invariants for pattern recognition
Chen, Guangyi; Xie, Wenfang
2011-07-01
Moment invariants have received a lot of attention as features for identification and inspection of two-dimensional shapes. In this paper, two sets of novel moments are proposed by using the auto-correlation of wavelet functions and the dual-tree complex wavelet functions. It is well known that the wavelet transform lacks the property of shift invariance. A little shift in the input signal will cause very different output wavelet coefficients. The autocorrelation of wavelet functions and the dual-tree complex wavelet functions, on the other hand, are shift-invariant, which is very important in pattern recognition. Rotation invariance is the major concern in this paper, while translation invariance and scale invariance can be achieved by standard normalization techniques. The Gaussian white noise is added to the noise-free images and the noise levels vary with different signal-to-noise ratios. Experimental results conducted in this paper show that the proposed wavelet-based moments outperform Zernike's moments and the Fourier-wavelet descriptor for pattern recognition under different rotation angles and different noise levels. It can be seen that the proposed wavelet-based moments can do an excellent job even when the noise levels are very high.
Adiabatic invariants of the extended KdV equation
Karczewska, Anna [Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Rozmej, Piotr, E-mail: p.rozmej@if.uz.zgora.pl [Institute of Physics, Faculty of Physics and Astronomy, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Infeld, Eryk [National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa (Poland); Rowlands, George [Department of Physics, University of Warwick, Coventry, CV4 7A (United Kingdom)
2017-01-30
When the Euler equations for shallow water are taken to the next order, beyond KdV, momentum and energy are no longer exact invariants. (The only one is mass.) However, adiabatic invariants (AI) can be found. When the KdV expansion parameters are zero, exact invariants are recovered. Existence of adiabatic invariants results from general theory of near-identity transformations (NIT) which allow us to transform higher order nonintegrable equations to asymptotically equivalent (when small parameters tend to zero) integrable form. Here we present a direct method of calculations of adiabatic invariants. It does not need a transformation to a moving reference frame nor performing a near-identity transformation. Numerical tests show that deviations of AI from constant values are indeed small. - Highlights: • We suggest a new and simple method for calculating adiabatic invariants of second order wave equations. • It is easy to use and we hope that it will be useful if published. • Interesting numerics included.
On the generally invariant Lagrangians for the metric field and other tensor fields
Novotny, J.
1978-01-01
The Krupka and Trautman method for the description of all generally invariant functions of the components of geometrical object fields is applied to the invariants of second degree of the metrical field and other tensor fields. The complete system of differential identities fulfilled by the invariants mentioned is found and it is proved that these invariants depend on the tensor quantities only. (author)
Engelhard, George, Jr.
1992-01-01
A historical perspective is provided of the concept of invariance in measurement theory, describing sample-invariant item calibration and item-invariant measurement of individuals. Invariance as a key measurement concept is illustrated through the measurement theories of E. L. Thorndike, L. L. Thurstone, and G. Rasch. (SLD)
Skyrme, T.H.R.
1994-01-01
A unified field theory of mesons and their particle sources is proposed and considered in its classical aspects. The theory has static solutions of a singular nature, but finite energy, characterized by spin directions; the number of such entities is a rigorously conserved constant of motion; they interact with an external meson field through a derivative-type coupling with the spins, akin to the formalism of strong-coupling meson theory. There is a conserved current identifiable with isobaric spin, and another that may be related to hypercharge. The postulates include one constant of the dimensions of length, and another that is conjecture necessarily to have the value (h/2π)c, or perhaps 1/2(h/2π)c, in the quantized theory. (author). 5 refs
Evidence for several dipolar quasi-invariants in liquid crystals
Bonin, C. J.; González, C. E.; Segnorile, H. H.; Zamar, R. C.
2013-10-01
The quasi-equilibrium states of an observed quantum system involve as many constants of motion as the dimension of the operator basis which spans the blocks of all the degenerate eigenvalues of the Hamiltonian that drives the system dynamics, however, the possibility of observing such quasi-invariants in solid-like spin systems in Nuclear Magnetic Resonance (NMR) is not a strictly exact prediction. The aim of this work is to provide experimental evidence of several quasi-invariants, in the proton NMR of small spin clusters, like nematic liquid crystal molecules, in which the use of thermodynamic arguments is not justified. We explore the spin states prepared with the Jeener-Broekaert pulse sequence by analyzing the time-domain signals yielded by this sequence as a function of the preparation times, in a variety of dipolar networks, solids, and liquid crystals. We observe that the signals can be explained with two dipolar quasi-invariants only within a range of short preparation times, however at longer times liquid crystal signals show an echo-like behaviour whose description requires assuming more quasi-invariants. We study the multiple quantum coherence content of such signals on a basis orthogonal to the z-basis and see that such states involve a significant number of correlated spins. Therefore, we show that the NMR signals within the whole preparation time-scale can only be reconstructed by assuming the occurrence of multiple quasi-invariants which we experimentally isolate.
SO(9,1) invariant matrix formulation of a supermembrane
Fujikawa, K.; Okuyama, K.
1998-01-01
An SO(9,1) invariant formulation of an 11-dimensional supermembrane is presented by combining an SO(10,1) invariant treatment of reparametrization symmetry with an SO(9,1) invariant θ R = 0 gauge of κ-symmetry. The Lagrangian thus defined consists of polynomials in dynamical variables (up to quartic terms in X μ and up to the eighth power in θ), and reparametrization BRST symmetry is manifest. The area preserving diffeomorphism is consistently incorporated and the area preserving gauge symmetry is made explicit. The SO(9,1) invariant theory contains terms which cannot be induced by a naive dimensional reduction of higher-dimensional supersymmetric Yang-Mills theory. The SO(9,1) invariant Hamiltonian and the generator of area preserving diffeomorphism together with the supercharge are matrix regularized by applying the standard procedure. As an application of the present formulation, we evaluate the possible central charges in superalgebra both in the path integral and in the canonical (Dirac) formalism, and we find only the two-form charge [ X μ , X ν ]. (orig.)
Phylogenetic mixtures and linear invariants for equal input models.
Casanellas, Marta; Steel, Mike
2017-04-01
The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).
An Advanced Rotation Invariant Descriptor for SAR Image Registration
Yuming Xiang
2017-07-01
Full Text Available The Scale-Invariant Feature Transform (SIFT algorithm and its many variants have been widely used in Synthetic Aperture Radar (SAR image registration. The SIFT-like algorithms maintain rotation invariance by assigning a dominant orientation for each keypoint, while the calculation of dominant orientation is not robust due to the effect of speckle noise in SAR imagery. In this paper, we propose an advanced local descriptor for SAR image registration to achieve rotation invariance without assigning a dominant orientation. Based on the improved intensity orders, we first divide a circular neighborhood into several sub-regions. Second, rotation-invariant ratio orientation histograms of each sub-region are proposed by accumulating the ratio values of different directions in a rotation-invariant coordinate system. The proposed descriptor is composed of the concatenation of the histograms of each sub-region. In order to increase the distinctiveness of the proposed descriptor, multiple image neighborhoods are aggregated. Experimental results on several satellite SAR images have shown an improvement in the matching performance over other state-of-the-art algorithms.
Multi-clues image retrieval based on improved color invariants
Liu, Liu; Li, Jian-Xun
2012-05-01
At present, image retrieval has a great progress in indexing efficiency and memory usage, which mainly benefits from the utilization of the text retrieval technology, such as the bag-of-features (BOF) model and the inverted-file structure. Meanwhile, because the robust local feature invariants are selected to establish BOF, the retrieval precision of BOF is enhanced, especially when it is applied to a large-scale database. However, these local feature invariants mainly consider the geometric variance of the objects in the images, and thus the color information of the objects fails to be made use of. Because of the development of the information technology and Internet, the majority of our retrieval objects is color images. Therefore, retrieval performance can be further improved through proper utilization of the color information. We propose an improved method through analyzing the flaw of shadow-shading quasi-invariant. The response and performance of shadow-shading quasi-invariant for the object edge with the variance of lighting are enhanced. The color descriptors of the invariant regions are extracted and integrated into BOF based on the local feature. The robustness of the algorithm and the improvement of the performance are verified in the final experiments.
Embedded graph invariants in Chern-Simons theory
Major, Seth A.
1999-01-01
Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines -- an embedded graph invariant. Using a generalization of the variational method, lowest-order results for invariants for graphs of arbitrary valence and general vertex tangent space structure are derived. Gauge invariant operators are introduced. Higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. However, without a global projection of the graph there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity -- as a way of relating frames at distinct vertices
Robust Frequency Invariant Beamforming with Low Sidelobe for Speech Enhancement
Zhu, Yiting; Pan, Xiang
2018-01-01
Frequency invariant beamformers (FIBs) are widely used in speech enhancement and source localization. There are two traditional optimization methods for FIB design. The first one is convex optimization, which is simple but the frequency invariant characteristic of the beam pattern is poor with respect to frequency band of five octaves. The least squares (LS) approach using spatial response variation (SRV) constraint is another optimization method. Although, it can provide good frequency invariant property, it usually couldn’t be used in speech enhancement for its lack of weight norm constraint which is related to the robustness of a beamformer. In this paper, a robust wideband beamforming method with a constant beamwidth is proposed. The frequency invariant beam pattern is achieved by resolving an optimization problem of the SRV constraint to cover speech frequency band. With the control of sidelobe level, it is available for the frequency invariant beamformer (FIB) to prevent distortion of interference from the undesirable direction. The approach is completed in time-domain by placing tapped delay lines(TDL) and finite impulse response (FIR) filter at the output of each sensor which is more convenient than the Frost processor. By invoking the weight norm constraint, the robustness of the beamformer is further improved against random errors. Experiment results show that the proposed method has a constant beamwidth and almost the same white noise gain as traditional delay-and-sum (DAS) beamformer.
Uniqueness of the gauge invariant action for cosmological perturbations
Prokopec, Tomislav; Weenink, Jan
2012-01-01
In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show that the cubic action for one choice of gauge invariant variables is unique in the following sense: the action for any other, non-linearly related variable can be brought to the same bulk action, plus additional boundary terms. These boundary terms correspond to the choice of hypersurface and generate extra, disconnected contributions to the bispectrum. We also discuss uniqueness of the action with respect to conformal frames. When expressed in terms of the gauge invariant curvature perturbation on uniform field hypersurfaces the action for cosmological perturbations has a unique form, independent of the original Einstein or Jordan frame. Crucial is that the gauge invariant comoving curvature perturbation is frame independent, which makes it extremely helpful in showing the quantum equivalence of the two frames, and therefore in calculating quantum effects in nonminimally coupled theories such as Higgs inflation
Perturbation to Unified Symmetry and Adiabatic Invariants for Relativistic Hamilton Systems
Zhang Mingjiang; Fang Jianhui; Lu Kai; Pang Ting; Lin Peng
2009-01-01
Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained. (general)
Size invariance of the granular Rayleigh-Taylor instability.
Vinningland, Jan Ludvig; Johnsen, Øistein; Flekkøy, Eirik G; Toussaint, Renaud; Måløy, Knut Jørgen
2010-04-01
The size scaling behavior of the granular Rayleigh-Taylor instability [J. L. Vinningland, Phys. Rev. Lett. 99, 048001 (2007)] is investigated experimentally, numerically, and theoretically. An upper layer of grains displaces a lower gap of air by organizing into dense fingers of falling grains separated by rising bubbles of air. The dependence of these structures on the system and grain sizes is investigated. A spatial measurement of the finger structures is obtained by the Fourier power spectrum of the wave number k. As the size of the grains increases the wave number decreases accordingly which leaves the dimensionless product of wave number and grain diameter, dk, invariant. A theoretical interpretation of the invariance, based on the scaling properties of the model equations, suggests a gradual breakdown of the invariance for grains smaller than approximately 70 microm or greater than approximately 570 microm in diameter.
Torsional Topological Invariants (and their relevance for real life)
Chandia, O; Chandia, Osvaldo; Zanelli, Jorge
1997-01-01
The existence of topological invariants analogous to Chern/Pontryagin classes for a standard $SO(D)$ or SU(N) connection, but constructed out of the torsion tensor, is discussed. These invariants exhibit many of the features of the Chern/Pontryagin invariants: they can be expressed as integrals over the manifold of local densities and take integer values on compact spaces without boundary; their spectrum is determined by the homotopy groups determined by the connection bundle but depend also on the bundle of local orthonormal frames on the tangent space of the manifold. It is shown that in spacetimes with nonvanishing torsion there can occur topologically stable configurations associated with the frame bundle which are independent of the curvature. Explicit examples of topologically stable configurations carrying nonvanishing instanton number in four and eight dimensions are given, and they can be conjectured to exist in dimension $4k$. It is also shown that the chiral anomaly in a spacetime with torsion rece...
Probability density functions for CP-violating rephasing invariants
Fortin, Jean-François; Giasson, Nicolas; Marleau, Luc
2018-05-01
The implications of the anarchy principle on CP violation in the lepton sector are investigated. A systematic method is introduced to compute the probability density functions for the CP-violating rephasing invariants of the PMNS matrix from the Haar measure relevant to the anarchy principle. Contrary to the CKM matrix which is hierarchical, it is shown that the Haar measure, and hence the anarchy principle, are very likely to lead to the observed PMNS matrix. Predictions on the CP-violating Dirac rephasing invariant |jD | and Majorana rephasing invariant |j1 | are also obtained. They correspond to 〈 |jD | 〉 Haar = π / 105 ≈ 0.030 and 〈 |j1 | 〉 Haar = 1 / (6 π) ≈ 0.053 respectively, in agreement with the experimental hint from T2K of | jDexp | ≈ 0.032 ± 0.005 (or ≈ 0.033 ± 0.003) for the normal (or inverted) hierarchy.
Implications of maximal Jarlskog invariant and maximal CP violation
Rodriguez-Jauregui, E.; Universidad Nacional Autonoma de Mexico
2001-04-01
We argue here why CP violating phase Φ in the quark mixing matrix is maximal, that is, Φ=90 . In the Standard Model CP violation is related to the Jarlskog invariant J, which can be obtained from non commuting Hermitian mass matrices. In this article we derive the conditions to have Hermitian mass matrices which give maximal Jarlskog invariant J and maximal CP violating phase Φ. We find that all squared moduli of the quark mixing elements have a singular point when the CP violation phase Φ takes the value Φ=90 . This special feature of the Jarlskog invariant J and the quark mixing matrix is a clear and precise indication that CP violating Phase Φ is maximal in order to let nature treat democratically all of the quark mixing matrix moduli. (orig.)
Symplectic invariants, entropic measures and correlations of Gaussian states
Serafini, Alessio; Illuminati, Fabrizio; Siena, Silvio De [Dipartimento di Fisica ' E R Caianiello' , Universita di Salerno, INFM UdR Salerno, INFN Sezione di Napoli, Gruppo Collegato di Salerno, Via S Allende, 84081 Baronissi, SA (Italy)
2004-01-28
We present a derivation of the Von Neumann entropy and mutual information of arbitrary two-mode Gaussian states, based on the explicit determination of the symplectic eigenvalues of a generic covariance matrix. The key role of the symplectic invariants in such a determination is pointed out. We show that the Von Neumann entropy depends on two symplectic invariants, while the purity (or the linear entropy) is determined by only one invariant, so that the two quantities provide two different hierarchies of mixed Gaussian states. A comparison between mutual information and entanglement of formation for symmetric states is considered, taking note of the crucial role of the symplectic eigenvalues in qualifying and quantifying the correlations present in a generic state. (letter to the editor)
Symplectic invariants, entropic measures and correlations of Gaussian states
Serafini, Alessio; Illuminati, Fabrizio; Siena, Silvio De
2004-01-01
We present a derivation of the Von Neumann entropy and mutual information of arbitrary two-mode Gaussian states, based on the explicit determination of the symplectic eigenvalues of a generic covariance matrix. The key role of the symplectic invariants in such a determination is pointed out. We show that the Von Neumann entropy depends on two symplectic invariants, while the purity (or the linear entropy) is determined by only one invariant, so that the two quantities provide two different hierarchies of mixed Gaussian states. A comparison between mutual information and entanglement of formation for symmetric states is considered, taking note of the crucial role of the symplectic eigenvalues in qualifying and quantifying the correlations present in a generic state. (letter to the editor)
SPEEDY: An Eclipse-based IDE for invariant inference
David R. Cok
2014-04-01
Full Text Available SPEEDY is an Eclipse-based IDE for exploring techniques that assist users in generating correct specifications, particularly including invariant inference algorithms and tools. It integrates with several back-end tools that propose invariants and will incorporate published algorithms for inferring object and loop invariants. Though the architecture is language-neutral, current SPEEDY targets C programs. Building and using SPEEDY has confirmed earlier experience demonstrating the importance of showing and editing specifications in the IDEs that developers customarily use, automating as much of the production and checking of specifications as possible, and showing counterexample information directly in the source code editing environment. As in previous work, automation of specification checking is provided by back-end SMT solvers. However, reducing the effort demanded of software developers using formal methods also requires a GUI design that guides users in writing, reviewing, and correcting specifications and automates specification inference.
ASIFT: An Algorithm for Fully Affine Invariant Comparison
Guoshen Yu
2011-02-01
Full Text Available If a physical object has a smooth or piecewise smooth boundary, its images obtained by cameras in varying positions undergo smooth apparent deformations. These deformations are locally well approximated by affine transforms of the image plane. In consequence the solid object recognition problem has often been led back to the computation of affine invariant image local features. The similarity invariance (invariance to translation, rotation, and zoom is dealt with rigorously by the SIFT method The method illustrated and demonstrated in this work, Affine-SIFT (ASIFT, simulates a set of sample views of the initial images, obtainable by varying the two camera axis orientation parameters, namely the latitude and the longitude angles, which are not treated by the SIFT method. Then it applies the SIFT method itself to all images thus generated. Thus, ASIFT covers effectively all six parameters of the affine transform.
Electric dipole moments with and beyond flavor invariants
Smith, Christopher; Touati, Selim
2017-11-01
In this paper, the flavor structure of quark and lepton electric dipole moments in the SM and beyond is investigated using tools inspired from Minimal Flavor Violation. While Jarlskog-like flavor invariants are adequate for estimating CP-violation from closed fermion loops, non-invariant structures arise from rainbow-like processes. Our goal is to systematically construct these latter flavor structures in the quark and lepton sectors, assuming different mechanisms for generating neutrino masses. Numerically, they are found typically much larger, and not necessarily correlated with, Jarlskog-like invariants. Finally, the formalism is adapted to deal with a third class of flavor structures, sensitive to the flavored U (1) phases, and used to study the impact of the strong CP-violating interaction and the interplay between the neutrino Majorana phases and possible baryon and/or lepton number violating interactions.
Electric dipole moments with and beyond flavor invariants
Christopher Smith
2017-11-01
Full Text Available In this paper, the flavor structure of quark and lepton electric dipole moments in the SM and beyond is investigated using tools inspired from Minimal Flavor Violation. While Jarlskog-like flavor invariants are adequate for estimating CP-violation from closed fermion loops, non-invariant structures arise from rainbow-like processes. Our goal is to systematically construct these latter flavor structures in the quark and lepton sectors, assuming different mechanisms for generating neutrino masses. Numerically, they are found typically much larger, and not necessarily correlated with, Jarlskog-like invariants. Finally, the formalism is adapted to deal with a third class of flavor structures, sensitive to the flavored U(1 phases, and used to study the impact of the strong CP-violating interaction and the interplay between the neutrino Majorana phases and possible baryon and/or lepton number violating interactions.
Machine learning strategies for systems with invariance properties
Ling, Julia; Jones, Reese; Templeton, Jeremy
2016-08-01
In many scientific fields, empirical models are employed to facilitate computational simulations of engineering systems. For example, in fluid mechanics, empirical Reynolds stress closures enable computationally-efficient Reynolds Averaged Navier Stokes simulations. Likewise, in solid mechanics, constitutive relations between the stress and strain in a material are required in deformation analysis. Traditional methods for developing and tuning empirical models usually combine physical intuition with simple regression techniques on limited data sets. The rise of high performance computing has led to a growing availability of high fidelity simulation data. These data open up the possibility of using machine learning algorithms, such as random forests or neural networks, to develop more accurate and general empirical models. A key question when using data-driven algorithms to develop these empirical models is how domain knowledge should be incorporated into the machine learning process. This paper will specifically address physical systems that possess symmetry or invariance properties. Two different methods for teaching a machine learning model an invariance property are compared. In the first method, a basis of invariant inputs is constructed, and the machine learning model is trained upon this basis, thereby embedding the invariance into the model. In the second method, the algorithm is trained on multiple transformations of the raw input data until the model learns invariance to that transformation. Results are discussed for two case studies: one in turbulence modeling and one in crystal elasticity. It is shown that in both cases embedding the invariance property into the input features yields higher performance at significantly reduced computational training costs.
The Invariant Properties of Two-Port Circuits
Alexandr A. Penin
2009-01-01
Application of projective geometry to the theory of two-ports and cascade circuits with a load change is considered. The equations linking the input and output of a two-port are interpreted as projective transformations which have the invariant as a cross-ratio of four points. This invariant has place for all regime parameters in all parts of a cascade circuit. This approach allows justifying the definition of a regime and its change, to calculate a circuit without explicitly finding the apar...
Object detection based on improved color and scale invariant features
Chen, Mengyang; Men, Aidong; Fan, Peng; Yang, Bo
2009-10-01
A novel object detection method which combines color and scale invariant features is presented in this paper. The detection system mainly adopts the widely used framework of SIFT (Scale Invariant Feature Transform), which consists of both a keypoint detector and descriptor. Although SIFT has some impressive advantages, it is not only computationally expensive, but also vulnerable to color images. To overcome these drawbacks, we employ the local color kernel histograms and Haar Wavelet Responses to enhance the descriptor's distinctiveness and computational efficiency. Extensive experimental evaluations show that the method has better robustness and lower computation costs.
Projection Operators and Moment Invariants to Image Blurring
Flusser, Jan; Suk, Tomáš; Boldyš, Jiří; Zitová, Barbara
2015-01-01
Roč. 37, č. 4 (2015), s. 786-802 ISSN 0162-8828 R&D Projects: GA ČR GA13-29225S; GA ČR GAP103/11/1552 Institutional support: RVO:67985556 Keywords : Blurred image * N-fold rotation symmetry * projection operators * image moments * moment invariants * blur invariants * object recognition Subject RIV: JD - Computer Applications, Robotics Impact factor: 6.077, year: 2015 http://library.utia.cas.cz/separaty/2014/ZOI/flusser-0434521.pdf
Polarization particle drift and quasi-particle invariants
Sosenko, P.P.
1995-01-01
The second-order approximation in quasi-particle description of magnetized plasmas is studied. Reduced particle and guiding-centre velocities are derived taking account of the second-order renormalization and polarization drift modified owing to finite-Larmor-radius effects. The second-order adiabatic invariant of quasi-particle motion is found. Global adiabatic invariants for the magnetized plasma are revealed, and their possible role in energy exchange between particles and fields, nonlinear mode cascades and global plasma stability is shown. 49 refs
Three-body forces mandated by Poincare invariance
Coester, F.
1986-01-01
Poincare invariant models for the three-nucleon system are examined which have the same heuristic relation to field theories as the nonrelativistic nuclear models. The generators of the infinitesimal dynamical transformations can be obtained as functions of the kinematic generators, the invariant mass operator of the interacting system, and additional operators. These additional operators are the components of the Newton-Wigner position operator in the instant form, and the transverse components of the spin in the front form. The relativistic dynamics of Poincare transformations is examined, and then these concepts are applied to two-nucleon systems. The transition to a fully interacting three-nucleon system is made
Smooth invariant densities for random switching on the torus
Bakhtin, Yuri; Hurth, Tobias; Lawley, Sean D.; Mattingly, Jonathan C.
2018-04-01
We consider a random dynamical system obtained by switching between the flows generated by two smooth vector fields on the 2d-torus, with the random switchings happening according to a Poisson process. Assuming that the driving vector fields are transversal to each other at all points of the torus and that each of them allows for a smooth invariant density and no periodic orbits, we prove that the switched system also has a smooth invariant density, for every switching rate. Our approach is based on an integration by parts formula inspired by techniques from Malliavin calculus.
On the Computation of Finite Invariant Sets of Mappings.
1988-02-01
for the calculation of such invariant cycles. We refer here only to Doedel [1], looss et al [3], Kevrekidis et al [4], Van Veldhuizen ,[6], where further... van Veldhuizen , On Polygonal Approximations of an Invariant Curve, Dept.of Mathem. and Comp. Science, Vrije Universiteit Amsterdam, Techni- cal Report 1987, Math. Comp. to appear DATE Fl .LMED ...of van der Pol’s equation " x2) x - A(l - x ) X’ + x - 0 (16) As shown, for example in [2], the solution satisfies x - 2 cos(wt)+ A (0.75 sin(wt
The conformally invariant Laplace-Beltrami operator and factor ordering
Ryan, Michael P.; Turbiner, Alexander V.
2004-01-01
In quantum mechanics the kinetic energy term for a single particle is usually written in the form of the Laplace-Beltrami operator. This operator is a factor ordering of the classical kinetic energy. We investigate other relatively simple factor orderings and show that the only other solution for a conformally flat metric is the conformally invariant Laplace-Beltrami operator. For non-conformally-flat metrics this type of factor ordering fails, by just one term, to give the conformally invariant Laplace-Beltrami operator
Gauge invariant treatment of the electroweak phase transition
Buchmueller, W.; Fodor, Z.; Hebecker, A.
1994-03-01
We evaluate the gauge invariant effective potential for the composite field σ = 2Φ † Φin the SU(2)-Higgs model at finite temperature. Symmetric and broken phases correspond to the domains σ ≤ T 2 /3 and σ > T 2 /3, respectively. The effective potential increases very steeply at small values of σ. Predictions for several observables, derived from the ordinary and the gauge invariant effective potential, are compared. Good agreement is found for the critical temperature and the jump in the order parameter. The results for the latent heat differ significantly for large Higgs masses. (orig.)
Darvas, Gyrgy
2009-01-01
The paper discusses the mathematical consequences of the application of derived variables in gauge fields. Physics is aware of several phenomena, which depend first of all on velocities (like e.g., the force caused by charges moving in a magnetic field, or the Lorentz transformation). Applying the property of the second Noether theorem, that allowed generalised variables, this paper extends the article by Al-Kuwari and Taha (1991) with a new conclusion. They concluded that there are no extra conserved currents associated with local gauge invariance. We show, that in a more general case, there are further conserved Noether currents. In its method the paper reconstructs the clue introduced by Utiyama (1956, 1959) and followed by Al-Kuwari and Taha (1991) in the presence of a gauge field that depends on the co-ordinates of the velocity space. In this course we apply certain (but not full) analogies with Mills (1989). We show, that handling the space-time coordinates as implicit variables in the gauge field, reproduces the same results that have been derived in the configuration space (i.e., we do not lose information), while the proposed new treatment gives additional information extending those. The result is an extra conserved Noether current.
The Loneliness Questionnaire: Establishing Measurement Invariance Across Ethnic Groups.
Ritchwood, Tiarney D; Ebesutani, Chad K; Chin, Eu Gene; Young, John
2017-09-01
A state of loneliness describes an individual's perception of having dissatisfying social connections to others. Though it is notable across the life span, it may have particularly deleterious effects in childhood and adolescence, leading to increased risk of emotional impairment. The current study evaluates a widely used test of loneliness, the Loneliness Questionnaire, for measurement invariance across ethnic groups in a large, representative sample of youth in the 2nd to 12th grades ( N = 12,344; 41% African American) in Mississippi. Analyses were conducted using multigroup confirmatory factor analysis following a published, sequential method to examine invariance in form, factor loadings, and item intercepts. Overall, our results indicated that the instrument was invariant across ethnicities, suggesting that youth with equivalent manifest scores can be discerned as having comparable levels of latent loneliness. The loneliness scores also corresponded significantly with depression and anxiety scores for most subsamples, with one exception. These findings are discussed in the context of previous results comparing levels of loneliness across ethnicities. Additionally, the broader context of the need to expand invariance studies in instrumentation work is highlighted.
Invariant set computation for constrained uncertain discrete-time systems
Athanasopoulos, N.; Bitsoris, G.
2010-01-01
In this article a novel approach to the determination of polytopic invariant sets for constrained discrete-time linear uncertain systems is presented. First, the problem of stabilizing a prespecified initial condition set in the presence of input and state constraints is addressed. Second, the
DU and UD-invariants of unitary groups
Aguilera-Navarro, M.C.K.
1977-01-01
Four distint ways of obtaining the eigenvalues of unitary groups, in any irreducible representation, are presented. The invariants are defined according to two different contraction conventions. Their eigenvalue can be given in terms of two classes of special partial hooks associated with the young diagram characterizing the irreducible representation considered
Spontaneous breaking of supersymmetry and gauge invariance in supergravity
Sohnius, M. (European Organization for Nuclear Research, Geneva (Switzerland)); West, P. (King' s Coll., London (UK). Dept. of Mathematics)
1982-08-09
Using the new minimal auxillary fields of N = 1 supergravity it is found possible to construct a model of local supersymmetry which spontaneously breaks both supersymmetry and gauge invariance. The status of the cosmological constant resulting from this breaking is discussed.
Spontaneous breaking of supersymmetry and gauge invariance in supergravity
Sohnius, M.; West, P.
1982-01-01
Using the new minimal auxillary fields of N = 1 supergravity it is found possible to construct a model of local supersymmetry which spontaneously breaks both supersymmetry and gauge invariance. The status of the cosmological constant resulting from this breaking is discussed. (orig.)
Gauge-invariant intense-field approximations to all orders
Faisal, F H M
2007-01-01
We present a gauge-invariant formulation of the so-called strong-field KFR approximations in the 'velocity' and 'length' gauges and demonstrate their equivalence in all orders. The theory thus overcomes a longstanding discrepancy between the strong-field velocity and the length-gauge approximations for non-perturbative processes in intense laser fields. (fast track communication)
Second-order gauge-invariant perturbations during inflation
Finelli, F.; Marozzi, G.; Vacca, G. P.; Venturi, G.
2006-01-01
The evolution of gauge invariant second-order scalar perturbations in a general single field inflationary scenario are presented. Different second-order gauge-invariant expressions for the curvature are considered. We evaluate perturbatively one of these second order curvature fluctuations and a second-order gauge-invariant scalar field fluctuation during the slow-roll stage of a massive chaotic inflationary scenario, taking into account the deviation from a pure de Sitter evolution and considering only the contribution of super-Hubble perturbations in mode-mode coupling. The spectra resulting from their contribution to the second order quantum correlation function are nearly scale-invariant, with additional logarithmic corrections with respect to the first order spectrum. For all scales of interest the amplitude of these spectra depends on the total number of e-folds. We find, on comparing first and second order perturbation results, an upper limit to the total number of e-folds beyond which the two orders are comparable
On transformations which leave invariant the Einstein equations
Pham Mau Quan
1983-01-01
The author defines and studies the invariance of Einstein equations and its relation with the causality of the space-time. By space-time is meant a smooth pseudo-riemannian manifold (M,g) of signature (1,n) for n = 3 one has the space-time of general relativity. (Auth.)
Complex dynamical invariants for two-dimensional complex potentials
Abstract. Complex dynamical invariants are searched out for two-dimensional complex poten- tials using rationalization method within the framework of an extended complex phase space characterized by x = x1 + ip3, y = x2 + ip4, px = p1 + ix3, py = p2 + ix4. It is found that the cubic oscillator and shifted harmonic oscillator ...
Selected papers on harmonic analysis, groups, and invariants
Nomizu, Katsumi
1997-01-01
This volume contains papers that originally appeared in Japanese in the journal Sūgaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication the Society has chosen to publish them as a volume of selected papers. The papers range over a variety of topics, including representation theory, differential geometry, invariant theory, and complex analysis.
Canonical transformations and exact invariants for dissipative systems
Pedrosa, I.A.
1986-01-01
A simple treatment to the problem of finding exact invariants and related auxiliary equations for time-dependent oscillators with friction is presented. The treatment is based on the use of a time-dependent canonical transformation and an auxiliary transformation. (Author) [pt
Discrete Velocity Models for Polyatomic Molecules Without Nonphysical Collision Invariants
Bernhoff, Niclas
2018-05-01
An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. Unlike for the Boltzmann equation, for DVMs there can appear extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and hence, without spurious ones, is called normal. The construction of such normal DVMs has been studied a lot in the literature for single species, but also for binary mixtures and recently extensively for multicomponent mixtures. In this paper, we address ways of constructing normal DVMs for polyatomic molecules (here represented by that each molecule has an internal energy, to account for non-translational energies, which can change during collisions), under the assumption that the set of allowed internal energies are finite. We present general algorithms for constructing such models, but we also give concrete examples of such constructions. This approach can also be combined with similar constructions of multicomponent mixtures to obtain multicomponent mixtures with polyatomic molecules, which is also briefly outlined. Then also, chemical reactions can be added.
Gauge-invariant cosmic structures---A dynamic systems approach
Woszczyna, A.
1992-01-01
Gravitational instability is expressed in terms of the dynamic systems theory. The gauge-invariant Ellis-Bruni equation and Bardeen's equation are discussed in detail. It is shown that in an open universe filled with matter of constant sound velocity the Jeans criterion does not adequately define the length scale of the gravitational structure
Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations
Waheed A. Ahmed
2017-11-01
Full Text Available Approximate symmetries of a class of perturbed nonlinear wave equations are computed using two newly-developed methods. Invariant solutions associated with the approximate symmetries are constructed for both methods. Symmetries and solutions are compared through discussing the advantages and disadvantages of each method.
Construction of exact complex dynamical invariant of a two ...
system possesses a complex invariant, namely u = ln(p + imωx) − iωt [6]. ... gaining importance for explaining several phenomena [10] such as the resonance .... then H1 and H2 satisfy the Cauchy–Riemann conditions [18] and after employing.
Invariant-based reasoning about parameterized security protocols
Mooij, A.J.
2010-01-01
We explore the applicability of the programming method of Feijen and van Gasteren to the domain of security protocols. This method addresses the derivation of concurrent programs from a formal specification, and it is based on common notions like invariants and pre- and post-conditions. We show that
On the Galilean Non-Invariance of Classical Electromagnetism
Preti, Giovanni; de Felice, Fernando; Masiero, Luca
2009-01-01
When asked to explain the Galilean non-invariance of classical electromagnetism on the basis of pre-relativistic considerations alone, students--and sometimes their teachers too--may face an impasse. Indeed, they often argue that a pre-relativistic physicist could most obviously have provided the explanation "at a glance", on the basis of the…
Dynamical constraints and adiabatic invariants in chemical reactions.
Lorquet, J C
2007-08-23
For long-range electrostatic potentials and, more generally, when the topography of the potential energy surface is locally simple, the reaction path coordinate is adiabatically separable from the perpendicular degrees of freedom. For the ion-permanent dipole and ion-quadrupole interactions, the Poisson bracket of the adiabatic invariant decreases with the interfragment distance more rapidly than the electrostatic potential. The smaller the translational momentum, the moment of inertia of the neutral fragment, and the dipole or quadrupole moments are, the more reliable the adiabatic approximation is, as expected from the usual argumentation. Closed-form expressions for an effective one-dimensional potential in an adiabatic Hamiltonian are given. Connection with a model where the decoupling is exact is obtained in the limit of an infinitely heavy dipole. The dynamics is also constrained by adiabatic invariance for a harmonic valley about a curved reaction path, as shown by the reaction path Hamiltonian method. The maximum entropy method reveals that, as a result of the invariance properties of the entropy, constraints whose validity has been demonstrated locally only subsist in all parts of phase space. However, their form varies continuously, and they are not necessarily expressed in simple terms as they are in the asymptotic region. Therefore, although the influence of adiabatic invariance has been demonstrated at asymptotically large values of the reaction coordinate only, it persists in more interesting ranges.
Three-dimensional low-energy topological invariants
Bakalarska, M.; Broda, B.
2000-01-01
A description of the one-loop approximation formula for the partition function of a three-dimensional abelian version of the Donaldson-Witten theory is proposed. The one-loop expression is shown to contain such topological invariants of a three-dimensional manifold M like the Reidemeister-Ray-Singer torsion τ R and Betti numbers. (orig.)
Measuring University Students' Approaches to Learning Statistics: An Invariance Study
Chiesi, Francesca; Primi, Caterina; Bilgin, Ayse Aysin; Lopez, Maria Virginia; del Carmen Fabrizio, Maria; Gozlu, Sitki; Tuan, Nguyen Minh
2016-01-01
The aim of the current study was to provide evidence that an abbreviated version of the Approaches and Study Skills Inventory for Students (ASSIST) was invariant across different languages and educational contexts in measuring university students' learning approaches to statistics. Data were collected on samples of university students attending…
Conformal Invariance, Dark Energy, and CMB Non-Gaussianity
Antoniadis, Ignatios; Mottola, Emil
2012-01-01
We show that in addition to simple scale invariance, a universe dominated by dark energy naturally gives rise to correlation functions possessing full conformal invariance. This is due to the mathematical isomorphism between the conformal group of certain three dimensional slices of de Sitter space and the de Sitter isometry group SO(4,1). In the standard homogeneous, isotropic cosmological model in which primordial density perturbations are generated during a long vacuum energy dominated de Sitter phase, the embedding of flat spatial R^3 sections in de Sitter space induces a conformal invariant perturbation spectrum and definite prediction for the shape of the non-Gaussian CMB bispectrum. In the case in which the density fluctuations are generated instead on the de Sitter horizon, conformal invariance of the S^2 horizon embedding implies a different but also quite definite prediction for the angular correlations of CMB non-Gaussianity on the sky. Each of these forms for the bispectrum is intrinsic to the sym...
An extension of Brosowski-Meinardus theorem on invariant approximation
Liaqat Ali Khan; Abdul Rahim Khan.
1991-07-01
We obtain a generalization of a fixed point theorem of Dotson for non-expansive mappings on star-shaped sets and then use it to prove a unified Brosowski-Meinardus theorem on invariant approximation in the setting of p-normed linear spaces. (author). 13 refs
Perturbation of frame sequences in shift-invariant spaces
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2005-01-01
We prove a new perturbation criteria for frame sequences, which generalizes previous results and is easier to apply. In the special case of frames infinitely generated shift-invariant subspaces of L2(ℝd) the condition can be formulated in terms of the norm of a finite Gram matrix and a correspond...
Isomorph invariance of the structure and dynamics of classical crystals
Albrechtsen, Dan; Olsen, Andreas Elmerdahl; Pedersen, Ulf Rørbæk
2014-01-01
This paper shows by computer simulations that some crystalline systems have curves in their thermodynamic phase diagrams, so-called isomorphs, along which structure and dynamics in reduced units are invariant to a good approximation. The crystals are studied in a classical-mechanical framework...
Another scheme for quantization of scale invariant gauge theories
Hortacsu, M.
1987-10-01
A new scheme is proposed for the quantization of scale invariant gauge theories for all even dimensions when they are minimally coupled to a spinor field. A cut-off procedure suggests an algorithm which may regularize the theory. (author). 10 refs
Numeraire Invariance and application to Option Pricing and Hedging
Jamshidian, F.; Vanmaele, Michèle; Deelstra, Griselda; De Schepper, Ann; Dhaene, Jan; Reynaerts, Huguette; Schoutens, Wim; Van Goethem, Paul
2008-01-01
Numeraire invariance is a well-known technique in option pricing and hedging theory. It takes a convenient asset as the numeraire, as if it were the medium of exchange, and expresses all other asset and option prices in units of this numeraire. Since the price of the numeraire relative to itself is
Deformed special relativity with an invariant minimum speed and its ...
On the other hand, according to special relativity (SR), the momentum cannot ... Deformed special relativity with an invariant minimum speed ..... However, we need to show that there is an anti-gravitational interaction between the ordinary proof mass m and the big sphere with a 'dark mass' of vacuum (MΛ), but let us first ...
Electromagnetic properties of off-shell particles and gauge invariance
Nagorny, S. I.; Dieperink, A. E. L.
1998-01-01
Abstract: Electromagnetic properties of off-shell particles are discussed on the basis of a purely electromagnetic reaction: virtual Compton scattering off a proton. It is shown that the definition of off-shell electromagnetic form factors is not gauge invariant and that these cannot be investigated
The Toledo invariant, and Seshadri constants of fake projective planes
DI CERBO, Luca F.
2017-01-01
The purpose of this paper is to explicitly compute the Seshadri constants of all ample line bundles on fake projective planes. The proof relies on the theory of the Toledo invariant, and more precisely on its characterization of $\\mathbb{C}$-Fuchsian curves in complex hyperbolic spaces.
On the invariant measure for the nonlinear Schroedinger equation
Zhidkov, P.R.
1991-01-01
The invariant measure for the nonlinear Schroedinger equation is constructed. In fact, it is assumed that the nonlinearity in the equation is semilinear. The main aim of the paper is the explanation of the Fermi - Past - Ulam phenomenon. Poincare theorem gives the answer to this question. 17 refs
Modular invariants for affine SU(3) theories at prime heights
Ruelle, P.; Thiran, E.; Weyers, J.
1990-01-01
A proof is given for the existence of two and only two modular invariant partition functions in affine SU(3) k theories at heights n=k+3 which are prime numbers. Arithmetic properties of the ring of algabraic integers Z(ω) which is related to SU(3) weights are extensively used. (orig.)
A bootstrap invariance principle for highly nonstationary long memory processes
Kapetanios, George
2004-01-01
This paper presents an invariance principle for highly nonstationary long memory processes, defined as processes with long memory parameter lying in (1, 1.5). This principle provides the tools for showing asymptotic validity of the bootstrap in the context of such processes.
Birkhoff-Kellogg theorems on invariant directions for multimaps
Donal O'Regan
2003-04-01
Full Text Available We establish Birkhoff-Kellogg type theorems on invariant directions for a general class of maps. Our results, in particular, apply to Kakutani, acyclic, O'Neill, approximable, admissible, and Ã°ÂÂ’Â°cÃŽÂº maps.
The Satisfaction with Life Scale: : Measurement invariance across immigrant groups
Ponizovsky, Y.; Dimitrova, R.; Schachner, M.K.; Van de Schoot, R.
2013-01-01
The current study examined measurement invariance of the Satisfaction With Life Scale (SWLS; Diener, Emmons, Larsen, & Griffin, 1985) across three immigrant groups, namely, immigrants from the Former Soviet Union (FSU) in Israel, Turkish-Bulgarians, and Turkish-Germans. The results demonstrate
The Satisfaction With Life Scale : Measurement invariance across immigrant groups
Ponizovsky, Y.; Dimitrova, R.; Schachner, M.; van de Schoot, R.
2013-01-01
The current study examined measurement invariance of the Satisfaction With Life Scale (SWLS; Diener, Emmons, Larsen, & Griffin, 1985) across three immigrant groups, namely, immigrants from the Former Soviet Union (FSU) in Israel, Turkish-Bulgarians, and Turkish-Germans. The results demonstrate
Linear complexity for multidimensional arrays - a numerical invariant
Gomez-Perez, Domingo; Høholdt, Tom; Moreno, Oscar
2015-01-01
Linear complexity is a measure of how complex a one dimensional sequence can be. In this paper we extend the concept of linear complexity to multiple dimensions and present a definition that is invariant under well-orderings of the arrays. As a result we find that our new definition for the proce...
Gauge invariance and equations of motion for closed string modes
B. Sathiapalan
2014-12-01
Full Text Available We continue earlier discussions on loop variables and the exact renormalization group on the string world sheet for closed and open string backgrounds. The world sheet action with a UV regulator is written in a generally background covariant way by introducing a background metric. It is shown that the renormalization group gives background covariant equations of motion – this is the gauge invariance of the graviton. Interaction is written in terms of gauge invariant and generally covariant field strength tensors. The basic idea is to work in Riemann normal coordinates and covariantize the final equation. It turns out that the equations for massive modes are gauge invariant only if the space–time curvature of the (arbitrary background is zero. The exact RG equations give quadratic equations of motion for all the modes including the physical graviton. The level (2,2¯ massive field equations are used to illustrate the techniques. At this level there are mixed symmetry tensors. Gauge invariant interacting equations can be written down. In flat space an action can also be written for the free theory.
A characterization of scale invariant responses in enzymatic networks.
Maja Skataric
Full Text Available An ubiquitous property of biological sensory systems is adaptation: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a prolonged change in their environment. Recently, it was shown theoretically and experimentally that many adapting systems, both at the organism and single-cell level, enjoy a remarkable additional feature: scale invariance, meaning that the initial, transient behavior remains (approximately the same even when the background signal level is scaled. In this work, we set out to investigate under what conditions a broadly used model of biochemical enzymatic networks will exhibit scale-invariant behavior. An exhaustive computational study led us to discover a new property of surprising simplicity and generality, uniform linearizations with fast output (ULFO, whose validity we show is both necessary and sufficient for scale invariance of three-node enzymatic networks (and sufficient for any number of nodes. Based on this study, we go on to develop a mathematical explanation of how ULFO results in scale invariance. Our work provides a surprisingly consistent, simple, and general framework for understanding this phenomenon, and results in concrete experimental predictions.
View Invariant Gesture Recognition using 3D Motion Primitives
Holte, Michael Boelstoft; Moeslund, Thomas B.
2008-01-01
This paper presents a method for automatic recognition of human gestures. The method works with 3D image data from a range camera to achieve invariance to viewpoint. The recognition is based solely on motion from characteristic instances of the gestures. These instances are denoted 3D motion...
SO(N) reformulated link invariants from topological strings
Borhade, Pravina; Ramadevi, P.
2005-01-01
Large N duality conjecture between U(N) Chern-Simons gauge theory on S 3 and A-model topological string theory on the resolved conifold was verified at the level of partition function and Wilson loop observables. As a consequence, the conjectured form for the expectation value of the topological operators in A-model string theory led to a reformulation of link invariants in U(N) Chern-Simons theory giving new polynomial invariants whose integer coefficients could be given a topological meaning. We show that the A-model topological operator involving SO(N) holonomy leads to a reformulation of link invariants in SO(N) Chern-Simons theory. Surprisingly, the SO(N) reformulated invariants also has a similar form with integer coefficients. The topological meaning of the integer coefficients needs to be explored from the duality conjecture relating SO(N) Chern-Simons theory to A-model closed string theory on orientifold of the resolved conifold background
Measurement Invariance of Expectancy-Value Questionnaire in Physical Education
Zhu, Xihe; Sun, Haichun; Chen, Ang; Ennis, Catherine
2012-01-01
Expectancy-Value Questionnaire (EVQ) measures student expectancy beliefs and task values of the domain content (Eccles & Wigfield, 1995). In this study the authors examine measurement invariance of EVQ in the domain of physical education between elementary and middle-school students. Participants included 811 students (3rd-5th grades) from 13…
Renormalization group invariance in the presence of an instanton
Ross, D.A.
1987-01-01
A pure Yang-Mills theory which admits an instanton is under discussion. n=1 supersymmetric (SU-2) Yang-Mills theory, both in the Wess-zumino gauge and in manifestly supersymmetric supergauge is considered. Two-loop vacuum graphs are calculated. The way a renormalization group invariance works under conditions of fermionic zero mode elimination is shown
Global operator expansions in conformally invariant relativistic quantum field theory
Schoer, B.; Swieca, J.A.; Voelkel, A.H.
1974-01-01
A global conformal operator expansions in the Minkowski region in several models and their formulation in the general theory is presented. Whereas the vacuum expansions are termwise manisfestly conformal invariant, the expansions away from the vacuum do not share this property
Residual gauge invariance of Hamiltonian lattice gauge theories
Ryang, S.; Saito, T.; Shigemoto, K.
1984-01-01
The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegengauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically. (orig.)
Lorentz Invariant Spectrum of Minimal Chiral Schwinger Model
Kim, Yong-Wan; Kim, Seung-Kook; Kim, Won-Tae; Park, Young-Jai; Kim, Kee Yong; Kim, Yongduk
We study the Lorentz transformation of the minimal chiral Schwinger model in terms of the alternative action. We automatically obtain a chiral constraint, which is equivalent to the frame constraint introduced by McCabe, in order to solve the frame problem in phase space. As a result we obtain the Lorentz invariant spectrum in any moving frame by choosing a frame parameter.
Invariant Handwriting Features Useful in Cursive-Script Recognition
Teulings, Hans-leo L; Schomaker, L R; Impedovo, S.
1994-01-01
A handwriting pattern is considered as a sequence of ballistic strokes. Replications of a pattern may be generated from a single, higher-level memory representation, acting as a motor program. Therefore, those stroke features which show the most invariant pattern are probably related to the
Non-singular cosmologies in the conformally invariant gravitation theory
Kembhavi, A.K.
1976-01-01
It is shown that in the framework of a conformally invariant gravitation theory, the singularity which is present in some anisotropic universes in general relativity is due to a wrong choice of conformal frame. Frames exist in which these models can be made singularity free. (author)
On Similarity Invariance of Balancing for Nonlinear Systems
Scherpen, Jacquelien M.A.
1995-01-01
A previously obtained balancing method for nonlinear systems is investigated on similarity in variance by generalization of the observations on the similarity invariance of the linear balanced realization theory. For linear systems it is well known that the Hankel singular values are similarity
Heavy ions acceleration in RF wells of 2-frequency electromagnetic field and in the inverted FEL
Dzergach, A.I.; Kabanov, V.S.; Nikulin, M.G.; Vinogradov, S.V.
1995-03-01
Last results of the study of heavy ions acceleration by electrons trapped in moving 2-frequency 3-D RF wells are described. A linearized theoretical model of ions acceleration in a polarized spheroidal plasmoid is proposed. The equilibrium state of this plasmoid is described by the modified microcanonical distribution of the Courant-Snyder invariant (open-quotes quasienergyclose quotes of electrons). Some new results of computational simulation of the acceleration process are given. The method of computation takes into account the given cylindrical field E 011 (var-phi,r,z) and the self fields of electrons and ions. The results of the computation at relatively short time intervals confirm the idea and estimated parameters of acceleration. The heavy ion accelerator using this principle may be constructed with the use of compact cm band iris-loaded and biperiodical waveguides with double-sided 2-frequency RF feeding. It can accelerate heavy ions with a charge number Z i from small initial energies ∼ 50 keV/a.u. with the rate ∼ Z i · 10 MeV/m. Semirelativistic ions may be accelerated with similar rate also in the inverted FEL
Global coupling and decoupling of the APS storage ring
Chae, Yong-Chul; Liu, Jianyang; Teng, L.C.
1995-01-01
This Paper describes a study of controlling the coupling between the horizontal and the vertical betatron oscillations in the APS storage ring. First, we investigate the strengthening of coupling using two families of skew quadrupoles. Using smooth approximation, we obtained the formulae to estimate the coupling ratio defined as the ratio of the vertical and horizontal emittances or, for a single particle, the ratio of the maximum values of the Courant Snyder invariants. Since we knew that the coupling is mostly enhanced by the 21st harmonic content of skew quadrupole distribution, we carried out the harmonic analysis in order to find the optimum arrangement of the skew quadrupoles. The numerical results from tracking a single particle are presented for the various configurations of skew quadrupoles. Second, we describe the global decoupling procedure to minimize the unwanted coupling effects. These are mainly due to the random roll errors of normal quadrupoles. It is shown that even with the rather large rms roll error of 2 mrad we can reduce the Coupling from 70 percent to 10 percent with a skew quadrupole strength which is one order of magnitude lower than the typical normal quadrupole strength
Metric invariance in object recognition: a review and further evidence.
Cooper, E E; Biederman, I; Hummel, J E
1992-06-01
Phenomenologically, human shape recognition appears to be invariant with changes of orientation in depth (up to parts occlusion), position in the visual field, and size. Recent versions of template theories (e.g., Ullman, 1989; Lowe, 1987) assume that these invariances are achieved through the application of transformations such as rotation, translation, and scaling of the image so that it can be matched metrically to a stored template. Presumably, such transformations would require time for their execution. We describe recent priming experiments in which the effects of a prior brief presentation of an image on its subsequent recognition are assessed. The results of these experiments indicate that the invariance is complete: The magnitude of visual priming (as distinct from name or basic level concept priming) is not affected by a change in position, size, orientation in depth, or the particular lines and vertices present in the image, as long as representations of the same components can be activated. An implemented seven layer neural network model (Hummel & Biederman, 1992) that captures these fundamental properties of human object recognition is described. Given a line drawing of an object, the model activates a viewpoint-invariant structural description of the object, specifying its parts and their interrelations. Visual priming is interpreted as a change in the connection weights for the activation of: a) cells, termed geon feature assemblies (GFAs), that conjoin the output of units that represent invariant, independent properties of a single geon and its relations (such as its type, aspect ratio, relations to other geons), or b) a change in the connection weights by which several GFAs activate a cell representing an object.
Deep generative learning of location-invariant visual word recognition.
Di Bono, Maria Grazia; Zorzi, Marco
2013-01-01
It is widely believed that orthographic processing implies an approximate, flexible coding of letter position, as shown by relative-position and transposition priming effects in visual word recognition. These findings have inspired alternative proposals about the representation of letter position, ranging from noisy coding across the ordinal positions to relative position coding based on open bigrams. This debate can be cast within the broader problem of learning location-invariant representations of written words, that is, a coding scheme abstracting the identity and position of letters (and combinations of letters) from their eye-centered (i.e., retinal) locations. We asked whether location-invariance would emerge from deep unsupervised learning on letter strings and what type of intermediate coding would emerge in the resulting hierarchical generative model. We trained a deep network with three hidden layers on an artificial dataset of letter strings presented at five possible retinal locations. Though word-level information (i.e., word identity) was never provided to the network during training, linear decoding from the activity of the deepest hidden layer yielded near-perfect accuracy in location-invariant word recognition. Conversely, decoding from lower layers yielded a large number of transposition errors. Analyses of emergent internal representations showed that word selectivity and location invariance increased as a function of layer depth. Word-tuning and location-invariance were found at the level of single neurons, but there was no evidence for bigram coding. Finally, the distributed internal representation of words at the deepest layer showed higher similarity to the representation elicited by the two exterior letters than by other combinations of two contiguous letters, in agreement with the hypothesis that word edges have special status. These results reveal that the efficient coding of written words-which was the model's learning objective
Deep generative learning of location-invariant visual word recognition
Di Bono, Maria Grazia; Zorzi, Marco
2013-01-01
It is widely believed that orthographic processing implies an approximate, flexible coding of letter position, as shown by relative-position and transposition priming effects in visual word recognition. These findings have inspired alternative proposals about the representation of letter position, ranging from noisy coding across the ordinal positions to relative position coding based on open bigrams. This debate can be cast within the broader problem of learning location-invariant representations of written words, that is, a coding scheme abstracting the identity and position of letters (and combinations of letters) from their eye-centered (i.e., retinal) locations. We asked whether location-invariance would emerge from deep unsupervised learning on letter strings and what type of intermediate coding would emerge in the resulting hierarchical generative model. We trained a deep network with three hidden layers on an artificial dataset of letter strings presented at five possible retinal locations. Though word-level information (i.e., word identity) was never provided to the network during training, linear decoding from the activity of the deepest hidden layer yielded near-perfect accuracy in location-invariant word recognition. Conversely, decoding from lower layers yielded a large number of transposition errors. Analyses of emergent internal representations showed that word selectivity and location invariance increased as a function of layer depth. Word-tuning and location-invariance were found at the level of single neurons, but there was no evidence for bigram coding. Finally, the distributed internal representation of words at the deepest layer showed higher similarity to the representation elicited by the two exterior letters than by other combinations of two contiguous letters, in agreement with the hypothesis that word edges have special status. These results reveal that the efficient coding of written words—which was the model's learning objective
Invariant recognition drives neural representations of action sequences.
Andrea Tacchetti
2017-12-01
Full Text Available Recognizing the actions of others from visual stimuli is a crucial aspect of human perception that allows individuals to respond to social cues. Humans are able to discriminate between similar actions despite transformations, like changes in viewpoint or actor, that substantially alter the visual appearance of a scene. This ability to generalize across complex transformations is a hallmark of human visual intelligence. Advances in understanding action recognition at the neural level have not always translated into precise accounts of the computational principles underlying what representations of action sequences are constructed by human visual cortex. Here we test the hypothesis that invariant action discrimination might fill this gap. Recently, the study of artificial systems for static object perception has produced models, Convolutional Neural Networks (CNNs, that achieve human level performance in complex discriminative tasks. Within this class, architectures that better support invariant object recognition also produce image representations that better match those implied by human and primate neural data. However, whether these models produce representations of action sequences that support recognition across complex transformations and closely follow neural representations of actions remains unknown. Here we show that spatiotemporal CNNs accurately categorize video stimuli into action classes, and that deliberate model modifications that improve performance on an invariant action recognition task lead to data representations that better match human neural recordings. Our results support our hypothesis that performance on invariant discrimination dictates the neural representations of actions computed in the brain. These results broaden the scope of the invariant recognition framework for understanding visual intelligence from perception of inanimate objects and faces in static images to the study of human perception of action sequences.
Jak, Suzanne; Oort, Frans J.; Dolan, Conor V.
2013-01-01
We present a test for cluster bias, which can be used to detect violations of measurement invariance across clusters in 2-level data. We show how measurement invariance assumptions across clusters imply measurement invariance across levels in a 2-level factor model. Cluster bias is investigated by testing whether the within-level factor loadings…
Infrared asymptotic behavior of gauge-invariant propagator in quantum electrodynamics
Skachkov, N.B.; Solovtsov, I.L.; Shevchenko, O.Yu.
1987-01-01
A new class of gauge-invariant fields is introduced. The Dyson-Schwinger equations are obtained for the gauge-invariant generalization of the spinor propagator. On the basis of these equations, and also by means of functional methods, it is shown that the gauge-invariant spinor propagator has a singularity in the form of a simple pole in the infrared region
Infrared asymptotics of a gauge-invariant propagator in quantum electrodynamics
Skachkov, N.B.; Shevchenko, O.Yu.; Solovtsov, I.l.
1987-01-01
A new class of gauge-invariant fields is introduced. For the gauge-invariant propagator of a spinor field the analogue of the Dyson-Schwinger equations is derived. With the help of these equations as well as the functional integration method it is shown that the gauge-invariant spinor propagator has a simple pole singularity in the infrared region
Infrared asymptotics of a gauge-invariant propagator in quantum electrodynamics
Skachkov, N.B.; Shevchenko, O.Yu.
1985-01-01
A new class of the gauge-invariant field is introduced. For the gauge-invariant propagator of a spinor field the analog of the Dyson-Schwinger equations is derived. By using these equations as well as the functional integration method it is shown that the gauge-invariant spinor propagator has a simple pole singularity in the infrared region
Normal Anti-Invariant Submanifolds of Paraquaternionic Kähler Manifolds
Novac-Claudiu Chiriac
2006-12-01
Full Text Available We introduce normal anti-invariant submanifolds of paraquaternionic Kähler manifolds and study the geometric structures induced on them. We obtain necessary and sufficient conditions for the integrability of the distributions defined on a normal anti-invariant submanifold. Also, we present characterizations of local (global anti-invariant products.
Quantum gravity vacuum and invariants of embedded spin networks
Mikovic, A
2003-01-01
We show that the path integral for the three-dimensional SU(2) BF theory with a Wilson loop or a spin network function inserted can be understood as the Rovelli-Smolin loop transform of a wavefunction in the Ashtekar connection representation, where the wavefunction satisfies the constraints of quantum general relativity with zero cosmological constant. This wavefunction is given as a product of the delta functions of the SU(2) field strength and therefore it can be naturally associated with a flat connection spacetime. The loop transform can be defined rigorously via the quantum SU(2) group, as a spin foam state sum model, so that one obtains invariants of spin networks embedded in a three-manifold. These invariants define a flat connection vacuum state in the q-deformed spin network basis. We then propose a modification of this construction in order to obtain a vacuum state corresponding to the flat metric spacetime
Black brane entropy and hydrodynamics: The boost-invariant case
Booth, Ivan; Heller, Michal P.; Spalinski, Michal
2009-01-01
The framework of slowly evolving horizons is generalized to the case of black branes in asymptotically anti-de Sitter spaces in arbitrary dimensions. The results are used to analyze the behavior of both event and apparent horizons in the gravity dual to boost-invariant flow. These considerations are motivated by the fact that at second order in the gradient expansion the hydrodynamic entropy current in the dual Yang-Mills theory appears to contain an ambiguity. This ambiguity, in the case of boost-invariant flow, is linked with a similar freedom on the gravity side. This leads to a phenomenological definition of the entropy of black branes. Some insights on fluid/gravity duality and the definition of entropy in a time-dependent setting are elucidated.
Can confinement ensure natural CP-invariance of strong interactions
Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I.
1979-01-01
P- and T-invariance violation in quantum chromodynamics (QCD) due to the so called THETA term Δα=THETAxgsub(s)sup(2)/32πsup(2)xGsub(μν)sup(a)xGsub(μν)sup(a) tilde, where Gsub(μν)sup(a) is the gluon field strength tensor, and gsub(s) is the quark-gluon coupling constant is discussed. It is shown that irrespectively of how the confinement works there emerge observable P- and T-odd effects. The proof is based on the assumption that QCD resolves the upsilon(1) problem, i.e. the mass of the singlet pseudoscalar meson does not vanish in the chiral limit. A modification of the axion scheme which restores the natural P and T invariance of the theory is suggested and cannot be ruled out experimentally
Tokunaga self-similarity arises naturally from time invariance
Kovchegov, Yevgeniy; Zaliapin, Ilya
2018-04-01
The Tokunaga condition is an algebraic rule that provides a detailed description of the branching structure in a self-similar tree. Despite a solid empirical validation and practical convenience, the Tokunaga condition lacks a theoretical justification. Such a justification is suggested in this work. We define a geometric branching process G (s ) that generates self-similar rooted trees. The main result establishes the equivalence between the invariance of G (s ) with respect to a time shift and a one-parametric version of the Tokunaga condition. In the parameter region where the process satisfies the Tokunaga condition (and hence is time invariant), G (s ) enjoys many of the symmetries observed in a critical binary Galton-Watson branching process and reproduces the latter for a particular parameter value.
Propagators for gauge-invariant observables in cosmology
Fröb, Markus B.; Lima, William C. C.
2018-05-01
We make a proposal for gauge-invariant observables in perturbative quantum gravity in cosmological spacetimes, building on the recent work of Brunetti et al (2016 J. High Energy Phys. JHEP08(2016)032). These observables are relational, and are obtained by evaluating the field operator in a field-dependent coordinate system. We show that it is possible to define this coordinate system such that the non-localities inherent in any higher-order observable in quantum gravity are causal, i.e. the value of the gauge-invariant observable at a point x only depends on the metric and inflation perturbations in the past light cone of x. We then construct propagators for the metric and inflaton perturbations in a gauge adapted to that coordinate system, which simplifies the calculation of loop corrections, and give explicit expressions for relevant cases: matter- and radiation-dominated eras and slow-roll inflation.
A gauge invariant theory for time dependent heat current
Chen, Jian; ShangGuan, Minhui; Wang, Jian
2015-01-01
In this work, we develop a general gauge-invariant theory for AC heat current through multi-probe systems. Using the non-equilibrium Green’s function, a general expression for time-dependent electrothermal admittance is obtained where we include the internal potential due to the Coulomb interaction explicitly. We show that the gauge-invariant condition is satisfied for heat current if the self-consistent Coulomb interaction is considered. It is known that the Onsager relation holds for dynamic charge conductance. We show in this work that the Onsager relation for electrothermal admittance is violated, except for a special case of a quantum dot system with a single energy level. We apply our theory to a nano capacitor where the Coulomb interaction plays an essential role. We find that, to the first order in frequency, the heat current is related to the electrochemical capacitance as well as the phase accumulated in the scattering event. (paper)
Symmetry, Invariance and Ontology in Physics and Statistics
Julio Michael Stern
2011-09-01
Full Text Available This paper has three main objectives: (a Discuss the formal analogy between some important symmetry-invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy principle in probability theory, and de Finetti-type theorems in Bayesian statistics; (b Discuss the epistemological and ontological implications of these theorems, as they are interpreted in physics and statistics. Specifically, we will focus on the positivist (in physics or subjective (in statistics interpretations vs. objective interpretations that are suggested by symmetry and invariance arguments; (c Introduce the cognitive constructivism epistemological framework as a solution that overcomes the realism-subjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion.
Computation of Quasiperiodic Normally Hyperbolic Invariant Tori: Rigorous Results
Canadell, Marta; Haro, Àlex
2017-12-01
The development of efficient methods for detecting quasiperiodic oscillations and computing the corresponding invariant tori is a subject of great importance in dynamical systems and their applications in science and engineering. In this paper, we prove the convergence of a new Newton-like method for computing quasiperiodic normally hyperbolic invariant tori carrying quasiperiodic motion in smooth families of real-analytic dynamical systems. The main result is stated as an a posteriori KAM-like theorem that allows controlling the inner dynamics on the torus with appropriate detuning parameters, in order to obtain a prescribed quasiperiodic motion. The Newton-like method leads to several fast and efficient computational algorithms, which are discussed and tested in a companion paper (Canadell and Haro in J Nonlinear Sci, 2017. doi: 10.1007/s00332-017-9388-z), in which new mechanisms of breakdown are presented.
Q-phonons, Q-invariants, and company
Brentano, P. von; Gade, A.; Pietralla, N.; Werner, V.
2002-01-01
The paper discusses the concept of Q-phonons and its connection to the concept of Q-invariants and the shape parameters of nuclei. It will also discuss some useful relations between Q-invariants and observables. These relations allow one to determine crucial nuclear observables such as the square of the quadrupole moment of the first 2+ state from lifetime data of the gamma- and ground band which may have applications, in future measurements with rare isotopes beams. These concepts are discussed for the Barium, Xenon and Cerium nuclei with mass numbers around A = 130, because some of these concepts were either introduced or at least heavily used in the discussion of the nuclear structure of these nuclei
External gauge invariance and anomaly in BS vertices and boundstates
Bando, Masako; Harada, Masayasu; Kugo, Taichiro
1994-01-01
A systematic method is given for obtaining consistent approximations to the Schwinger-Dyson (SD) and Bethe-Salpeter (BS) equations which maintain the external gauge invariance. We show that for any order of approximation to the SD equation there is a corresponding approximation to the BS equations such that the solutions to those equations satisfy the Ward-Takahashi identities of the external gauge symmetry. This formulation also clarifies the way how we can calculate the Green functions of current operators in a consistent manner with the gauge invariance and the axial anomaly. We show which type of diagrams for the π 0 → γγ amplitude using the pion BS amplitude give result consistent with the low-energy theorem. An interesting phenomenon is observed in the ladder approximation that the low-energy theorem is saturated by the zeroth order terms in the external momenta of the pseudoscalar BS amplitude and the vector vertex functions. (author)
Evaluating Forecasts, Narratives and Policy Using a Test of Invariance
Jennifer L. Castle
2017-09-01
Full Text Available Economic policy agencies produce forecasts with accompanying narratives, and base policy changes on the resulting anticipated developments in the target variables. Systematic forecast failure, defined as large, persistent deviations of the outturns from the numerical forecasts, can make the associated narrative false, which would in turn question the validity of the entailed policy implementation. We establish when systematic forecast failure entails failure of the accompanying narrative, which we call forediction failure, and when that in turn implies policy invalidity. Most policy regime changes involve location shifts, which can induce forediction failure unless the policy variable is super exogenous in the policy model. We propose a step-indicator saturation test to check in advance for invariance to policy changes. Systematic forecast failure, or a lack of invariance, previously justified by narratives reveals such stories to be economic fiction.
The visual system supports online translation invariance for object identification.
Bowers, Jeffrey S; Vankov, Ivan I; Ludwig, Casimir J H
2016-04-01
The ability to recognize the same image projected to different retinal locations is critical for visual object recognition in natural contexts. According to many theories, the translation invariance for objects extends only to trained retinal locations, so that a familiar object projected to a nontrained location should not be identified. In another approach, invariance is achieved "online," such that learning to identify an object in one location immediately affords generalization to other locations. We trained participants to name novel objects at one retinal location using eyetracking technology and then tested their ability to name the same images presented at novel retinal locations. Across three experiments, we found robust generalization. These findings provide a strong constraint for theories of vision.
Local Relation Map: A Novel Illumination Invariant Face Recognition Approach
Lian Zhichao
2012-10-01
Full Text Available In this paper, a novel illumination invariant face recognition approach is proposed. Different from most existing methods, an additive term as noise is considered in the face model under varying illuminations in addition to a multiplicative illumination term. High frequency coefficients of Discrete Cosine Transform (DCT are discarded to eliminate the effect caused by noise. Based on the local characteristics of the human face, a simple but effective illumination invariant feature local relation map is proposed. Experimental results on the Yale B, Extended Yale B and CMU PIE demonstrate the outperformance and lower computational burden of the proposed method compared to other existing methods. The results also demonstrate the validity of the proposed face model and the assumption on noise.
Path-integral invariants in abelian Chern–Simons theory
Guadagnini, E.; Thuillier, F.
2014-01-01
We consider the U(1) Chern–Simons gauge theory defined in a general closed oriented 3-manifold M; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The non-perturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent U(1) principal bundles over M; the different sectors of configuration space are labelled by the elements of the first homology group of M and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the non-perturbative contributions to the mean values. The functional integration is carried out in any 3-manifold M, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin–Turaev surgery invariants
Assessment of Rotationally-Invariant Clustering Using Streamlet Tractography
Liptrot, Matthew George; Lauze, François
2016-01-01
We present a novel visualisation-based strategy for the assessment of a recently proposed clustering technique for raw DWI volumes which derives rotationally-invariant metrics to classify voxels. The validity of the division of all brain tissue voxels into such classes was assessed using the rece......We present a novel visualisation-based strategy for the assessment of a recently proposed clustering technique for raw DWI volumes which derives rotationally-invariant metrics to classify voxels. The validity of the division of all brain tissue voxels into such classes was assessed using...... the recently developed streamlets visualisation technique, which aims to represent brain fibres by collections of many short streamlines. Under the assumption that streamlines seeded in a cluster should stay within it, we were able to assess how well perceptual tracing could occur across the boundaries...... of the clusters....
Cartesian integration of Grassmann variables over invariant functions
Kieburg, Mario; Kohler, Heiner; Guhr, Thomas [Universitaet Duisburg-Essen, Duisburg (Germany)
2009-07-01
Supersymmetry plays an important role in field theory as well as in random matrix theory and mesoscopic physics. Anticommuting variables are the fundamental objects of supersymmetry. The integration over these variables is equivalent to the derivative. Recently[arxiv:0809.2674v1[math-ph] (2008)], we constructed a differential operator which only acts on the ordinary part of the superspace consisting of ordinary and anticommuting variables. This operator is equivalent to the integration over all anticommuting variables of an invariant function. We present this operator and its applications for functions which are rotation invariant under the supergroups U(k{sub 1}/k{sub 2}) and UOSp(k{sub 1}/k{sub 2}).
Statistical analysis of complex systems with nonclassical invariant measures
Fratalocchi, Andrea
2011-02-28
I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by employing a general formalism based on the Ablowitz-Kaup-Newell-Segur scheme, I demonstrate how to build an invariant measure and, within a one-dimensional phase space, how to develop a suitable thermodynamics. A detailed example is provided with a universal model of wave propagation, with reference to a transparent potential sustaining gray solitons. The system shows a rich thermodynamic scenario, with a free-energy landscape supporting phase transitions and controllable emergent properties. I finally discuss the origin of such behavior, trying to identify common denominators in the area of complex dynamics.
From modular invariants to graphs: the modular splitting method
Isasi, E; Schieber, G
2007-01-01
We start with a given modular invariant M of a two-dimensional su-hat(n) k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction (1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; (2) the quantum symmetries of the higher ADE graph G associated with the initial modular invariant M. Note that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyse several su-hat(3) k exceptional cases at levels 5 and 9
On invariant MASAs for endomorphisms of the Cuntz algebras
Hong, Jeong Hee; Skalski, Adam; Szymanski, Wojciech
2010-01-01
The problem of existence of standard (i.e. product-type) invariant MASAs for endomorphisms of the Cuntz algebras O_n is studied. In particular, endomorphisms which preserve the canonical diagonal MASA D_n are investigated. Conditions on a unitary w equivalent to the fact that the corresponding...... endomorphism λ_w preserves D_n are found, and it is shown that they may be satisfied by unitaries which do not normalize D_n. Unitaries giving rise to endomorphisms which leave all standard MASAs invariant and have identical actions on them are characterized. Finally, some properties of examples of finite......-index endomorphisms of O_n given by Izumi and related to sector theory are discussed and it is shown that they lead to an endomorphism of O_2 associated to a matrix unitary which does not preserve any standard MASA....
CPT invariance and the spin-statistics connection
Bain, Jonathan
2016-01-01
This book seeks to answer the question "What explains CPT invariance and the spin-statistics connection?" These properties play foundational roles in relativistic quantum field theories (RQFTs), are supported by high-precision experiments, and figure into explanations of a wide range of phenomena, from antimatter, to the periodic table of the elements, to superconductors and superfluids. They can be derived in RQFTs by means of the famous CPT and Spin-Statistics theorems; but, the author argues, these theorems cannot be said to explain these properties, at least under standard philosophical accounts of scientific explanation. This is because there are multiple, in some cases incompatible, ways of deriving these theorems, and, secondly, because the theorems fail for the types of theories that underwrite the empirical evidence: non-relativistic quantum theories, and realistic interacting RQFTs. The goal of this book is to work towards an understanding of CPT invariance and the spin-statistics connection by firs...
Basin of Attraction through Invariant Curves and Dominant Functions
Ziyad AlSharawi
2015-01-01
Full Text Available We study a second-order difference equation of the form zn+1=znF(zn-1+h, where both F(z and zF(z are decreasing. We consider a set of invariant curves at h=1 and use it to characterize the behaviour of solutions when h>1 and when 01 is related to the Y2K problem. For 0
η-INVARIANT AND CHERN-SIMONS CURRENT
ZHANG WEIPING
2005-01-01
The author presents an alternate proof of the Bismut-Zhang localization formula of ηinvariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the aualytically defined η invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles,and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.
Invariant length scale in relativistic kinematics: lessons from Dirichlet branes
Schuller, Frederic P.; Pfeiffer, Hendryk
2004-01-01
Dirac-Born-Infeld theory is shown to possess a hidden invariance associated with its maximal electric field strength. The local Lorentz symmetry O(1,n) on a Dirichlet-n-brane is thereby enhanced to an O(1,n)xO(1,n) gauge group, encoding both an invariant velocity and acceleration (or length) scale. The presence of this enlarged gauge group predicts consequences for the kinematics of observers on Dirichlet branes, with admissible accelerations being bounded from above. An important lesson is that the introduction of a fundamental length scale into relativistic kinematics does not enforce a deformation of Lorentz boosts, as one might assume naively. The exhibited structures further show that Moffat's non-symmetric gravitational theory qualifies as a candidate for a consistent Born-Infeld type gravity with regulated solutions
Scale-invariant entropy-based theory for dynamic ordering
Mahulikar, Shripad P.; Kumari, Priti
2014-01-01
Dynamically Ordered self-organized dissipative structure exists in various forms and at different scales. This investigation first introduces the concept of an isolated embedding system, which embeds an open system, e.g., dissipative structure and its mass and/or energy exchange with its surroundings. Thereafter, scale-invariant theoretical analysis is presented using thermodynamic principles for Order creation, existence, and destruction. The sustainability criterion for Order existence based on its structured mass and/or energy interactions with the surroundings is mathematically defined. This criterion forms the basis for the interrelationship of physical parameters during sustained existence of dynamic Order. It is shown that the sufficient condition for dynamic Order existence is approached if its sustainability criterion is met, i.e., its destruction path is blocked. This scale-invariant approach has the potential to unify the physical understanding of universal dynamic ordering based on entropy considerations
Hamiltonian approach to second order gauge invariant cosmological perturbations
Domènech, Guillem; Sasaki, Misao
2018-01-01
In view of growing interest in tensor modes and their possible detection, we clarify the definition of tensor modes up to 2nd order in perturbation theory within the Hamiltonian formalism. Like in gauge theory, in cosmology the Hamiltonian is a suitable and consistent approach to reduce the gauge degrees of freedom. In this paper we employ the Faddeev-Jackiw method of Hamiltonian reduction. An appropriate set of gauge invariant variables that describe the dynamical degrees of freedom may be obtained by suitable canonical transformations in the phase space. We derive a set of gauge invariant variables up to 2nd order in perturbation expansion and for the first time we reduce the 3rd order action without adding gauge fixing terms. In particular, we are able to show the relation between the uniform-ϕ and Newtonian slicings, and study the difference in the definition of tensor modes in these two slicings.
Invariants and labels for Lie-Poisson Systems
Thiffeault, J.L.; Morrison, P.J.
1998-04-01
Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket obtained is not of the canonical type. Specifically, we give two examples that give rise to brackets of the noncanonical Lie-Poisson form: the rigid body and the two-dimensional ideal fluid. From these simple cases, we then use the semidirect product extension of algebras to describe more complex physical systems. The Casimir invariants in these systems are examined, and some are shown to be linked to the recovery of information about the configuration of the system. We discuss a case in which the extension is not a semidirect product, namely compressible reduced MHD, and find for this case that the Casimir invariants lend partial information about the configuration of the system
Application of Geometric Polarization to Invariance Properties in Bistatic Scattering
D. H. O. Bebbington
2005-01-01
Full Text Available Bistatic polarimetric radars provide target properties which just one monostatic system can not reveal. Moreover, augmentation of monostatic systems through the provision of bistatic receive-only stations can be a cheap way to increase the amount of remote sensing data. However, bistatic scattering needs to be investigated in order to properly define target properties such as symmetries and invariance, especially regarding choices of polarization basis. In this paper we discuss how the geometric theory of polarization, in which the geometry of the Poincaré sphere is directly related to 3-D geometry of space rather than the 2-D geometry of the wavefront plane, can be used to reduce the ambiguities in the interpretation of data. We also show how in the coherent case a complex scalar invariant can be determined irrespective of the basis combinations.
Completed Local Ternary Pattern for Rotation Invariant Texture Classification
Taha H. Rassem
2014-01-01
Full Text Available Despite the fact that the two texture descriptors, the completed modeling of Local Binary Pattern (CLBP and the Completed Local Binary Count (CLBC, have achieved a remarkable accuracy for invariant rotation texture classification, they inherit some Local Binary Pattern (LBP drawbacks. The LBP is sensitive to noise, and different patterns of LBP may be classified into the same class that reduces its discriminating property. Although, the Local Ternary Pattern (LTP is proposed to be more robust to noise than LBP, however, the latter’s weakness may appear with the LTP as well as with LBP. In this paper, a novel completed modeling of the Local Ternary Pattern (LTP operator is proposed to overcome both LBP drawbacks, and an associated completed Local Ternary Pattern (CLTP scheme is developed for rotation invariant texture classification. The experimental results using four different texture databases show that the proposed CLTP achieved an impressive classification accuracy as compared to the CLBP and CLBC descriptors.
Pomeron-Quark Coupling from Charge Conjugation Invariance
Zhou Lijuan; Wu Qing; Ma Weixing; Gu Yunting
2006-01-01
Based on the charge conjugation invariance and the vacuum property of the Pomeron, we point out that the commonly used vector vertex of the Pomeron coupling to quark is incorrect since it contradicts with the Pomeron property. We also claim that the soft Pomeron could be a tensor glueball ξ(2230) with quantum numbers I G J PC = 0 + 2 ++ and total decay width Γ tot ≅100 MeV, which lies on the soft Pomeron trajectory α p = 1.08+0.20t. Therefore, the coupling vertex of the soft Pomeron to quark should be tensorial which is invariant under the charge conjugation and can explain why the inadequate vector coupling, γ μ , of the soft Pomeron to quark is successful in dealing with Pomeron physics.
Globally conformal invariant gauge field theory with rational correlation functions
Nikolov, N M; Todorov, I T; CERN. Geneva; Todorov, Ivan T.
2003-01-01
Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields $V_{\\kappa} (x_1, x_2)$ of dimension $(\\kappa, \\kappa)$. For a {\\it globally conformal invariant} (GCI) theory we write down the OPE of $V_{\\kappa}$ into a series of {\\it twist} (dimension minus rank) $2\\kappa$ symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field. We argue that the theory of a GCI hermitian scalar field ${\\cal L} (x)$ of dimension 4 in $D = 4$ Minkowski space such that the 3-point functions of a pair of ${\\cal L}$'s and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density ${\\cal L} (x)$.
MEG source localization using invariance of noise space.
Junpeng Zhang
Full Text Available We propose INvariance of Noise (INN space as a novel method for source localization of magnetoencephalography (MEG data. The method is based on the fact that modulations of source strengths across time change the energy in signal subspace but leave the noise subspace invariant. We compare INN with classical MUSIC, RAP-MUSIC, and beamformer approaches using simulated data while varying signal-to-noise ratios as well as distance and temporal correlation between two sources. We also demonstrate the utility of INN with actual auditory evoked MEG responses in eight subjects. In all cases, INN performed well, especially when the sources were closely spaced, highly correlated, or one source was considerably stronger than the other.
Invariant hyperplanes and Darboux integrability of polynomial vector fields
Zhang Xiang
2002-01-01
This paper is composed of two parts. In the first part, we provide an upper bound for the number of invariant hyperplanes of the polynomial vector fields in n variables. This result generalizes those given in Artes et al (1998 Pac. J. Math. 184 207-30) and Llibre and Rodriguez (2000 Bull. Sci. Math. 124 599-619). The second part gives an extension of the Darboux theory of integrability to polynomial vector fields on algebraic varieties
Invariant subspaces in some function spaces on symmetric spaces. II
Platonov, S S
1998-01-01
Let G be a semisimple connected Lie group with finite centre, K a maximal compact subgroup of G, and M=G/K a Riemannian symmetric space of non-compact type. We study the problem of describing the structure of closed linear subspaces in various function spaces on M that are invariant under the quasiregular representation of the group G. We consider the case when M is a symplectic symmetric space of rank 1
Dualities and signatures of G++-invariant theories
Buyl, Sophie de; Houart, Laurent; Tabti, Nassiba
2005-01-01
The G ++ -content of the formulation of gravity and M-theories as very-extended Kac-Moody invariant theories is further analysed. The different exotic phases of all the G ++ B -theories, which admit exact solutions describing intersecting branes smeared in all directions but one, are derived. This is achieved by analysing for all G ++ the signatures which are related to the conventional one (1,D-1) by 'dualities' generated by the Weyl reflections
An Affine Invariant Bivariate Version of the Sign Test.
1987-06-01
words: affine invariance, bivariate quantile, bivariate symmetry, model,. generalized median, influence function , permutation test, normal efficiency...calculate a bivariate version of the influence function , and the resulting form is bounded, as is the case for the univartate sign test, and shows the...terms of a blvariate analogue of IHmpel’s (1974) influence function . The latter, though usually defined as a von-Mises derivative of certain
Invariant molecular-dynamics approach to structural phase transitions
Wentzcovitch, R.M.
1991-01-01
Two fictitious Lagrangians to be used in molecular-dynamics simulations with variable cell shape and suitable to study problems like structural phase transitions are introduced. Because they are invariant with respect to the choice of the simulation cell edges and eliminate symmetry breaking associated with the fictitious part of the dynamics, they improve the physical content of numerical simulations that up to now have been done by using Parrinello-Rahman dynamics