Partial Isometries and an Invariant of C*-algebras
Institute of Scientific and Technical Information of China (English)
Hong Liang YAO; Xiao Chun FANG
2011-01-01
In this paper, we will discuss some properties of biprojection-commutative elements which are relevant to the classification of certain infinite C*-algebras,.and define an important invariant s(A)of C*-algebra A as well as give some basic properties with regard to s(A). Moreover we prove that the invariant s(A) has continuity.
C, P, and T invariance of noncommutative gauge theories
Sheikh-Jabbari
2000-06-05
In this paper we study the invariance of the noncommutative gauge theories under C, P, and T transformations. For the noncommutative space (when only the spatial part of straight theta is nonzero) we show that noncommutative QED (NCQED) is parity invariant. In addition, we show that under charge conjugation the theory on noncommutative R(4)(straight theta) is transformed to the theory on R(4)(-straight theta), so NCQED is a CP violating theory. The theory remains invariant under time reversal if, together with proper changes in fields, we also change straight theta by -straight theta. Hence altogether NCQED is CPT invariant. Moreover, we show that the CPT invariance holds for general noncommutative space-time.
Perturbations of C*-algebraic Invariants
DEFF Research Database (Denmark)
Christensen, Erik; Sinclair, Allan M.; Smith, Roger R.;
2010-01-01
The setting of the article is the so-called theory of perturbations of algebras of operators. It is shown that several of the properties a C*-algebra may have are preseved under pertubations. The main result states that Pisier's concept finite length is a stasble property.......The setting of the article is the so-called theory of perturbations of algebras of operators. It is shown that several of the properties a C*-algebra may have are preseved under pertubations. The main result states that Pisier's concept finite length is a stasble property....
Problem of invariant subspaces in C*-algebras
Institute of Scientific and Technical Information of China (English)
张伦传
2002-01-01
Let A be a separable simple C*-algebra. For each a(≠0) in A, there exists a separable faithful and irreducible * representation (π, Hπ) on A such that π(a) has a non-trivial invariant subspace in Hπ.
RGIsearch: A C++ program for the determination of Renormalization Group Invariants
Verheyen, Rob
2015-01-01
RGIsearch is a C++ program that searches for invariants of a user-defined set of renormalization group equations. Based on the general shape of the $\\beta$-functions of quantum field theories, RGIsearch searches for several types of invariants that require different methods. Additionally, it supports the computation of invariants up to two-loop level. A manual for the program is given, including the settings and set-up of the program, as well as a test case.
d $\\leq$ 1 U d $\\geq$ 25 and W constraints from BRST invariance in the C $\
Gato-Rivera, Beatriz
1992-01-01
The BRST invariance condition in a highest-weight representation of the topological ($\\equiv$ twisted $N=2$) algebra captures the `invariant' content of two-dimensional gravity coupled to matter. The standard DDK formulation is recovered by splitting the topological generators into $c=-26$ reparametrization ghosts+matter +`Liouville', while a similar splitting involving $c=-2$ ghosts gives rise to the matter dressed in exactly the way required in order that the theory be equivalent to Virasoro constraints on the KP hierarchy. The two dressings of matter with the `Liouville' differ also by their `ghost numbers', which is similar to the existence of representatives of BRST cohomologies with different ghost numbers. The topological central charge $\\ctop\
Conformal invariance and QCD Pomeron vertices in the $1/N_{c}$ limit
Janik, R A
1999-01-01
Using the dipole framework for QCD at small x in the 1/N_c limit, we derive the expression of the 1 -> p dipole multiplicity density in momentum space. This gives an analytical expression for the 1 -> p QCD Pomeron amplitudes in terms of one-loop integration of effective vertices in transverse momentum. Conformal invariance and a Hilbert space construction for dipole correlation functions are the main tools of the derivation. Relations with conformal field theories in the classical limit are discussed.
Time-reversal-invariance-violating nucleon-nucleon potential in the 1/N_c expansion
Samart, Daris; Schindler, Matthias R; Phillips, Daniel R
2016-01-01
We apply the large-$N_c$ expansion to the time-reversal-invariance-violating (TV) nucleon-nucleon potential. The operator structures contributing to next-to-next-to-leading order in the large-$N_c$ counting are constructed. For the TV and parity-violating case we find a single operator structure at leading order. The TV but parity-conserving potential contains two leading-order terms, which however are suppressed by 1/$N_c$ compared to the parity-violating potential. Comparison with phenomenological potentials, including the chiral EFT potential in the TV parity-violating case, leads to large-$N_c$ scaling relations for TV meson-nucleon and nucleon-nucleon couplings.
Dye, H A
2011-01-01
We construct two knot invariants. The first knot invariant is a sum constructed using linking numbers. The second is an invariant of flat knots and is a formal sum of flat knots obtained by smoothing pairs of crossings. This invariant can be used in conjunction with other flat invariants, forming a family of invariants. Both invariants are constructed using the parity of a crossing.
A resonance structure in the $\\gamma\\gamma$ invariant mass spectrum in $p$C- and $d$C-interactions
Abraamyan, Kh U; Friesen, A V; Gudima, K K; Kozhin, M A; Lebedev, S A; Nazarenko, M A; Nikitin, S A; Ososkov, G A; Reznikov, S G; Sissakian, A N; Sorin, A S; Toneev, V D
2008-01-01
Along with $\\pi^0$ and $\\eta$ mesons, a resonance structure in the invariant mass spectrum of two photons at $M_{\\gamma\\gamma}= 360 \\pm 7 \\pm 9$ MeV is observed in the reaction $d C\\to\\gamma + \\gamma +X$ at momentum 2.75 GeV/c per nucleon. Estimates of its width and production cross section are $\\Gamma = 49.2 \\pm 18.6$ MeV and $\\sigma_{\\gamma\\gamma}=98\\pm24^{+93}_{-67} {\\rm \\mu b}$, respectively. The collected statistics amount to $2339 \\pm 340$ events of $1.5\\cdot 10^6$ triggered interactions of a total number $\\sim 10^{12}$ of $d$C-interactions. This resonance structure is not observed in $p$C collisions at the beam momentum 5.5 GeV/c. Possible mechanisms of this ABC-like effect are discussed.
Diagonal Invariant Ideals of Topologically Graded C*-algebras%拓扑分次C*-代数中的对角不变理想
Institute of Scientific and Technical Information of China (English)
许庆祥; 张小波
2005-01-01
We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.
Invariant mass spectroscopy of 17C via one-neutron knockout reaction from 18C
Kim, Sunji; Samurai Collaboration
2014-09-01
The nuclei away from the β-stability line are expected to have exotic nuclear structures. For example, the ground states of neutron-rich carbon isotopes, 15C, 17C, and 19C, have been predicted to be 5/2+ states in the naive shell model. However, they were identified as 1/2+, 3/2+, and 1/2+, respectively, due to the halo structure and/or nuclear deformation. To understand the properties of the valence orbit relative to the inner orbit in those neutron-rich carbon isotopes, the study of the negative parity states is decisive. The present study focuses on the low-lying negative parity states in 17C above the neutron decay threshold. The experiment was performed for the C(18C,17C*) one-neutron knockout reaction channel at 250 MeV/nucleon using the SAMURAI spectrometer at RIKEN-RIBF, during the first physics runs of the apparatus. The nucleon knockout reaction utilizing the secondary beams in inverse kinematics has become recognized as a sensitive tool for spectroscopy of the nuclei far from the β-stability line. In the presentation, details of the measurement and analysis will be reported together with new results on the low-lying negative parity states in 17C.
Matching of gauge invariant dimension 6 operators for $b\\to s$ and $b\\to c$ transitions
Aebischer, Jason; Fael, Matteo; Greub, Christoph
2016-01-01
New physics realized above the electroweak scale can be encoded in a model independent way in the Wilson coefficients of higher dimensional operators which are invariant under the Standard Model gauge group. In this article, we study the matching of the $SU(3)_C \\times SU(2)_L \\times U(1)_Y$ gauge invariant dim-6 operators on the standard $B$ physics Hamiltonian relevant for $b \\to s$ and $b\\to c$ transitions. The matching is performed at the electroweak scale (after spontaneous symmetry breaking) by integrating out the top quark, $W$, $Z$ and the Higgs particle. We first carry out the matching of the dim-6 operators that give a contribution at tree level to the low energy Hamiltonian. In a second step, we identify those gauge invariant operators that do not enter $b \\to s$ transitions already at tree level, but can give relevant one-loop matching effects.
Kervaire Invariant One [after M. A. Hill, M. J. Hopkins, and D. C. Ravenel
Miller, Haynes
2011-01-01
The question of when the Kervaire invariant is nontrivial was the only question left unresolved by Kervaire and Milnor in their 1963 study of the relationship between groups of homotopy spheres and stable homotopy groups. In 2009, Mike Hill, Mike Hopkins, and Doug Ravenel resolved this question except in one dimension, by a highly innovative attack using large amounts of equivariant stable homotopy theory and small amounts of computation. The present paper is a Seminaire Bourbaki report on this work.
Combinatorial decoding of the invariant C. elegans embryonic lineage in space and time.
Zacharias, Amanda L; Murray, John Isaac
2016-04-01
Understanding how a single cell, the zygote, can divide and differentiate to produce the diverse animal cell types is a central goal of developmental biology research. The model organism Caenorhabditis elegans provides a system that enables a truly comprehensive understanding of this process across all cells. Its invariant cell lineage makes it possible to identify all of the cells in each individual and compare them across organisms. Recently developed methods automate the process of cell identification, allowing high-throughput gene expression characterization and phenotyping at single cell resolution. In this Review, we summarize the sequences of events that pattern the lineage including establishment of founder cell identity, the signaling pathways that diversify embryonic fate, and the regulators involved in patterning within these founder lineages before cells adopt their terminal fates. We focus on insights that have emerged from automated approaches to lineage tracking, including insights into mechanisms of robustness, context-specific regulation of gene expression, and temporal coordination of differentiation. We suggest a model by which lineage history produces a combinatorial code of transcription factors that act, often redundantly, to ensure terminal fate.
Ham, Ji-Young; Lee, Joongul
2016-11-01
We calculate the Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation C(2n, 3) using the Schläfli formula for the generalized Chern-Simons function on the family of C(2n, 3) cone-manifold structures. We present the concrete and explicit formula of them. We apply the general instructions of Hilden, Lozano, and Montesinos-Amilibia and extend the Ham and Lee's methods. As an application, we calculate the Chern-Simons invariants of cyclic coverings of the hyperbolic C(2n, 3) orbifolds.
Origin of Invariant Gel Melting Temperatures in the c-T Phase Diagram of an Organogel.
Christ, Elliot; Blanc, Christophe; Al Ouahabi, Abdelaziz; Maurin, David; Le Parc, Rozenn; Bantignies, Jean-Louis; Guenet, Jean-Michel; Collin, Dominique; Mésini, Philippe J
2016-05-17
Binary c-T phase diagrams of organogelators in solvent are frequently simplified to two domains, gel and sol, even when the melting temperatures display two distinct regimes, an increase with T and a plateau. Herein, the c-T phase diagram of an organogelator in solvent is elucidated by rheology, DSC, optical microscopy, and transmitted light intensity measurements. We evidence a miscibility gap between the organogelator and the solvent above a threshold concentration, cL. In this domain the melting or the formation of the gel becomes a monotectic transformation, which explains why the corresponding temperatures are nonvariant above cL. As shown by further studies by variable temperature FTIR and NMR, different types of H-bonds drive both the liquid-liquid phase separation and the gelation.
THE TRACE SPACE INVARIANT AND UNITARY GROUP OF C*-ALGEBRA
Institute of Scientific and Technical Information of China (English)
方小春
2003-01-01
Let A be a unital C*-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n :Un0(A)/DUn0(A) → AffT(A)/△n0(π1(Un0(A))) is isometric for some suitable distances. Asan application, the author has the split exact sequence 0 → AffT(A)/△n0(π1(Un0(A))) iA→Un(A)/DUn(A) πA→ Un(A)/Un0(A) → 0 with iA contractive (and isometric if n = ∞) under certain condition of A.
Morphisms of Extensions of C*-algebras: Pushing Forward the Busby Invariant
DEFF Research Database (Denmark)
Eilers, Søren; Loring, Terry A.; Pedersen, Gert Kjærgård
1999-01-01
of varying severity, on the given vertical maps and describe the solutions in terms of push-outs and pull-backs of certain diagrams. Our characterization of the universal solution to one of the diagrams yields a concrete description of various amalgamated free products. This leads to new results about the K......-theory of amalgamated free products, verifying the Cuntz conjecture in certain cases. We also obtain new results about extensions of matricial fieldC*-algebras, verifying partially a conjecture of Blackadar and Kirchberg. Finally, we show that almost commuting unitary matrices can be uniformly approximated by commuting...
Frank, Steven A.
2016-01-01
In nematodes, environmental or physiological perturbations alter death’s scaling of time. In human cancer, genetic perturbations alter death’s curvature of time. Those changes in scale and curvature follow the constraining contours of death’s invariant geometry. I show that the constraints arise from a fundamental extension to the theories of randomness, invariance and scale. A generalized Gompertz law follows. The constraints imposed by the invariant Gompertz geometry explain the tendency of perturbations to stretch or bend death’s scaling of time. Variability in death rate arises from a combination of constraining universal laws and particular biological processes.
Zong, Zhengyu
2012-01-01
We give a formula of the framed one-leg orbifold Gromov-Witten vertex where the leg is gerby with isotropy group $\\bZ_m$. Then we use this formula to compute the Gromov-Witten invariants of the local $\\cB\\bZ_m$ gerbe. We will also compute some examples of the degree 1 and degree 2 $\\bZ_2$-Hodge integrals.
Invariant manifolds for flows in Banach Spaces
Energy Technology Data Exchange (ETDEWEB)
Lu Kening.
1989-01-01
The author considers the existence, smoothness and exponential attractivity of global invariant manifolds for flow in Banach Spaces. He shows that every global invariant manifold can be expressed as a graph of a C{sup k} map, provided that the invariant manifolds are exponentially attractive. Applications go to the Reaction-Diffusion equation, the Kuramoto-Sivashinsky equation, and singular perturbed wave equation.
Current forms and gauge invariance
Energy Technology Data Exchange (ETDEWEB)
Lopez, M Castrillon [Departemento de GeometrIa y TopologIa, Facultad de Matematicas, Universidad Complutense de Madrid, 28040-Madrid (Spain); Masque, J Munoz [Instituto de FIsica Aplicada, CSIC, C/Serrano 144, 28006-Madrid (Spain)
2004-05-14
Let C be the bundle of connections of a principal G-bundle {pi}:P {yields} M, and let V be the vector bundle associated with P by a linear representation G {yields} GL(V) on a finite-dimensional vector space V. The Lagrangians on J{sup 1}(C x {sub M}V) whose current form is gauge invariant, are described and the gauge-invariant Lagrangians on J{sup 1}(V) are classified.
Buchmann, Nicolas; Rouvier, Sylvain; Soria, Julio
2010-11-01
The study of coherent structures (CS) in turbulent flows is essential for understanding turbulence mechanisms in technological and theoretical relevant flows. The recent advent of instantaneous three-component and three-dimensional (3C-3D) measurement techniques now permits detailed experimental investigation into the dynamics and topology of CSs by for example analysis of the invariants of the velocity gradient tensor. For this purpose, the present work presents instantaneous, high-resolution 3C-3D Tomographic Particle Image Velocimetry (TPIV) measurements in a grid-generated, homogeneous isotropic turbulent flow (Reλ 140). The experiments are conducted in a larger water tunnel facility using a passive grid, four high-resolution digital cameras and a pulsed Nd:YAG laser for volume illumination. The invariants of the velocity gradient, rate of strain and rate of rotation tensor are used to characterize the dynamics and topology of the turbulent flow field and in particular its dissipation and vortex structure. Preliminary results are in agreement with previous literature and DNS simulations. The objective of this work is to measure these quantities experimentally and directly without additional assumptions pertaining to the structure and dynamics of the turbulent flow field.
Test of Charge Conjugation Invariance
Nefkens, B. M.; Prakhov, S.; Gårdestig, A.; Allgower, C. E.; Bekrenev, V.; Briscoe, W. J.; Clajus, M.; Comfort, J. R.; Craig, K.; Grosnick, D.; Isenhower, D.; Knecht, N.; Koetke, D.; Koulbardis, A.; Kozlenko, N.; Kruglov, S.; Lolos, G.; Lopatin, I.; Manley, D. M.; Manweiler, R.; Marušić, A.; McDonald, S.; Olmsted, J.; Papandreou, Z.; Peaslee, D.; Phaisangittisakul, N.; Price, J. W.; Ramirez, A. F.; Sadler, M.; Shafi, A.; Spinka, H.; Stanislaus, T. D.; Starostin, A.; Staudenmaier, H. M.; Supek, I.; Tippens, W. B.
2005-02-01
We report on the first determination of upper limits on the branching ratio (BR) of η decay to π0π0γ and to π0π0π0γ. Both decay modes are strictly forbidden by charge conjugation (C) invariance. Using the Crystal Ball multiphoton detector, we obtained BR(η→π0π0γ)<5×10-4 at the 90% confidence level, in support of C invariance of isoscalar electromagnetic interactions of the light quarks. We have also measured BR(η→π0π0π0γ)<6×10-5 at the 90% confidence level, in support of C invariance of isovector electromagnetic interactions.
Kubo, Toshihisa
2011-01-01
In earlier work, Barchini, Kable, and Zierau constructed a number of conformally invariant systems of differential operators associated to Heisenberg parabolic subalgebras in simple Lie algebras. The construction was systematic, but the existence of such a system was left open in two cases, namely, the $\\Omega_3$ system for type $A_2$ and type $D_4$. Here, such a system is shown to exist for both cases. The construction of the system may also be interpreted as giving an explicit homomorphism between generalized Verma modules.
Test of charge conjugation invariance.
Nefkens, B M K; Prakhov, S; Gårdestig, A; Allgower, C E; Bekrenev, V; Briscoe, W J; Clajus, M; Comfort, J R; Craig, K; Grosnick, D; Isenhower, D; Knecht, N; Koetke, D; Koulbardis, A; Kozlenko, N; Kruglov, S; Lolos, G; Lopatin, I; Manley, D M; Manweiler, R; Marusić, A; McDonald, S; Olmsted, J; Papandreou, Z; Peaslee, D; Phaisangittisakul, N; Price, J W; Ramirez, A F; Sadler, M; Shafi, A; Spinka, H; Stanislaus, T D S; Starostin, A; Staudenmaier, H M; Supek, I; Tippens, W B
2005-02-04
We report on the first determination of upper limits on the branching ratio (BR) of eta decay to pi0pi0gamma and to pi0pi0pi0gamma. Both decay modes are strictly forbidden by charge conjugation (C) invariance. Using the Crystal Ball multiphoton detector, we obtained BR(eta-->pi0pi0gamma)pi0pi0pi0gamma)<6 x 10(-5) at the 90% confidence level, in support of C invariance of isovector electromagnetic interactions.
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 ...
Invariants and submanifolds in almost complex geometry
Kruglikov, Boris
2007-01-01
In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of higher-dimensional pseudoholomorphic submanifolds.
Gauge Invariance for the Massive Axion
Arias, P J; Arias, Pio Jose; Khoudeir, Adel
1997-01-01
A massive gauge invariant formulation for scalar ($\\phi$) and antisymmetric ($C_{mnp}$) fields with a topological coupling, which provides a mass for the axion field, is considered. The dual and local equivalence with the non-gauge invariant proposal is established, but on manifolds with non-trivial topological structure both formulations are not globally equivalent.
On Invariant Decompositions, Dominated Splittings and Sectional-Hyperbolicity
Araujo, Vitor; Salgado, Luciana
2011-01-01
We obtain sufficient conditions for an invariant splitting over a compact invariant subset of a $C^1$ flow $X_t$ to be dominated. For a $C^1$ flow $X_t$ on a compact manifold $M$ and a compact invariant subset $\\Lambda$, with a continuous and $DX_t$-invariant splitting $E\\oplus F$ of the tangent bundle $T_\\Lambda M$ over $\\Lambda$, we consider the relation between weak forms of hyperbolicity along each subbundle and domination.
Oancea, Alexandru
2011-01-01
This is an overview of some of the invariants that were discovered by Welschinger in the context of enumerative real algebraic geometry. Their definition finds a natural setup in real symplectic geometry. In particular, they can be studied using techniques from symplectic field theory, of which we also give a sample. Welschinger invariants are real analogues of certain Gromov-Witten invariants. This article is an extended set of notes for a talk at the Bourbaki seminar in April 2011.
Conformal projective invariants in the problem of image recognition.
Directory of Open Access Journals (Sweden)
Надежда Григорьевна Коновенко
2014-11-01
Full Text Available In this paper we reduce local classification of differential 1-forms on the plane with respect to group SL_2(C of Mobius transformations. We find the field of rational conformal differential invariants and show that the field is generated by two differential invariant derivations and by differential invariants of the first and second orders.
On multipartite invariant states
Chruscinski, D; Chruscinski, Dariusz; Kossakowski, Andrzej
2006-01-01
We propose a natural generalization of bipartite Werner and isotropic states to multipartite systems consisting of an arbitrary even number of d-dimensional subsystems (qudits). These generalized states are invariant under the action of local unitary operations. We study basic properties of multipartite invariant states: separability criteria and multi-PPT conditions.
Generalized Donaldson-Thomas invariants
Joyce, Dominic
2009-01-01
This is a summary of the much longer paper arXiv:0810.5645 with Yinan Song. Let X be a Calabi-Yau 3-fold over C. The Donaldson-Thomas invariants of X are integers DT^a(t) which count stable sheaves with Chern character a on X, with respect to a Gieseker stability condition t. They are defined only for Chern characters a for which there are no strictly semistable sheaves on X. They have the good property that they are unchanged under deformations of X. Their behaviour under change of stability condition t was not understood until now. We discuss "generalized Donaldson-Thomas invariants" \\bar{DT}^a(t). These are rational numbers, defined for all Chern characters a, and are equal to DT^a(t) if there are no strictly semistable sheaves in class a. They are deformation-invariant, and have a known transformation law under change of stability condition. We conjecture they can be written in terms of integral "BPS invariants" \\hat{DT}^a(t) when the stability condition t is "generic". We extend the theory to abelian cat...
Measurement invariance versus selection invariance : Is fair selection possible?
Borsboom, Denny; Romeijn, Jan-Willem; Wicherts, Jelte 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 instrume
Neutrinos and electromagnetic gauge invariance
Energy Technology Data Exchange (ETDEWEB)
Pisano, F.; Silva-Sobrinho, J.A. [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Tonasse, M.D. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica
1996-02-01
It is discussed a recently proposed connection among electromagnetic gauge invariance U(1){sub em} and the nature of the neutrino mass terms in the framework of SU(3){sub C} x G{sub W} x U(1){sub N}, G{sub W} SU(3){sub L}, extensions of the Standard Model. The impossibility of that connection, also in the case G{sub W} = SU(4){sub L}, is demonstrated. (author). 7 refs.
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
Lorentz invariance with an invariant energy scale
Magueijo, J; Magueijo, Joao; Smolin, Lee
2002-01-01
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 non-linear 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, and we highlight the similarities between the group action found and a transformation previously proposed by Fock. 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.
Cosmological disformal invariance
Domènech, Guillem; Sasaki, Misao
2015-01-01
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 d...
Lifting quasianalytic mappings over invariants
Rainer, Armin
2010-01-01
Let $\\rho : G \\to \\operatorname{GL}(V)$ be a rational finite dimensional complex representation of a reductive linear algebraic group $G$, and let $\\sigma_1,\\ldots,\\sigma_n$ be a system of generators of the algebra of invariant polynomials $\\mathbb{C}[V]^G$. We study the problem of lifting mappings $f : \\mathbb{R}^q \\supseteq U \\to \\sigma(V) \\subseteq \\mathbb{C}^n$ over the mapping of invariants $\\sigma=(\\sigma_1,\\ldots,\\sigma_n) : V \\to \\sigma(V)$. Note that $\\sigma(V)$ can be identified with the categorical quotient $V /\\!\\!/ G$ and its points correspond bijectively to the closed orbits in $V$. We prove that, if $f$ belongs to a quasianalytic subclass $\\mathcal{C} \\subseteq C^\\infty$ satisfying some mild closedness properties which guarantee resolution of singularities in $\\mathcal{C}$ (e.g.\\ the real analytic class), then $f$ admits a lift of the same class $\\mathcal{C}$ after desingularization by local blow-ups and local power substitutions. As a consequence we show that $f$ itself allows for a lift which...
Bera, Sudesna; Chakrabarti, Barnali; Das, T. K.
2017-04-01
We show that the conditional shape invariance symmetry can be used as a very powerful tool to calculate the eigenvalues of the mixed potential V (r) = ar + br2 + c/r + l (l + 1)/r2 for a restricted set of potential parameters. The energy for any state can be obtained algebraically, albeit for a severely restricted set of potential parameters. We also indicate that each member of the hierarchy of Hamiltonians is basically conditionally translational shape invariant. Comparison of analytically obtained results with numerical results is also presented. Our present methodology can be taken as an alternative treatment for the calculation of any higher order excited states of conditionally exactly solvable (CES) potentials.
Elementary examples of adiabatic invariance
Energy Technology Data Exchange (ETDEWEB)
Crawford, F.S. (Physics Department, University of California, Berkeley, CA (USA) Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720 (USA))
1990-04-01
Simple classical one-dimensional systems subject to adiabatic (gradual) perturbations are examined. The first examples are well known: the adiabatic invariance of the product {ital E}{tau} of energy {ital E} and period {tau} for the simple pendulum and for the simple harmonic oscillator. Next, the adiabatic invariants of the vertical bouncer are found---a ball bouncing elastically from the floor of a rising elevator having slowly varying velocity and acceleration. These examples lead to consideration of adiabatic invariance for one-dimensional systems with potentials of the form {ital V}={ital ax}{sup {ital n}}, with {ital a}={ital a}({ital t}) slowly varying in time. Then, the horizontal bouncer is considered---a mass sliding on a smooth floor, bouncing back and forth between two impenetrable walls, one of which is slowly moving. This example is generalized to a particle in a bound state of a general potential with one slowly moving turning point.'' Finally, circular motion of a charged particle in a magnetic field slowly varying in time under three different configurations is considered: (a) a free particle in a uniform field; (b) a free particle in a nonuniform betatron'' field; and (c) a particle constrained to a circular orbit in a uniform field.
Transformation invariant sparse coding
DEFF Research Database (Denmark)
Mørup, Morten; Schmidt, Mikkel Nørgaard
2011-01-01
Sparse coding is a well established principle for unsupervised learning. Traditionally, features are extracted in sparse coding in specific locations, however, often we would prefer invariant representation. This paper introduces a general transformation invariant sparse coding (TISC) model....... The model decomposes images into features invariant to location and general transformation by a set of specified operators as well as a sparse coding matrix indicating where and to what degree in the original image these features are present. The TISC model is in general overcomplete and we therefore invoke...... sparse coding to estimate its parameters. We demonstrate how the model can correctly identify components of non-trivial artificial as well as real image data. Thus, the model is capable of reducing feature redundancies in terms of pre-specified transformations improving the component identification....
Pérez-Nadal, Guillem
2016-01-01
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, with the metric of each space 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.
Supersymmetric invariant theories
Esipova, S R; Radchenko, O V
2013-01-01
We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.
Supersymmetric invariant theories
Esipova, S. R.; Lavrov, P. M.; Radchenko, O. V.
2014-04-01
We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is a direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.
Kobayashi, Tatsuo; Nitta, Daisuke; Urakawa, Yuko
2016-08-01
Modular invariance is a striking symmetry in string theory, which may keep stringy corrections under control. In this paper, we investigate a phenomenological consequence of the modular invariance, assuming that this symmetry is preserved as well as in a four dimensional (4D) low energy effective field theory. As a concrete setup, we consider a modulus field T whose contribution in the 4D effective field theory remains invariant under the modular transformation and study inflation drived by T. The modular invariance restricts a possible form of the scalar potenntial. As a result, large field models of inflation are hardly realized. Meanwhile, a small field model of inflation can be still accomodated in this restricted setup. The scalar potential traced during the slow-roll inflation mimics the hilltop potential Vht, but it also has a non-negligible deviation from Vht. Detecting the primordial gravitational waves predicted in this model is rather challenging. Yet, we argue that it may be still possible to falsify this model by combining the information in the reheating process which can be determined self-completely in this setup.
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.
Kobayashi, Tatsuo; Urakawa, Yuko
2016-01-01
Modular invariance is a striking symmetry in string theory, which may keep stringy corrections under control. In this paper, we investigate a phenomenological consequence of the modular invariance, assuming that this symmetry is preserved as well as in a four dimensional (4D) low energy effective field theory. As a concrete setup, we consider a modulus field $T$ whose contribution in the 4D effective field theory remains invariant under the modular transformation and study inflation drived by $T$. The modular invariance restricts a possible form of the scalar potenntial. As a result, large field models of inflation are hardly realized. Meanwhile, a small field model of inflation can be still accomodated in this restricted setup. The scalar potential traced during the slow-roll inflation mimics the hilltop potential $V_{ht}$, but it also has a non-negligible deviation from $V_{ht}$. Detecting the primordial gravitational waves predicted in this model is rather challenging. Yet, we argue that it may be still po...
Exact invariants and adiabatic invariants of the singular Lagrange system
Institute of Scientific and Technical Information of China (English)
陈向炜; 李彦敏
2003-01-01
Based on the theory of symmetries and conserved quantities of the singular Lagrange system,the perturbations to the symmetries and adiabatic invariants of the singular Lagrange systems are discussed.Firstly,the concept of higher-order adiabatic invariants of the singular Lagrange system is proposed.Then,the conditions for the existence of the exact invariants and adiabatic invariants are proved,and their forms are given.Finally,an example is presented to illustrate these results.
Hojman Exact Invariants and Adiabatic Invariants of Hamilton System
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The perturbation to Lie symmetry and adiabatic invariants are studied. Based on the concept of higherorder adiabatic invariants of mechanical systems with action of a small perturbation, the perturbation to Lie symmetry is studied, and Hojman adiabatic invariants of Hamilton system are obtained. An example is given to illustrate the application of the results.
Continuous Integrated Invariant Inference Project
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...
Reducing Lookups for Invariant Checking
DEFF Research Database (Denmark)
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 sti...
Permutationally invariant state reconstruction
Moroder, Tobias; Toth, Geza; Schwemmer, Christian; Niggebaum, Alexander; Gaile, Stefanie; Gühne, Otfried; Weinfurter, Harald
2012-01-01
Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, also an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a non-linear large-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 likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed n...
Invariant Scattering Convolution Networks
Bruna, Joan
2012-01-01
A wavelet scattering network computes a translation invariant image representation, which is stable to deformations and preserves high frequency information for classification. It cascades wavelet transform convolutions with non-linear modulus and averaging operators. The first network layer outputs SIFT-type descriptors whereas the next layers provide complementary invariant information which improves classification. The mathematical analysis of wavelet scattering networks explains important properties of deep convolution networks for classification. A scattering representation of stationary processes incorporates higher order moments and can thus discriminate textures having the same Fourier power spectrum. State of the art classification results are obtained for handwritten digits and texture discrimination, using a Gaussian kernel SVM and a generative PCA classifier.
Vollmer, Gerhard
2010-10-01
Scientific knowledge should not only be true, it should be as objective as possible. It should refer to a reality independent of any subject. What can we use as a criterion of objectivity? Intersubjectivity (i.e., intersubjective understandability and intersubjective testability) is necessary, but not sufficient. Other criteria are: independence of reference system, independence of method, non-conventionality. Is there some common trait? Yes, there is: invariance under some specified transformations. Thus, we say: A proposition is objective only if its truth is invariant against a change in the conditions under which it was formulated. We give illustrations from geometry, perception, neurobiology, relativity theory, and quantum theory. Such an objectivist position has many advantages.
Invariants for Parallel Mapping
Institute of Scientific and Technical Information of China (English)
YIN Yajun; WU Jiye; FAN Qinshan; HUANG Kezhi
2009-01-01
This paper analyzes the geometric quantities that remain unchanged during parallel mapping (i.e., mapping from a reference curved surface to a parallel surface with identical normal direction). The second gradient operator, the second class of integral theorems, the Gauss-curvature-based integral theorems, and the core property of parallel mapping are used to derive a series of parallel mapping invadants or geometri-cally conserved quantities. These include not only local mapping invadants but also global mapping invari-ants found to exist both in a curved surface and along curves on the curved surface. The parallel mapping invadants are used to identify important transformations between the reference surface and parallel surfaces. These mapping invadants and transformations have potential applications in geometry, physics, biome-chanics, and mechanics in which various dynamic processes occur along or between parallel surfaces.
2010-12-02
evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in
Braaten, Eric
2015-01-01
XEFT is a low-energy effective field theory for charm mesons and pions that provides a systematically improvable description of the X(3872) resonance. A Galilean-invariant formulation of XEFT is introduced to exploit the fact that mass is very nearly conserved in the transition D*0 --> D0 pi0. The transitions D*0 --> D0 pi0 and X --> D0 D0-bar pi0 are described explicitly in XEFT. The effects of the decay D*0 --> D0 gamma and of short-distance decay modes of the X(3872), such as J/psi --> pi+ pi-, can be taken into account by using complex on-shell renormalization schemes for the D*0 propagator and for the D*0 D0-bar propagator in which the positions of their complex poles are specified. Galilean-invariant XEFT is used to calculate the D*0 D0-bar scattering length to next-to-leading order. Galilean invariance ensures the cancellation of ultraviolet divergences without the need for truncating an expansion in powers of the ratio of the pion and charm meson masses.
On the Invariance of Residues of Feynman Graphs
Bierenbaum, I; Kreimer, D; Bierenbaum, Isabella; Kreckel, Richard; Kreimer, Dirk
2002-01-01
We use simple iterated one-loop graphs in massless Yukawa theory and QED to pose the following question: what are the symmetries of the residues of a graph under a permutation of places to insert subdivergences. The investigation confirms partial invariance of the residue under such permutations: the highest weight transcendental is invariant under such a permutation. For QED this result is gauge invariant, ie the permutation invariance holds for any gauge. Computations are done making use of the Hopf algebra structure of graphs and employing GiNaC to automate the calculations.
Uniformly Most Powerful Invariant Test and Its Application
Institute of Scientific and Technical Information of China (English)
ZHANG Shuang-lin; SHA Qui-ying; ZHOU Wen-hai
2001-01-01
The authors consider the uniformly most powerful invariant test of the testing problems (Ⅰ)H0: μ′∑-1μ ≥ C H1: μ＇∑-1μ ＜ C and(Ⅱ) H00: ≥ C H11: ＜C under m-dimensional normal population Nm (μ, ∑ ) and normal linear model ( Y, Xβ, σ2 ) respectively.Furthermore, an application of the uniformly most powerful invariant test is given.
Anistropic Invariant FRW Cosmology
Chagoya, J F
2015-01-01
In this paper we study the effects of including anisotropic scaling invariance in the minisuperspace Lagrangian for a universe modelled by the Friedman-Robertson-Walker metric, a massless scalar field and cosmological constant. We find that canonical quantization of this system leads to a Schroedinger type equation, thus avoiding the frozen time problem of the usual Wheeler-DeWitt equation. Furthermore, we find numerical solutions for the classical equations of motion, and we also find evidence that under some conditions the big bang singularity is avoided in this model.
Invariant connections and vortices
García-Prada, Oscar
1993-10-01
We study the vortex equations on a line bundle over a compact Kähler manifold. These are a generalization of the classical vortex equations over ℝ2. We first prove an invariant version of the theorem of Donaldson, Uhlenbeck and Yau relating the existence of a Hermitian-Yang-Mills metric on a holomorphic bundle to the stability of such a bundle. We then show that the vortex equations are a dimensional reduction of the Hermitian-Yang-Mills equation. Using this fact and the theorem above we give a new existence proof for the vortex equations and describe the moduli space of solutions.
Singularities of invariant connections
Energy Technology Data Exchange (ETDEWEB)
Amores, A.M. (Universidad Complutense, Madrid (Spain)); Gutierrez, M. (Universidad Politecnica, Madrid (Spain))
1992-12-01
A reductive homogeneous space M = P/G is considered, endowed with an invariant connection, i.e., such that all left translations of M induced by members of P preserve it. The authors study the set of singularities of such connections giving sufficient conditions for it to be empty, or, in other cases, familities of b-incomplete curves converging to singularities. A full description of the b-completion of a connection with M = R[sup m] (or a quotient of it) is given with information on its topology. 5 refs.
Entanglement, Invariants, and Phylogenetics
Sumner, J. G.
2007-10-01
This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units from biomolecular sequence data. The techniques of mathematical physics are plethora and have been developed for some time. The Markov model of phylogenetics and its analysis is a relatively new technique where most progress to date has been achieved by using discrete mathematics. This thesis takes a group theoretical approach to the problem by beginning with a remarkable mathematical parallel to the process of scattering in particle physics. This is shown to equate to branching events in the evolutionary history of molecular units. The major technical result of this thesis is the derivation of existence proofs and computational techniques for calculating polynomial group invariant functions on a multi-linear space where the group action is that relevant to a Markovian time evolution. The practical results of this thesis are an extended analysis of the use of invariant functions in distance based methods and the presentation of a new reconstruction technique for quartet trees which is consistent with the most general Markov model of sequence evolution.
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...
Palmer, T N
2016-01-01
Invariant Set Theory (IST) is a realistic, locally causal theory of fundamental physics which assumes a much stronger synergy between cosmology and quantum physics than exists in contemporary theory. In IST the (quasi-cyclic) universe $U$ is treated as a deterministic dynamical system evolving precisely on a measure-zero fractal invariant subset $I_U$ of its state space. In this approach, the geometry of $I_U$, and not a set of differential evolution equations in space-time $\\mathcal M_U$, provides the most primitive description of the laws of physics. As such, IST is non-classical. The geometry of $I_U$ is based on Cantor sets of space-time trajectories in state space, homeomorphic to the algebraic set of $p$-adic integers, for large but finite $p$. In IST, the non-commutativity of position and momentum observables arises from number theory - in particular the non-commensurateness of $\\phi$ and $\\cos \\phi$. The complex Hilbert Space and the relativistic Dirac Equation respectively are shown to describe $I_U$...
Invariants for minimal conformal supergravity in six dimensions
Butter, Daniel; Novak, Joseph; Theisen, Stefan
2016-01-01
We develop a new off-shell formulation for six-dimensional conformal supergravity obtained by gauging the 6D ${\\cal N} = (1, 0)$ superconformal algebra in superspace. This formulation is employed to construct two invariants for 6D ${\\cal N} = (1, 0)$ conformal supergravity, which contain $C^3$ and $C\\Box C$ 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 $F \\Box F$ invariant in curved superspace.
Tractors, Mass and Weyl Invariance
Gover, A R; Waldron, A
2008-01-01
Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describe massive and gauge invariant theories using Weyl invariance. The key idea is to introduce a new scalar field which is constant when evaluated at the scale corresponding to the metric of physical interest. This technique relies on being able to efficiently construct Weyl invariant theories. This is achieved using tractor calculus--a mathematical machinery designed for the study of conformal geometry. From a physics standpoint, this amounts to arranging fields in multiplets with respect to the conformal group but with novel Weyl transformation laws. Our approach gives a mechanism for generating masses from Weyl weights. Breitenlohner--Freedman stability bounds for Anti de Sitter theories arise na...
Tractors, mass, and Weyl invariance
Gover, A. R.; Shaukat, A.; Waldron, A.
2009-05-01
Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describe massive and gauge invariant theories using Weyl invariance. The key idea is to introduce a new scalar field which is constant when evaluated at the scale corresponding to the metric of physical interest. This technique relies on being able to efficiently construct Weyl invariant theories. This is achieved using tractor calculus—a mathematical machinery designed for the study of conformal geometry. From a physics standpoint, this amounts to arranging fields in multiplets with respect to the conformal group but with novel Weyl transformation laws. Our approach gives a mechanism for generating masses from Weyl weights. Breitenlohner-Freedman stability bounds for Anti-de Sitter theories arise naturally as do direct derivations of the novel Weyl invariant theories given by Deser and Nepomechie. In constant curvature spaces, partially massless theories—which rely on the interplay between mass and gauge invariance—are also generated by our method. Another simple consequence is conformal invariance of the maximal depth partially massless theories. Detailed examples for spins s⩽2 are given including tractor and component actions, on-shell and off-shell approaches and gauge invariances. For all spins s⩾2 we give tractor equations of motion unifying massive, massless, and partially massless theories.
Invariant and Absolute Invariant Means of Double Sequences
Directory of Open Access Journals (Sweden)
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.
Lorentz invariant intrinsic decoherence
Milburn, G J
2003-01-01
Quantum decoherence can arise due to classical fluctuations in the parameters which define the dynamics of the system. In this case decoherence, and complementary noise, is manifest when data from repeated measurement trials are combined. Recently a number of authors have suggested that fluctuations in the space-time metric arising from quantum gravity effects would correspond to a source of intrinsic noise, which would necessarily be accompanied by intrinsic decoherence. This work extends a previous heuristic modification of Schr\\"{o}dinger dynamics based on discrete time intervals with an intrinsic uncertainty. The extension uses unital semigroup representations of space and time translations rather than the more usual unitary representation, and does the least violence to physically important invariance principles. Physical consequences include a modification of the uncertainty principle and a modification of field dispersion relations, in a way consistent with other modifications suggested by quantum grav...
Permutationally invariant state reconstruction
DEFF Research Database (Denmark)
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......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...... likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex...
Invariants of Quartic Plane Curves as Automorphic Forms
Looijenga, E.
2007-01-01
We identify the algebra of regular functions on the space of quartic polynomials in three complex variables invariant under SL(3; C) with an algebra of meromorphic automorphic forms on the complex 6-ball. We also discuss the underlying geometry.
Invariant visual object recognition: biologically plausible approaches.
Robinson, Leigh; Rolls, Edmund T
2015-10-01
Key properties of inferior temporal cortex neurons are described, and then, the biological plausibility of two leading approaches to invariant visual object recognition in the ventral visual system is assessed to investigate whether they account for these properties. Experiment 1 shows that VisNet performs object classification with random exemplars comparably to HMAX, except that the final layer C neurons of HMAX have a very non-sparse representation (unlike that in the brain) that provides little information in the single-neuron responses about the object class. Experiment 2 shows that VisNet forms invariant representations when trained with different views of each object, whereas HMAX performs poorly when assessed with a biologically plausible pattern association network, as HMAX has no mechanism to learn view invariance. Experiment 3 shows that VisNet neurons do not respond to scrambled images of faces, and thus encode shape information. HMAX neurons responded with similarly high rates to the unscrambled and scrambled faces, indicating that low-level features including texture may be relevant to HMAX performance. Experiment 4 shows that VisNet can learn to recognize objects even when the view provided by the object changes catastrophically as it transforms, whereas HMAX has no learning mechanism in its S-C hierarchy that provides for view-invariant learning. This highlights some requirements for the neurobiological mechanisms of high-level vision, and how some different approaches perform, in order to help understand the fundamental underlying principles of invariant visual object recognition in the ventral visual stream.
Invariant Measures for Cherry Flows
Saghin, Radu; Vargas, Edson
2013-01-01
We investigate the invariant probability measures for Cherry flows, i.e. flows on the two-torus which have a saddle, a source, and no other fixed points, closed orbits or homoclinic orbits. In the case when the saddle is dissipative or conservative we show that the only invariant probability measures are the Dirac measures at the two fixed points, and the Dirac measure at the saddle is the physical measure. In the other case we prove that there exists also an invariant probability measure supported on the quasi-minimal set, we discuss some situations when this other invariant measure is the physical measure, and conjecture that this is always the case. The main techniques used are the study of the integrability of the return time with respect to the invariant measure of the return map to a closed transversal to the flow, and the study of the close returns near the saddle.
Hidden scale invariance of metals
DEFF Research Database (Denmark)
Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.
2015-01-01
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...... 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......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...
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
Sohrab, Siavash
2017-01-01
According to a scale-invariant statistical theory of fields electromagnetic photon mass is given as mem , k =√{ hk /c3 } . Since electromagnetic energy of photon is identified as amu =√{ hkc } , all baryonic matter is composed of light (photons) Eem = Nmem , kc2 =Mem , kc2 [ Joule ] or equivalently Mem , kc2 / 8338 [ kcal ] = Namu =Ma [ kg ] where 8338 is De Pretto number. Besides particle electromagnetic energy one requires potential energy associated with Poincaré stress for particle stability leading to rest enthalpy \\hcirco =\\ucirco +po \\vcirc =\\ucirco +\\ucirco / 3 = (4 / 3)mem , kc2 in accordance with Hasenöhrl. The 4/3 problem of electrodynamics (T. H. Boyer, Phys. Rev. Lett. 25, 1982) is also related to Poincaré stress thus the potential energy po \\vcirc =\\ucirco / 3 . Hence, the factor 4/3 is identified as Poisson polytropic index b =cp /cv and total particle rest mass will be composed of electromagnetic and gravitational parts mo =mem +mgr = (3 / 4) Eo /c2 + (1 / 4) Eo /c2 . At cosmological scale, respectively 3/4 and 1/4 of the total mass of closed universe will be electromagnetic (dark energy) and gravitational (dark matter) in nature as was emphasized by Pauli (Theory of Relativity, Dover, 1958). Also, Poincaré-Lorentz dynamic versus Einstein kinematic theory of relativity will be discussed.
Conformal invariant saturation
Navelet, H
2002-01-01
We show that, in onium-onium scattering at (very) high energy, a transition to saturation happens due to quantum fluctuations of QCD dipoles. This transition starts when the order alpha^2 correction of the dipole loop is compensated by its faster energy evolution, leading to a negative interference with the tree level amplitude. After a derivation of the the one-loop dipole contribution using conformal invariance of the elastic 4-gluon amplitude in high energy QCD, we obtain an exact expression of the saturation line in the plane (Y,L) where Y is the total rapidity and L, the logarithm of the onium scale ratio. It shows universal features implying the Balitskyi - Fadin - Kuraev - Lipatov (BFKL) evolution kernel and the square of the QCD triple Pomeron vertex. For large L, only the higher BFKL Eigenvalue contributes, leading to a saturation depending on leading log perturbative QCD characteristics. For initial onium scales of same order, however, it involves an unlimited summation over all conformal BFKL Eigen...
Mechanized derivation of linear invariants.
Cavender, J A
1989-05-01
Linear invariants, discovered by Lake, promise to provide a versatile way of inferring phylogenies on the basis of nucleic acid sequences (the method that he called "evolutionary parsimony"). A semigroup of Markov transition matrices embodies the assumptions underlying the method, and alternative semigroups exist. The set of all linear invariants may be derived from the semigroup by using an algorithm described here. Under assumptions no stronger than Lake's, there are greater than 50 independent linear invariants for each of the 15 rooted trees linking four species.
Invariant manifolds and global bifurcations.
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M; Sandstede, Björn
2015-09-01
Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to global bifurcations. Bifurcation manifolds in the parameter spaces of multi-parameter families of dynamical systems also play a prominent role in dynamical systems theory. Much progress has been made in developing theory and computational methods for invariant manifolds during the past 25 years. This article highlights some of these achievements and remaining open problems.
Invariant and semi-invariant probabilistic normed spaces
Energy Technology Data Exchange (ETDEWEB)
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.
On density of the Vassiliev invariants
DEFF Research Database (Denmark)
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...
Cubic surfaces and their invariants: Some memories of Raymond Stora
Directory of Open Access Journals (Sweden)
Michel Bauer
2016-11-01
I then turn to the study of the family of cubic surfaces. They depend on 20 parameters, and the action of the 15 parameter group SL4(C splits the family in orbits depending on 5 parameters. This takes us into the realm of (geometric invariant theory. I review briefly the classical theorems on the structure of the ring of polynomial invariants and illustrate its many facets by looking at a simple example, before turning to the already involved case of cubic surfaces. The invariant ring was described in the 19th century. I show how to retrieve this description via counting/generating functions and character formulae.
Invariant measures for Cherry flows
Saghin, Radu
2011-01-01
We investigate the invariant probability measures for Cherry flows, i.e. flows on the two-torus which have a saddle, a source, and no other fixed points, closed orbits or homoclinic orbits. In the case when the saddle is dissipative or conservative we show that the only invariant probability measures are the Dirac measures at the two fixed points, and the Dirac measure at the saddle is the physical measure. In the other case we discuss some situations when there exists another invariant measure supported on the quasi-minimal set, which is the physical measure, and conjecture that this is always the case. The main techniques used are the study of the integrability of the return time with respect to the invariant measure of the return map to a closed transversal to the flow, and the study of the close returns near the saddle.
Scaling Equation for Invariant Measure
Institute of Scientific and Technical Information of China (English)
LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; REN Kui
2003-01-01
An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.
Invariants from classical field theory
Diaz, Rafael
2007-01-01
We introduce a method that generates invariant functions from classical field theories depending on external parameters. We apply our method to several field theories such as abelian BF, Chern-Simons and 2-dimensional Yang-Mills theory.
Invariant foliations for parabolic equations
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
It is proved for parabolic equations that under certain conditions the weak (un-)stable manifolds possess invariant foliations, called strongly (un-)stable foliations. The relevant results on center manifolds are generalized to weak hyperbolic manifolds.
Local Scale Invariance and Inflation
Singh, Naveen K
2016-01-01
We study the inflation and the cosmological perturbations generated during the inflation in a local scale invariant model. The local scale invariant model introduces a vector field $S_{\\mu}$ in this theory. In this paper, for simplicity, we consider the temporal part of the vector field $S_t$. We show that the temporal part is associated with the slow roll parameter of scalar field. Due to local scale invariance, we have a gauge degree of freedom. In a particular gauge, we show that the local scale invariance provides sufficient number of e-foldings for the inflation. Finally, we estimate the power spectrum of scalar perturbation in terms of the parameters of the theory.
Invariants of broken discrete symmetries
Kalozoumis, P.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-01-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic ...
Invariants of broken discrete symmetries
Kalozoumis, P; Diakonos, F K; Schmelcher, P
2014-01-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
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.)
Invariant Manifolds and Collective Coordinates
Papenbrock, T
2001-01-01
We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction.
Operator equations and invariant subspaces
Directory of Open Access Journals (Sweden)
Valentin Matache
1994-05-01
Full Text Available Banach space operators acting on some fixed space X are considered. If two such operators A and B verify the condition A2=B2 and if A has nontrivial hyperinvariant subspaces, then B has nontrivial invariant subspaces. If A and B commute and satisfy a special type of functional equation, and if A is not a scalar multiple of the identity, the author proves that if A has nontrivial invariant subspaces, then so does B.
Invariant measures for Chebyshev maps
Directory of Open Access Journals (Sweden)
Abraham Boyarsky
2001-01-01
Full Text Available Let Tλ(x=cos(λarccosx, −1≤x≤1, where λ>1 is not an integer. For a certain set of λ's which are irrational, the density of the unique absolutely continuous measure invariant under Tλ is determined exactly. This is accomplished by showing that Tλ is differentially conjugate to a piecewise linear Markov map whose unique invariant density can be computed as the unique left eigenvector of a matrix.
Gauge-invariant approach to quark dynamics
Sazdjian, H
2016-01-01
The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of QCD are first reviewed. In particular, the role of the parallel transport operation in constructing gauge-invariant Green's functions is presented, and the relevance of Wilson loops for the representation of the interaction is emphasized. Recent developments, based on the use of polygonal lines for the parallel transport operation, are then presented. An integro-differential equation is obtained for the quark Green's function defined with a phase factor along a single, straight line segment. It is solved exactly and analytically in the case of two-dimensional QCD in the large $N_c$ limit. The solution displays the dynamical mass generation phenomenon for quarks, with an infinite number of branch-cut singularities that are stronger than simple poles.
Generalized Formalism in Gauge-Invariant Gravitational Perturbations
Cai, Rong-Gen
2013-01-01
By use of the gauge-invariant variables proposed by Kodama and Ishibashi, we obtain the most general perturbation equations in the $(m+n)$-dimensional spacetime with a warped product metric. These equations do not depend on the spectral expansions of the Laplace-type operators on the $n$-dimensional Einstein manifold. These equations enable us to have a complete gauge-invariant perturbation theory and a well-defined spectral expansion for all modes and the gauge invariance is kept for each mode. By studying perturbations of some projections of Weyl tensor in the case of $m=2$, we define three Teukolsky-like gauge-invariant variables and obtain the perturbation equations of these variables by considering perturbations of the Penrose wave equations in the $(2+n)$-dimensional Einstein spectime. In particular, we find the relations between the Teukolsky-like gauge-invariant variables and the Kodama-Ishibashi gauge-invariant variables. These relations imply that the Kodama-Ishibashi gauge-invariant variables all c...
Invarient patterns in articulatory movements
Bonaventura, Patrizia
2004-04-01
The purpose of the reported study is to discover an effective method of characterizing movement patterns of the crucial articulator as the function of an abstract syllable magnitude and the adjacent boundary, and at the same time to investigate effects of prosodic control on utterance organization. In particular, the speed of movement when a flesh point on the tongue blade or the lower lip crosses a selected position relative to the occlusion plane is examined. The time of such crossing provides an effective measure of syllable timing and syllable duration according to previous work. In the present work, using a very limited vocabulary with only a few consonants and one vowel as the key speech materials, effects of contrastive emphasis on demisyllabic movement patterns were studied. The theoretical framework for this analysis is the C/D model of speech production in relation to the concept of an invariant part of selected articulatory movements. The results show evidence in favor of the existence of ``iceberg'' patterns, but a linear dependence of slope on the total excursion of the demisyllabic movement, instead of the approximate constancy of the threshold crossing speed as suggested in the original proposal of the iceberg, has been found. Accordingly, a revision of the original concept of iceberg, seems necessary. This refinement is consistent with the C/D model assumption on ``prominence control'' that the syllable magnitude determines the movement amplitude, accompanying directly related syllable duration change. In this assumption, the movement of a consonantal component should also be proportional to syllable magnitude. The results suggests, however, systematic outliers deviating from the linear dependence of movement speed on excursion. This deviation may be caused by the effect of the immediately following boundary, often referred to as phrase-final elongation. Thesis advisor: Osamu Fujimura Copies of this thesis written in English can be obtained from
On Gauge Invariant Descriptions of Gluon Polarization
Guo, Zhi-Qiang
2012-01-01
We propose methods to construct gauge invariant decompositions of nucleon spin, especially gauge invariant descriptions of gluon polarization. We show that gauge invariant decompositions of nucleon spin can be derived naturally from the conserved current of a generalized Lorentzian transformation by Noether theorem. We also examine the problem of gauge dependence with a gauge invariant extension of the Chern-Simons current.
On higher rank Donaldson-Thomas invariants
Nagao, Kentaro
2010-01-01
We study higher rank Donaldson-Thomas invariants of a Calabi-Yau 3-fold using Joyce-Song's wall-crossing formula. We construct quivers whose counting invariants coincide with the Donaldson-Thomas invariants. As a corollary, we prove the integrality and a certain symmetry for the higher rank invariants.
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 Broken Discrete Symmetries
Kalozoumis, P. A.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-08-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
Neutrino mixing and Lorentz invariance
Blasone, M; Pires-Pacheco, P; Blasone, Massimo; Magueijo, Joao; Pires-Pacheco, Paulo
2003-01-01
We use previous work on the Hilbert space for mixed fields to derive deformed dispersion relations for neutrino flavor states. We then discuss how these dispersion relations may be incorporated into frameworks encoding the breakdown of Lorentz invariance. We consider non-linear relativity schemes (of which doubly special relativity is an example), and also frameworks allowing for the existence of a preferred frame. In both cases we derive expressions for the spectrum and end-point of beta decay, which may be used as an experimental probe of the peculiar way in which neutrinos experience Lorentz invariance.
Simple Algebras of Invariant Operators
Institute of Scientific and Technical Information of China (English)
Xiaorong Shen; J.D.H. Smith
2001-01-01
Comtrans algebras were introduced in as algebras with two trilinear operators, a commutator [x, y, z] and a translator , which satisfy certain identities. Previously known simple comtrans algebras arise from rectangular matrices, simple Lie algebras, spaces equipped with a bilinear form having trivial radical, spaces of hermitian operators over a field with a minimum polynomial x2+1. This paper is about generalizing the hermitian case to the so-called invariant case. The main result of this paper shows that the vector space of n-dimensional invariant operators furnishes some comtrans algebra structures, which are simple provided that certain Jordan and Lie algebras are simple.
Invariant manifolds and collective coordinates
Energy Technology Data Exchange (ETDEWEB)
Papenbrock, T. [Centro Internacional de Ciencias, Cuernavaca, Morelos (Mexico); Institute for Nuclear Theory, University of Washington, Seattle, WA (United States); Seligman, T.H. [Centro Internacional de Ciencias, Cuernavaca, Morelos (Mexico); Centro de Ciencias Fisicas, University of Mexico (UNAM), Cuernavaca (Mexico)
2001-09-14
We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction. (author)
Asymptotic Analysis of Invariant Density of Randomly Perturbed Dynamical Systems
Mikami, Toshio
1990-01-01
The invariant density of diffusion processes which are small random perturbations of dynamical systems can be expanded in W.K.B. type, as the random effect disappears, in the set in which the Freidlin-Wentzell quasipotential $V(\\cdot)$ is of $C^\\infty$-class and each coefficient which appears in the expansion is of $C^\\infty$-class.
Singular conformally invariant trilinear forms and generalized Rankin Cohen operators
Jean-Louis, Clerc
2011-01-01
The most singular residues of the standard meromorphic family of trilinear conformally invariant forms on $\\mathcal C^\\infty_c(\\mathbb R^d)$ are computed. Their expression involves covariant bidifferential operators (generalized Rankin Cohen operators), for which new formul\\ae \\ are obtained. The main tool is a Bernstein-Sato identity for the kernel of the forms.
Invariant Classification of Gait Types
DEFF Research Database (Denmark)
Fihl, Preben; Moeslund, Thomas B.
2008-01-01
This paper presents a method of classifying human gait in an invariant manner based on silhouette comparison. A database of artificially generated silhouettes is created representing the three main types of gait, i.e. walking, jogging, and running. Silhouettes generated from different camera angles...
Galilean invariance in Lagrangian mechanics
Mohallem, J. R.
2015-10-01
The troublesome topic of Galilean invariance in Lagrangian mechanics is discussed in two situations: (i) A particular case involving a rheonomic constraint in uniform motion and (ii) the general translation of an entire system and the constants of motion involved. A widespread impropriety in most textbooks is corrected, concerning a condition for the equality h = E to hold.
Scale invariance and superfluid turbulence
Energy Technology Data Exchange (ETDEWEB)
Sen, Siddhartha, E-mail: siddhartha.sen@tcd.ie [CRANN, Trinity College Dublin, Dublin 2 (Ireland); R.K. Mission Vivekananda University, Belur 711 202, West Bengal (India); Ray, Koushik, E-mail: koushik@iacs.res.in [Department of Theoretical Physics, Indian Association for the Cultivation of Science, Calcutta 700 032 (India)
2013-11-11
We construct a Schroedinger field theory invariant under local spatial scaling. It is shown to provide an effective theory of superfluid turbulence by deriving, analytically, the observed Kolmogorov 5/3 law and to lead to a Biot–Savart interaction between the observed filament excitations of the system as well.
Conjectured enumeration of Vassiliev invariants
Broadhurst, D J
1997-01-01
These conjectures are motivated by successful enumerations of irreducible Euler sums. Predictions for $\\beta_{15,10}$, $\\beta_{16,12}$ and $\\beta_{19,16}$ suggest that the action of sl and osp Lie algebras, on baguette diagrams with ladder insertions, fails to detect an invariant in each case.
A Many Particle Adiabatic Invariant
DEFF Research Database (Denmark)
Hjorth, Poul G.
1999-01-01
For a system of N charged particles moving in a homogeneous, sufficiently strong magnetic field, a many-particle adiabatic invariant constrains the collisional exchange of energy between the degrees of freedom perpendicular to and parallel to the magnetic field. A description of the phenomenon...
Xiao, Jing; Bai, Yu; He, Yini; McWhinnie, Chad M.; Ling, Yu; Smith, Hannah; Huebner, E. Scott
2016-01-01
The aim of this study was to test the gender invariance of the Chinese version of the Achievement Goal Questionnaire (AGQ-C) utilizing a sample of 1,115 Chinese university students. Multi-group confirmatory factor analysis supported the configural, metric, and scalar invariance of the AGQ-C across genders. Analyses also revealed that the latent…
Scale invariance of parity-invariant three-dimensional QED
Karthik, Nikhil; Narayanan, Rajamani
2016-09-01
We present numerical evidences using overlap fermions for a scale-invariant behavior of parity-invariant three-dimensional QED with two flavors of massless two-component fermions. Using finite-size scaling of the low-lying eigenvalues of the massless anti-Hermitian overlap Dirac operator, we rule out the presence of a bilinear condensate and estimate the mass anomalous dimension. The eigenvectors associated with these low-lying eigenvalues suggest critical behavior in the sense of a metal-insulator transition. We show that there is no mass gap in the scalar and vector correlators in the infinite-volume theory. The vector correlator does not acquire an anomalous dimension. The anomalous dimension associated with the long-distance behavior of the scalar correlator is consistent with the mass anomalous dimension.
Test of Lorentz Invarience from Compton Scattering
Mohanmurthy, Prajwal; Narayan, Amrendra
2015-01-01
In the recent times, test of Lorentz Invariance has been used as a means to probe theories of physics beyond the standard model, especially those such as extensions to String Theory and Quantum Gravity. Tests of Lorentz invariance could go a long way in setting the stage for possible quantum gravity theories which are beyond the standard model. We describe a simple way of utilizing the polarimeters, which are a critical beam instrument at precision and intensity frontier nuclear physics labs such as Stanford Linear Accelerator Center (SLAC) and Jefferson Lab (JLab), to limit the dependence of speed of light with the energy of the photons. Furthermore, we also describe a way of limiting directional dependence of speed of light at previously unprecedented levels of precision by studying the sidereal variations. We obtain a limit of MSME parameters: $\\sqrt{\\kappa_X^2 + \\kappa_Y^2} < 2.4 \\times 10^{-17}$ and $\\sqrt{\\left( 2c_{TX} - (\\tilde{\\kappa}_{0^+}^{YZ} \\right)^2 + \\left( 2c_{TY} - (\\tilde{\\kappa}_{0^+}^{...
Shift-invariant optical associative memories
Energy Technology Data Exchange (ETDEWEB)
Psaltis, D.; Hong, J.
1987-01-01
Shift invariance in the context of associative memories is discussed. Two optical systems that exhibit shift invariance are described in detail with attention given to the analysis of storage capacities. It is shown that full shift invariance cannot be achieved with systems that employ only linear interconnections to store the associations.
Finite type invariants and fatgraphs
DEFF Research Database (Denmark)
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...... from an appropriate vector space of homology cylinders to a certain algebra of Jacobi diagrams. Via composition for any pair of fatgraph spines G,G′ of Σ, we derive a representation of the Ptolemy groupoid, i.e., the combinatorial model for the fundamental path groupoid of Teichmüller space, as a group...... of automorphisms of this algebra. The space comes equipped with a geometrically natural product induced by stacking cylinders on top of one another and furthermore supports related operations which arise by gluing a homology handlebody to one end of a cylinder or to another homology handlebody. We compute how G...
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.
Proton spin: A topological invariant
Tiwari, S. C.
2016-11-01
Proton spin problem is given a new perspective with the proposition that spin is a topological invariant represented by a de Rham 3-period. The idea is developed generalizing Finkelstein-Rubinstein theory for Skyrmions/kinks to topological defects, and using non-Abelian de Rham theorems. Two kinds of de Rham theorems are discussed applicable to matrix-valued differential forms, and traces. Physical and mathematical interpretations of de Rham periods are presented. It is suggested that Wilson lines and loop operators probe the local properties of the topology, and spin as a topological invariant in pDIS measurements could appear with any value from 0 to ℏ 2, i.e. proton spin decomposition has no meaning in this approach.
Invariance of the Noether charge
Silagadze, Z K
2016-01-01
Surprisingly, an interesting property of the Noether charge that it is by itself invariant under the corresponding symmetry transformation is never discussed in quantum field theory or classical mechanics textbooks we have checked. This property is also almost never mentioned in articles devoted to Noether's theorem. Nevertheless, to prove this property in the context of Lagrangian formalism is not quite trivial and the proof, outlined in this article, can constitute an useful and interesting exercise for students.
Holographic multiverse and conformal invariance
Energy Technology Data Exchange (ETDEWEB)
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.
Volume conjecture for $SU(n)$-invariants
Chen, Qingtao; Zhu, Shengmao
2015-01-01
This paper discuss an intrinsic relation among congruent relations \\cite{CLPZ}, cyclotomic expansion and Volume Conjecture for $SU(n)$ invariants. Motivated by the congruent relations for $SU(n)$ invariants obtained in our previous work \\cite{CLPZ}, we study certain limits of the $SU(n)$ invariants at various roots of unit. First, we prove a new symmetry property for the $SU(n)$ invariants by using a symmetry of colored HOMFLYPT invariants. Then we propose some conjectural formulas including the cyclotomic expansion conjecture and volume conjecture for $SU(n)$ invariants (specialization of colored HOMFLYPT invariants). We also give the proofs of these conjectural formulas for the case of figure-eight knot.
A spectral invariant representation of spectral reflectance
Ibrahim, Abdelhameed; Tominaga, Shoji; Horiuchi, Takahiko
2011-03-01
Spectral image acquisition as well as color image is affected by several illumination factors such as shading, gloss, and specular highlight. Spectral invariant representations for these factors were proposed for the standard dichromatic reflection model of inhomogeneous dielectric materials. However, these representations are inadequate for other characteristic materials like metal. This paper proposes a more general spectral invariant representation for obtaining reliable spectral reflectance images. Our invariant representation is derived from the standard dichromatic reflection model for dielectric materials and the extended dichromatic reflection model for metals. We proof that the invariant formulas for spectral images of natural objects preserve spectral information and are invariant to highlights, shading, surface geometry, and illumination intensity. It is proved that the conventional spectral invariant technique can be applied to metals in addition to dielectric objects. Experimental results show that the proposed spectral invariant representation is effective for image segmentation.
Role of gauge invariance in B -> V gamma radiative weak decays
Riazuddin, M
2002-01-01
The role of gauge invariance in calculating B -> V gamma radiative weak decays is clarified. It is shown that the gauge invariance severely restricts the contributions mediated by the usual weak non-leptonic Hamiltonian dominated by u and c quaks with one photon attachment. Such contributions are found to be almost negligible.
SPEEDY: An Eclipse-based IDE for invariant inference
Directory of Open Access Journals (Sweden)
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.
Quantum Weyl invariance and cosmology
Directory of Open Access Journals (Sweden)
Atish Dabholkar
2016-09-01
Full Text Available Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly decaying vacuum energy. A natural generalization to four dimensions implies a quantum modification of Einstein field equations at long distances. It offers a new perspective on time-dependence of couplings and naturalness with potentially far-reaching consequences for the cosmological constant problem, inflation, and dark energy.
Quantum Weyl invariance and cosmology
Dabholkar, Atish
2016-09-01
Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly decaying vacuum energy. A natural generalization to four dimensions implies a quantum modification of Einstein field equations at long distances. It offers a new perspective on time-dependence of couplings and naturalness with potentially far-reaching consequences for the cosmological constant problem, inflation, and dark energy.
Weierstrass preparation and algebraic invariants
Harbater, David; Krashen, Daniel
2011-01-01
We prove a form of the Weierstrass Preparation Theorem for normal algebraic curves over complete discrete valuation rings. While the more traditional algebraic form of Weierstrass Preparation applies just to the projective line over a base, our version allows more general curves. This result is then used to obtain applications concerning the values of u-invariants, and on the period-index problem for division algebras, over fraction fields of complete two-dimensional rings. Our approach uses patching methods and matrix factorization results that can be viewed as analogs of Cartan's Lemma.
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.
Duality and universality for stable pair invariants of surfaces
Kool, M
2013-01-01
Let $\\beta$ be a curve class on a surface $S$. The moduli space of stable pairs on $S$ with class $\\beta$ carries a natural reduced virtual cycle \\cite{KT1, KT2}. This cycle is defined when $h^2(L) = 0$ for any \\emph{effective} $L \\in \\mathrm{Pic}^\\beta(S)$ (weak assumption). When $h^2(L) = 0$ for \\emph{any} $L \\in \\mathrm{Pic}^{\\beta}(S)$ (strong assumption), the associated invariants are given by universal functions in $\\beta^2$, $\\beta.c_1(S)$, $c_1(S)^2$, $c_2(S)$, and certain invariants of the ring structure of $H^*(S,\\Z)$. In this paper, we show the following. (1) Universality \\emph{no longer} holds when just the weak assumption is satisfied. (2) For any $S,\\beta$ (no conditions), the BPS spectrum of the non-reduced stable pair invariants of $S,\\beta$ with maximal number of point insertions consists of a single number. This number is the Seiberg-Witten invariant of $S, \\beta$. (3) The GW/PT correspondence for $X = K_S$ implies Taubes' GW/SW correspondence in certain cases, e.g. when $\\beta$ is irreducib...
Age-invariant face recognition.
Park, Unsang; Tong, Yiying; Jain, Anil K
2010-05-01
One of the challenges in automatic face recognition is to achieve temporal invariance. In other words, the goal is to come up with a representation and matching scheme that is robust to changes due to facial aging. Facial aging is a complex process that affects both the 3D shape of the face and its texture (e.g., wrinkles). These shape and texture changes degrade the performance of automatic face recognition systems. However, facial aging has not received substantial attention compared to other facial variations due to pose, lighting, and expression. We propose a 3D aging modeling technique and show how it can be used to compensate for the age variations to improve the face recognition performance. The aging modeling technique adapts view-invariant 3D face models to the given 2D face aging database. The proposed approach is evaluated on three different databases (i.g., FG-NET, MORPH, and BROWNS) using FaceVACS, a state-of-the-art commercial face recognition engine.
Lorentz Invariant CPT Violating Effects for a Class of Gauge-invariant Nonlocal Thirring Models
Patra, Pinaki
2013-01-01
CPT violation and Lorentz invariance can coexist in the framework of non-local field theory. Local gauge-invariance may not hold for the few non-local interaction terms. However, the gauge-invariance for the non-local interaction term can be formulated by the inclusion of Swinger non-integrable phase factor. In this article we have proposed a class of CPT violating Lorentz invariant Nonlocal Gauge-invariant models which can be termed as non-local gauge-invariant Thirring models. The inclusion of non-locality will modify the current conservation laws. Also, the possible particle antiparticle mass-splitting in this respect is discussed.
Synthesizing Modular Invariants for Synchronous Code
Directory of Open Access Journals (Sweden)
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.
On the Galilean non-invariance of classical electromagnetism
Energy Technology Data Exchange (ETDEWEB)
Preti, Giovanni; De Felice, Fernando; Masiero, Luca [Dipartimento di Fisica ' Galileo Galilei' , Universita degli Studi di Padova (Italy)], E-mail: giovanni.preti@pd.infn.it, E-mail: fernando.defelice@pd.infn.it, E-mail: masieroluca@yahoo.it
2009-03-15
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 presence of a parameter c with the dimensions of a velocity in Maxwell's equations, being well aware of the fact that any velocity is non-invariant in Galilean relativity. This 'obvious' answer, however popular, is not correct due to the actual observer-invariance of the Maxwell parameter c in pre-relativistic physics too. A pre-relativistic physicist would therefore have needed a different explanation. Playing the role of this physicist, we pedagogically show how a proof of the Galilean non-invariance of classical electromagnetism can be obtained, resting on simple pre-relativistic considerations alone.
Conformal invariance conserved quantity of Hamilton systems
Institute of Scientific and Technical Information of China (English)
Cai Jian-Le; Luo Shao-Kai; Mei Feng-Xiang
2008-01-01
This paper studies conformal invariance and comserved quantRies of Hamilton system.The definition and the determining equation of conformal invariance for Hamilton system are provided.The relationship between the conformal invariance and the Lie symmetry are discussed,and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced.It gives the conserved quantities of the system and an example for illustration.
Wilson loop invariants from WN conformal blocks
Directory of Open Access Journals (Sweden)
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.
Optimized Set of RST Moment Invariants
Directory of Open Access Journals (Sweden)
Khalid M. Hosny
2008-01-01
Full Text Available Moment invariants are widely used in image processing, pattern recognition and computer vision. Several methods and algorithms have been proposed for fast and efficient calculation of moment's invariants where numerical approximation errors are involved in most of these methods. In this paper, an optimized set of moment invariants with respect to rotation, scaling and translation is presented. An accurate method is used for exact computation of moment invariants for gray level images. A fast algorithm is applied to accelerate the process of computation. Error analysis is presented and a comparison with other conventional methods is performed. The obtained results explain the superiority of the proposed method.
Geometric invariance in describing color features
Tran, Linh Viet; Lenz, Reiner
2003-01-01
We present a projective geometry framework for color invariants using the Extended Dichromatic Reflection Model, in which more realistic and complicated illuminations are considered. Many assumptions which have been used by other methods are relaxed in our framework. Specifically some of the proposed invariants do not require any additional assumption except the ones assumed by the Extended Dichromatic Reflection Model. By putting the color invariance into the projective geometry framework, we can generate different types of invariants and clarify the assumptions under which they are valid. Experiments are presented that illustrate the results derived within our framework.
Gauge Invariant Cosmological Perturbation Theory
Durrer, R
1993-01-01
After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum ``conservation''. Furthermore, the perturbations of Liouville's equation for collisionless particles and Boltzmann's equation for Compton scattering are worked out. We fully discuss the propagation of photons in a perturbed Friedmann universe, calculating the Sachs--Wolfe effect and light deflection. The perturbation equations are extended to accommodate also perturbations induced by seeds. With these general results we discuss some of the main aspects of the texture model for the formation of large scale structure in the Universe (galaxies, clusters, sheets, voids). In this model, perturbations in the dark matter are induced by texture seeds. The gravitational effects of a spherically symmetric collapsing texture on dark matter, baryonic matter and photons are calculated in first orde...
Inflation and classical scale invariance
Racioppi, Antonio
2014-01-01
BICEP2 measurement of primordial tensor modes in CMB suggests that cosmological inflation is due to a slowly rolling inflaton taking trans-Planckian values and provides further experimental evidence for the absence of large $M_{\\rm P}$ induced operators. We show that classical scale invariance solves the problem and allows for a remarkably simple scale-free inflaton model without any gauge group. Due to trans-Planckian inflaton values and VEVs, a dynamically induced Coleman-Weinberg-type inflaton potential of the model can predict tensor-to-scalar ratio $r$ in a large range. Precise determination of $r$ in future experiments will allow to test the proposed field-theoretic framework.
Pattern Recognition by Combined Invariants
Institute of Scientific and Technical Information of China (English)
WANG Xiaohong; ZHAO Rongchun
2001-01-01
A feature-based recognition of objectsor patterns independent of their position, size, orien-tation and other variations has been the goal of muchrecent research. The existing approaches to invarianttwo-dimensional pattern recognition are useless whenpattern is blurred. In this paper, we present a novelpattern recognition system which can solve the prob-lem by using combined invariants as image features.The classification technique we choose for our systemis weighted normalized cross correlation. The mean ofthe intraclass standard deviations of the kth featureover the total number of prototypes for each class isused as a weighting factor during the classification pro-cess to improve recognition accuracy. The feasibilityof our pattern recognition system and the invarianceof the combined features with respect to translation,scaling, rotation and blurring are approved by numer-ical experiments on head images.
Hrushovski, Ehud
2007-01-01
We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of $NIP$ (not the independence property), continuing aspects of math.LO/0607442. Among key results are: (i) if $p = tp(b/A)$ does not fork over $A$ then the Lascar strong type of $b$ over $A$ coincides with the compact strong type of $b$ over $A$ and any global nonforking extension of $p$ is Borel definable over $bdd(A)$ (ii) analogous statements for Keisler measures and definable groups, including the fact that $G^{000} = G^{00}$ for $G$ definably amenable, (iii) definitions, characterizations and properties of "generically stable" types and groups (iv) uniqueness of translation invariant Keisler measures on groups with finitely satisfiable generics (v) ``generic compact domination" for groups with finitely satisfiable generics (vi) A proof of the compact domination conjecture for definably compact commutative groups in $o$-minimal expansions of real closed fields.
Negation switching invariant signed graphs
Directory of Open Access Journals (Sweden)
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.
Cardinal invariants on Boolean algebras
Monk, J Donald
2014-01-01
This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the...
Dynamical invariance for random matrices
Unterberger, Jeremie
2016-01-01
We consider a general Langevin dynamics for the one-dimensional N-particle Coulomb gas with confining potential $V$ at temperature $\\beta$. These dynamics describe for $\\beta=2$ the time evolution of the eigenvalues of $N\\times N$ random Hermitian matrices. The equilibrium partition function -- equal to the normalization constant of the Laughlin wave function in fractional quantum Hall effect -- is known to satisfy an infinite number of constraints called Virasoro or loop constraints. We introduce here a dynamical generating function on the space of random trajectories which satisfies a large class of constraints of geometric origin. We focus in this article on a subclass induced by the invariance under the Schr\\"odinger-Virasoro algebra.
Gromov-Witten invariants of $\\bp^1$ and Eynard-Orantin invariants
Norbury, Paul
2011-01-01
We prove that stationary Gromov-Witten invariants of $\\bp^1$ arise as the Eynard-Orantin invariants of the spectral curve $x=z+1/z$, $y=\\ln{z}$. As an application we show that tautological intersection numbers on the moduli space of curves arise in the asymptotics of large degree Gromov-Witten invariants of $\\bp^1$.
Whitney smooth families of invariant tori within the reversible context 2 of KAM theory
Sevryuk, Mikhail B.
2016-11-01
We prove a general theorem on the persistence of Whitney C ∞-smooth families of invariant tori in the reversible context 2 of KAM theory. This context refers to the situation where dim Fix G Fix G is the fixed point manifold of the reversing involution G and T is the invariant torus in question. Our result is obtained as a corollary of the theorem by H. W.Broer, M.-C.Ciocci, H.Hanßmann, and A.Vanderbauwhede (2009) concerning quasi-periodic stability of invariant tori with singular "normal" matrices in reversible systems.
Invariance of the distributional curvature of the cone under smooth diffeomorphisms
Vickers, J A
1999-01-01
An explicit calculation is carried out to show that the distributional curvature of a 2-cone, calculated by Clarke et al. (1996), using Colombeau's new generalised functions is invariant under non-linear $C^\\infty$ coordinate transformations.
Scale invariant Volkov–Akulov supergravity
Energy Technology Data Exchange (ETDEWEB)
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.
Singularity invariants related to Milnor fibers: survey
Budur, Nero
2010-01-01
This brief survey of some singularity invariants related to Milnor fibers should serve as a quick guide to references. We attempt to place things into a wide geometric context while leaving technicalities aside. We focus on relations among different invariants and on the practical aspect of computing them.
Parton model in Lorentz invariant noncommutative space
Haghighat, M.; Ettefaghi, M. M.
2004-08-01
We consider the Lorentz invariant noncommutative QED and complete the Feynman rules for the theory up to the order θ2. In the Lorentz invariant version of the noncommutative QED the particles with fractional charges can be also considered. We show that in the parton model, even at the lowest order, the Bjorken scaling violates as ˜θ2Q4.
Polynomial Invariant Theory of the Classical Groups
Westrich, Quinton
2011-01-01
The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \\emph{basic invariants}. In particular, we set out to find the set of basic invariants for the classical groups GL$(V)$, O$(n)$, and Sp$(n)$ for $n$ even. In the first half of the paper we set up relevant definitions and theorems for our search for the set of basic invariants, starting with linear algebraic groups and then discussing associative algebras. We then state and prove a monumental theorem that will allow us to proceed with hope: it says that the set of basic invariants is finite if $G$ is reductive. Finally we state without proof the First Fundamental Theorems, which aim to list explicitly the relevant sets of basic invariants, for the classical groups above. We end by commenting on some applications of invariant theory, on the history of its development, and stating a useful theorem in the appendix whose proof lies beyond the scope ...
INVARIANT RANDOM APPROXIMATION IN NONCONVEX DOMAIN
Directory of Open Access Journals (Sweden)
R. Shrivastava
2012-05-01
Full Text Available Random fixed point results in the setup of compact and weakly compact domain of Banach spaces which is not necessary starshaped have been obtained in the present work. Invariant random approximation results have also been determined asits application. In this way, random version of invariant approximation results due toMukherjee and Som [13] and Singh [17] have been given.
Scale invariant Volkov–Akulov supergravity
Directory of Open Access Journals (Sweden)
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.
Gauge-invariant perturbations of Schwarzschild spacetime
Shah, Abhay G; Aksteiner, Steffen; Andersson, Lars; Bäckdahl, Thomas
2016-01-01
We study perturbations of Schwarzschild spacetime in a coordinate-free, covariant form. The GHP formulation, having the advantage of not only being covariant but also tetrad-rotation invariant, is used to write down the previously known odd- and even-parity gauge-invariants and the equations they satisfy. Additionally, in the even-parity sector, a new invariant and the second order hyperbolic equation it satisfies are presented. Chandrasekhar's work on transformations of solutions for perturbation equations on Schwarzschild spacetime is translated into the GHP form, i.e., solutions for the equations of the even- and odd-parity invariants are written in terms of one another, and the extreme Weyl scalars; and solutions for the equations of these latter invariants are also written in terms of one another. Recently, further gauge invariants previously used by Steven Detweiler have been described. His method is translated into GHP form and his basic invariants are presented here. We also show how these invariants ...
Spectral properties of supersymmetric shape invariant potentials
Indian Academy of Sciences (India)
Barnali Chakrabarti
2008-01-01
We present the spectral properties of supersymmetric shape invariant potentials (SIPs). Although the folded spectrum is completely random, unfolded spectrum shows that energy levels are highly correlated and absolutely rigid. All the SIPs exhibit harmonic oscillator-type spectral statistics in the unfolded spectrum. We conjecture that this is the reflection of shape invariant symmetry.
On multipartite invariant states II. Orthogonal symmetry
Chruściński, Dariusz; Kossakowski, Andrzej
2006-01-01
We construct a new class of multipartite states possessing orthogonal symmetry. This new class defines a convex hull of multipartite states which are invariant under the action of local unitary operations introduced in our previous paper "On multipartite invariant states I. Unitary symmetry". We study basic properties of multipartite symmetric states: separability criteria and multi-PPT conditions.
Borromean surgery formula for the Casson invariant
DEFF Research Database (Denmark)
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, li...
A Family of Invariant Stress Surfaces
DEFF Research Database (Denmark)
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...
Testing Lorentz invariance in weak decays
Energy Technology Data Exchange (ETDEWEB)
Sytema, Auke; Dijck, Elwin; Hoekstra, Steven; Jungmann, Klaus; Mueller, Stefan; Noordmans, Jacob; Onderwater, Gerco; Pijpker, Coen; Timmermans, Rob; Vos, Keri; Willmann, Lorenz; Wilschut, Hans [Van Swinderen Institute, University of Groningen (Netherlands)
2015-07-01
Lorentz invariance is the invariance of physical laws under orientations and boosts. It is a key assumption in Special Relativity and the Standard Model of Particle Physics. Several theories unifying General Relativity and Quantum Mechanics allow breaking of Lorentz invariance. At the Van Swinderen Institute in Groningen a theoretical and experimental research program was started to study Lorentz invariance violation (LIV) in weak interactions. The theoretical work allowed a systematic approach to LIV in weak decays. Limits could be set on parameters that quantify LIV. A novel beta decay experiment was designed which tests rotational invariance with respect to the orientation of nuclear spin. In particular, using the isotope {sup 20}Na, the decay rate dependence on the nuclear polarization direction was measured. Searching for sidereal variations, systematic errors can be suppressed. The result of the experiment is presented.
Constructing Invariant Fairness Measures for Surfaces
DEFF Research Database (Denmark)
Gravesen, Jens; Ungstrup, Michael
1998-01-01
This paper presents a general method which from an invariant curve fairness measure constructs an invariant surface fairness measure. Besides the curve fairness measure one only needs a class of curves on the surface for which one wants to apply the curve measure. The surface measure at a point...... variation.The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family of curves. Such a family is generated by the flow of a vector field, orthogonal to the curves. The first, respectively the second order derivative along the curve...... 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...
Factorial invariance in multilevel confirmatory factor analysis.
Ryu, Ehri
2014-02-01
This paper presents a procedure to test factorial invariance in multilevel confirmatory factor analysis. When the group membership is at level 2, multilevel factorial invariance can be tested by a simple extension of the standard procedure. However level-1 group membership raises problems which cannot be appropriately handled by the standard procedure, because the dependency between members of different level-1 groups is not appropriately taken into account. The procedure presented in this article provides a solution to this problem. This paper also shows Muthén's maximum likelihood (MUML) estimation for testing multilevel factorial invariance across level-1 groups as a viable alternative to maximum likelihood estimation. Testing multilevel factorial invariance across level-2 groups and testing multilevel factorial invariance across level-1 groups are illustrated using empirical examples. SAS macro and Mplus syntax are provided.
Hamiltonian Formalism of de-Sitter Invariant Special Relativity
Yan, Mu-Lin; Xiao, Neng-Chao; Huang, Wei; Li, Si
2007-07-01
The Lagrangian of Einstein's special relativity with universal parameter c (Script SRc) is invariant under Poincaré transformation, which preserves Lorentz metric ημν. The Script SRc has been extended to be one which is invariant under de Sitter transformation that preserves so-called Beltrami metric Bμν. There are two universal parameters, c and R, in this Special Relativity (denoted as Script SRcR). The Lagrangian-Hamiltonian formulism of Script SRcR is formulated in this paper. The canonic energy, canonic momenta, and 10 Noether charges corresponding to the space-time's de Sitter symmetry are derived. The canonical quantization of the mechanics for Script SRcR-free particle is performed. The physics related to it is discussed.
Hamiltonian Formalism of de-Sitter Invariant Special Relativity
Institute of Scientific and Technical Information of China (English)
YAN Mu-Lin; XIAO Neng-Chao; HUANG Wei; LI Si
2007-01-01
The Lagrangian of Einstein's special relativity with universal parameter c (SRc) is invariant under Poincaré transformation, which preserves Lorentz metric ημν. The SRc has been extended to be one which is invariant under de Sitter transformation that preserves so-called Beltrami metric Bμν. There are two universal parameters, c and R, in this Special Relativity (denoted as SRcR). The Lagrangian-Hamiltonian formulism of SRcR is formulated in this paper.The canonic energy, canonic momenta, and 10 Noether charges corresponding to the space-time's de Sitter symmetry are derived. The canonical quantization of the mechanics for SRcR-free particle is performed. The physics related to it is discussed.
Smoothness of invariant density for expanding transformations in higher dimensions
Directory of Open Access Journals (Sweden)
Kourosh Adl-Zarabi
2000-01-01
Full Text Available Let Ω be a bounded region in ℝn and let ={Pi}i=1m be a partition of Ω into a finite number of closed subsets having piecewise C2 boundaries of finite (n−1-dimensional measure. Let τ:Ω→Ω be an expanding transformation on where, τi:τ|Pi, and τi∈CM, m≥2. We show that the τ-invariant density h∈CM−2.
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.
A scale invariance criterion for LES parametrizations
Directory of Open Access Journals (Sweden)
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.
The invariator principle in convex geometry
DEFF Research Database (Denmark)
Thórisdóttir, Ólöf; Kiderlen, Markus
look at rotational Crofton-type formulae that are obtained by combining the invariator principle and classical Crofton formulae. This results in geometrical quantities represented as averages over weighted Crofton-type integrals in linear sections. We refer to these weighted integrals as measurement......The invariator principle is a measure decomposition that was rediscovered in local stereology in 2005 and has since been used widely in the stereological literature. We give an exposition of invariator related results where existing formulae are generalized and new ones proposed. In particular, we...
Knot Invariants from Classical Field Theories
Leal, L C
1999-01-01
We consider the Non-Abelian Chern-Simons term coupled to external particles, in a gauge and diffeomorphism invariant form. The classical equations of motion are perturbativelly studied, and the on-shell action is shown to produce knot-invariants associated with the sources. The first contributions are explicitly calculated, and the corresponding knot-invariants are recognized. We conclude that the interplay between Knot Theory and Topological Field Theories is manifested not only at the quantum level, but in a classical context as well.
Graph Invariants of Vassiliev Type and Application to 4D Quantum Gravity
Hayashi, Nobuharu
1995-01-01
We consider a special class of Kauffman's graph invariants of rigid vertex isotopy (graph invariants of Vassiliev type). They are given by a functor from a category of colored and oriented graphs embedded into a 3-space to a category of representations of the quasi-triangular ribbon Hopf algebra $U_q(sl(2,\\bf C))$. Coefficients in expansions of them with respect to $x$ ($q=e^x$) are known as the Vassiliev invariants of finite type. In the present paper, we construct two types of tangle operat...
Estimating the ultimate bound and positively invariant set for a generalized Lorenz system
Institute of Scientific and Technical Information of China (English)
SHU Yong-lu; ZHANG Yong-hao
2008-01-01
A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system. We derived an ellipsoidal estimate of the ultimate bound and positively invariant set for the generalized Lorenz system, for all the positive values of system parameters a, b, and c. Our results extend the related result of Li, et al. [Li DM, Lu JA, Wu XQ, et al., Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system, Journal of Mathematical Analysis and Application, 2006, 323(2): 844-653].
On link invariants and topological string amplitudes
Energy Technology Data Exchange (ETDEWEB)
Ramadevi, P. E-mail: rama@phy.iitb.ernet.in; Sarkar, Tapobrata E-mail: tapo@theory.tifr.res.in
2001-04-30
We explicitly show that the new polynomial invariants for knots, upto nine crossings, agree with the Ooguri-Vafa conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold.
On Link Invariants and Topological String Amplitudes
Ramadevi, P.; Sarkar, Tapobrata
2000-01-01
We explicitly show that the new polynomial invariants for knots, upto nine crossings, agree with the Ooguri-Vafa conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold.
Local and gauge invariant observables in gravity
Khavkine, Igor
2015-01-01
It is well known that General Relativity (GR) does not possess any non-trivial local (in a precise standard sense) and diffeomorphism invariant observables. We propose a generalized notion of local observables, which retain the most important properties that follow from the standard definition of locality, yet is flexible enough to admit a large class of diffeomorphism invariant observables in GR. The generalization comes at a small price, that the domain of definition of a generalized local observable may not cover the entire phase space of GR and two such observables may have distinct domains. However, the subset of metrics on which generalized local observables can be defined is in a sense generic (its open interior is non-empty in the Whitney strong topology). Moreover, generalized local gauge invariant observables are sufficient to separate diffeomorphism orbits on this admissible subset of the phase space. Connecting the construction with the notion of differential invariants, gives a general scheme for...
Ermakov–Lewis invariants and Reid systems
Energy Technology Data Exchange (ETDEWEB)
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.
Edge and corner detection by color invariants
Chu, Jun; Miao, Jun; Zhang, Guimei; Wang, Lu
2013-02-01
Gray-based features are widely used in computer vision applications, while image color is a very important source, which can provide more feature information. To fully exploit color data, a color saturation invariant based on dichromatic reflection model is first constructed. The invariant is an object reflectance property independent of viewpoint and illumination direction. The saturation invariant is then synthesized with existing hue invariant to detect edge and corner features in color image. Experiments show that the detection method proposed here can more effectively tap into color information and achieve true target features due to its lower sensitivity to shadow, shading and highlight. Moreover, when comparing with many other existing edges and corners detecting methods, experimental results demonstrate that the proposed method performs better in detection accurate and effective.
Testing gauge-invariant perturbation theory
Törek, Pascal
2016-01-01
Gauge-invariant perturbation theory for theories with a Brout-Englert-Higgs effect, as developed by Fr\\"ohlich, Morchio and Strocchi, starts out from physical, exactly gauge-invariant quantities as initial and final states. These are composite operators, and can thus be considered as bound states. In case of the standard model, this reduces almost entirely to conventional perturbation theory. This explains the success of conventional perturbation theory for the standard model. However, this is due to the special structure of the standard model, and it is not guaranteed to be the case for other theories. Here, we review gauge-invariant perturbation theory. Especially, we show how it can be applied and that it is little more complicated than conventional perturbation theory, and that it is often possible to utilize existing results of conventional perturbation theory. Finally, we present tests of the predictions of gauge-invariant perturbation theory, using lattice gauge theory, in three different settings. In ...
Wall-Crossing Invariants from Spectral Networks
Longhi, Pietro
2016-01-01
A new construction of BPS monodromies for 4d ${\\mathcal N}=2$ theories of class S is introduced. A novel feature of this construction is its manifest invariance under Kontsevich-Soibelman wall crossing, in the sense that no information on the 4d BPS spectrum is employed. The BPS monodromy is encoded by topological data of a finite graph, embedded into the UV curve $C$ of the theory. The graph arises from a degenerate limit of spectral networks, constructed at maximal intersections of walls of marginal stability in the Coulomb branch of the gauge theory. The topology of the graph, together with a notion of framing, encode equations that determine the monodromy. We develop an algorithmic technique for solving the equations, and compute the monodromy in several examples. The graph manifestly encodes the symmetries of the monodromy, providing some support for conjectural relations to specializations of the superconformal index. For $A_1$-type theories, the graphs encoding the monodromy are "dessins d'enfants" on ...
A relationship between twisted conjugacy classes and the geometric invariants $\\Omega^n$
Koban, Nic
2009-01-01
A group $G$ is said to have the property $R_\\infty$ if every automorphism $\\varphi \\in {\\rm Aut}(G)$ has an infinite number of $\\varphi$-twisted conjugacy classes. Recent work of Gon\\c{c}alves and Kochloukova uses the $\\Sigma^n$ (Bieri-Neumann-Strebel-Renz) invariants to show the $R_{\\infty}$ property for a certain class of groups, including the generalized Thompson's groups $F_{n,0}$. In this paper, we make use of the $\\Omega^n$ invariants, analogous to $\\Sigma^n$, to show $R_{\\infty}$ for certain finitely generated groups. In particular, we give an alternate and simpler proof of the $R_{\\infty}$ property for BS(1,n). Moreover, we give examples for which the $\\Omega^n$ invariants can be used to determine the $R_{\\infty}$ property while the $\\Sigma^n$ invariants techniques cannot.
Weyl Invariance and the Origins of Mass
Gover, A R; Waldron, A
2008-01-01
By a uniform and simple Weyl invariant coupling of scale and matter fields, we construct theories that unify massless, massive, and partially massless excitations. Masses are related to tractor Weyl weights, and Breitenlohner-Freedman stability bounds in anti de Sitter amount to reality of these weights. The method relies on tractor calculus -- mathematical machinery allowing Weyl invariance to be kept manifest at all stages. The equivalence between tractor and higher spin systems with arbitrary spins and masses is also considered.
Applications of new affine invariant for polytopes
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
To study the Schneider's projection problem,Lutwak,Yang and Zhang recently introduced a new .affine invariant functional U(P) for convex polytopes in Rn.In the paper,we obtain the analytic expression of the affine-invariant U(P) defined on a specific subclass of origin-symmetric convex polytopes in Rn and give an application of U(P) to the Lp-Minkowski problem.
Invariance and stability for bounded uncertain systems.
Peng, T. K. C.
1972-01-01
The positive limit sets of the solutions of a contingent differential equation are shown to possess an invariance property. In this connection the 'invariance principle' in the theory of Lyapunov stability is extended to systems with unknown, bounded, time-varying parameters, and thus to a large and important class of nonautonomous systems. Asymptotic stability criteria are obtained and applied to guaranteed cost control problems.
Invariants of Fokker-Planck equations
Abe, Sumiyoshi
2016-01-01
A weak invariant of a stochastic system is defined in such a way that its expectation value with respect to the distribution function as a solution of the associated Fokker-Planck equation is constant in time. A general formula is given for time evolution of fluctuations of the invariants. An application to the problem of share price in finance is illustrated. It is shown how this theory makes it possible to reduce the growth rate of the fluctuations.
On the -Invariant of Hermitian Forms
Indian Academy of Sciences (India)
Sudeep S Parihar; V Suresh
2013-08-01
Let be a field of characteristic not 2 and a central simple algebra with an involution . A result of Mahmoudi provides an upper bound for the -invariants of hermitian forms and skew-hermitian forms over (,) in terms of the -invariant of . In this paper we give a different upper bound when is a tensor product of quaternion algebras and is a the tensor product of canonical involutions. We also show that our bounds are sharper than those of Mahmoudi.
Test of time reversal invariance with TRINE
Soldner, T; Schreckenbach, K; Bussière, A; Kossakowski, R; Liaud, P; Zimmer, O
2000-01-01
The new detector TRINE (time reversal invariance neutron experiment) was developed to test the time reversal invariance in the neutron decay. The precision of former experiments can be improved by one order of magnitude with an improved proton detection, a better background suppression and an angular resolving measurement using multiwire proportional chambers in coincidence with plastic scintillators, and the higher neutron flux and polarization available today. The concept of the detector and the status of the project is discussed.
Test of time reversal invariance with TRINE
Energy Technology Data Exchange (ETDEWEB)
Soldner, T.; Beck, L.; Schreckenbach, K.; Bussiere, A.; Kossakowski, R.; Liaud, P.; Zimmer, O
2000-02-11
The new detector TRINE (time reversal invariance neutron experiment) was developed to test the time reversal invariance in the neutron decay. The precision of former experiments can be improved by one order of magnitude with an improved proton detection, a better background suppression and an angular resolving measurement using multiwire proportional chambers in coincidence with plastic scintillators, and the higher neutron flux and polarization available today. The concept of the detector and the status of the project is discussed.
On invariant sets in Lagrangian graphs
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this exposition, we show that the Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are sufficiently smooth. We also provide some counterexamples to show that if the Hamiltonian function is not smooth enough, then it may be non-constant on a compact invariant connected subset which lies in a Lagrangian graph.
From scale invariance to Lorentz symmetry
Sibiryakov, Sergey
2014-01-01
It is shown that a unitary translationally invariant field theory in (1+1) dimensions satisfying isotropic scale invariance, standard assumptions about the spectrum of states and operators and the requirement that signals propagate with finite velocity possesses an infinite dimensional symmetry given by one or a product of several copies of conformal algebra. In particular, this implies presence of one or several Lorentz groups acting on the operator algebra of the theory.
On Lorentz invariants in relativistic magnetic reconnection
Yang, Shu-Di; Wang, Xiao-Gang
2016-08-01
Lorentz invariants whose nonrelativistic correspondences play important roles in magnetic reconnection are discussed in this paper. Particularly, the relativistic invariant of the magnetic reconnection rate is defined and investigated in a covariant two-fluid model. Certain Lorentz covariant representations for energy conversion and magnetic structures in reconnection processes are also investigated. Furthermore, relativistic measures for topological features of reconnection sites, particularly magnetic nulls and separatrices, are analyzed.
On some applications of invariant manifolds
Institute of Scientific and Technical Information of China (English)
Xi-Yun Hou; Lin Liu; Yu-Hui Zhao
2011-01-01
Taking transfer orbits of a collinear libration point probe, a lunar probe and an interplanetary probe as examples, some applications of stable and unstable invariant manifolds of the restricted three-body problem are discussed. Research shows that transfer energy is not necessarily conserved when invariant manifolds are used. For the cases in which the transfer energy is conserved, the cost is a much longer transfer time.
Symmetry, Invariance and Ontology in Physics and Statistics
Directory of Open Access Journals (Sweden)
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.
Gauge coupling unification in a classically scale invariant model
Haba, Naoyuki; Ishida, Hiroyuki; Takahashi, Ryo; Yamaguchi, Yuya
2016-02-01
There are a lot of works within a class of classically scale invariant model, which is motivated by solving the gauge hierarchy problem. In this context, the Higgs mass vanishes at the UV scale due to the classically scale invariance, and is generated via the Coleman-Weinberg mechanism. Since the mass generation should occur not so far from the electroweak scale, we extend the standard model only around the TeV scale. We construct a model which can achieve the gauge coupling unification at the UV scale. In the same way, the model can realize the vacuum stability, smallness of active neutrino masses, baryon asymmetry of the universe, and dark matter relic abundance. The model predicts the existence vector-like fermions charged under SU(3) C with masses lower than 1 TeV, and the SM singlet Majorana dark matter with mass lower than 2.6 TeV.
Gauge coupling unification in a classically scale invariant model
Haba, Naoyuki; Takahashi, Ryo; Yamaguchi, Yuya
2015-01-01
There are a lot of works within a class of classically scale invariant model, which is motivated by solving the gauge hierarchy problem. In this context, the Higgs mass vanishes at the UV scale due to the classically scale invariance, and is generated via the Coleman-Weinberg mechanism. Since the mass generation should occur not so far from the electroweak scale, we extend the standard model only around the TeV scale. We construct a model which can achieve the gauge coupling unification at the UV scale. In the same way, the model can realize the vacuum stability, smallness of active neutrino masses, baryon asymmetry of the universe, and dark matter relic abundance. The model predicts the existence vector-like fermions charged under $SU(3)_C$ with masses lower than $1\\,{\\rm TeV}$, and the SM singlet Majorana dark matter with mass lower than $2.6\\,{\\rm TeV}$.
Exact invariants and adiabatic invariants of dynamical system of relative motion
Institute of Scientific and Technical Information of China (English)
Chen Xiang-Wei; Wang Xin-Min; Wang Ming-Quan
2004-01-01
Based on the theory of symmetries and conserved quantities, the exact inwriants and adiabatic inwriants of a dynamical system of relative motion are studied. The perturbation to symmetries for the dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
Shift-invariant target in allocation problems.
Mandal, Saumen; Biswas, Atanu
2014-07-10
We provide a template for finding target allocation proportions in optimal allocation designs where the target will be invariant for both shifts in location and scale of the response distributions. One possible application of such target allocation proportions is to carry out a response-adaptive allocation. While most of the existing designs are invariant for any change in scale of the underlying distributions, they are not location invariant in most of the cases. First, we indicate this serious flaw in the existing literature and illustrate how this lack of location invariance makes the performance of the designs very poor in terms of allocation for any drastic change in location, such as the changes from degrees centigrade to degrees Fahrenheit. We illustrate that unless a target allocation is location invariant, it might lead to a completely irrelevant and useless target for allocation. Then we discuss how such location invariance can be achieved for general continuous responses. We illustrate the proposed method using some real clinical trial data. We also indicate the possible extension of the procedure for more than two treatments at hand and in the presence of covariates.
Helicity is the only integral invariant of volume-preserving transformations.
Enciso, Alberto; Peralta-Salas, Daniel; de Lizaur, Francisco Torres
2016-02-23
We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional I defined on exact divergence-free vector fields of class C(1) on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that I is invariant under arbitrary volume-preserving diffeomorphisms if and only if it is a function of the helicity.
Test of Lorentz invariance in β decay of polarized 20Na
Sytema, A.; van den Berg, J. E.; Böll, O.; Chernowitz, D.; Dijck, E. A.; Grasdijk, J. O.; Hoekstra, S.; Jungmann, K.; Mathavan, S. C.; Meinema, C.; Mohanty, A.; Müller, S. E.; Noordmans, J. P.; Nuñez Portela, M.; Onderwater, C. J. G.; Pijpker, C.; Timmermans, R. G. E.; Vos, K. K.; Willmann, L.; Wilschut, H. W.
2016-08-01
Background: Lorentz invariance is key in our understanding of nature, yet relatively few experiments have tested Lorentz invariance in weak interactions. Purpose: Our goal is to obtain limits on Lorentz-invariance violation in weak interactions, in particular rotational invariance in β decay. Method: We search for a dependence of the lifetime of 20Na nuclei on the nuclear spin direction. Such directional dependence would be evidence for Lorentz-invariance violation in weak interactions. A difference in lifetime between nuclei that are polarized in the east and west direction is searched for. This difference is maximally sensitive to the rotation of the Earth, while the sidereal dependence is free from most systematic errors. Results: The experiment sets a limit of 2 ×10-4 at 90% C.L. on the amplitude of the sidereal variation of the relative lifetime differences, an improvement by a factor 15 compared to an earlier result. Conclusions: No significant violation of Lorentz invariance is found. The result sets limits on parameters of theories describing Lorentz-invariance violation.
Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
Eldering, J
2012-01-01
We prove a persistence result for noncompact normally hyperbolic invariant manifolds in the setting of Riemannian manifolds of bounded geometry. Bounded geometry of the ambient manifold is a crucial assumption required to control the uniformity of all estimates throughout the proof. The $C^{k,\\alpha}$-smoothness result is optimal with respect to the spectral gap condition involved. The core of the persistence proof is based on the Perron method. In the process we derive new results on noncompact submanifolds in bounded geometry: a uniform tubular neighborhood theorem and uniform smooth approximation of a submanifold. The submanifolds considered are assumed to be uniformly $C^k$ bounded in an appropriate sense.
Teleparallel Conformal Invariant Models induced by Kaluza-Klein Reduction
Geng, Chao-Qiang
2016-01-01
We study the extensions of teleparallism in the Kaluza-Klein (KK) scenario by writing the analogous form to the torsion scalar $T_{\\text{NGR}}$ in terms of the corresponding antisymmetric tensors, given by $T_{\\text{NGR}} = a\\,T_{ijk} \\, T^{ijk} + b\\,T_{ijk} \\,T^{kji} + c\\,T^{j}{}_{ji} \\, T^{k}{}_{k}{}^{i}$, in the four-dimensional New General Relativity (NGR) with arbitrary coefficients $a$, $b$ and $c$. After the KK dimensional reduction, the Lagrangian in the Einstein-frame can be realized by taking $2a+b+c=0$ with the ghost-free condition $c\\leq0$ for the one-parameter family of teleparallelism. We demonstrate that the conformal invariant gravity models can be constructed by the requirement of $2a+b+4c=0$ or $2a+b=0$. In particular, this conformal gravity is described on the Weyl-Cartan geometry $Y_4$ with the ghost-free condition $c>0$. We also consider the weak field approximation and discuss the non-minimal coupled term of the scalar current and torsion vector. For the conformal invariant models with $...
Invariant Object Recognition Based on Extended Fragments
Directory of Open Access Journals (Sweden)
Evgeniy eBart
2012-08-01
Full Text Available Visual appearance of natural objects is profoundly affected by viewing conditions such as viewpoint and illumination. Human subjects can nevertheless compensate well for variations in these viewing conditions. The strategies that the visual system uses to accomplish this are largely unclear. Previous computational studies have suggested that in principle, certain types of object fragments (rather than whole objects can be used for invariant recognition. However, whether the human visual system is actually capable of using this strategy remains unknown. Here, we show that human observers can achieve illumination invariance by using object fragments that carry the relevant information. To determine this, we have used novel, but naturalistic, 3-D visual objects called ‘digital embryos’. Using novel instances of whole embryos, not fragments, we trained subjects to recognize individual embryos across illuminations. We then tested the illumination-invariant object recognition performance of subjects using fragments. We found that the performance was strongly correlated with the mutual information (MI of the fragments, provided that MI value took variations in illumination into consideration. This correlation was not attributable to any systematic differences in task difficulty between different fragments. These results reveal two important principles of invariant object recognition. First, the subjects can achieve invariance at least in part by compensating for the changes in the appearance of small local features, rather than of whole objects. Second, the subjects do not always rely on generic or pre-existing invariance of features (i.e., features whose appearance remains largely unchanged by variations in illumination, and are capable of using learning to compensate for appearance changes when necessary. These psychophysical results closely fit the predictions of earlier computational studies of fragment-based invariant object recognition.
Invariants of solvable rigid Lie algebras up to dimension 8
Energy Technology Data Exchange (ETDEWEB)
Campoamor-Stursberg, Rutwig [Depto Geometria y Topologia, Fac. CC Matematicas UCM, Madrid (Spain)]. E-mail: rutwig@nfssrv.mat.ucm.es
2002-08-02
The invariants of all complex solvable rigid Lie algebras up to dimension 8 are computed. Moreover we show, for rank 1 solvable algebras, some criteria to deduce the non-existence of nontrivial invariants or the existence of fundamental sets of invariants formed by rational functions of the Casimir invariants of the associated nilradical. (author)
Invariants of 3-Manifolds derived from finite dimensional hopf algebras
Kauffman, L H; Louis H Kauffman; David E Radford
1994-01-01
Abstract: This paper studies invariants of 3-manifolds derived from certain fin ite dimensional Hopf algebras. The invariants are based on right integrals for these algebras. It is shown that the resulting class of invariants is distinct from the class of Witten-Reshetikhin-Turaev invariants.
Cubic surfaces and their invariants: Some memories of Raymond Stora
Bauer, Michel
2016-11-01
Cubic surfaces embedded in complex projective 3-space are a classical illustration of the use of old and new methods in algebraic geometry. Recently, they made their appearance in physics, and in particular aroused the interest of Raymond Stora, to the memory of whom these notes are dedicated, and to whom I'm very much indebted. Each smooth cubic surface has a rich geometric structure, which I review briefly, with emphasis on the 27 lines and the combinatorics of their intersections. Only elementary methods are used, relying on first order perturbation/deformation theory. I then turn to the study of the family of cubic surfaces. They depend on 20 parameters, and the action of the 15 parameter group SL4 (C) splits the family in orbits depending on 5 parameters. This takes us into the realm of (geometric) invariant theory. I review briefly the classical theorems on the structure of the ring of polynomial invariants and illustrate its many facets by looking at a simple example, before turning to the already involved case of cubic surfaces. The invariant ring was described in the 19th century. I show how to retrieve this description via counting/generating functions and character formulae.
The fundamental theorem via derived Morita invariance, localization, and A^1-homotopy invariance
Tabuada, Goncalo
2011-01-01
We prove that every functor defined on dg categories, which is derived Morita invariant, localizing, and A^1-homotopy invariant, satisfies the fundamental theorem. As an application, we recover in a unified and conceptual way, Weibel and Kassel's fundamental theorems in homotopy algebraic K-theory, and periodic cyclic homology, respectively.
The First Fundamental Theorem of Invariant Theory for the Orthosymplectic Supergroup
Lehrer, G. I.; Zhang, R. B.
2016-08-01
We give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of Atiyah, Bott and Patodi to the supergroup context. We use methods from super-algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space. In this way, super Schur-Weyl-Brauer duality is established between the orthosymplectic supergroup of superdimension (m|2n) and the Brauer algebra with parameter m - 2n. The result may be interpreted either in terms of the group scheme OSp(V) over C, where V is a finite dimensional super space, or as a statement about the orthosymplectic Lie supergroup over the infinite dimensional Grassmann algebra {Λ} . We take the latter point of view here, and also state a corresponding theorem for the orthosymplectic Lie superalgebra, which involves an extra invariant generator, the super-Pfaffian.
The First Fundamental Theorem of Invariant Theory for the Orthosymplectic Supergroup
Lehrer, G. I.; Zhang, R. B.
2017-01-01
We give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of Atiyah, Bott and Patodi to the supergroup context. We use methods from super-algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space. In this way, super Schur-Weyl-Brauer duality is established between the orthosymplectic supergroup of superdimension ( m|2 n) and the Brauer algebra with parameter m - 2 n. The result may be interpreted either in terms of the group scheme OSp( V) over C, where V is a finite dimensional super space, or as a statement about the orthosymplectic Lie supergroup over the infinite dimensional Grassmann algebra {Λ}. We take the latter point of view here, and also state a corresponding theorem for the orthosymplectic Lie superalgebra, which involves an extra invariant generator, the super-Pfaffian.
Forgoston, Eric; Yecko, Philip; Schwartz, Ira B
2011-01-01
We consider the problem of stochastic prediction and control in a time-dependent stochastic environment, such as the ocean, where escape from an almost invariant region occurs due to random fluctuations. We determine high-probability control-actuation sets by computing regions of uncertainty, almost invariant sets, and Lagrangian Coherent Structures. The combination of geometric and probabilistic methods allows us to design regions of control that provide an increase in loitering time while minimizing the amount of control actuation. We show how the loitering time in almost invariant sets scales exponentially with respect to the control actuation, causing an exponential increase in loitering times with only small changes in actuation force. The result is that the control actuation makes almost invariant sets more invariant.
Invariant properties of representations under cleft extensions
Institute of Scientific and Technical Information of China (English)
2007-01-01
The main aim of this paper is to give the invariant properties of representations of algebras under cleft extensions over a semisimple Hopf algebra. Firstly, we explain the concept of the cleft extension and give a relation between the cleft extension and the crossed product which is the approach we depend upon. Then, by making use of them, we prove that over an algebraically closed field k, for a finite dimensional Hopf algebra H which is semisimple as well as its dual H*, the representation type of an algebra is an invariant property under a finite dimensional H-cleft extension . In the other part, we still show that over an arbitrary field k, the Nakayama property of a k-algebra is also an invariant property under an H -cleft extension when the radical of the algebra is H-stable.
Some Cosmological Consequences of Weyl Invariance
Álvarez, Enrique; Herrero-Valea, Mario
2015-01-01
Some Weyl invariant cosmological models are examined in the framework of dilaton gravity. It will be shown that When the FRW ansatz for the spacetime metric is assumed, the Ward identity for conformal invariance guarantees that the gravitational equations hold whenever the matter EM do so. It follows that any scale factor can solve the theory provided a non-trivial profile for a dilaton field. In particular, accelerated expansion is a natural solution to the full set of equations. When two or more scalar fields are coupled to gravity in a Weyl invariant way there is an antigravity phase in which the effective Newton constant is negative. This phase is separated from the atractive gravity phase by a strong coupling barrier. Nevertheles, and perhaps contradicting na\\"ive beliefs, the antigravity phase does not imply accelerated expansion, although it is compatible with it.
Weyl's Scale Invariance And The Standard Model
Gold, B S
2005-01-01
This paper is an extension of the work by Dr. Subhash Rajpoot, Ph.D. and Dr. Hitoshi Nishino, Ph.D. I introduce Weyl's scale invariance as an additional local symmetry in the standard model of electroweak interactions. An inevitable consequence is the introduction of general relativity coupled to scalar fields a la Dirac and an additional vector particle called the Weylon. This paper shows that once Weyl's scale invariance is broken, the phenomenon (a) generates Newton's gravitational constant GN and (b) triggers spontaneous symmetry breaking in the normal manner resulting in masses for the conventional fermions and bosons. The scale at which Weyl's sclale symmetry breaks is of order Planck mass. If right-handed neutrinos are also introduced, their absence at present energy scales is attributed to their mass which is tied to the scale where scale invariance breaks.
Scale-Invariant Random Spatial Networks
Aldous, David J
2012-01-01
Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\\em exactly} invariant under Euclidean scaling? This requires working in the continuum plane. We introduce an axiomatization of a class of processes we call {\\em scale-invariant random spatial networks}, whose primitives are routes between each pair of points in the plane. We prove that one concrete model, based on minimum-time routes in a binary hierarchy of roads with different speed limits, satisfies the axioms, and note informally that two other constructions (based on Poisson line processes and on dynamic proximity graphs) are expected also to satisfy the axioms. We initiate study of structure theory and summary statistics for general processes in this class.
Gravity as the breakdown of conformal invariance
Amelino-Camelia, Giovanni; Gubitosi, Giulia; Magueijo, Joao
2015-01-01
We propose that at the beginning of the universe gravity existed in a limbo either because it was switched off or because it was only conformally coupled to all particles. This picture can be reverse-engineered from the requirement that the cosmological perturbations be (nearly) scale-invariant without the need for inflation. It also finds support in recent results in quantum gravity suggesting that spacetime becomes two-dimensional at super-Planckian energies. We advocate a novel top-down approach to cosmology based on the idea that gravity and the Big Bang Universe are relics from the mechanism responsible for breaking the fundamental conformal invariance. Such a mechanism should leave clear signatures in departures from scale-invariance in the primordial power spectrum and the level of gravity waves generated.
Rainbow gravity and scale-invariant fluctuations
Amelino-Camelia, Giovanni; Gubitosi, Giulia; Magueijo, Joao
2013-01-01
We re-examine a recently proposed scenario where the deformed dispersion relations associated with a flow of the spectral dimension to a UV value of 2 leads to a scale-invariant spectrum of cosmological fluctuations, without the need for inflation. In that scenario Einstein gravity was assumed. The theory displays a wavelength-dependent speed of light but by transforming to a suitable "rainbow frame" this feature can be removed, at the expense of modifying gravity. We find that the ensuing rainbow gravity theory is such that gravity switches off at high energy (or at least leads to a universal conformal coupling). This explains why the fluctuations are scale-invariant on all scales: there is no horizon scale as such. For dispersion relations that do not lead to exact scale invariance we find instead esoteric inflation in the rainbow frame. We argue that these results shed light on the behaviour of gravity under the phenomenon of dimensional reduction.
Phylogenetic invariants for group-based models
Donten-Bury, Maria
2010-01-01
In this paper we investigate properties of algebraic varieties representing group-based phylogenetic models. We give the (first) example of a nonnormal general group-based model for an abelian group. Following Kaie Kubjas we also determine some invariants of group-based models showing that the associated varieties do not have to be deformation equivalent. We propose a method of generating many phylogenetic invariants and in particular we show that our approach gives the whole ideal of the claw tree for 3-Kimura model under the assumption of the conjecture of Sturmfels and Sullivant. This, combined with the results of Sturmfels and Sullivant, would enable to determine all phylogenetic invariants for any tree for 3-Kimura model and possibly for other group-based models.
Gauge-invariant massive BF models
Energy Technology Data Exchange (ETDEWEB)
Bizdadea, Constantin; Saliu, Solange-Odile [University of Craiova, Department of Physics, Craiova (Romania)
2016-02-15
Consistent interactions that can be added to a free, Abelian gauge theory comprising a BF model and a finite set of massless real scalar fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of analyticity in the coupling constant, Lorentz covariance, spacetime locality, and Poincare invariance, supplemented with the requirement of the preservation of the number of derivatives on each field with respect to the free theory, we see that the deformation procedure leads to two classes of gauge-invariant interacting theories with a mass term for the BF vector field A{sub μ} with U(1) gauge invariance. In order to derive this result we have not used the Higgs mechanism based on spontaneous symmetry breaking. (orig.)
Gauge-invariant massive BF models
Bizdadea, Constantin; Saliu, Solange-Odile
2016-02-01
Consistent interactions that can be added to a free, Abelian gauge theory comprising a BF model and a finite set of massless real scalar fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of analyticity in the coupling constant, Lorentz covariance, spacetime locality, and Poincaré invariance, supplemented with the requirement of the preservation of the number of derivatives on each field with respect to the free theory, we see that the deformation procedure leads to two classes of gauge-invariant interacting theories with a mass term for the BF vector field A_{μ } with U(1) gauge invariance. In order to derive this result we have not used the Higgs mechanism based on spontaneous symmetry breaking.
Gauge-invariant massive BF models
Bizdadea, Constantin
2015-01-01
Consistent interactions that can be added to a free, Abelian gauge theory comprising a BF model and a finite set of massless real scalar fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of analyticity in the coupling constant, Lorentz covariance, spacetime locality, Poincare invariance, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure leads to two classes of gauge-invariant interacting theories with a mass term for the BF vector field $A_{\\mu }$ with U(1) gauge invariance. In order to derive this result we have not used the Higgs mechanism based on spontaneous symmetry breaking.
INVARIANTS UNDER STABLE EQUIVALENCES OF MORITA TYPE
Institute of Scientific and Technical Information of China (English)
Li Fang; Sun Longgang
2012-01-01
The aim of this article is to study some invariants of associative algebras under stable equivalences of Morita type.First of all,we show that,if two finite-dimensional selfinjective k-algebras are stably equivalent of Morita type,then their orbit algebras are isomorphic.Secondly,it is verified that the quasitilted property of an algebra is invariant under stable equivalences of Morita type.As an application of this result,it is obtained that if an algebra is of finite representation type,then its tilted property is invariant under stable equivalences of Morita type; the other application to partial tilting modules is given in Section 4. Finally,we prove that when two finite-dimensional k-algebras are stably equivalent of Morita type,their repetitive algebras are also stably equivalent of Morita type under certain conditions.
Resonance varieties and Dwyer-Fried invariants
Suciu, Alexander I
2011-01-01
The Dwyer-Fried invariants of a finite cell complex X are the subsets \\Omega^i_r(X) of the Grassmannian of r-planes in H^1(X,\\Q) which parametrize the regular \\Z^r-covers of X having finite Betti numbers up to degree i. In previous work, we showed that each \\Omega-invariant is contained in the complement of a union of Schubert varieties associated to a certain subspace arrangement in H^1(X,\\Q). Here, we identify a class of spaces for which this inclusion holds as equality. For such "straight" spaces X, all the data required to compute the \\Omega-invariants can be extracted from the resonance varieties associated to the cohomology ring H^*(X,\\Q). In general, though, translated components in the characteristic varieties affect the answer.
Burning invariant manifolds in reactive front propagation
Mahoney, John; Mitchell, Kevin; Solomon, Tom
2011-01-01
We present theory and experiments on the dynamics of reaction fronts in a two-dimensional flow composed of a chain of alternating vortices. Inspired by the organization of passive transport by invariant manifolds, we introduce burning invariant manifolds (BIMs), which act as one-sided barriers to front propagation. The BIMs emerge from the theory when the advection-reaction- diffusion system is recast as an ODE for reaction front elements. Experimentally, we demonstrate how these BIMs can be measured and compare their behavior with simulation. Finally, a topological BIM formalism yields a maximum front propagation speed.
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
Automatic CP invariance and flavor symmetry
Dutta, G; Dutta, Gautam; Joshipura, Anjan S
1996-01-01
The approximate conservation of CP can be naturally understood if it arises as an automatic symmetry of the renormalizable Lagrangian. We present a specific realistic example with this feature. In this example, the global Peccei-Quinn symmetry and gauge symmetries of the model make the renormalizable Lagrangian CP invariant but allow non zero hierarchical masses and mixing among the three generations. The left-right and a horizontal U(1)_H symmetry is imposed to achieve this. The non-renormalizable interactions invariant under these symmetries violate CP whose magnitude can be in the experimentally required range if U(1)_H is broken at very high, typically, near the grand unification scale.
Holonomy invariance, orbital resonances, and kilohertz QPOs
Abramowicz, M A; Kluzniak, W; Thampan, A V; Wallinder, F
2002-01-01
Quantized orbital structures are typical for many aspects of classical gravity (Newton's as well as Einstein's). The astronomical phenomenon of orbital resonances is a well-known example. Recently, Rothman, Ellis and Murugan (2001) discussed quantized orbital structures in the novel context of a holonomy invariance of parallel transport in Schwarzschild geometry. We present here yet another example of quantization of orbits, reflecting both orbital resonances and holonomy invariance. This strong-gravity effect may already have been directly observed as the puzzling kilohertz quasi-periodic oscillations (QPOs) in the X-ray emission from a few accreting galactic black holes and several neutron stars.
SU(2) Invariants of Symmetric Qubit States
Sirsi, Swarnamala
2011-01-01
Density matrix for N-qubit symmetric state or spin-j state (j = N/2) is expressed in terms of the well known Fano statistical tensor parameters. Employing the multiaxial representation [1], wherein a spin-j density matrix is shown to be characterized by j(2j+1) axes and 2j real scalars, we enumerate the number of invariants constructed out of these axes and scalars. These invariants are explicitly calculated in the particular case of pure as well as mixed spin-1 state.
On adiabatic invariant in generalized Galileon theories
Ema, Yohei; Mukaida, Kyohei; Nakayama, Kazunori
2015-01-01
We consider background dynamics of generalized Galileon theories in the context of inflation, where gravity and inflaton are non-minimally coupled to each other. In the inflaton oscillation regime, the Hubble parameter and energy density oscillate violently in many cases, in contrast to the Einstein gravity with minimally coupled inflaton. However, we find that there is an adiabatic invariant in the inflaton oscillation regime in any generalized Galileon theory. This adiabatic invariant is useful in estimating the expansion law of the universe and also the particle production rate due to the oscillation of the Hubble parameter.
On inequalities among some cardinal invariants
Directory of Open Access Journals (Sweden)
Joanna Jureczko
2016-03-01
Full Text Available The strong sequences method was introduced by B. A. Efimov, as a useful method for proving famous theorems in dyadic spaces: Marczewski theorem on cellularity, Shanin theorem on a calibre and Esenin-Volpin theorem. In this paper there will be considered strong sequences on a set with arbitrary relation as generalization of a partially ordered set. In this paper there will be introduced a new cardinal invariant s-length of the strong sequence and investigated relations among s and other well known invariants like: saturation, boundeness, density, calibre.
Unitarily invariant norms related to factors
Fang, Junsheng
2007-01-01
Let $\\M$ be a semi-finite von Neumann algebra and $\\J(\\M)$ be the set of operators in $\\M$ with finite range projections. In this paper we obtain a representation theorem for unitarily invariant norms on $\\J(\\M)$ of semi-finite factors $\\M$ in terms of Ky Fan norms. As an application, we prove that the class of unitarily invariant norms on $\\J(\\M)$ of a type ${\\rm II}\\sb \\infty$ (or type ${\\rm I}\\sb \\infty$) factor $\\M$ coincides with the class of symmetric gauge norms on $\\J(L^\\infty[0,\\infty))$ (or $\\J(l^\\infty(\
Comments on Holography with Broken Lorentz Invariance
Gordeli, Ivan
2009-01-01
Recently a family of solutions of the Einstein equations in backgrounds with broken Lorentz invariance was found ArXiv:0712.1136. We show that the gravitational solution recently obtained by Kachru, Liu and Mulligan in ArXiv:0808.1725 is a part of the former solution which was derived earlier in the framework of extra dimensional theories. We show how the energy-momentum and Einstein tensors are related and establish a correspondence between parameters which govern Lorentz invariance violation. At the end we speculate on relations between the RG flow of a boundary theory and asymptotic behavior of gravitational solutions in the bulk.
Scaling theory of {{{Z}}_{2}} topological invariants
Chen, Wei; Sigrist, Manfred; Schnyder, Andreas P.
2016-09-01
For inversion-symmetric topological insulators and superconductors characterized by {{{Z}}2} topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling schemes renormalize either the phase gradient or the second derivative of the Pfaffian of the time-reversal operator, through which the renormalization group flow of the driving energy parameter can be obtained. The Pfaffian near the time-reversal invariant momentum is revealed to display a universal critical behavior for a great variety of models examined.
Hidden invariance of the free classical particle
García, S
1993-01-01
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.
Affine Invariant Character Recognition by Progressive Removing
Iwamura, Masakazu; Horimatsu, Akira; Niwa, Ryo; Kise, Koichi; Uchida, Seiichi; Omachi, Shinichiro
Recognizing characters in scene images suffering from perspective distortion is a challenge. Although there are some methods to overcome this difficulty, they are time-consuming. In this paper, we propose a set of affine invariant features and a new recognition scheme called “progressive removing” that can help reduce the processing time. Progressive removing gradually removes less feasible categories and skew angles by using multiple classifiers. We observed that progressive removing and the use of the affine invariant features reduced the processing time by about 60% in comparison to a trivial one without decreasing the recognition rate.
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; 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 or applications in quantum optics and quantum information.
Invariant measures on multimode quantum Gaussian states
Energy Technology Data Exchange (ETDEWEB)
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.
Application of invariant embedding to reactor physics
Shimizu, Akinao; Parsegian, V L
1972-01-01
Application of Invariant Embedding to Reactor Physics describes the application of the method of invariant embedding to radiation shielding and to criticality calculations of atomic reactors. The authors intend to show how this method has been applied to realistic problems, together with the results of applications which will be useful to shielding design. The book is organized into two parts. Part A deals with the reflection and transmission of gamma rays by slabs. The chapters in this section cover topics such as the reflection and transmission problem of gamma rays; formulation of the probl
Rotationally Invariant Singular Solutions to the Kapustin-Witten Equations
He, Siqi
2015-01-01
In the present paper, we find a system of non-linear ODEs that gives rotationally invariant solutions to the Kapustin-Witten equations in 4-dimensional Euclidean space. We explicitly solve these ODEs in some special cases and find decaying rational solutions, which provide solutions to the Kapustin-Witten equations. The imaginary parts of the solutions are singular. By rescaling, we can prove the existence of the Uhlenbeck bubbling phenomenon for these solutions. In addition, for any integer $k$, we can construct a 5$|k|$ dimensional family of $C^1$ solutions to the Kapustin-Witten equations on Euclidean space, again with singular imaginary parts.
Momentum Routing Invariance in Extended QED: Assuring Gauge Invariance Beyond Tree Level
Vieira, A R; Sampaio, Marcos
2015-01-01
We address the study of gauge invariance in the Standard Model Extension which encompasses all Lorentz-violating terms originated by spontaneous symmetry breaking at the Planck scale. In particular, we fully evaluate Ward identities involving two and three point functions and derive the conditions which assure gauge invariance of the electromagnetic sector of the Standard Model Extension at one-loop. We show that momentum routing invariance is sufficient to fix arbitrary and regularization dependent parameters intrinsic to perturbation theory in the diagrams involved. A scheme which judiciously collects finite but undetermined quantum corrections is employed, a particularly subtle issue in the presence of $\\gamma_5$ matrices.
Knot invariants and higher representation theory II: the categorification of quantum knot invariants
Webster, Ben
2010-01-01
We construct knot invariants categorifying the quantum knot variants for all representations of quantum groups. We show that these invariants coincide with previous invariants defined by Khovanov for sl_2 and sl_3 and by Mazorchuk-Stroppel and Sussan for sl_n. We also suggest an approach to showing that these knot homologies are functorial. Our technique uses categorifications of the tensor products of integrable representations of Kac-Moody algebras and quantum groups, constructed a prequel to this paper. In particular, we construct functors on these categorifying the action of the braiding and duality of quantum group representations. These categories are based on the pictorial approach of Khovanov and Lauda.
Modular invariance and the fusion algebra
Dijkgraaf, Robbert; Verlinde, Erik
1988-12-01
We discuss the relation between modular transformations and the fusion algebra, and explain its proof. It is shown that the existence of off-diagonal modular invariant partition functions imply the existence of a non-trivial automorphism of the fusion algebra. This is illustrated using the SU(2) affine models.
Invariant algebraic surfaces for a virus dynamics
Valls, Claudia
2015-08-01
In this paper, we provide a complete classification of the invariant algebraic surfaces and of the rational first integrals for a well-known virus system. In the proofs, we use the weight-homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations.
On Integrable Quantum Group Invariant Antiferromagnets
Cuerno, R; Gómez, C
1992-01-01
A new open spin chain hamiltonian is introduced. It is both integrable (Sklyanin`s type $K$ matrices are used to achieve this) and invariant under ${\\cal U}_{\\epsilon}(sl(2))$ transformations in nilpotent irreps for $\\epsilon^3=1$. Some considerations on the centralizer of nilpotent representations and its representation theory are also presented.
Topologically Left Invariant Means on Semigroup Algebras
Indian Academy of Sciences (India)
Ali Ghaffari
2005-11-01
Let $M(S)$ be the Banach algebra of all bounded regular Borel measures on a locally compact Hausdorff semitopological semigroup with variation norm and convolution as multiplication. We obtain necessary and sufficient conditions for $M(S)^∗$ to have a topologically left invariant mean.
Shape invariant potentials in SUSY quantum mechanics
Directory of Open Access Journals (Sweden)
A. Dadkhah
2007-12-01
Full Text Available We give a brief review on the known shape invariant potentials. We derive the all of them by introducing a general superpotential with two constant and four variable parameters. Finally we examine those potentials which lead to the equally-spaced energy spectrum for the Klein-Gordon equation.
Emergent Lorentz invariance in fermion sector
Directory of Open Access Journals (Sweden)
Kharuk Ivan
2016-01-01
Full Text Available By using holographic description of strongly interacting field theories we show that under common assumptions Lorentz invariance emerges as an effective low–energy symmetry of the theory, despite fundamental theory at hight energies being Lorentz–violating. We consider fermions sector and show that the notion of chirality also automatically arises in the infrared.
Diffeomorphism Invariant Theories and Vector Supersymmetry
Piguet, O
2000-01-01
Einstein gravity in the Palatini first order formalism is shown to possess a vector supersymmetry of the type encountered in the topological gauge theories. A peculiar feature of the gravitationel theory is the link of this vector supersymmetry with the field equation of motion of the Faddeev-Popov ghost associated to diffeomorphism invariance.
q-exchangeability via quasi-invariance
Gnedin, A.V.; Olshanski, G.
2010-01-01
For positive q is not 1, the q-exchangeability of an infinite random word is introduced as quasi-invariance under permutations of letters, with a special cocycle which accounts for inversions in the word. This framework allows us to extend the q-analog of de Finetti’s theorem for binary sequences—se
Average sampling theorems for shift invariant subspaces
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.
Invariant properties between stroke features in handwriting
Teulings, H L; Schomaker, L R
1993-01-01
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 paramete
Constitutive laws, tensorial invariance and chocolate cake
Energy Technology Data Exchange (ETDEWEB)
Rundle, J.B.; Passman, S.L.
1982-01-01
Although constitutive modeling is a well-established branch of mathematics which has found wide industrial application, geophysicists often do not take full advantage of its known results. We present a synopsis of the theory of constitutive modeling, couched in terms of the simple material, which has been extensively studied and is complex enough to include most of the correct models proposed to describe the behavior of geological materials. Critical in the development of the theory are various invariance requirements, the principal ones being coordinate invariance, peer group invariance (isotropy), and frame-indifference. Each places distinct restrictions on constitutive equations. A noncomprehensive list of properly invariant and commonly used constitutive equations is given. To exemplify use of the equations, we consider two problems in detail: steady extension, which models the commonly performed constant strain rate triaxial test, and simple shearing. We note that each test is so restricted kinematically that only the most trivial aspects of material behavior are manifested in these tests, no matter how complex the material. Furthermore, the results of one test do not generally determine the results of the other.
Invariant metric for nonlinear symplectic maps
Indian Academy of Sciences (India)
Govindan Rangarajan; Minita Sachidanand
2002-03-01
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 demonstrate that the performance of a nonlinear Hamiltonian system is enhanced.
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
Electromagnetic fields with vanishing scalar invariants
Ortaggio, Marcello
2015-01-01
We determine the class of $p$-forms $F$ which possess vanishing scalar invariants (VSI) at arbitrary order in a $n$-dimensional spacetime. Namely, we prove that $F$ is VSI if and only if it is of type N, its multiple null direction $l$ is "degenerate Kundt", and $\
Invariance Properties for General Diagnostic Classification Models
Bradshaw, Laine P.; Madison, Matthew J.
2016-01-01
In item response theory (IRT), the invariance property states that item parameter estimates are independent of the examinee sample, and examinee ability estimates are independent of the test items. While this property has long been established and understood by the measurement community for IRT models, the same cannot be said for diagnostic…
A functional LMO invariant for Lagrangian cobordisms
DEFF Research Database (Denmark)
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...
η-Invariant and Flat Vector Bundles
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
We present an alternate definition of the mod Z component of the AtiyahPatodi-Singer η invariant associated to (not necessary unitary) fiat vector bundles, which identifies explicitly its real and imaginary parts. This is done by combining a deformation of flat connections introduced in a previous paper with the analytic continuation procedure appearing in the original article of Atiyah, Parodi and Singer.
Invariant functionals in higher-spin theory
Vasiliev, M. A.
2017-03-01
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.
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
Joint Local Quasinilpotence and Common Invariant Subspaces
Indian Academy of Sciences (India)
A Fernández Valles
2006-08-01
In this article we obtain some positive results about the existence of a common nontrivial invariant subspace for -tuples of not necessarily commuting operators on Banach spaces with a Schauder basis. The concept of joint quasinilpotence plays a basic role. Our results complement recent work by Kosiek [6] and Ptak [8].
Multipartite invariant states. II. Orthogonal symmetry
Chruściński, Dariusz; Kossakowski, Andrzej
2006-06-01
We construct a class of multipartite states possessing orthogonal symmetry. This new class contains multipartite states which are invariant under the action of local unitary operations introduced in our preceding paper [Phys. Rev. A 73, 062314 (2006)]. We study basic properties of multipartite symmetric states: separability criteria and multi-PPT conditions.
Testing Lorentz and CPT invariance with neutrinos
Diaz, Jorge S
2016-01-01
Neutrino experiments can be considered sensitive tools to test Lorentz and CPT invariance. Taking advantage of the great variety of neutrino experiments, including neutrino oscillations, weak decays, and astrophysical neutrinos, the generic experimental signatures of the breakdown of these fundamental symmetries in the neutrino sector are presented.
Kontsevich integral for knots and Vassiliev invariants
Dunin-Barkowski, P.; Sleptsov, A.; Smirnov, A.
2013-01-01
We review quantum field theory approach to the knot theory. Using holomorphic gauge, we obtain the Kontsevich integral. It is explained how to calculate Vassiliev invariants and coefficients in Kontsevich integral in a combinatorial way which can be programmed on a computer. We discuss experimental
Complete Cohomologies and Some Homological Invariants
Institute of Scientific and Technical Information of China (English)
Javad Asadollahi; Shokrollah Salarian
2007-01-01
There is a complete cohomology theory developed over a commutative noetherian ring in which injectives take the role of projectives in Vogel's construction of complete cohomology theory. We study the interaction between this complete cohomology, that is referred to as I-complete cohomology, and Vogel's one and give some sufficient conditions for their equivalence. Using I-complete functors, we assign a new homological invariant to any finitely generated module over an arbitrary commutative noetherian local ring,that would generalize Auslander's delta invariant. We generalize the results about the δ-invariant to arbitrary rings and give a sufficient condition for the vanishing of this new invariant. We also introduce an analogue of the notion of the index of a Gorenstein local ring, introduced by Auslander, for arbitrary local rings and study its behavior under flat extensions of local rings. Finally, we study the connection between the index and Loewy length of a local ring and generalize the main result of [11] to arbitrary rings.
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 us
Adaptivity and group invariance in mathematical morphology
Roerdink, Jos B.T.M.
2009-01-01
The standard morphological operators are (i) defined on Euclidean space, (ii) based on structuring elements, and (iii) invariant with respect to translation. There are several ways to generalise this. One way is to make the operators adaptive by letting the size or shape of structuring elements depe
Testing local Lorentz invariance with gravitational waves
Energy Technology Data Exchange (ETDEWEB)
Kostelecký, V. Alan, E-mail: kostelec@indiana.edu [Physics Department, Indiana University, Bloomington, IN 47405 (United States); Mewes, Matthew [Physics Department, California Polytechnic State University, San Luis Obispo, CA 93407 (United States)
2016-06-10
The effects of local Lorentz violation on dispersion and birefringence of gravitational waves are investigated. The covariant dispersion relation for gravitational waves involving gauge-invariant Lorentz-violating operators of arbitrary mass dimension is constructed. The chirp signal from the gravitational-wave event GW150914 is used to place numerous first constraints on gravitational Lorentz violation.
Nonlinear Differential Systems with Prescribed Invariant Sets
DEFF Research Database (Denmark)
Sandqvist, Allan
1999-01-01
We present a class of nonlinear differential systems for which invariant sets can be prescribed.Moreover,we show that a system in this class can be explicitly solved if a certain associated linear homogeneous system can be solved.As a simple application we construct a plane autonomous system having...
Scale invariant density perturbations from cyclic cosmology
Frampton, Paul Howard
2016-04-01
It is shown how quantum fluctuations of the radiation during the contraction era of a comes back empty (CBE) cyclic cosmology can provide density fluctuations which re-enter the horizon during the subsequent expansion era and at lowest order are scale invariant, in a Harrison-Zel’dovich-Peebles sense. It is necessary to be consistent with observations of large scale structure.
Permutation centralizer algebras and multimatrix invariants
Mattioli, Paolo; Ramgoolam, Sanjaye
2016-03-01
We introduce a class of permutation centralizer algebras which underly the combinatorics of multimatrix gauge-invariant observables. One family of such noncommutative algebras is parametrized by two integers. Its Wedderburn-Artin decomposition explains the counting of restricted Schur operators, which were introduced in the physics literature to describe open strings attached to giant gravitons and were subsequently used to diagonalize the Gaussian inner product for gauge invariants of two-matrix models. The structure of the algebra, notably its dimension, its center and its maximally commuting subalgebra, is related to Littlewood-Richardson numbers for composing Young diagrams. It gives a precise characterization of the minimal set of charges needed to distinguish arbitrary matrix gauge invariants, which are related to enhanced symmetries in gauge theory. The algebra also gives a star product for matrix invariants. The center of the algebra allows efficient computation of a sector of multimatrix correlators. These generate the counting of a certain class of bicoloured ribbon graphs with arbitrary genus.
Global invariant methods for object recognition
Stiller, Peter F.
2001-11-01
The general problem of single-view recognition is central to man image understanding and computer vision tasks; so central, that it has been characterized as the holy grail of computer vision. In previous work, we have shown how to approach the general problem of recognizing three dimensional geometric configurations (such as arrangements of lines, points, and conics) from a single two dimensional view, in a manner that is view independent. Our methods make use of advanced mathematical techniques from algebraic geometry, notably the theory of correspondences, and a novel equivariant geometric invariant theory. The machinery gives us a way to understand the relationship that exists between the 3D geometry and its residual in a 2D image. This relationship is shown to be a correspondence in the technical sense of algebraic geometry. Exploiting this, one can compute a set of fundamental equations in 3D and 2D invariants which generate the ideal of the correspondence, and which completely describe the mutual 3D/2D constraints. We have chosen to call these equations object/image equations. They can be exploited in a number of ways. For example, from a given 2D configuration, we can determine a set of non-linear constraints on the geometric invariants of a 3D configurations capable of imaging to the given 2D configuration (features on an object), we can derive a set of equations that constrain the images of that object; helping us to determine if that particular object appears in various images. One previous difficulty has been that the usual numerical geometric invariants get expressed as rational functions of the geometric parameters. As such they are not always defined. This leads to degeneracies in algorithms based on these invariants. We show how to replace these invariants by certain toric subvarieties of Grassmannians where the object/image equations become resultant like expressions for the existence of a non- trivial intersection of these subvarieties with
Dimensional analysis using toric ideals: primitive invariants.
Atherton, Mark A; Bates, Ronald A; Wynn, Henry P
2014-01-01
Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units [Formula: see text] etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Buckingham approach. Some textbook examples are revisited and the full set of primitive invariants found. First, a worked example based on convection is introduced to recall the Buckingham method, but using computer algebra to obtain an integer [Formula: see text] matrix from the initial integer [Formula: see text] matrix holding the exponents for the derived quantities. The [Formula: see text] matrix defines the dimensionless variables. But, rather than this integer linear algebra approach it is shown how, by staying with the power product representation, the full set of invariants (dimensionless groups) is obtained directly from the toric ideal defined by [Formula: see text]. One candidate for the set of invariants is a simple basis of the toric ideal. This, although larger than the rank of [Formula: see text], is typically not unique. However, the alternative Graver basis is unique and defines a maximal set of invariants, which are primitive in a simple sense. In addition to the running example four examples are taken from: a windmill, convection, electrodynamics and the hydrogen atom. The method reveals some named invariants. A selection of computer algebra packages is used to show the considerable ease with which both a simple basis and a Graver basis can be found.
Dimensional analysis using toric ideals: primitive invariants.
Directory of Open Access Journals (Sweden)
Mark A Atherton
Full Text Available Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units [Formula: see text] etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Buckingham approach. Some textbook examples are revisited and the full set of primitive invariants found. First, a worked example based on convection is introduced to recall the Buckingham method, but using computer algebra to obtain an integer [Formula: see text] matrix from the initial integer [Formula: see text] matrix holding the exponents for the derived quantities. The [Formula: see text] matrix defines the dimensionless variables. But, rather than this integer linear algebra approach it is shown how, by staying with the power product representation, the full set of invariants (dimensionless groups is obtained directly from the toric ideal defined by [Formula: see text]. One candidate for the set of invariants is a simple basis of the toric ideal. This, although larger than the rank of [Formula: see text], is typically not unique. However, the alternative Graver basis is unique and defines a maximal set of invariants, which are primitive in a simple sense. In addition to the running example four examples are taken from: a windmill, convection, electrodynamics and the hydrogen atom. The method reveals some named invariants. A selection of computer algebra packages is used to show the considerable ease with which both a simple basis and a Graver basis can be found.
Li, Chonghong
2012-01-01
We study cosmological perturbation spectra using the dynamical equations of gauge invariant perturbations with a generalized blue/red-shift term. Combined with the power-law index of cosmological background, {\
Directory of Open Access Journals (Sweden)
José Antonio Martínez García
2009-04-01
Full Text Available ResumenEsta investigación presenta un nuevo método para el estudio de la invarianza de escala que complementa otros métodos existentes, lo que contribuye a realizar un análisis ecléctico y multifocal de un problema importante en la investigación de marketing, y en particular en la investigación de servicios deportivos. Este método está basado en la utilización del cálculo integral y tiene una sencilla interpretación geométrica. Se describen y comparan varios procedimientos para testar la invarianza de escala, y se realiza un re-análisis de la investigación de Martínez y Martínez (2008b sobre la percepción de calidad del consumidor de servicios deportivos. Los resultados muestran cómo existen diferencias sobre las conclusiones originales de estos autores. De este modo, las escalas de siete opciones de respuesta sí son invariantes, mientras que la de cinco opciones no lo son. Finalmente, se discuten las bondades y las limitaciones del método integral, abogando por la triangulación estadística para dar robustez a los resultados empíricos.AbstractThis research introduces a new method to analyse scale invariance, which overcomes some shortcomings of other procedures. Under an eclectic perspective, this method must help to provide insights in the marketing research discipline, and specifically in the sports service management. The method is grounded on the use of definite integrals to compute the area between two functions. In addition, several procedures for testing scale invariance are depicted and compared. An empirical application is achieved by re-analysing the study of Martínez & Martínez (2008b on perceived quality in sports services. Results shows that misleading conclusions were derived from the original study of those authors. Finally, advantages and shortcomings of the new method are discussed.
Cardinal invariants associated with Fubini product of ideals
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We prove some results displaying the relationship between Fubini product of ideals and its factor ideals, and study a partial order using the cardinal invariant of the continuum. The relationships among transitive cardinal invariants of abelian group are also investigated.
Markov invariants, plethysms, and phylogenetics (the long version)
Sumner, J G; Jermiin, L S; Jarvis, P D
2008-01-01
We explore model based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, although we establish a commonality in some special cases. We show that the simplest Markov invariant forms the foundation of the Log-Det distance measure. We take as our primary tool group representation theory, and show that it provides a general framework for analysing Markov processes on trees. From this algebraic perspective, the inherent symmetries of these processes become apparent, and focusing on plethysms, we are able to define Markov invariants and give existence proofs. We give an explicit technique for constructing the invariants, valid for any number of character states and taxa. For phylogenetic trees with three and four leaves, we demonstrate that the corresponding Markov invariants can be fruitfully exploited in applied phylogenetic studies.
An approach to dark energy problem through linear invariants
Institute of Scientific and Technical Information of China (English)
Jeong Ryeol Choi
2011-01-01
The time evolution of vacuum energy density is investigated in the coherent states of inflationary universe using a linear invariant approach. The linear invariants we derived are represented in terms of annihilation operators. On account of the fact that
A perturbative and gauge invariant treatment of gravitational wave memory
Bieri, Lydia
2013-01-01
We present a perturbative treatment of gravitational wave memory. The coordinate invariance of Einstein's equations leads to a type of gauge invariance in perturbation theory. As with any gauge invariant theory, results are more clear when expressed in terms of manifestly gauge invariant quantities. Therefore we derive all our results from the perturbed Weyl tensor rather than the perturbed metric. We derive gravitational wave memory for the Einstein equations coupled to a general energy-momentum tensor that reaches null infinity.
Conformal invariance and Hojman conserved quantities of canonical Hamilton systems
Institute of Scientific and Technical Information of China (English)
Liu Chang; Liu Shi-Xing; Mei Feng-Xiang; Guo Yong-Xin
2009-01-01
This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invariance being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.
Embedded graph invariants in Chern-Simons theory
Major, Seth A.
1998-01-01
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 slight generalization of the variational method, lowest-order results for invariants for arbitrary valence graphs are derived; gauge invariant operators are introduced; and some higher order ...
Form invariance for systems of generalized classical mechanics
Institute of Scientific and Technical Information of China (English)
张毅; 梅凤翔
2003-01-01
This paper presents a form invariance of canonical equations for systems of generalized classical mechanics. According to the invariance of the form of differential equations of motion under the infinitesimal transformations, this paper gives the definition and criterion of the form invariance for generalized classical mechanical systems, and establishes relations between form invariance, Noether symmetry and Lie symmetry. At the end of the paper, an example is given to illustrate the application of the results.
Image indexing using composite color and shape invariant features
Gevers, Th.; Smeulders, A.W.M.
1998-01-01
New sets of color models are proposed for object recognition invariant to a change in view point, object geometry and illumination. Further, computational methods are presented to combine color and shape invariants to produce a high-dimensional invariant feature set for discriminatory object recogni
Extended Weyl Invariance in a Bimetric Model
Hassan, S F; von Strauss, Mikael
2015-01-01
We revisit a particular ghost-free bimetric model which is related to both partial masslessness as well conformal gravity. Its equations of motion can be recast in the form of a perturbative series in derivatives which exhibits a remarkable amount of structure. In a perturbative (but fully nonlinear) analysis, we demonstrate that the equations are invariant under scalar gauge transformations up to six orders in derivatives, the lowest-order term being a local Weyl scaling of the metrics. More specifically, we develop a procedure for constructing terms in the gauge transformations order by order in the perturbative framework. This allows us to derive sufficient conditions for the existence of a gauge symmetry at the nonlinear level. It is explicitly demonstrated that these conditions are satisfied at the first relevant order and, consequently, the equations are gauge invariant up to six orders in derivatives. We furthermore show that the model propagates six instead of seven degrees of freedom not only around ...
Scale-invariant nonlinear optics in gases
Heyl, C M; Miranda, M; Louisy, M; Kovacs, K; Tosa, V; Balogh, E; Varjú, K; L'Huillier, A; Couairon, A; Arnold, C L
2015-01-01
Nonlinear optical methods are becoming ubiquitous in many areas of modern photonics. They are, however, often limited to a certain range of input parameters, such as pulse energy and average power, since restrictions arise from, for example, parasitic nonlinear effects, damage problems and geometrical considerations. Here, we show that many nonlinear optics phenomena in gaseous media are scale-invariant if spatial coordinates, gas density and laser pulse energy are scaled appropriately. We develop a general scaling model for (3+1)-dimensional wave equations, demonstrating the invariant scaling of nonlinear pulse propagation in gases. Our model is numerically applied to high-order harmonic generation and filamentation as well as experimentally verified using the example of pulse post-compression via filamentation. Our results provide a simple recipe for up-or downscaling of nonlinear processes in gases with numerous applications in many areas of science.
Non-boost-invariant dissipative hydrodynamics
Florkowski, Wojciech; Strickland, Michael; Tinti, Leonardo
2016-01-01
The one-dimensional non-boost-invariant evolution of the quark-gluon plasma, presumably produced during the early stages of heavy-ion collisions, is analyzed within the frameworks of viscous and anisotropic hydrodynamics. We neglect transverse dynamics and assume homogeneous conditions in the transverse plane but, differently from Bjorken expansion, we relax longitudinal boost invariance in order to study the rapidity dependence of various hydrodynamical observables. We compare the results obtained using several formulations of second-order viscous hydrodynamics with a recent approach to anisotropic hydrodynamics, which treats the large initial pressure anisotropy in a non-perturbative fashion. The results obtained with second-order viscous hydrodynamics depend on the particular choice of the second-order terms included, which suggests that the latter should be included in the most complete way. The results of anisotropic hydrodynamics and viscous hydrodynamics agree for the central hot part of the system, ho...
Gauge Invariant Perturbations of the Schwarzschild Spacetime
Chen, Hector; Whiting, Bernard F
2016-01-01
Beginning with the pioneering work of Regge and Wheeler (Phys. Rev. 108, 1957), there have been many studies of perturbations away from the Schwarzschild spacetime background. In particular several authors (e.g. Moncrief, Ann. Phys 88, 1974) have investigated gauge invariant quantities of the Regge-Wheeler (RW) gauge. Steven Detweiler also investigated perturbations of Schwarzschild in his own gauge, which he denoted the "easy (EZ) gauge", and which he was in the process of adapting for use in the second-order self-force problem. We present here a compilation of some of his working results, arising from notes for which there seems to have been no manuscript in preparation. In particular, we list the gauge invariant quantities used by Detweiler, as well as explain the process by which he found them.
Field redefinition invariance in quantum field theory
Apfeldorf, K M; Apfeldorf, Karyn M; Ordonez, Carlos
1994-01-01
We investigate the consequences of field redefinition invariance in quantum field theory by carefully performing nonlinear transformations in the path integral. We first present a ``paradox'' whereby a 1+1 freemassless scalar theory on a Minkowskian cylinder is reduced to an effectively quantum mechanical theory. We perform field redefinitions both before and after reduction to suggest that one should not ignore operator ordering issues in quantum field theory. We next employ a discretized version of the path integral for a free massless scalar quantum field in d dimensions to show that beyond the usual jacobian term, an infinite series of divergent ``extra'' terms arises in the action whenever a nonlinear field redefinition is made. The explicit forms for the first couple of these terms are derived. We evaluate Feynman diagrams to illustrate the importance of retaining the extra terms, and conjecture that these extra terms are the exact counterterms necessary to render physical quantities invariant under fie...
Mutation, Witten Index, and Quiver Invariant
Kim, Heeyeon; Yi, Piljin
2015-01-01
We explore Seiberg-like dualities, or mutations, for ${\\cal N}=4$ 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.
Unimodular Gravity with Pseudo-scale Invariance
Jain, Pankaj; Singh, Naveen K
2011-01-01
We consider a model of gravity and matter fields which is invariant only under unimodular general coordinate transformations (GCT). The determinant of the metric is treated as a separate field which transforms as a scalar under unimodular GCT. Furthermore we also demand that the theory obeys pseudo-scale invariance. We study the implications of the resulting theory. We solve the resulting field equations for a sperically symmetric system in vacuum. We find that the resulting solution contains an additional term in comparison to the standard Schwarzchild solution. We also study the cosmological implications of the model. We find that both in case of radiation and matter dominated universe it predicts an accelerated expansion. Furthermore the model does not admit a cosmological constant, thereby solving its fine tuning problem.
Autonomous Ship Classification By Moment Invariants
Zvolanek, Budimir
1981-12-01
An algorithm to classify ships from images generated by an infrared (IR) imaging sensor is described. The algorithm is based on decision-theoretic classification of Moment Invariant Functions (MIFs). The MIFs are computed from two-dimensional gray-level images to form a feature vector uniquely describing the ship. The MIF feature vector is classified by a Distance-Weighted k-Nearest Neighbor (D-W k-NN) decision rule to identify the ship type. Significant advantage of the MIF feature extraction coupled with D-W k-NN classification is the invariance of the classification accuracies to ship/sensor orienta-tion - aspect, depression, roll angles and range. The accuracy observed from a set of simulated IR test images reveals a good potential of the classifier algorithm for ship screening.
On degree bounds for separating invariants
Kohls, Martin
2010-01-01
Let a group $G$ act on a finite dimensional vector space $V$ over an algebraically closed field $K$ of characteristic $p$. Then $\\beta_{\\sep}(G)$ is the minimal number such that, for any $V$, the invariants of degree less or equal than this number have the same separating properties as the whole invariant ring $K[V]^{G}$. Derksen and Kemper have shown $\\beta_{\\sep}(G)\\le |G|$. We show $\\beta_{\\sep}(G)=|G|$ for $p$-groups and cyclic groups, and $\\beta_{\\sep}(G)=\\infty$ for infinite unipotent groups. We also show $\\beta_{\\sep}(G)\\le \\beta_{\\sep}(G/N)\\beta_{\\sep}(N)$ for a normal divisor $N$ of finite index.
Multipole invariants and non-Gaussianity
Land, K; Land, Kate; Magueijo, Joao
2004-01-01
We propose a framework for separating the information contained in the CMB multipoles, $a_{\\ell m}$, into its algebraically independent components. Thus we cleanly separate information pertaining to the power spectrum, non-Gaussianity and preferred axis effects. The formalism builds upon the recently proposed multipole vectors (Copi, Huterer & Starkman 2003; Schwarz & al 2004; Katz & Weeks 2004), and we elucidate a few features regarding these vectors, namely their lack of statistical independence for a Gaussian random process. In a few cases we explicitly relate our proposed invariants to components of the $n$-point correlation function (power spectrum, bispectrum). We find the invariants' distributions using a mixture of analytical and numerical methods. We also evaluate them for the co-added WMAP first year map.
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 ...
Near Scale Invariance with Modified Dispersion Relations
Armendariz-Picon, C
2006-01-01
We describe a novel mechanism to seed a nearly scale invariant spectrum of adiabatic perturbations during a non-inflationary stage. It relies on a modified dispersion relation that contains higher powers of the spatial momentum of matter perturbations. We implement this idea in the context of a massless scalar field in an otherwise perfectly homogeneous universe. The couplings of the field to background scalars and tensors give rise to the required modification of its dispersion relation, and the couplings of the scalar to matter result in an adiabatic primordial spectrum. This work is meant to explicitly illustrate that it is possible to seed nearly scale invariant primordial spectra without inflation, within a conventional expansion history.
The relativistic virial theorem and scale invariance
Gaite, Jose
2013-01-01
The virial theorem is related to the dilatation properties of bound states. This is realized, in particular, by the Landau-Lifshitz formulation of the relativistic virial theorem, in terms of the trace of the energy-momentum tensor. We construct a Hamiltonian formulation of dilatations in which the relativistic virial theorem naturally arises as the condition of stability against dilatations. A bound state becomes scale invariant in the ultrarelativistic limit, in which its energy vanishes. However, for very relativistic bound states, scale invariance is broken by quantum effects and the virial theorem must include the energy-momentum tensor trace anomaly. This quantum field theory virial theorem is directly related to the Callan-Symanzik equations. The virial theorem is applied to QED and then to QCD, focusing on the bag model of hadrons. In massless QCD, according to the virial theorem, 3/4 of a hadron mass corresponds to quarks and gluons and 1/4 to the trace anomaly.
Role of Lifshitz Invariants in Liquid Crystals
Directory of Open Access Journals (Sweden)
Amelia Sparavigna
2009-06-01
Full Text Available The interaction between an external action and the order parameter, via a dependence described by a so-called Lifshitz invariant, is very important to determine the final configuration of liquid crystal cells. The external action can be an electric field applied to the bulk or the confinement due to free surfaces or cell walls. The Lifshitz invariant includes the order parameter in the form of an elastic strain. This coupling between elastic strains and fields, inserted in a Landau-Ginzburg formalism, is well known and gives rise to striction effects causing undulations in the director configuration. We want to discuss here the role of Lifshitz coupling terms, following an approach similar to that introduced by Dzyaloshinskii for magnetic materials. Case studies on nematics in planar and cylindrical cells are also proposed.
Revisiting R-invariant Direct Gauge Mediation
Chiang, Cheng-Wei; Ibe, Masahiro; Yanagida, Tsutomu T
2015-01-01
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 \\mu-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 \\mu-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 3\\sigma excess of the Z+jets+$E_T^{\\rm miss}$ events reported by the ATLAS Collaboration.
Spherical harmonics, invariant theory and Maxwell's poles
Dowker, J S
2008-01-01
I discuss the relation between harmonic polynomials and invariant theory and show that homogeneous, harmonic polynomials correspond to ternary forms that are apolar to a base conic (the absolute). The calculation of Schlesinger that replaces such a form by a polarised binary form is reviewed. It is suggested that Sylvester's theorem on the uniqueness of Maxwell's pole expression for harmonics is renamed the Clebsch-Sylvester theorem. The relation between certain constructs in invariant theory and angular momentum theory is enlarged upon and I resurrect the Joos--Weinberg matrices. Hilbert's projection operators are considered and their generalisations by Story and Elliott are related to similar, more recent constructions in group theory and quantum mechanics, the ternary case being equivalent to SU(3).
More Modular Invariant Anomalous U(1) Breaking
Gaillard, Mary Katherin; 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 Kahler 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 o...
Scale-invariant geometric random graphs
Xie, Zheng
2015-01-01
We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to an influence zone that depends on node position in space and time, capturing the heterogeneity and increased specialization found in growing networks. Through calculations and numerical simulations we explore the consequences of scale-invariance for geometric graphs generated this way. Our analysis reveals a dichotomy between scale-free and Poisson distributions of in- and out-degree, the existence of a random number of hub nodes, high clustering, and unusual percolation behaviour. Moreover, we show how these properties provide a good fit to those of empirically observed web graphs.
Complete Pick Positivity and Unitary Invariance
Bhattacharya, Angshuman
2009-01-01
The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel $k_S(z,w) = (1 - z\\ow)^{-1}$ for $|z|, |w| < 1$, by means of $(1/k_S)(T,T^*) \\ge 0$, we consider an arbitrary open connected domain $\\Omega$ in $\\BC^n$, a complete Nevanilinna-Pick kernel $k$ on $\\Omega$ and a tuple $T = (T_1, ..., T_n)$ of commuting bounded operators on a complex separable Hilbert space $\\clh$ such that $(1/k)(T,T^*) \\ge 0$. For a complete Pick kernel the $1/k$ functional calculus makes sense in a beautiful way. It turns out that the model theory works very well and a characteristic function can be associated with $T$. Moreover, the characteristic function then is a complete unitary invariant for a suitable class of tuples $T$.
Fast forward to the classical adiabatic invariant
Jarzynski, Christopher; Patra, Ayoti; Subaşı, Yiğit
2016-01-01
We show how the classical action, an adiabatic invariant, can be preserved under non-adiabatic conditions. Specifically, for a time-dependent Hamiltonian $H = p^2/2m + U(q,t)$ in one degree of freedom, and for an arbitrary choice of action $I_0$, we construct a "fast-forward" potential energy function $V_{\\rm FF}(q,t)$ that, when added to $H$, guides all trajectories with initial action $I_0$ to end with the same value of action. We use this result to construct a local dynamical invariant $J(q,p,t)$ whose value remains constant along these trajectories. We illustrate our results with numerical simulations. Finally, we sketch how our classical results may be used to design approximate quantum shortcuts to adiabaticity.
Real object recognition using moment invariants
Indian Academy of Sciences (India)
Muharrem Mercimek; Kayhan Gulez; Tarik Veli Mumcu
2005-12-01
Moments and functions of moments have been extensively employed as invariant global features of images in pattern recognition. In this study, a flexible recognition system that can compute the good features for high classiﬁcation of 3-D real objects is investigated. For object recognition, regardless of orientation, size and position, feature vectors are computed with the help of nonlinear moment invariant functions. Representations of objects using two-dimensional images that are taken from different angles of view are the main features leading us to our objective. After efﬁcient feature extraction, the main focus of this study, the recognition performance of classiﬁers in conjunction with moment–based feature sets, is introduced.
Invariant line and crystallography of HCP→BCC precipitation
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
［1］Luo,C.P.,Weatherly,G.C.,The precipitation behavior of a Zr-2.5%wt.%pct Nb alloy,Metall.Trans.,1988,19A: 1153-1162.［2］Lang,J.M.,Dahmen,U.,Westmacott,K.H.,The origin of Mo2C precipitate morphology in molybdenum,Phys.Stat.Sol.(a),1983,75: 409-420.［3］Luo,C.P.,Dahmen,U.,Wesmacott,K.H.,Morphology,and crestallography of precipitates in a Cu-0.33wt.%Cr alloy,Acta Metall.,1994,42,1923-1932.［4］Luo,C.P.,Wu,D.X.,Xiao,X.L.,Crystallography of the BCCFCC transformation in a Cr-10wt.%Ni alloy,Abstract (Letters) of Science and Technology of China,1996,2 (10): 121-127.［5］Xiao,X.L.,Luo,C.P.,Nie,J.F.,Morphology and crystallography of β-(Mg17Al12) precipitate in an AZ91 magnesium-aluminum alloy,Acta Metall.Sinica,2001,in press.［6］Wechsler,M.S.,Lieberman,D.S.,Read,T.A.,On the theory of formation of martensite,Trans.Am.Inst.Min.Engrs.,1953,197: 1503-1515.［7］Bowles,J.S.,Mackenzine,J.K.,The crystallography of martensite transformation,Acta Metall.,1954,2: 129-147.［8］Wayman,C.M.,Introduction to the Crystallography of Martensitic Transformations,New York: Macmillan Co.,1964.76-80.［9］Luo,C.P.,Weatherly,G.C.,The invariant line and precipitation in a Ni-25wt.%Cr alloy,Acta Metall.,1987,35: 1963-1972.［10］Luo,C.P.,Xiao,X.L.,Wu,D.X.,Invariant line strain theory and its application to the crystallography of solid-state phase transformations,Progress in Natural Science,2000,10(3): 193-200.［11］Luo,C.P.,Weatherly,G.C.,The interphase boundary structure of precipitates in a Ni-Cr alloy,Philos.Mag.,1988,58: 445-462.［12］Luo,C.P.,Dahmen,U.,Interface structure of faceted lath-shaped Cr precipitates in a Cu-0.33wt.%Cr alloy,Acta Metall.,1998,46: 2063-2081.
Ghost Equations and Diffeomorphism Invariant Theories
Piguet, O
2000-01-01
Four-dimensional Einstein gravity in the Palatini first order formalism is shown to possess a vector supersymmetry of the same type as found in the topological theories for Yang-Mills fields. A peculiar feature of the gravitational theory, characterized by diffeomorphism invariance, is a direct link of vector supersymmetry with the field equation of motion for the Faddeev-Popov ghost of diffeomorphisms.
O(3)-invariant tunneling in general relativity
Energy Technology Data Exchange (ETDEWEB)
Berezin, V.A.; Tkachev, I.I.; Kuzmin, V.A.
1988-06-30
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.
Overcomplete steerable pyramid filters and rotation invariance
1994-01-01
A given (overcomplete) discrete oriented pyramid may be converted into a steerable pyramid by interpolation. We present a technique for deriving the optimal interpolation functions (otherwise called 'steering coefficients'). The proposed scheme is demonstrated on a computationally efficient oriented pyramid, which is a variation on the Burt and Adelson (1983) pyramid. We apply the generated steerable pyramid to orientation-invariant texture analysis in order to demonstrate its excellent rotat...
Conformal Invariance and Quantum Nature of Particles
Salehi, H; Salehi, Hadi; Bisabr, Yousef
2003-01-01
We investigate a gravitational model whose vacuum sector is invariant under conformal transformations. In this model, matter is taken to be coupled with a metric which is different but conformally related to the metric appearing explicitly in the vacuum sector. It is then show that the effect of a conformal symmetry breaking would lead to a particle concept. In particular, a correspondence between quantum nature of the particles and the gravitational interaction of matter is established.
Invariant holomorphic extension in several complex variables
Institute of Scientific and Technical Information of China (English)
ZHOU; Xiangyu
2006-01-01
Two fundamental problems on the invariant holomorphic extensions have been posed, which are naturally arose from our solution of the extended future tube conjecture and closely and deeply related to the general theory of Stein manifolds due to Cartan-Serre. In this paper, the relationship is presented between the two problems, the motivation of considering the problems, and the methods to approach the problems. We have also posed some questions and conjectures related to this two problems.
CLASSIFICATION OF MPSK SIGNALS USING CUMULANT INVARIANTS
Institute of Scientific and Technical Information of China (English)
Yang Shaoquan; Chen Weidong
2002-01-01
A new feature based on higher order statistics is proposed for classification of MPSKsignals, which is invariant with respect to translation (shift), scale and rotation transforms of MPSK signal constellations, and can suppress additive color or white Gaussian noise. Application of the new feature to classification of MPSK signals, at medium signal-to-noise ratio with specified sample size, results in high probability of correct identification. Finally, computer simulations and comparisons with existing algorithms are given.
CLASSIFICATION OF MPSK SIGNALS USING CUMULANT INVARIANTS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A new feature based on higher order statistics is proposed for classification of MPSK signals, which is invariant with respect to translation(shift),scale and rotation transforms of MPSK signal constellations, and can suppress additive color or white Gaussian noise.Application of the new feature to classification of MPSK signals, at medium signal-to-noise ratio with specified sample size, results in high probability of correct identification.Finally, computer simulations and comparisons with existing algorithms are given.
Switched Systems With Multiple Invariant Sets
2015-05-06
Motor Control Mode Figure 1: Schematic of mode switching with non-equilibrium limit sets. with σ = 1. For a positive rate of convergence λ > 0, it...while utilizing steady-state control strategies for static balancing or tasks requiring fine motor control . Mode-switching also implicates a large...Switched Systems With Multiple Invariant SetsI Michael Dorothy, Soon-Jo Chung∗ Department of Aerospace Engineering, University of Illinois at Urbana
Conformally Invariant Spinorial Equations in Six Dimensions
Batista, Carlos
2016-01-01
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for some of these equations are established. Moreover, in the course of the article, some useful identities involving the curvature of the spinorial connection are attained and a digression about harmonic forms and more general massless fields is made.
Test of CP invariance in decay
Energy Technology Data Exchange (ETDEWEB)
Chauvat, P.; Erhan, S.; Hayes, K.; Smith, A.M.; Meritet, L.; Reyrolle, M.; Vazeille, F.; Bonino, R.; Cousins, R.; Kroll, I.J.; Medinnis, M.; Schlein, P.E.; Sherwood, P.; Zweizig, J.G.; Alitti, J.; Bloch-Devaux, B.; Cheze, J.B.; Montag, A.; Pichard, B.; Zsembery, J.; R608 Collaboration.
1985-11-21
In an experiment at the CERN intersecting storage rings with s = 31 GeV, we have measured P, the product of asymmetry parameter and polarization, for anti 's and 's produced in anti pp interactions, respectively. The ratio, ( P)anti /( P)sub( ) = -1.04+-0.29, is consistent with the value -1, and constitutes the first test of CP invariance in decay. (orig.).
Efficient Learning of Sparse Invariant Representations
Gregor, Karol
2011-01-01
We propose a simple and efficient algorithm for learning sparse invariant representations from unlabeled data with fast inference. When trained on short movies sequences, the learned features are selective to a range of orientations and spatial frequencies, but robust to a wide range of positions, similar to complex cells in the primary visual cortex. We give a hierarchical version of the algorithm, and give guarantees of fast convergence under certain conditions.
Gromov-Witten Invariants and Quantum Cohomology
Indian Academy of Sciences (India)
Amiya Mukherjee
2006-11-01
This article is an elaboration of a talk given at an international conference on Operator Theory, Quantum Probability, and Noncommutative Geometry held during December 20--23, 2004, at the Indian Statistical Institute, Kolkata. The lecture was meant for a general audience, and also prospective research students, the idea of the quantum cohomology based on the Gromov-Witten invariants. Of course there are many important aspects that are not discussed here.
Invariant indentities in the Heisenberg algebra
Turbiner, A V
1994-01-01
Polynomial relations between the generators of q--deformed Heisenberg algebra invariant under the quantization and q-deformation are discovered. One of the examples of such relations is the following: if two elements a and b, obeying the relation \\[ ab - q ba = p, \\] where p, q are any complex numbers, then for any p,q and natural n \\[ (aba)^n = a^n b^n a^n \\
Nonequilibrium invariant measure under heat flow.
Delfini, Luca; Lepri, Stefano; Livi, Roberto; Politi, Antonio
2008-09-19
We provide an explicit representation of the nonequilibrium invariant measure for a chain of harmonic oscillators with conservative noise in the presence of stationary heat flow. By first determining the covariance matrix, we are able to express the measure as the product of Gaussian distributions aligned along some collective modes that are spatially localized with power-law tails. Numerical studies show that such a representation applies also to a purely deterministic model, the quartic Fermi-Pasta-Ulam chain.
q-Exchangeability via quasi-invariance
Gnedin, Alexander
2009-01-01
For positive q, the q-exchangeability is introduced as quasi-invariance under permutations, with a special cocycle. This allows us to extend the q-analogue of de Finetti's theorem for binary sequences (arXiv:0905.0367) to the general real-valued sequences. In contrast to the classical case with q=1, the order on the reals plays for the q-analogues a significant role. An explicit construction of ergodic q-exchangeable measures involves a random shuffling of the set N={1,2,..} by iteration of the geometric choice. For q distinct from 1, the shuffling yields a probability measure Q that is supported by the group of bijections of N, and has the property of quasi-invariance under both left and right multiplications by finite permutations. We establish connections of the q-exchangeability to certain transient Markov chains on the q-Pascal pyramids and to invariant random flags over the Galois fields.
Localization via Automorphisms of the CARs. Local gauge invariance
Grundling, Hendrik
2010-01-01
The classical matter fields are sections of a vector bundle E with base manifold M. The space L^2(E) of square integrable matter fields w.r.t. a locally Lebesgue measure on M, has an important module action of C_b^\\infty(M) on it. This module action defines restriction maps and encodes the local structure of the classical fields. For the quantum context, we show that this module action defines an automorphism group on the algebra A, of the canonical anticommutation relations on L^2(E), with which we can perform the analogous localization. That is, the net structure of the CAR, A, w.r.t. appropriate subsets of M can be obtained simply from the invariance algebras of appropriate subgroups. We also identify the quantum analogues of restriction maps. As a corollary, we prove a well-known "folk theorem," that the algebra A contains only trivial gauge invariant observables w.r.t. a local gauge group acting on E.
Watson-Crick pairing, the Heisenberg group and Milnor invariants.
Gadgil, Siddhartha
2009-07-01
We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.
Watson-Crick pairing, the Heisenberg group and Milnor invariants
Gadgil, Siddhartha
2008-01-01
We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict \\emph{allosteric structures} for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.
Towards a third-order topological invariant for magnetic fields
Hornig, G
2002-01-01
An expression for a third-order link integral of three magnetic fields is presented. It is a topological invariant and therefore an invariant of ideal magnetohydrodynamics. The integral generalizes existing expressions for third-order invariants which are obtained from the Massey triple product, where the three fields are restricted to isolated flux tubes. The derivation and interpretation of the invariant shows a close relationship with the well-known magnetic helicity, which is a second-order topological invariant. Using gauge fields with an SU(2) symmetry, helicity and the new third-order invariant originate from the same identity, an identity which relates the second Chern class and the Chern-Simons three-form. We present an explicit example of three magnetic fields with non-disjunct support. These fields, derived from a vacuum Yang-Mills field with a non-vanishing winding number, possess a third-order linkage detected by our invariant.
Endpoints of invariant mass distribution in SUSY particle decays into massive particles
DiBello, J; Lavini, N; Laurent, T St
2010-01-01
Kinematic limits on an invariant mass distribution of bc-pairs for a three-step decay chain A -> bB -> bcC involving all massive particles are found. It is shown that an application of these limits to a stop quark production at the LHC could reduce significantly Standard Model background contribution.
A geometrical take on invariants of low-dimensional manifolds found by integration
Wintraecken, M.H.M.J.; Vegter, G.
2013-01-01
An elementary geometrical proof of the fact that the Euler characteristic is the only topological invariant of a surface that can be found by integration (using Gauss-Bonnet) is given. A similar method is also applied to three-dimensional manifolds. (C) 2013 Elsevier B.V. All rights reserved.
Scaling symmetry and conserved charge for shape-invariant optical fields
El Gawhary, O.; Severini, S.
2013-01-01
In this work we present an extensive study of the scaling symmetry typical of a paraxial wave theory. In particular, by means of a Lagrangian approach we derive the conservation law and the corresponding generalized charge associated with the scale invariance symmetry. In general, such a conserved c
Alg\\`ebres de Jordan et th\\'eorie des invariants
Blind, Bruno
2009-01-01
If V is a simple complex euclidean Jordan algebra and G the subgroup of GL(V) fixing the determinant of V, we give a unified description of the invariant algebras C[pV]^G, for p not greater than three.
The relativistic invariant Lie algebra for the kinematical observables in quantum space-time
Khrushchov, V V
2003-01-01
The deformation of the canonical algebra for the kinematical observables in Minkowski space has been considered under the condition of Lorentz invariance. A new relativistic invariant algebra depends on the fundamental constants $M$, $L$ and $H$ with the dimensionality of mass, length and action, respectively. In some limit cases the algebra obtained goes over into the well-known Snyder or Yang algebras. In general case the algebra represents a class of Lie algebras, which are either simple algebras, or semidirect sums of simple algebras integrable ones. T and C noninvariance for certain algebras of this class have been elucidated.
Do scale-invariant fluctuations imply the breaking of de Sitter invariance?
Energy Technology Data Exchange (ETDEWEB)
Youssef, A., E-mail: youssef@mathematik.hu-berlin.de [Institut fuer Mathematik und Institut fuer Physik, Humboldt-Universitaet zu Berlin, Johann von Neumann-Haus, Rudower Chaussee 25, 12489 Berlin (Germany)
2013-01-08
The quantization of the massless minimally coupled (mmc) scalar field in de Sitter spacetime is known to be a non-trivial problem due to the appearance of strong infrared (IR) effects. In particular, the scale-invariance of the CMB power-spectrum - certainly one of the most successful predictions of modern cosmology - is widely believed to be inconsistent with a de Sitter invariant mmc two-point function. Using a Cesaro-summability technique to properly define an otherwise divergent Fourier transform, we show in this Letter that de Sitter symmetry breaking is not a necessary consequence of the scale-invariant fluctuation spectrum. We also generalize our result to the tachyonic scalar fields, i.e. the discrete series of representations of the de Sitter group, that suffer from similar strong IR effects.
Bradley, Michael; Ramos, M P Machado
2008-01-01
Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by presenting a simple and transparent complete invariant classification of the conformally flat pure radiation metrics (except plane waves) in such intrinsic coordinates; in particular we confirm that the three apparently non-redundant functions of one variable are genuinely non-redundant, and easily identify the subclasses which admit a Killing and/or a homothetic Killing vector. Most of our results agree with the earlier classification carried out by Skea in the different Koutras-McIntosh coordinates, which required much more involved calculations; but there are some subtle differences. Therefore, we also rework the classification in the Koutras-McIntosh coordinates, and by paying attention to some of the subtleties involving arbitrary functions, we are able to obtain complete a...
Shape invariance and SUSY separation of variables
Directory of Open Access Journals (Sweden)
Ioffe M.V.
2016-01-01
Full Text Available The main ingredients of conventional Supersymmetrical Quantum Mechanics (SUSY QM are presented. The generalization with supercharges of second order in derivatives - Second Order SUSY - is formulated, and the property of shape invariance is defined. The generalization to two-dimensional coordinate space, after using just these two elements of the modern SUSY QM approach, provides the opportunity to solve analytically some two-dimensional problems. Two different procedures of supersymmetrical separation of variables are formulated. They are illustrated by two-dimensional generalization of the Morse model.
Conformal invariance in quantum field theory
Todorov, Ivan T; Petkova, Valentina B
1978-01-01
The present volume is an extended and up-to-date version of two sets of lectures by the first author and it reviews more recent work. The notes aim to present a self-contained exposition of a constructive approach to conformal invariant quantum field theory. Other parts in application of the conformal group to quantum physics are only briefly mentioned. The relevant mathematical material (harmonic analysis on Euclidean conformal groups) is briefly summarized. A new exposition of physical applications is given, which includes an explicit construction of the vacuum operator product expansion for the free zero mass fields.
Invariant Regularization of Supersymmetric Chiral Gauge Theory
Suzuki, H
1999-01-01
We present a regularization scheme which respects the supersymmetry and the maximal background gauge covariance in supersymmetric chiral gauge theories. When the anomaly cancellation condition is satisfied, the effective action in the superfield background field method automatically restores the gauge invariance without counterterms. The scheme also provides a background gauge covariant definition of composite operators that is especially useful in analyzing anomalies. We present several applications: The minimal consistent gauge anomaly; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.
The Axion Mass in Modular Invariant Supergravity
Butter, D; 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).
Broken Lifshitz invariance, spin waves and hydrodynamics
Roychowdhury, Dibakar
2016-01-01
In this paper, based on the basic principles of thermodynamics, we explore the hydrodynamic regime of interacting Lifshitz field theories in the presence of broken rotational invariance. We compute the entropy current and discover new dissipative effects those are consistent with the principle of local entropy production in the fluid. In our analysis, we consider both the parity even as well as the parity odd sector upto first order in the derivative expansion. Finally, we argue that the present construction of the paper could be systematically identified as that of the hydrodynamic description associated with \\textit{spin waves} (away from the domain of quantum criticality) under certain limiting conditions.
Thermodynamic Entropy as a Noether Invariant
Sasa, Shin-ichi; Yokokura, Yuki
2016-04-01
We study a classical many-particle system with an external control represented by a time-dependent extensive parameter in a Lagrangian. We show that thermodynamic entropy of the system is uniquely characterized as the Noether invariant associated with a symmetry for an infinitesimal nonuniform time translation t →t +η ℏβ , where η is a small parameter, ℏ is the Planck constant, β is the inverse temperature that depends on the energy and control parameter, and trajectories in the phase space are restricted to those consistent with quasistatic processes in thermodynamics.
Relevant phylogenetic invariants of evolutionary models
Casanellas, Marta
2009-01-01
Recently there have been several attempts to provide a whole set of generators of the ideal of the algebraic variety associated to a phylogenetic tree evolving under an algebraic model. These algebraic varieties have been proven to be useful in phylogenetics. In this paper we prove that, for phylogenetic reconstruction purposes, it is enough to consider generators coming from the edges of the tree, the so-called edge invariants. This is the algebraic analogous to Buneman's Splits Equivalence Theorem. The interest of this result relies on its potential applications in phylogenetics for the widely used evolutionary models such as Jukes-Cantor, Kimura 2 and 3 parameters, and General Markov models.
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. We analyse briefly the OPERA results and show that they could be reproduced with chameleon models. We suggest that neutrinos emitted radially, at different energies, and observed on the other side of the earth would provide a test of these models.
Gauge Invariance of Thermal Transport Coefficients
Ercole, Loris; Marcolongo, Aris; Umari, Paolo; Baroni, Stefano
2016-10-01
Thermal transport coefficients are independent of the specific microscopic expression for the energy density and current from which they can be derived through the Green-Kubo formula. We discuss this independence in terms of a kind of gauge invariance resulting from energy conservation and extensivity, and demonstrate it numerically for a Lennard-Jones fluid, where different forms of the microscopic energy density lead to different time correlation functions for the heat flux, all of them, however, resulting in the same value for the thermal conductivity.
QCD, conformal invariance and the two Pomerons
Munier, S
1998-01-01
Using the solution of the BFKL equation including the leading and subleading conformal spin components, we show how the conformal invariance underlying the leading log (1/x) expansion of perturbative QCD leads to elastic amplitudes described by two effective Pomeron singularities. One Pomeron is the well-known "hard" BFKL leading singularity while the new one appears from a shift of the higher conformal spin BFKL singularities from subleading to leading position. This new effective singularity is compatible with the "soft" Pomeron and thus, together with the "hard" Pomeron, meets at large $Q^{2}$ the "double Pomeron" solution which has been recently conjectured by Donnachie and Landshoff.
Cobordism invariance of the family index
Carvalho, Catarina
2008-01-01
We give a K-theory proof of the invariance under cobordism of the family index. We consider elliptic pseudodifferential families on a continuous fibre bundle with smooth fibres over a compact base space B, and define a notion of cobordant families using K^1-groups on fibrations with boundary. We show that the index of two such families is the same using properties of the push-forward map in K-theory to reduce it to families on B x R^n.
Weyl invariance and black hole evaporation
Navarro-Salas, J; Talavera, C F
1995-01-01
We consider the semiclassical dynamics of CGHS black holes with a Weyl-invariant effective action for conformal matter. The trace anomaly of Polyakov effective action is converted into the Virasoro anomaly thus leading to the same flux of Hawking radiation. The covariance of semiclassical equations can be restored through a non-local redefinition of the metric-dilaton fields. The resulting theory turns out to be equivalent to the RST model. This provides a mechanism to solve semiclassical equations of 2D dilaton gravity coupled to conformal matter for classically soluble models.
Riccati group invariants of linear hamiltonian systems
Garzia, M. R.; Loparo, K. A.; Martin, C. F.
1983-01-01
The action of the Riccati group on the Riccati differential equation is associated with the action of a subgroup of the symplectic group on a set of hamiltonian matrices. Within this framework various sets of canonical forms are developed for the matrix coefficients of the Riccati differential equation. The canonical forms presented are valid for arbitrary Kronecker indices, and it is shown that the Kronecker indices are invariants for this group action. These canonical forms are useful for studying problems arising in the areas of optimal decentralized control and the spectral theory of optimal control problems.
Green's Functions for Translation Invariant Star Products
Lizzi, Fedele; Vitale, Patrizia
2015-01-01
We calculate the Green functions for a scalar field theory with quartic interactions for which the fields are multiplied with a generic translation invariant star product. Our analysis involves both noncommutative products, for which there is the canonical commutation relation among coordinates, and nonlocal commutative products. We give explicit expressions for the one-loop corrections to the two and four point functions. We find that the phenomenon of ultraviolet/infrared mixing is always a consequence of the presence of noncommuting variables. The commutative part of the product does not have the mixing.
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.
Singular Masas and Measure-Multiplicity Invariant
Mukherjee, Kunal
2011-01-01
In this paper we study relations between the \\emph{left-right-measure} and properties of singular masas. Part of the analysis is mainly concerned with masas for which the \\emph{left-right-measure} is the class of product measure. We provide examples of Tauer masas in the hyperfinite $\\rm{II}_{1}$ factor whose \\emph{left-right-measure} is the class of Lebesgue measure. We show that for each subset $S\\subseteq \\mathbb{N}$, there exist uncountably many pairwise non conjugate singular masas in the free group factors with \\emph{Puk\\'{a}nszky invariant} $S\\cup\\{\\infty\\}$.
Visual Distinctness Determined by Partially Invariant Features
2000-03-01
DISTINCTNESS DETERMINED BY PARTIALLY INVARIANT FEATURES. J.A. Garcia, J. Fdez-Valdivia Departamento de Ciencias de la Computacion e I.A. Univ. de Granada...E.T.S. de Ingenieria Informatica. 18071 Granada. Spain E-mail: jagsadecsai.ugr.es, J.Fdez-Valdivia@decsai.ugr.es Xose R. Fdez-Vidal Departamento de... Fisica Aplicada. Univ. de Santiago de Compostela. Facultad de Fisica . 15706 Santiago de Compostela. Spain E-mail: faxose@usc.es Rosa Rodriguez-Sanchez
Higher helicity invariants and solar dynamo
Sokolov, D. D.; Illarionov, E. A.; Akhmet'ev, P. M.
2017-01-01
Modern models of nonlinear dynamo saturation in celestial bodies (specifically, on the Sun) are largely based on the consideration of the balance of magnetic helicity. This physical variable has also a topological meaning: it is associated with the linking coefficient of magnetic tubes. In addition to magnetic helicity, magnetohydrodynamics has a number of topological integrals of motion (the so-called higher helicity moments). We have compared these invariants with magnetic helicity properties and concluded that they can hardly serve as nonlinear constraints on dynamo action.
Gauge invariance, causality and gluonic poles
Energy Technology Data Exchange (ETDEWEB)
Anikin, I.V., E-mail: anikin@theor.jinr.r [Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Russian Federation); Teryaev, O.V., E-mail: teryaev@theor.jinr.r [Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Russian Federation)
2010-07-05
We explore the electromagnetic gauge invariance of the hadron tensor of the Drell-Yan process with one transversely polarized hadron. The special role is played by the contour gauge for gluon fields. The prescription for the gluonic pole in the twist 3 correlator is related to causality property and compared with the prescriptions for exclusive hard processes. As a result we get the extra contributions, which naively do not have an imaginary phase. The single spin asymmetry for the Drell-Yan process is accordingly enhanced by the factor of two.
SO(n)-Invariant Special Lagrangian Submanifolds of Cn+1 with Fixed Loci
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Let SO(n) act in the standard way on Cn and extend this action in the usual way toCn+1=C((+))Cn.It is shown that a nonsingular special Lagrangian submanifold L (∩) Cn+1 that is invariant under this SO(n)-action intersects the fixed C (∩) Cn+1 in a nonsingular real-analytic arc A (which may be empty). If n ＞ 2, then A has no compact component.Conversely, an embedded, noncompact nonsingular real-analytic arc A (∩) C lies in an embedded nonsingular special Lagrangian submanifold that is SO(n)-invariant. The same existence result holds for compact A if n = 2. If A is connected, there exist n distinct nonsingular SO(n)-invariant special Lagrangian extensions of A such that any embedded nonsingular SO(n)-invariant special Lagrangian extension of A agrees with one of these n extensions in some open neighborhood of A.The method employed is an analysis of a singular nonlinear PDE and ultimately calls on the work of Gérard and Tahara to prove the existence of the extension.
A filter bank for rotationally invariant image recognition
Directory of Open Access Journals (Sweden)
S Rodtook
2005-12-01
Full Text Available We present new rotation moment invariants based on multiresolution filter bank techniques. The multiresolution pyramid motivates our simple but efficient feature selection procedure based on the fuzzy C-mean clustering methodology combined with the Mahalanobis distance measure. The proposed procedure verifies an impact of random noise as well as an interesting, less known impact of noise due to spatial transformations. The recognition accuracy of the proposed technique has been tested with the Zernike moments, the Fourier-Mellin moments as well as with wavelet based schemes. The numerical experiments, with more than 30 000 images, demonstrate a tangible accuracy increase of about 3% for low level noise, 8% for the average level noise and 15% for high level noise.
INVARIANT FORM AND INTEGRAL INVARIANTS ON K(A)HLER MANIFOLD
Institute of Scientific and Technical Information of China (English)
ZHANG Rong-ye
2006-01-01
The important notions and results of the integral invariants of Poincaré and lished first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on K(a)hler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider and deeper results.
Translational invariance in nucleation theories: Theoretical formulation
Energy Technology Data Exchange (ETDEWEB)
Drossinos, Y.; Kevrekidis, P. G.; Georgopoulos, P. G.
2001-03-01
The consequences of spontaneously broken translational invariance on the nucleation-rate statistical prefactor in theories of first-order phase transitions are analyzed. A hybrid, semiphenomenological approach based on field-theoretic analyses of condensation and modern density-functional theories of nucleation is adopted to provide a unified prescription for the incorporation of translational-invariance corrections to nucleation-rate predictions. A connection between these theories is obtained starting from a quantum-mechanical Hamiltonian and using methods developed in the context of studies on Bose-Einstein condensation. An extremum principle is used to derive an integro-differential equation for the spatially nonuniform mean-field order-parameter profile; the appropriate order parameter becomes the square root of the fluid density. The importance of the attractive intermolecular potential is emphasized, whereas the repulsive two-body potential is approximated by considering hard-sphere collisions. The functional form of the degenerate translational eigenmodes in three dimensions is related to the mean-field order parameter, and their contribution to the nucleation-rate prefactor is evaluated. The solution of the Euler-Lagrange variational equation is discussed in terms of either a proposed variational trial function or the complete numerical solution of the associated boundary-value integro-differential problem. Alternatively, if the attractive potential is not explicitly known, an approach that allows its formal determination from its moments is presented.
Natural Inflation with Hidden Scale Invariance
Barrie, Neil D; Liang, Shelley
2016-01-01
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: $n_s-1\\approx 0.025\\left(\\frac{N_{\\star}}{60}\\right)^{-1}$ and $r\\approx 0.0667\\left(\\frac{N_{\\star}}{60}\\right)^{-1}$, where $N_{\\star}\\approx 30-65$ 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.
Natural inflation with hidden scale invariance
Directory of Open Access Journals (Sweden)
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.
Translation Invariant Extensions of Finite Volume Measures
Goldstein, S.; Kuna, T.; Lebowitz, J. L.; Speer, E. R.
2017-02-01
We investigate the following questions: Given a measure μ _Λ on configurations on a subset Λ of a lattice L, where a configuration is an element of Ω ^Λ for some fixed set Ω , does there exist a measure μ on configurations on all of L, invariant under some specified symmetry group of L, such that μ _Λ is its marginal on configurations on Λ ? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which L=Z^d and the symmetries are the translations. For the case in which Λ is an interval in Z we give a simple necessary and sufficient condition, local translation invariance ( LTI), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which L is the Bethe lattice. On Z we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When Λ subset Z is not an interval, or when Λ subset Z^d with d>1, the LTI condition is necessary but not sufficient for extendibility. For Z^d with d>1, extendibility is in some sense undecidable.
Using Invariant Translation to Denoise Electroencephalogram Signals
Directory of Open Access Journals (Sweden)
Janett Walters-Williams
2011-01-01
Full Text Available Problem statement: Because of the distance between the skull and the brain and their different resistivitys, Electroencephalogram (EEG recordings on a machine is usually mixed with the activities generated within the area called noise. EEG signals have been used to diagnose major brain diseases such as Epilepsy, narcolepsy and dementia. The presence of these noises however can result in misdiagnosis, as such it is necessary to remove them before further analysis and processing can be done. Denoising is often done with Independent Component Analysis algorithms but of late Wavelet Transform has been utilized. Approach: In this study we utilized one of the newer Wavelet Transform methods, Translation-Invariant, to deny EEG signals. Different EEG signals were used to verify the method using the MATLAB software. Results were then compared with those of renowned ICA algorithms Fast ICA and Radical and evaluated using the performance measures Mean Square Error (MSE, Percentage Root Mean Square Difference (PRD and Signal to Noise Ratio (SNR. Results: Experiments revealed that Translation-Invariant Wavelet Transform had the smallest MSE and PRD while having the largest SNR. Conclusion/Recommendations: This indicated that it performed superior to the ICA algorithms producing cleaner EEG signals which can influence diagnosis as well as clinical studies of the brain.
Translation Invariant Extensions of Finite Volume Measures
Goldstein, S.; Kuna, T.; Lebowitz, J. L.; Speer, E. R.
2016-08-01
We investigate the following questions: Given a measure μ _Λ on configurations on a subset Λ of a lattice L, where a configuration is an element of Ω ^Λ for some fixed set Ω , does there exist a measure μ on configurations on all of L, invariant under some specified symmetry group of L, such that μ _Λ is its marginal on configurations on Λ ? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which L=Z^d and the symmetries are the translations. For the case in which Λ is an interval in Z we give a simple necessary and sufficient condition, local translation invariance (LTI), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which L is the Bethe lattice. On Z we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When Λ subset Z is not an interval, or when Λ subset Z^d with d>1 , the LTI condition is necessary but not sufficient for extendibility. For Z^d with d>1 , extendibility is in some sense undecidable.
The Manifestly Gauge Invariant Exact Renormalisation Group
Rosten, O J
2005-01-01
We construct a manifestly gauge invariant Exact Renormalisation Group (ERG) whose form is suitable for computation in SU(N) Yang-Mills theory, beyond one-loop. An effective cutoff is implemented by embedding the physical SU(N) theory in a spontaneously broken SU(N|N) Yang-Mills theory. To facilitate computations within this scheme, which proceed at every step without fixing the gauge, we develop a set of diagrammatic techniques. As an initial test of the formalism, the one-loop SU(N) Yang-Mills beta-function, beta_1, is computed, and the standard, universal answer is reproduced. It is recognised that the computational technique can be greatly simplified. Using these simplifications, a partial proof is given that, to all orders in perturbation theory, the explicit dependence of perturbative $\\beta$-function coefficients, beta_n, on certain non-universal elements of the manifestly gauge invariant ERG cancels out. This partial proof yields an extremely compact, diagrammatic form for the surviving contributions t...
Stackable groups, tame filling invariants, and algorithmic properties of groups
Brittenham, Mark
2011-01-01
We introduce a combinatorial property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a canonical finite presentation. We also define algorithmically stackable groups, for which this procedure is an effective algorithm. This property gives a uniform model for algorithms arising from both rewriting systems and almost convexity for groups. We also introduce a new pair of asymptotic invariants that are filling inequalities refining the notions of intrinsic and extrinsic diameter inequalities for finitely presented groups. These tame filling invariants are quasi-isometry invariants, up to Lipschitz equivalence of functions (and, in the case of the intrinsic tame filling invariant, up to choice of a sufficiently large set of defining relators). We show that radial tameness functions are equivalent to the extrinsic tame filling invariant condition, and so intrinsic tame filling invariants can be viewed as the in...
Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations
Directory of Open Access Journals (Sweden)
Chunrong Zhu
2016-11-01
Full Text Available In this paper, we develop the symmetry-related methods to study invariant subspaces of the two-dimensional nonlinear differential operators. The conditional Lie–Bäcklund symmetry and Lie point symmetry methods are used to construct invariant subspaces of two-dimensional differential operators. We first apply the multiple conditional Lie–Bäcklund symmetries to derive invariant subspaces of the two-dimensional operators. As an application, the invariant subspaces for a class of two-dimensional nonlinear quadratic operators are provided. Furthermore, the invariant subspace method in one-dimensional space combined with the Lie symmetry reduction method and the change of variables is used to obtain invariant subspaces of the two-dimensional nonlinear operators.
Conformal invariance in the long-range Ising model
Energy Technology Data Exchange (ETDEWEB)
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.
Conformal invariance in the long-range Ising model
Directory of Open Access Journals (Sweden)
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.
The Kubelka-Munk Theory for Color Image Invariant Properties
Geusebroek, J.M.; Gevers, Th.; Smeulders, A.W.M.
2002-01-01
A fundamental problem in color image processing is the integration of the physical laws of light reflection into image processing results, the probem known as photometric invariance. The derivation of object properties from color images yields the extraction of geometric and photometric invariants from color images. Photometric invariance is to be derived from the physics of refelection. In this paper, we rehearse the results from radiative transfer theory to model the reflection and transmis...
Spectral Invariants in Rabinowitz Floer homology and Global Hamiltonian perturbations
Albers, Peter
2010-01-01
Spectral invariant were introduced in Hamiltonian Floer homology by Viterbo, Oh, and Schwarz. We extend this concept to Rabinowitz Floer homology. As an application we derive new quantitative existence results for leaf-wise intersections. The importance of spectral invariants for the presented application is that spectral invariants allow us to derive existence of critical points of the Rabinowitz action functional even in degenerate situations where the functional is not Morse.
Adiabatic invariants of the extended KdV equation
Karczewska, Anna; Infeld, Eryk; Rowlands, George
2015-01-01
When the Euler equations for shallow water are taken to the next order, beyond KdV, $\\eta^2$ is no longer an invariant. (It would seem that $\\eta$ is the only one.) However, two adiabatic invariants akin to $\\eta^2$ can be found. Here we present and test them. When the KdV expansion parameters are zero, $\\eta^2$ is recovered from both adiabatic invariants.
Lie symmetries and invariants of constrained Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
Liu Rong-Wan; Chen Li-Qun
2004-01-01
According to the theory of the invariance of ordinary differential equations under the infinitesimal transformations of group, the relations between Lie symmetries and invariants of the mechanical system with a singular Lagrangian are investigated in phase space. New dynamical equations of the system are given in canonical form and the determining equations of Lie symmetry transformations are derived. The proposition about the Lie symmetries and invariants are presented. An example is given to illustrate the application of the result in this paper.
Chern-Simons Invariants of Torus Knots and Links
Stevan, Sébastien
2010-01-01
We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus links and we obtain an analogous formula for Kauffman invariants. We also derive a formula for cable knots. We use our results to test a recently proposed conjecture that relates HOMFLY and Kauffman invariants.
Complex dynamical invariants for two-dimensional complex potentials
Indian Academy of Sciences (India)
J S Virdi; F Chand; C N Kumar; S C Mishra
2012-08-01
Complex dynamical invariants are searched out for two-dimensional complex potentials using rationalization method within the framework of an extended complex phase space characterized by $x = x_{1} + ip_{3}. y = x_{2} + ip_{4}, p_{x} = p_{1} + ix_{3}, p_{y} = p_{2} + ix_{4}$. It is found that the cubic oscillator and shifted harmonic oscillator admit quadratic complex invariants. THe obtained invariants may be useful for studying non-Hermitian Hamiltonian systems.
Scale-invariant correlations and the distribution of prime numbers
Holdom, B.
2009-08-01
Negative correlations in the distribution of prime numbers are found to display a scale invariance. This occurs in conjunction with a nonstationary behavior. We compare the prime number series to a type of fractional Brownian motion which incorporates both the scale invariance and the nonstationary behavior. Interesting discrepancies remain. The scale invariance also appears to imply the Riemann hypothesis and we study the use of the former as a test of the latter.
Vassiliev invariants a new framework for quantum gravity
Gambini, R; Pullin, J; Gambini, Rodolfo; Griego, Jorge; Pullin, Jorge
1998-01-01
We show that Vassiliev invariants of knots, appropriately generalized to the spin network context, are loop differentiable in spite of being diffeomorphism invariant. This opens the possibility of defining rigorously the constraints of quantum gravity as geometrical operators acting on the space of Vassiliev invariants of spin nets. We show how to explicitly realize the diffeomorphism constraint on this space and present proposals for the construction of Hamiltonian constraints.
BIFURCATIONS OF INVARIANT CURVES OF A DIFFERENCE EQUATION
Institute of Scientific and Technical Information of China (English)
贺天兰
2001-01-01
Bifurcation of the invariant curves of a difference equation is studied. The system defined by the difference equation is integrable , so the study of the invariant curves of the difference system can become the study of topological classification of the planar phase portraits defined by a planar Hamiltonian system. By strict qualitative analysis, the classification of the invariant curves in parameter space can be obtained.
On Scale Invariance and Anomalies in Quantum Mechanics
Cabo-Montes de Oca, Alejandro; Mercado, H
1997-01-01
We re-consider the quantum mechanics of scale invariant potentials in two dimensions. The breaking of scale invariance by quantum effects is analyzed by the explicit evaluation of the phase shift and the self-adjoint extension method. We argue that the breaking of scale invariance reported in the literature for the $\\delta$(r) potential, is an example of explicit and not an anomaly or quantum mechanical symmetry breaking.
Cotton-Type and Joint Invariants for Linear Elliptic Systems
Directory of Open Access Journals (Sweden)
A. Aslam
2013-01-01
that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results.
ESTIMATION OF SEAGRASS COVERAGE BY DEPTH INVARIANT INDICES ON QUICKBIRD IMAGERY
Directory of Open Access Journals (Sweden)
Muhammad Anshar Amran
2010-01-01
Full Text Available Management of seagrass ecosystem requires availability of information on the actual condition of seagrass coverage. Remote sensing technology for seagrass mapping has been used to detect the presence of seagrass coverage, but so far no information on the condition of seagrass could be obtained. Therefore, a research is required using remote sensing imagery to obtain information on the condition of seagrass coverage.The aim of this research is to formulate mathematical relationship between seagrass coverage and depth invariant indices on Quickbird imagery. Transformation was done on multispectral bands which could detect sea floor objects that are in the region of blue, green and red bands.The study areas covered are the seas around Barranglompo Island and Barrangcaddi Island, westward of Makassar city, Indonesia. Various seagrass coverages were detected within the region under study.Mathematical relationship between seagrass coverage and depth invariant indices was obtained by multiple linear regression method. Percentage of seagrass coverage (C was obtained by transformation of depth invariant indices (Xij on Quickbird imagery, with transformation equation as follows:C = 19.934 – 63.347 X12 + 23.239 X23.A good accuracy of 75% for the seagrass coverage was obtained by transformation of depth invariant indices (Xij on Quickbird imagery.
Metric Ranking of Invariant Networks with Belief Propagation
Energy Technology Data Exchange (ETDEWEB)
Tao, Changxia [Xi' an Jiaotong University, China; Ge, Yong [University of North Carolina, Charlotte; Song, Qinbao [Xi' an Jiaotong University, China; Ge, Yuan [Anhui Polytechnic University, China; Omitaomu, Olufemi A [ORNL
2014-01-01
The management of large-scale distributed information systems relies on the effective use and modeling of monitoring data collected at various points in the distributed information systems. A promising approach is to discover invariant relationships among the monitoring data and generate invariant networks, where a node is a monitoring data source (metric) and a link indicates an invariant relationship between two monitoring data. Such an invariant network representation can help system experts to localize and diagnose the system faults by examining those broken invariant relationships and their related metrics, because system faults usually propagate among the monitoring data and eventually lead to some broken invariant relationships. However, at one time, there are usually a lot of broken links (invariant relationships) within an invariant network. Without proper guidance, it is difficult for system experts to manually inspect this large number of broken links. Thus, a critical challenge is how to effectively and efficiently rank metrics (nodes) of invariant networks according to the anomaly levels of metrics. The ranked list of metrics will provide system experts with useful guidance for them to localize and diagnose the system faults. To this end, we propose to model the nodes and the broken links as a Markov Random Field (MRF), and develop an iteration algorithm to infer the anomaly of each node based on belief propagation (BP). Finally, we validate the proposed algorithm on both realworld and synthetic data sets to illustrate its effectiveness.
A scale invariant covariance structure on jet space
DEFF Research Database (Denmark)
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 part...... of the derivation, we introduce a blurring operator At that acts on jet space contrary to doing spatial filtering and a scaling operator Ss. The stochastic Brownian image model is an example of a class of functions which are scale invariant with respect to the operators At and Ss. This paper also includes empirical...
On the hierarchy of partially invariant submodels of differential equations
Energy Technology Data Exchange (ETDEWEB)
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.
Conformal transformations and conformal invariance in gravitation
Dabrowski, Mariusz P; Blaschke, David B
2008-01-01
Conformal transformations are frequently used tools in order to study relations between various theories of gravity and Einstein relativity. Because of that, in this paper we discuss the rules of conformal transformations for geometric quantities in general relativity. In particular, we discuss the conformal transformations of the matter energy-momentum tensor. We thoroughly discuss the latter and show the subtlety of the conservation law (i.e., the geometrical Bianchi identity) imposed in one of the conformal frames in reference to the other. The subtlety refers to the fact that conformal transformation ``creates'' an extra matter term composed of the conformal factor which enters the conservation law. In an extreme case of the flat original spacetime the matter is ``created'' due to work done by the conformal transformation to bend the spacetime which was originally flat. We also discuss how to construct the conformally invariant gravity which, in the simplest version, is a special case of the Brans-Dicke t...
Kahler stabilized, modular invariant heterotic string models
Energy Technology Data Exchange (ETDEWEB)
Gaillard, Mary K.; Gaillard, Mary K.; Nelson, Brent D.
2007-03-19
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 Binétruy, 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.
Lorentz Invariance Violation and Generalized Uncertainty Principle
Tawfik, A; Ali, A Farag
2016-01-01
Recent approaches for quantum gravity are conjectured to give predictions for a minimum measurable length, a maximum observable momentum and an essential generalization for the Heisenberg uncertainty principle (GUP). The latter is based on a momentum-dependent modification in the standard dispersion relation and leads to Lorentz invariance violation (LIV). The main features of the controversial OPERA measurements on the faster-than-light muon neutrino anomaly are used to calculate the time of flight delays $\\Delta t$ and the relative change $\\Delta v$ in the speed of neutrino in dependence on the redshift $z$. The results are compared with the OPERA measurements. We find that the measurements are too large to be interpreted as LIV. Depending on the rest mass, the propagation of high-energy muon neutrino can be superluminal. The comparison with the ultra high energy cosmic rays seems to reveals an essential ingredient of the approach combining string theory, loop quantum gravity, black hole physics and doubly ...
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.
Rotationally invariant ensembles of integrable matrices
Yuzbashyan, Emil A.; Shastry, B. Sriram; Scaramazza, Jasen A.
2016-05-01
We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT)—a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M family of integrable matrices consists of exactly N -M independent commuting N ×N matrices linear in a real parameter. We first develop a rotationally invariant parametrization of such matrices, previously only constructed in a preferred basis. For example, an arbitrary choice of a vector and two commuting Hermitian matrices defines a type-1 family and vice versa. Higher types similarly involve a random vector and two matrices. The basis-independent formulation allows us to derive the joint probability density for integrable matrices, similar to the construction of Gaussian ensembles in the RMT.
Gravitomagnetism and the Lorentz Invariance of Gravity
Kopeikin, S M
2006-01-01
Experimental discovery of the gravitomagnetic fields generated by translational and/or rotational currents of matter is one of primary goals of modern gravitational physics. The rotational (intrinsic) gravitomagnetic field of the Earth is currently measured by the Gravity Probe B. The present paper makes use of a parametrized post-Newtonian (PN) expansion of the Einstein equations to demonstrate how the extrinsic gravitomagnetic field generated by the translational current of matter can be measured by observing the relativistic time delay caused by a moving gravitational lens. We prove that measuring the extrinsic gravitomagnetic field is equivalent to testing of the relativistic effect of the aberration of gravity caused by the Lorentz transformation of the gravitational field. We unfold that the recent Jovian deflection experiment is a null-type experiment testing the Lorentz invariance of the gravitational field (aberration of gravity), thus, confirming existence of the extrinsic gravitomagnetic field asso...
Fourier-Bessel rotational invariant eigenimages.
Zhao, Zhizhen; Singer, Amit
2013-05-01
We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two-dimensional images and, for each image, the set of its uniform rotations in the plane and its reflection. The algorithm starts by expanding each image, originally given on a Cartesian grid, in the Fourier-Bessel basis for the disk. Because the images are essentially band limited in the Fourier domain, we use a sampling criterion to truncate the Fourier-Bessel expansion such that the maximum amount of information is preserved without the effect of aliasing. The constructed covariance matrix is invariant to rotation and reflection and has a special block diagonal structure. PCA is efficiently done for each block separately. This Fourier-Bessel-based PCA detects more meaningful eigenimages and has improved denoising capability compared to traditional PCA for a finite number of noisy images.
Weights on cohomology and invariants of singularities
Arapura, Donu; Włodarczyk, Jarosław
2011-01-01
In this paper, we extract natural invariants of a singularity by using the Deligne weight filtration on the cohomology of an exceptional fibre of a resolution, and also on the intersection cohomology of the link. Our primary goal is to study and give natural bounds on the weights in terms of direct images of differential forms. These bounds can be made explicit for various standard classes such as rational, isolated normal Cohen-Macaulay and toroidal singularities, and lead to strong restrictions on the topology of these singularities. A secondary goal of this paper is to make the weight filtration, and related constructions, more widely accessible. So we have tried to make the presentation somewhat self contained. This is supersedes our earlier preprint arXiv:0902.4234.
Rotationally invariant ensembles of integrable matrices.
Yuzbashyan, Emil A; Shastry, B Sriram; Scaramazza, Jasen A
2016-05-01
We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT)-a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M family of integrable matrices consists of exactly N-M independent commuting N×N matrices linear in a real parameter. We first develop a rotationally invariant parametrization of such matrices, previously only constructed in a preferred basis. For example, an arbitrary choice of a vector and two commuting Hermitian matrices defines a type-1 family and vice versa. Higher types similarly involve a random vector and two matrices. The basis-independent formulation allows us to derive the joint probability density for integrable matrices, similar to the construction of Gaussian ensembles in the RMT.
A simple Proof of Stolarsky's Invariance Principle
Brauchart, Johann S
2011-01-01
Stolarsky [Proc. Amer. Math. Soc. 41 (1973), 575--582] showed a beautiful relation that balances the sums of distances of points on the unit sphere and their spherical cap $\\mathbb{L}_2$-discrepancy to give the distance integral of the uniform measure on the sphere a potential-theoretical quantity (Bj{\\"o}rck [Ark. Mat. 3 (1956), 255--269]). Read differently it expresses the worst-case numerical integration error for functions from the unit ball in a certain Hilbert space setting in terms of the $\\mathbb{L}_2$-discrepancy and vice versa (first author and Womersley [Preprint]). In this note we give a simple proof of the invariance principle using reproducing kernel Hilbert spaces.
Constructing invariant fairness measures for surfaces
DEFF Research Database (Denmark)
Gravesen, Jens; Ungstrup, Michael
2002-01-01
The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given...... curves should be fair with respect to an appropriate curve fairness measure. The method is applied to the field of ship hull design where the curves are plane intersections. The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family...... of curves. Six basic third order invariants by which the fairing measures can be expressed are defined. Furthermore, the geometry of a plane intersection curve is studied, and the variation of the total, the normal, and the geodesic curvature and the geodesic torsion is determined....
Structural invariance and the energy spectrum
Energy Technology Data Exchange (ETDEWEB)
Leyvraz, F.; Mendez, R.A.; Seligman, T.H. [Laboratorio de Cuernavaca, Instituto de Fisica, Unam (Italy)
1999-10-01
We extend the application of the concept of structural invariance to bounded time-independent systems. This concept, previously introduced by two of us to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the semiclassical limit is extended to the energy spectra of bounded time-independent systems. We proceed by showing that the results obtained previously for the quasi-energies and eigenphases of the S-matrix can be extended to the eigenphases of the quantum Poincare map which is unitary in the semiclassical limit. We then show that its eigenphases in the chaotic case move rather stiffly around the unit circle and thus their local statistical fluctuations transfer to the energy spectrum via Bogomolny's prescription. We verify our results by studying numerically the properties of the eigenphases of the quantum Poincare map for billiards by using the boundary integral method. (author)
Structural Invariance and the Energy Spectrum
Leyvraz, F; Seligman, T H
1999-01-01
We extend the application of the concept of structural invariance to bounded time independent systems. This concept, previously introduced by two of us to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the semiclassical limit, is extended to the energy spectra of bounded time independent systems. We proceed by showing that the results obtained previously for the quasi-energies and eigenphases of the S-matrix can be extended to the eigenphases of the quantum Poincare map which is unitary in the semiclassical limit. We then show that its eigenphases in the chaotic case move rather stiffly around the unit circle and thus their local statistical fluctuations transfer to the energy spectrum via Bogomolny's prescription. We verify our results by studying numerically the properties of the eigenphases of the quantum Poincare map for billiards by using the boundary integral method.
Onboard Image Registration from Invariant Features
Wang, Yi; Ng, Justin; Garay, Michael J.; Burl, Michael C
2008-01-01
This paper describes a feature-based image registration technique that is potentially well-suited for onboard deployment. The overall goal is to provide a fast, robust method for dynamically combining observations from multiple platforms into sensors webs that respond quickly to short-lived events and provide rich observations of objects that evolve in space and time. The approach, which has enjoyed considerable success in mainstream computer vision applications, uses invariant SIFT descriptors extracted at image interest points together with the RANSAC algorithm to robustly estimate transformation parameters that relate one image to another. Experimental results for two satellite image registration tasks are presented: (1) automatic registration of images from the MODIS instrument on Terra to the MODIS instrument on Aqua and (2) automatic stabilization of a multi-day sequence of GOES-West images collected during the October 2007 Southern California wildfires.
Controlling acquiescence bias in measurement invariance tests
Directory of Open Access Journals (Sweden)
Aichholzer Julian
2015-01-01
Full Text Available Assessing measurement invariance (MI is an important cornerstone in establishing equivalence of instruments and comparability of constructs. However, a common concern is that respondent differences in acquiescence response style (ARS behavior could entail a lack of MI for the measured constructs. This study investigates if and how ARS impacts MI and the level of MI achieved. Data from two representative samples and two popular short Big Five personality scales were analyzed to study hypothesized ARS differences among educational groups. Multiple-group factor analysis and the random intercept method for controlling ARS are used to investigate MI with and without controlling for ARS. Results suggest that, contrary to expectations, controlling for ARS had little impact on conclusions regarding the level of MI of the instruments. Thus, the results suggest that testing MI is not an appropriate means for detecting ARS differences per se. Implications and further research areas are discussed.
Parabolic refined invariants and Macdonald polynomials
Chuang, Wu-yen; Donagi, Ron; Pantev, Tony
2013-01-01
A string theoretic derivation is given for the conjecture of Hausel, Letellier, and Rodriguez-Villegas on the cohomology of character varieties with marked points. Their formula is identified with a refined BPS expansion in the stable pair theory of a local root stack, generalizing previous work of the first two authors in collaboration with G. Pan. Haiman's geometric construction for Macdonald polynomials is shown to emerge naturally in this context via geometric engineering. In particular this yields a new conjectural relation between Macdonald polynomials and refined local orbifold curve counting invariants. The string theoretic approach also leads to a new spectral cover construction for parabolic Higgs bundles in terms of holomorphic symplectic orbifolds.
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...
Coordinate-invariant incremental Lyapunov functions
Zamani, Majid
2011-01-01
The notion of incremental stability was proposed by several researchers as a strong property of dynamical and control systems. In this type of stability, the focus is on the convergence of trajectories with respect to themselves, rather than with respect to an equilibrium point or a particular trajectory. Similarly to stability, Lyapunov functions play an important role in the study of incremental stability. In this paper, we propose coordinate-invariant notions of incremental Lyapunov function and provide the description of incremental stability in terms of existence of the proposed Lyapunov functions. Moreover, we develop a backstepping design approach providing a recursive way of constructing controllers as well as incremental Lyapunov functions. The effectiveness of our method is illustrated by synthesizing a controller rendering a single-machine infinite-bus electrical power system incrementally stable.
Invariant conserved currents in generalized gravity
Obukhov, Yuri N; Puetzfeld, Dirk; Rubilar, Guillermo F
2015-01-01
We study conservation laws for gravity theories invariant under general coordinate transformations. The class of models under consideration includes Einstein's general relativity theory as a special case as well as its generalizations to non-Riemannian spacetime geometry and nonminimal coupling. We demonstrate that an arbitrary vector field on the spacetime manifold generates a current density that is conserved under certain conditions, and find the expression of the corresponding superpotential. For a family of models including nonminimal coupling between geometry and matter, we discuss in detail the differential conservation laws and the conserved quantities defined in terms of covariant multipole moments. We show that the equations of motion for the multipole moments of extended microstructured test bodies lead to conserved quantities that are closely related to the conserved currents derived in the field-theoretic framework.
Time-Scale Invariant Audio Data Embedding
Directory of Open Access Journals (Sweden)
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.
Lorentz invariance violation and generalized uncertainty principle
Tawfik, Abdel Nasser; Magdy, H.; Ali, A. Farag
2016-01-01
There are several theoretical indications that the quantum gravity approaches may have predictions for a minimal measurable length, and a maximal observable momentum and throughout a generalization for Heisenberg uncertainty principle. The generalized uncertainty principle (GUP) is based on a momentum-dependent modification in the standard dispersion relation which is conjectured to violate the principle of Lorentz invariance. From the resulting Hamiltonian, the velocity and time of flight of relativistic distant particles at Planck energy can be derived. A first comparison is made with recent observations for Hubble parameter in redshift-dependence in early-type galaxies. We find that LIV has two types of contributions to the time of flight delay Δ t comparable with that observations. Although the wrong OPERA measurement on faster-than-light muon neutrino anomaly, Δ t, and the relative change in the speed of muon neutrino Δ v in dependence on redshift z turn to be wrong, we utilize its main features to estimate Δ v. Accordingly, the results could not be interpreted as LIV. A third comparison is made with the ultra high-energy cosmic rays (UHECR). It is found that an essential ingredient of the approach combining string theory, loop quantum gravity, black hole physics and doubly spacial relativity and the one assuming a perturbative departure from exact Lorentz invariance. Fixing the sensitivity factor and its energy dependence are essential inputs for a reliable confronting of our calculations to UHECR. The sensitivity factor is related to the special time of flight delay and the time structure of the signal. Furthermore, the upper and lower bounds to the parameter, a that characterizes the generalized uncertainly principle, have to be fixed in related physical systems such as the gamma rays bursts.
Time reversal invariance in polarized neutron decay
Energy Technology Data Exchange (ETDEWEB)
Wasserman, E.G.
1994-03-01
An experiment to measure the time reversal invariance violating (T-violating) triple correlation (D) in the decay of free polarized neutrons has been developed. The detector design incorporates a detector geometry that provides a significant improvement in the sensitivity over that used in the most sensitive of previous experiments. A prototype detector was tested in measurements with a cold neutron beam. Data resulting from the tests are presented. A detailed calculation of systematic effects has been performed and new diagnostic techniques that allow these effects to be measured have been developed. As the result of this work, a new experiment is under way that will improve the sensitivity to D to 3 {times} 10{sup {minus}4} or better. With higher neutron flux a statistical sensitivity of the order 3 {times} 10{sup {minus}5} is ultimately expected. The decay of free polarized neutrons (n {yields} p + e + {bar v}{sub e}) is used to search for T-violation by measuring the triple correlation of the neutron spin polarization, and the electron and proton momenta ({sigma}{sub n} {center_dot} p{sub p} {times} p{sub e}). This correlation changes sign under reversal of the motion. Since final state effects in neutron decay are small, a nonzero coefficient, D, of this correlation indicates the violation of time reversal invariance. D is measured by comparing the numbers of coincidences in electron and proton detectors arranged symmetrically about a longitudinally polarized neutron beam. Particular care must be taken to eliminate residual asymmetries in the detectors or beam as these can lead to significant false effects. The Standard Model predicts negligible T-violating effects in neutron decay. Extensions to the Standard Model include new interactions some of which include CP-violating components. Some of these make first order contributions to D.
Noise-assisted estimation of attractor invariants.
Restrepo, Juan F; Schlotthauer, Gastón
2016-07-01
In this article, the noise-assisted correlation integral (NCI) is proposed. The purpose of the NCI is to estimate the invariants of a dynamical system, namely the correlation dimension (D), the correlation entropy (K_{2}), and the noise level (σ). This correlation integral is induced by using random noise in a modified version of the correlation algorithm, i.e., the noise-assisted correlation algorithm. We demonstrate how the correlation integral by Grassberger et al. and the Gaussian kernel correlation integral (GCI) by Diks can be thought of as special cases of the NCI. A third particular case is the U-correlation integral proposed herein, from which we derived coarse-grained estimators of the correlation dimension (D_{m}^{U}), the correlation entropy (K_{m}^{U}), and the noise level (σ_{m}^{U}). Using time series from the Henon map and the Mackey-Glass system, we analyze the behavior of these estimators under different noise conditions and data lengths. The results show that the estimators D_{m}^{U} and σ_{m}^{U} behave in a similar manner to those based on the GCI. However, for the calculation of K_{2}, the estimator K_{m}^{U} outperforms its GCI-based counterpart. On the basis of the behavior of these estimators, we have proposed an automatic algorithm to find D,K_{2}, and σ from a given time series. The results show that by using this approach, we are able to achieve statistically reliable estimations of those invariants.
Scale invariance and universality of economic fluctuations
Stanley, H. E.; Amaral, L. A. N.; Gopikrishnan, P.; Plerou, V.
2000-08-01
In recent years, physicists have begun to apply concepts and methods of statistical physics to study economic problems, and the neologism “econophysics” is increasingly used to refer to this work. Much recent work is focused on understanding the statistical properties of time series. One reason for this interest is that economic systems are examples of complex interacting systems for which a huge amount of data exist, and it is possible that economic time series viewed from a different perspective might yield new results. This manuscript is a brief summary of a talk that was designed to address the question of whether two of the pillars of the field of phase transitions and critical phenomena - scale invariance and universality - can be useful in guiding research on economics. We shall see that while scale invariance has been tested for many years, universality is relatively less frequently discussed. This article reviews the results of two recent studies - (i) The probability distribution of stock price fluctuations: Stock price fluctuations occur in all magnitudes, in analogy to earthquakes - from tiny fluctuations to drastic events, such as market crashes. The distribution of price fluctuations decays with a power-law tail well outside the Lévy stable regime and describes fluctuations that differ in size by as much as eight orders of magnitude. (ii) Quantifying business firm fluctuations: We analyze the Computstat database comprising all publicly traded United States manufacturing companies within the years 1974-1993. We find that the distributions of growth rates is different for different bins of firm size, with a width that varies inversely with a power of firm size. Similar variation is found for other complex organizations, including country size, university research budget size, and size of species of bird populations.
Scale-invariance of parity-invariant three-dimensional QED
Karthik, Nikhil
2016-01-01
We present numerical evidences using overlap fermions for a scale-invariant behavior of parity-invariant three-dimensional QED with two flavors of massless two-component fermions. Using finite-size scaling of the low-lying eigenvalues of the massless anti-Hermitian overlap Dirac operator, we rule out the presence of bilinear condensate and estimate the mass anomalous dimension. The eigenvectors associated with these low-lying eigenvalues suggest critical behavior in the sense of a metal-insulator transition. We show that there is no mass gap in the scalar and vector correlators in the infinite volume theory. The vector correlator does not acquire an anomalous dimension. The anomalous dimension associated with the long-distance behavior of the scalar correlator is consistent with the mass anomalous dimension.
2015-09-01
VBA module. In our model , we assumed that all variables are independent from other variables inside the same invariant and that their names are...propose a new model for formal verification by using five online games. CSFV aims to explore whether an online game player with no formal verification...Advanced Research Projects Agency (DARPA) started the Crowd Sourced Formal Verification (CSFV) program to propose a new model for formal verification by
A test of local Lorentz invariance with Compton scattering asymmetry
Mohanmurthy, P; Dutta, D
2016-01-01
We report on a measurement of the constancy and anisotropy of the speed of light relative to the electrons in photon-electron scattering. We used the Compton scattering asymmetry measured by the new Compton polarimeter in Hall~C at Jefferson Lab to test for deviations from unity of the vacuum refractive index ($n$). For photon energies in the range of 9 - 46 MeV, we obtain a new limit of $1-n < 1.4 \\times 10^{-8}$. In addition, the absence of sidereal variation over the six month period of the measurement constrains any anisotropies in the speed of light. These constitute the first study of Lorentz invariance using Compton asymmetry. Within the minimal standard model extension framework, our result yield limits on the photon and electron coefficients $\\tilde{\\kappa}_{0^+}^{YZ}, c_{TX}, \\tilde{\\kappa}_{0^+}^{ZX}$, and $c_{TY}$. Although, these limits are several orders of magnitude larger than the current best limits, they demonstrate the feasibility of using Compton asymmetry for tests of Lorentz invarianc...
A test of local Lorentz invariance with Compton scattering asymmetry
Mohanmurthy, Prajwal; Narayan, Amrendra; Dutta, Dipangkar
2016-11-01
We report on a measurement of the constancy and anisotropy of the speed of light relative to the electrons in photon-electron scattering. We used the Compton scattering asymmetry measured by the new Compton polarimeter in Hall C at Jefferson Lab (JLab) to test for deviations from unity of the vacuum refractive index (n). For photon energies in the range of 9-46 MeV, we obtain a new limit of 1 - n speed of light. These constitute the first study of Lorentz invariance (LI) using Compton asymmetry. Within the minimal Standard Model extension (MSME) framework, our result yield limits on the photon and electron coefficients κ˜0+Y Z, cTX, κ˜0+ZX and cTY. Although these limits are several orders of magnitude larger than the current best limits, they demonstrate the feasibility of using Compton asymmetry for tests of LI. Future parity-violating electron-scattering experiments at JLab will use higher energy electrons enabling better constraints.
Sinninghe Damsté, J.S.; Schouten, S.; Volkman, J.K.
2014-01-01
A limited suite of C-27, C-29 and C-30 rearranged hopenes identified as neohop-13(18)-enes have been reported in immature Recent and ancient marine/lacustrine sediments and their presence has been explained by dehydration and isomerisation of ubiquitous hopanols or hopenes. Here we investigated the
The Kubelka-Munk Theory for Color Image Invariant Properties
Geusebroek, J.M.; Gevers, Th.; Smeulders, A.W.M.
2002-01-01
A fundamental problem in color image processing is the integration of the physical laws of light reflection into image processing results, the probem known as photometric invariance. The derivation of object properties from color images yields the extraction of geometric and photometric invariants f
Finding Mutual Exclusion Invariants in Temporal Planning Domains
Bernardini, Sara; Smith, David E.
2011-01-01
We present a technique for automatically extracting temporal mutual exclusion invariants from PDDL2.2 planning instances. We first identify a set of invariant candidates by inspecting the domain and then check these candidates against properties that assure invariance. If these properties are violated, we show that it is sometimes possible to refine a candidate by adding additional propositions and turn it into a real invariant. Our technique builds on other approaches to invariant synthesis presented in the literature, but departs from their limited focus on instantaneous discrete actions by addressing temporal and numeric domains. To deal with time, we formulate invariance conditions that account for both the entire structure of the operators (including the conditions, rather than just the effects) and the possible interactions between operators. As a result, we construct a technique that is not only capable of identifying invariants for temporal domains, but is also able to find a broader set of invariants for non-temporal domains than the previous techniques.
Invariant Measures for a Random Evolution Equation with Small Perturbations
Institute of Scientific and Technical Information of China (English)
Fu Bao XI
2001-01-01
In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions to the equation. As applications, we prove the Feller continuity of the solutions and the existence and uniqueness of invariant measures. Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero.
Gauge-invariance in one-loop quantum cosmology
Vasilevich, D V
1995-01-01
We study the problem of gauge-invariance and gauge-dependence in one-loop quantum cosmology. We formulate some requirements which should be satisfied by boundary conditions in order to give gauge-independent path integral. The case of QED is studied in some detail. We outline difficulties in gauge-invariant quantization of gravitational field in a bounded region.
RELAXATION OF FUNCTIONALS INVOLVING HOMOGENEOUS FUNCTIONS AND INVARIANCE OF ENVELOPES
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The authors compute the quasiconvex envelope of certain functions defined on the space Mmn of real m× n matrices via a homogeneous function on Mmn. They also deduce invariance properties for various convex envelopes from corresponding invariance properties satisfied by a function. Some applications related in particular to nonlinear elasticity are given.
The Geometric Invariants of Group Extensions Part II: Split Extensions
Koban, Nic
2011-01-01
We compute the {\\Omega}^1(G) invariant when 1 {\\to} H {\\to} G {\\to} K {\\to} 1 is a split short exact sequence. We use this result to compute the invariant for pure and full braid groups on compact surfaces. Applications to twisted conjugacy classes and to finite generation of commutator subgroups are also discussed.
Modular invariants and fusion rule automorphisms from Galois theory
Fuchs, J; Schellekens, Adrian Norbert; Schweigert, C; Beatriz Gato-Rivera; Bert Schellekens; Christoph Schweigert
1994-01-01
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.
Testing Lorentz Invariance with neutrino burst from supernova neutronization
Chakraborty, Sovan; Sigl, Günter
2012-01-01
Quantum-gravity (QG) effects might generate Lorentz invariance violation by the interaction of energetic particles with the foamy structure of the space-time. As a consequence, particles may not travel at the universal speed of light. We propose to constrain Lorentz invariance violation for energetic neutrinos exploiting the $\
On Action Invariance under Linear Spinor-Vector Supersymmetry
Directory of Open Access Journals (Sweden)
Kazunari Shima
2006-01-01
Full Text Available We show explicitly that a free Lagrangian expressed in terms of scalar, spinor, vector and Rarita-Schwinger (RS fields is invariant under linear supersymmetry transformations generated by a global spinor-vector parameter. A (generalized gauge invariance of the Lagrangian for the RS field is also discussed.
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…
Lorentz invariance and the semiclassical approximation of loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Kozameh, Carlos N; Parisi, Florencia [Facultad de Matematica, AstronomIa y FIsica, Universidad Nacional de Cordoba, Ciudad Universitaria (5000) Cordoba (Argentina)
2004-06-07
It is shown that the field equations derived from an effective interaction Hamiltonian for Maxwell and gravitational fields in the semiclassical approximation of loop quantum gravity using rotational invariant states (such as weave states) are Lorentz invariant. To derive this result, which is in agreement with the observational evidence, we use the geometrical properties of the electromagnetic field.
Evaluating color and shape invariant image indexing for consumer photography
Th. Gevers; A.W.M. Smeulders
1995-01-01
In this paper, indexing is used as a common framework to represent, index and retrieve images on the basis of color and shape invariants.To evaluate the use of color and shape invariants for the purpose of image retrieval, experiments have been conducted on a database consisting of 500 images of mul
Differential invariants of second-order ordinary differential equations
Rosado Maria, Maria Eugenia
2011-01-01
The notion of a differential invariant for systems of second-order differential equations on a manifold M with respect to the group of vertical automorphisms of the projection is de?ned and the Chern connection attached to a SODE allows one to determine a basis for second-order differential invariants of a SODE.
Graph invariants of Vassiliev type and application to 4D quantum gravity
Hayashi, N
1995-01-01
We consider a special class of Kauffman's graph invariants of rigid vertex isotopy (graph invariants of Vassiliev type). They are given by a functor from a category of colored and oriented graphs embedded into a 3-space to a category of representations of the quasi-triangular ribbon Hopf algebra U_q(sl(2,\\bf C)). Coefficients in expansions of them with respect to x (q=e^x) are known as the Vassiliev invariants of finite type. In the present paper, we construct two types of tangle operators of vertices. One of them corresponds to a Casimir operator insertion at a transverse double point of Wilson loops. This paper proposes a non-perturbative generalization of Kauffman's recent result based on a perturbative analysis of the Chern-Simons quantum field theory. As a result, a quantum group analog of Penrose's spin network is established taking into account of the orientation. We also deal with the 4-dimensional canonical quantum gravity of Ashtekar. It is verified that the graph invariants of Vassiliev type are co...
Scale invariant alternatives to General Relativity II: Dilaton properties
Karananas, Georgios K
2016-01-01
In the present paper we revisit gravitational theories which are invariant under TDiffs - transverse (volume preserving) diffeomorphisms and global scale transformations. It is known that these theories can be rewritten in an equivalent diffeomorphism-invariant form with an action including an integration constant (cosmological constant for the particular case of non scale-invariant unimodular gravity). The presence of this integration constant, in general, breaks explicitly scale invariance and induces a run-away potential for (otherwise massless) dilaton, associated with the determinant of the metric tensor. We show, however, that if the metric carries mass dimension $\\left[\\text{GeV}\\right]^{-2}$, the scale invariance of the system is preserved, unlike the situation in theories in which the metric has mass dimension different from $-2$. The dilaton remains massless and couples to other fields only through derivatives, without any conflict with observations. We observe that one can define a specific limit f...
Invariant regularization of anomaly-free chiral theories
Chang, L N; Chang, Lay Nam; Soo, Chopin
1997-01-01
We present a generalization of the Frolov-Slavnov invariant regularization scheme for chiral fermion theories in curved spacetimes. The Lagrangian level regularization is explicitly invariant under all the local gauge symmetries of the theory, including local Lorentz invariance. The perturbative scheme works for {\\it arbitrary} representations which satisfy the chiral gauge anomaly and mixed Lorentz-gauge anomaly cancellation conditions. Anomalous theories on the other hand manifest themselves by having divergent fermion loops which remain unregularized by the scheme. Since the invariant scheme is promoted to also include local Lorentz invariance, spectator fields which do not couple to gravity cannot be, and are not, introduced. Furthermore, the scheme is truly Weyl(chiral) in that {\\it all} fields, including the regulators, are left-handed; and {\\it only the left-handed spin connection} is needed. The scheme is therefore well-suited for the perturbative study of all four known forces in a completely chiral ...
Unit Invariance as a Unifying Principle of Physics
Shaukat, Abrar
2010-01-01
A basic principle of physics is the freedom to locally choose any unit system when describing physical quantities. Its implementation amounts to treating Weyl invariance as a fundamental symmetry of all physical theories. In this thesis, we study the consequences of this "unit invariance" principle and find that it is a unifying one. Unit invariance is achieved by introducing a gauge field called the scale, designed to measure how unit systems vary from point to point. In fact, by a uniform and simple Weyl invariant coupling of scale and matter fields, we unify massless, massive, and partially massless excitations. As a consequence, masses now dictate the response of physical quantities to changes of scale. This response is calibrated by certain "tractor Weyl weights". Reality of these weights yield Breitenlohner-Freedman stability bounds in anti de Sitter spaces. Another valuable outcome of our approach is a general mechanism for constructing conformally invariant theories. In particular, we provide direct d...
From dynamical scaling to local scale-invariance: a tutorial
Henkel, Malte
2016-01-01
Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced. Schr\\"odinger-invariance, the most simple example of local scale-invariance, will be introduced as a dynamical symmetry in the Edwards-Wilkinson universality class of interface growth. The Lie algebra construction, its representations and the Bargman superselection rules will be combined with non-equilibrium Janssen-de Dominicis field-theory to produce explicit predictions for responses and correlators, which can be compared to the results of explicit model studies. At the next level, the study of non-stationary states requires to go over, from Schr\\"odinger-invariance, to ageing-invariance. The ageing algebra admits new representations, which acts as dynamical symmetries on more general equations, and imply that each non-equilibrium scaling operator is characterised by two distinct, ind...
Effective QED Actions Representations, Gauge Invariance, Anomalies and Mass Expansions
Deser, Stanley D; Seminara, D
1998-01-01
We analyze and give explicit representations for the effective abelian vector gauge field actions generated by charged fermions with particular attention to the thermal regime in odd dimensions, where spectral asymmetry can be present. We show, through $\\zeta-$function regularization, that both small and large gauge invariances are preserved at any temperature and for any number of fermions at the usual price of anomalies: helicity/parity invariance will be lost in even/odd dimensions, and in the latter even at zero mass. Gauge invariance dictates a very general ``Fourier'' representation of the action in terms of the holonomies that carry the novel, large gauge invariant, information. We show that large (unlike small) transformations and hence their Ward identities, are not perturbative order-preserving, and clarify the role of (properly redefined) Chern-Simons terms in this context. From a powerful representation of the action in terms of massless heat kernels, we are able to obtain rigorous gauge invariant...
S— and T—Invariants in Cyber Net Systems
Institute of Scientific and Technical Information of China (English)
袁崇义
1995-01-01
Cyber nets are also known as self-modifying nets.Though proposed and defined some 20 years ago.They have never been under thorough study ever since.The reason for this is simple:the nonlinear nature of such nets keeps them away from applications of well developed methods known to the whole Petri Net Society in the world.This paper attempts to make a start of studying cyber nets in depth by proposing a way to defing and to verify S-invariants and T-invariants in such nets.These invariants reflect important dynamic properties of cyber nets.Invariants in cyber nets play a role similar to loop invariants proposed and studied by E.W.Dijkstra and D.Gries when cyber nets are used for program specification.
Discussion on Neutrino Oscillation and CPT/Lorentz Invariance Violation
Luo, Cui-Bai; Du, Yi-Lun; Wang, Yong-Long; Zong, Hong-Shi
2016-01-01
Depending on deformed canonical anticommutation relations, massless neutrino oscillation based on CPT /Lorentz invariance viol ation is discussed. It is found that the deformed canonical anti-commutation relations should satisfy the condition of new Moy al product and new non standard commutation relations. Furthermore, by comparing the neutrino experimental data and the above relations, we find that the orders of magnitude of noncommutative parameters or Lorentz invariant Violation parameters $\\mathi t{A}$ is not self-consistent. This means that the previous studies about Lorentz invariance violation in noncommutative field theory may not naturally explain massless neutrino oscillation. In other words, it should be impossible to explain neutrino os cillation by lorentz invariance violation. This conclusion is supported by the latest atmospheric neutrinos experimental resul ts from Super-Kamiokande Collaboration, which show that no evidence of Lorentz invariance violation on atmospheric neutrinos w as observe...
Covariant and locally Lorentz-invariant varying speed of light theories
Magueijo, J
2000-01-01
We propose definitions for covariance and local Lorentz invariance applicable when the speed of light $c$ is allowed to vary. They have the merit of retaining only those aspects of the usual definitions which are invariant under unit transformations, and which can therefore legitimately represent the outcome of an experiment. We then discuss some possibilities for invariant actions governing the dynamics of such theories. We consider first the classical action for matter fields and the effects of a changing $c$ upon quantization. We discover a peculiar form of quantum particle creation due to a varying $c$. We then study actions governing the dynamics of gravitation and the speed of light. We find the free, empty-space, no-gravity solution, to be interpreted as the counterpart of Minkowksi space-time, and highlight its similarities with Fock-Lorentz space-time. We also find flat-space string-type solutions, in which near the string core $c$ is much higher. We label them fast-tracks and compare them with gravi...
The Low Level Modular Invariant Partition Functions of Rank-Two Algebras
Gannon, T; Gannon, Terry
1994-01-01
Using the self-dual lattice method, we make a systematic search for modular invariant partition functions of the affine algebras $g\\*{(1)}$ of $g=A_2$, $A_1+A_1$, $G_2$, and $C_2$. Unlike previous computer searches, this method is necessarily complete. We succeed in finding all physical invariants for $A_2$ at levels $\\le 32$, for $G_2$ at levels $\\le 31$, for $C_2$ at levels $\\le 26$, and for $A_1+A_1$ at levels $k_1=k_2\\le 21$. This work thus completes a recent $A_2$ classification proof, where the levels $k=3,5,6,9,12,15,21$ had been left out. We also compute the dimension of the (Weyl-folded) commutant for these algebras and levels.
Search for Violation of Lorentz Invariance in Top Quark Pair Production and Decay
Energy Technology Data Exchange (ETDEWEB)
Abazov V. M.; Abbott, B.; Acharya, B. S.; Adams, M.; Adams, T.; Alexeev, G. D.; Alkhazov, G.; Alton, A.; Alverson, G.; Aoki, M.; Askew, A.; Atkins, S.; Augsten, K.; Avila, C.; Badaud, F.; Bagby, L.; Baldin, B.; Bandurin, D. V.; Banerjee, S.; Barberis, E.; Baringer, P.; Barreto, J.; Bartlett, J. F.; Bassler, U.; Bazterra, V.; Bean, A.; Begalli, M.; Bellantoni, L.; Berger, M. S.; Beri, S. B.; Bernardi, G.; Bernhard, R.; Bertram, I.; Besancon, M.; Beuselinck, R.; Bezzubov, V. A.; Bhat, P. C.; Bhatia, S.; Bhatnagar, V.; Blazey, G.; Blessing, S.; Bloom, K.; Boehnlein, A.; Boline, D.; Boos, E. E.; Borissov, G.; Bose, T.; Brandt, A.; Brandt, O.; Brock, R.; Brooijmans, G.; Bross, A.; Brown, D.; Brown, J.; Bu, X. B.; Buehler, M.; Buescher, V.; Bunichev, V.; Burdin, S.; Buszello, C. P.; Camacho-Perez, E.; Casey, B. C. K.; Castilla-Valdez, H.; Caughron, S.; Chakrabarti, S.; Chakraborty, D.; Chan, K. M.; Chandra, A.; Chapon, E.; Chen, G.; Chevalier-Thery, S.; Cho, D. K.; Cho, S. W.; Choi, S.; Choudhary, B.; Cihangir, S.; Claes, D.; Clutter, J.; Cooke, M.; Cooper, W. E.; Corcoran, M.; Couderc, F.; Cousinou, M. -C.; Croc, A.; Cutts, D.; Das, A.; Davies, G.; de Jong, S. J.; De La Cruz-Burelo, E.; Deliot, F.; Demina, R.; Denisov, D.; Denisov, S. P.; Desai, S.; Deterre, C.; DeVaughan, K.; Diehl, H. T.; Diesburg, M.; Ding, P. F.; Dominguez, A.; Dubey, A.; Dudko, L. V.; Duggan, D.; Duperrin, A.; Dutt, S.; Dyshkant, A.; Eads, M.; Edmunds, D.; Ellison, J.; Elvira, V. D.; Enari, Y.; Evans, H.; Evdokimov, A.; Evdokimov, V. N.; Facini, G.; Feng, L.; Ferbel, T.; Fiedler, F.; Filthaut, F.; Fisher, W.; Fisk, H. E.; Fortner, M.; Fox, H.; Fuess, S.; Garcia-Bellido, A.; Garcia-Gonzalez, J. A.; Garcia-Guerra, G. A.; Gavrilov, V.; Gay, P.; Geng, W.; Gerbaudo, D.; Gerber, C. E.; Gershtein, Y.; Ginther, G.; Golovanov, G.; Goussiou, A.; Grannis, P. D.; Greder, S.; Greenlee, H.; Grenier, G.; Gris, Ph.; Grivaz, J. -F.; Grohsjean, A.; Gruenendahl, S.; Gruenewald, M. W.; Guillemin, T.; Gutierrez, G.; Gutierrez, P.; Haas, A.; Hagopian, S.; Haley, J.; Han, L.; Harder, K.; Harel, A.; Hauptman, J. M.; Hays, J.; Head, T.; Hebbeker, T.; Hedin, D.; Hegab, H.; Heinson, A. P.; Heintz, U.; Hensel, C.; Heredia-De La Cruz, I.; Herner, K.; Hesketh, G.; Hildreth, M. D.; Hirosky, R.; Hoang, T.; Hobbs, J. D.; Hoeneisen, B.; Hohlfeld, M.; Howley, I.; Hubacek, Z.; Hynek, V.; Iashvili, I.; Ilchenko, Y.; Illingworth, R.; Ito, A. S.; Jabeen, S.; Jaffre, M.; Jayasinghe, A.; Jesik, R.; Johns, K.; Johnson, E.; Johnson, M.; Jonckheere, A.; Jonsson, P.; Joshi, J.; Jung, A. W.; Juste, A.; Kaadze, K.; Kajfasz, E.; Karmanov, D.; Kasper, P. A.; Katsanos, I.; Kehoe, R.; Kermiche, S.; Khalatyan, N.; Khanov, A.; Kharchilava, A.; Kharzheev, Y. N.; Kiselevich, I.; Kohli, J. M.; Kostelecky, V. A.; Kozelov, A. V.; Kraus, J.; Kulikov, S.; Kumar, A.; Kupco, A.; Kurca, T.; Kuzmin, V. A.; Lammers, S.; Landsberg, G.; Lebrun, P.; Lee, H. S.; Lee, S. W.; Lee, W. M.; Lellouch, J.; Li, H.; Li, L.; Li, Q. Z.; Lim, J. K.; Lincoln, D.; Linnemann, J.; Lipaev, V. V.; Lipton, R.; Liu, H.; Liu, Y.; Lobodenko, A.; Lokajicek, M.; de Sa, R. Lopes; Lubatti, H. J.; Luna-Garcia, R.; Lyon, A. L.; Maciel, A. K. A.; Madar, R.; Magana-Villalba, R.; Malik, S.; Malyshev, V. L.; Maravin, Y.; Martinez-Ortega, J.; McCarthy, R.; McGivern, C. L.; Meijer, M. M.; Melnitchouk, A.; Menezes, D.; Mercadante, P. G.; Merkin, M.; et al.
2012-06-27
Using data collected with the D0 detector at the Fermilab Tevatron Collider, corresponding to 5.3 fb{sup -1} of integrated luminosity, we search for violation of Lorentz invariance by examining the t{bar t} production cross section in lepton+jets final states. We quantify this violation using the standard-model extension framework, which predicts a dependence of the t{bar t} production cross section on sidereal time as the orientation of the detector changes with the rotation of the Earth. Within this framework, we measure components of the matrices (c{sub Q}){sub {mu}{nu}33} and (c{sub U}){sub {mu}{nu}33} containing coefficients used to parametrize violation of Lorentz invariance in the top quark sector. Within uncertainties, these coefficients are found to be consistent with zero.
AN ILLUMINATION INVARIANT TEXTURE BASED FACE RECOGNITION
Directory of Open Access Journals (Sweden)
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.
MERIT: Minutiae Extraction using Rotation Invariant Algorithm
Directory of Open Access Journals (Sweden)
Avinash Pokhriyal,
2010-07-01
Full Text Available Thinning a fingerprint makes its ridges as thin as one pixel and still retaining its basic structure. So many algorithms are devised by researchers to extract skeleton of a fingerprint image, but the problem is that they produce different results with different rotations of the same fingerprint image. This results in inefficient minutiae extraction. In this paper, a new way of thinning a fingerprint image is proposed. This method is called MERIT (Minutiae Extraction using Rotation Invariant Thinning, as it thins a fingerprint image irrespective of the fingerprint's position and then extracts minutiae points from a fingerprint image. First of all, we binarize the fingerprint image and convert it into a 0-1 pattern. Then, we apply some morphological operations like dilation and erosion, and also some if-then rules governing a 3x3 mask that is to be convoluted throughout the image to skeletonize it. In the end,some postprocessing is done on the thinned fingerprint image to remove false minutiae structures from it. Finally genuine minutiae points are extracted from the thinned fingerprint image along with their directions. Results show that the proposed method extracts genuine minutiae points even from low-quality fingerprint images.
Invariant measures and the soliton resolution conjecture
Chatterjee, Sourav
2012-01-01
The soliton resolution conjecture for the focusing nonlinear Schrodinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually resolve into a radiation component that disperses like a linear solution, plus a localized component that behaves like a soliton or multi-soliton solution. Considered to be one of the fundamental open problems in the area of nonlinear dispersive equations, this conjecture has eluded a proof or even a precise formulation till date. This paper proves a "statistical version" of this conjecture at mass-subcritical nonlinearity, in the following sense. The uniform probability distribution on the set of all functions with a given mass and energy, if such a thing existed, would be a natural invariant measure for the NLS flow and would reflect the long-term behavior for "generic initial data" with that mass and energy. Unfortunately, such a probability measure does not exist. We circumvent this problem by constructing a sequenc...
Higgs Triplet Model with Classically Conformal Invariance
Okada, Hiroshi; Yagyu, Kei
2015-01-01
We discuss an extension of the minimal Higgs triplet model with a classically conformal invariance and with a gauged $U(1)_{B-L}$ symmetry. In our scenario, tiny masses of neutrinos are generated by a hybrid contribution from the type-I and type-II seesaw mechanisms. The shape of the Higgs potential at low energies is determined by solving one-loop renormalization group equations for all the scalar quartic couplings with a set of initial values of parameters at the Planck scale. We find a successful set of the parameters in which the $U(1)_{B-L}$ symmetry is radiatively broken via the Coleman-Weinberg mechanism at the ${\\cal O}$(10) TeV scale, and the electroweak symmetry breaking is also triggered by the $U(1)_{B-L}$ breaking. Under this configuration, we can predict various low energy observables such as the mass spectrum of extra Higgs bosons, and the mixing angles. Furthermore, using these predicted mass parameters, we obtain upper limits on Yukawa couplings among an isospin triplet Higgs field and lepton...
Computing with scale-invariant neural representations
Howard, Marc; Shankar, Karthik
The Weber-Fechner law is perhaps the oldest quantitative relationship in psychology. Consider the problem of the brain representing a function f (x) . Different neurons have receptive fields that support different parts of the range, such that the ith neuron has a receptive field at xi. Weber-Fechner scaling refers to the finding that the width of the receptive field scales with xi as does the difference between the centers of adjacent receptive fields. Weber-Fechner scaling is exponentially resource-conserving. Neurophysiological evidence suggests that neural representations obey Weber-Fechner scaling in the visual system and perhaps other systems as well. We describe an optimality constraint that is solved by Weber-Fechner scaling, providing an information-theoretic rationale for this principle of neural coding. Weber-Fechner scaling can be generated within a mathematical framework using the Laplace transform. Within this framework, simple computations such as translation, correlation and cross-correlation can be accomplished. This framework can in principle be extended to provide a general computational language for brain-inspired cognitive computation on scale-invariant representations. Supported by NSF PHY 1444389 and the BU Initiative for the Physics and Mathematics of Neural Systems,.
Right-invariant Sobolev metrics ${H}^{s}$ on the diffeomorphisms group of the circle
Escher, Joachim
2012-01-01
We study the geodesic flow on the diffeomorphisms group of the circle with respect to the right-invariant metric induced by the fractional Sobolev norm $H^s$ for $s\\ge1/2$. We show that the corresponding initial value problem possesses a maximal solution in the smooth category and that the Riemannian exponential mapping is a smooth diffeomorphism from a neighbourhood of 0 in $C^{\\infty}(S)$ onto a neighbourhood of the identity in $Diff^{\\infty}(S)$.
A Vanishing Result for Donaldson Thomas Invariants of P1 Scroll
Institute of Scientific and Technical Information of China (English)
Huai Liang CHANG
2014-01-01
Let S be a smooth algebraic surface and let L be a line bundle on S. Suppose there is a holomorphic two form over S with zero loci to be a curve C. We show that the Donaldson-Thomas invariant of the P1 scroll X =P (L⊕OS ) vanishes unless the curves being enumerated lie in D=P (L|C⊕OC ). Our method is cosection localization of Y.-H. Kiem and J. Li.
Conformal Invariance and Conserved Quantities of General Holonomic Systems
Institute of Scientific and Technical Information of China (English)
CAI Jian-Le
2008-01-01
Conformal invarianee and conserved quantities of general holonomic systems are studied. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators are described.The definition of conformal invariance and determining equation for the system are provided.The conformal factor expression is deduced from conformal invariance and Lie symmetry.The necessary and sufficient condition,that conformal invariance of the system would be Lie symmetry,is obtained under the infinitesimal one-parameter transformation group. The corresponding conserved quantity is derived with the aid of a structure equation.Lastly,an example is given to demonstrate the application of the result.
Invariant Gait Continuum Based on the Duty-Factor
DEFF Research Database (Denmark)
Fihl, Preben; Moeslund, Thomas B.
2008-01-01
In this paper we present a method to describe the continuum of human gait in an invariant manner. The gait description is based on the duty-factor which is adopted from the biomechanics literature. We generate a database of artificial silhouettes representing the three main types of gait, i.......e. walking, jogging, and running. By generating silhouettes from different camera angles we make the method invariant to camera viewpoint and to changing directions of movement. Silhouettes are extracted using the Code-book method and represented in a scale- and translation-invariant manner by using shape...
Link Invariants from Classical Chern-Simons Theory
Leal, L C
2002-01-01
Taking as starting point a perturbative study of the classical equations of motion of the non-Abelian Chern-Simons Theory with non-dynamical sources, we search for analytical expressions for link invarians. In order to present this expressions in a manifestly diffeomorphism-invariant form, we introduce a set of differential forms associated with submanifolds in Euclidean three-space that allow us to write the link invariants as a kind of surface-dependent diffeomorphism-invariants that present certain Abelian gauge symmetry.
False Signals of CP-Invariance Violation at DUNE
de Gouvêa, André
2016-01-01
One of the main goals of the Deep Underground Neutrino Experiment (DUNE) is to look for new sources of CP-invariance violation. Another is to significantly test the three-massive-neutrinos paradigm. Here, we show that there are CP-invariant new physics scenarios which, as far as DUNE data are concerned, cannot be distinguished from the three-massive-neutrinos paradigm with very large CP-invariance violating effects. We discuss examples with non-standard neutrino interactions and with a fourth neutrino mass eigenstate. We briefly discuss how ambiguities can be resolved by combining DUNE data with data from other long-baseline experiments, including Hyper-Kamiokande.
Diagonal invariant ideals of Toeplitz algebras on discrete groups
Institute of Scientific and Technical Information of China (English)
许庆祥
2002-01-01
Diagonal invariant ideals of Toeplitz algebras defined on discrete groups are introduced and studied. In terms of isometric representations of Toeplitz algebras associated with quasi-ordered groups, a character of a discrete group to be amenable is clarified. It is proved that when G is Abelian, a closed two-sided non-trivial ideal of the Toeplitz algebra defined on a discrete Abelian ordered group is diagonal invariant if and only if it is invariant in the sense of Adji and Murphy, thus a new proof of their result is given.
Mapping of shape invariant potentials by the point canonical transformation
Setare, M R
2008-01-01
In this paper by using the method of point canonical transformation we find that the Coulomb and Kratzer potentials can be mapped to the Morse potential. Then we show that the P\\"{o}schl-Teller potential type I belongs to the same subclass of shape invariant potentials as Hulth\\'{e}n potential. Also we show that the shape-invariant algebra for Coulomb, Kratzer, and Morse potentials is SU(1,1), while the shape-invariant algebra for P\\"{o}schl-Teller type I and Hulth\\'{e}n is SU(2).
Evolution of Brain Tumor and Stability of Geometric Invariants
Directory of Open Access Journals (Sweden)
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.
Gauge invariant perturbations of Petrov type D space-times
Whiting, Bernard; Shah, Abhay
2016-03-01
The Regge-Wheeler and Zerilli equations are satisfied by gauge invariant perturbations of the Schwarzschild black hole geometry. Both the perturbation of the imaginary part of Ψ2 (a component of the Weyl curvature), and its time derivative, are gauge invariant and solve the Regge-Wheeler equation with different sources. The Ψ0 and Ψ4 perturbations of the Weyl curvature are not only gauge, but also tetrad, invariant. We explore the framework in which these results hold, and consider what generalizations may extend to the Kerr geometry, and presumably to Petrov type D space-times in general. NSF Grants PHY 1205906 and 1314529, ERC (EU) FP7 Grant 304978.
Shift-modulation invariant spaces on LCA groups
Cabrelli, Carlos
2011-01-01
A $(K,\\Lambda)$ shift-modulation invariant space is a subspace of $L^2(G)$, that is invariant by translations along elements in $K$ and modulations by elements in $\\Lambda$. Here $G$ is a locally compact abelian group, and $K$ and $\\Lambda$ are closed subgroups of $G$ and the dual group $\\hat G$, respectively. In this article we provide a characterization of shift-modulation invariant spaces in this general context when $K$ and $\\Lambda$ are uniform lattices. This extends previous results known for $L^2(\\R^d)$. We develop fiberization techniques and suitable range functions adapted to LCA groups needed to provide the desired characterization.
Tuning the cosmological constant, broken scale invariance, unitarity
Energy Technology Data Exchange (ETDEWEB)
Förste, Stefan; Manz, Paul [Bethe Center for Theoretical Physics,Nussallee 12, 53115 Bonn (Germany); Physikalisches Institut der Universität Bonn,Nussallee 12, 53115 Bonn (Germany)
2016-06-10
We study gravity coupled to a cosmological constant and a scale but not conformally invariant sector. In Minkowski vacuum, scale invariance is spontaneously broken. We consider small fluctuations around the Minkowski vacuum. At the linearised level we find that the trace of metric perturbations receives a positive or negative mass squared contribution. However, only for the Fierz-Pauli combination the theory is free of ghosts. The mass term for the trace of metric perturbations can be cancelled by explicitly breaking scale invariance. This reintroduces fine-tuning. Models based on four form field strength show similarities with explicit scale symmetry breaking due to quantisation conditions.
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 ways of construction of PISs is proved. In this framework the complete classification of regular partially invariant solutions of ideal MHD equations is given.
Two Lagrange-like optical invariants and some applications.
Corrente, Fabio; Onorato, Pasquale
2011-05-01
Geometric optics can be completely derived from Fermat's principle, as classical mechanics can be obtained by the application of the Hamilton principle. In Lagrangian optics, for optical systems with rotational symmetry, is known the invariant L₃, the Lagrange optical invariant. For systems built only with spherical lenses, we demonstrate there are two other optical invariants, L₁ and L₂, analogous to L₃. A proof based on Snell's law, the Weierstrass-Erdman jump condition, and the expression of the ray between two optical surfaces in the Hamiltonian formalism is reported. The presence of a conserved vector, L, allows us to write the equation of an emerging ray without any approximation.
Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space
Directory of Open Access Journals (Sweden)
Mahmut Mak
2014-01-01
Full Text Available We consider hyperbolic rotation (G0, hyperbolic translation (G1, and horocyclic rotation (G2 groups in H3, which is called Minkowski model of hyperbolic space. Then, we investigate extrinsic differential geometry of invariant surfaces under subgroups of G0 in H3. Also, we give explicit parametrization of these invariant surfaces with respect to constant hyperbolic curvature of profile curves. Finally, we obtain some corollaries for flat and minimal invariant surfaces which are associated with de Sitter and hyperbolic shape operator in H3.
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.
Isospin Invariance and the Vacuum Polarization Energy of Cosmic Strings
Weigel, H; Graham, N
2016-01-01
We corroborate the previously applied spectral approach to compute the vacuum polarization energy of string configurations in models similar to the standard model of particle physics. The central observation underlying this corroboration is the existence of a particular global isospin transformation of the string configuration. Under this transformation the single particle energies of the quantum fluctuations are invariant, while the inevitable implementation of regularization and renormalization requires operations that are not invariant. We verify numerically that all such variances eventually cancel, and that the vacuum polarization energy obtained in the spectral approach is indeed gauge invariant.
Noncommutative field theory and violation of translation invariance
Bertolami, O
2003-01-01
Noncommutative field theories with commutator of the coordinates of the form $[x^{mu},x^{nu}]=i Lambda_{quad omega}^{mu nu}x^{omega}$ are studied. Explicit Lorentz invariance is mantained considering $Lambda $ a Lorentz tensor. It is shown that a free quantum field theory is not affected. Since invariance under translations is broken, the conservation of energy-momentum is violated, obeying a new law which is expressed by a Poincar'e-invariant equation. The resulting new kinematics is studied and applied to simple examples and to astrophysical puzzles, such as the observed violation of the GZK cutoff. The $lambda
EXACT AND ADIABATIC INVARIANTS OF FIRST-ORDER LAGRANGE SYSTEMS
Institute of Scientific and Technical Information of China (English)
陈向炜; 尚玫; 梅凤翔
2001-01-01
A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.
The rank four heterotic modular invariant partition functions
Gannon, T
1994-01-01
In this paper, we develop several general techniques to investigate modular invariants of conformal field theories whose algebras of the holomorphic and anti-holomorphic sectors are different. As an application, we find all such "heterotic" WZNW physical invariants of (horizontal) rank four: there are exactly seven of these, two of which seem to be new. Previously, only those of rank $\\le 3$ have been completely classified. We also find all physical modular invariants for $su(2)_{k_1}\\times su(2)_{k_2}$, for $22>k_1>k_2$, and $k_1=28$, $k_2<22$, completing the classification of ref.{} \\SUSU.
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.
Noncommutative Field Theory With General Translation Invariant Star Products
Rivera, Manolo
2015-01-01
We compute the two-point and four-point Green's function of the noncommutative $\\phi^{4}$ field theory; first with the s-ordered star products and then with a general translation invariant star product. We derive the differential expression for any translation invariant star product, and with the help of this expression we show that any of these products can be written in terms of a twist. Finally, using the notion of the twisted action of the infinitesimal Poincar\\'e transformations, we show that the commutator between the coordinate functions is invariant under Poincar\\'e transformations at a deformed level.
On projective invariants of the complex Finsler spaces
Aldea, Nicoleta
2011-01-01
In this paper the projective curvature invariants of a complex Finsler space are obtained. By means of these invariants the notion of complex Douglas space is then defined. A special approach is devoted to obtain the equivalence conditions that a complex Finsler space should be Douglas. It is shown that any weakly K\\"{a}hler Douglas space is a complex Berwald space. A projective curvature invariant of Weyl type characterizes the complex Berwald spaces. They must be either purely Hermitian of constant holomorphic curvature or non purely Hermitian of vanish holomorphic curvature. The locally projectively flat complex Finsler metrics are also studied
Rotational invariant similarity measurement for content-based image indexing
Ro, Yong M.; Yoo, Kiwon
2000-04-01
We propose a similarity matching technique for contents based image retrieval. The proposed technique is invariant from rotated images. Since image contents for image indexing and retrieval would be arbitrarily extracted from still image or key frame of video, the rotation invariant property of feature description of image is important for general application of contents based image indexing and retrieval. In this paper, we propose a rotation invariant similarity measurement in cooperating with texture featuring base on HVS. To simplify computational complexity, we employed hierarchical similarity distance searching. To verify the method, experiments with MPEG-7 data set are performed.
Optimal affine-invariant matching: performance characterization
Costa, Mauro S.; Haralick, Robert M.; Shapiro, Linda G.
1992-04-01
The geometric hashing scheme proposed by Lamdan and Wolfson can be very efficient in a model-based matching system, not only in terms of the computational complexity involved, but also in terms of the simplicity of the method. In a recent paper, we discussed errors that can occur with this method due to quantization, stability, symmetry, and noise problems. These errors make the original geometric hashing technique unsuitable for use on the factory floor. Beginning with an explicit noise model, which the original Lamdan and Wolfson technique lacks, we derived an optimal approach that overcomes these problems. We showed that the results obtained with the new algorithm are clearly better than the results from the original method. This paper addresses the performance characterization of the geometric hashing technique, more specifically the affine-invariant point matching, applied to the problem of recognizing and determining the pose of sheet metal parts. The experiments indicate that with a model having 10 to 14 points, with 2 points of the model undetected and 10 extraneous points detected, and with the model points perturbed by Gaussian noise of standard deviation 3 (0.58 of range), the average amount of computation required to obtain an answer is equivalent to trying 11 of the possible three-point bases. The misdetection rate, measured by the percentage of correct bases matches that fail to verify, is 0.9. The percentage of incorrect bases that successfully produced a match that did verify (false alarm rate) is 13. And, finally, 2 of the experiments failed to find a correct match and verify it. Results for experiments with real images are also presented.
Invariant natural killer T cells and mucosal-associated invariant T cells in multiple sclerosis.
Bianchini, Elena; De Biasi, Sara; Simone, Anna Maria; Ferraro, Diana; Sola, Patrizia; Cossarizza, Andrea; Pinti, Marcello
2017-03-01
Multiple sclerosis (MS) is a chronic progressive inflammatory demyelinating disorder of the central nervous system, and in several countries is a leading cause of permanent neurological disability in young adults, particularly women. MS is considered an autoimmune disease, caused by an aberrant immune response to environmental triggers in genetically susceptible subjects. However, the contribution of the innate or of the adaptive immune system to the development and progression of the disease has not yet been fully elucidated. Innate-like T lymphocytes are unconventional T cells that bridge the innate and adaptive arms of the immune system, because they use a T cell receptor to sense external ligands, but behave like innate cells when they rapidly respond to stimuli. These cells could play an important role in the pathogenesis of MS. Here, we focus on invariant natural killer T (iNKT) cells and mucosal-associated invariant T (MAIT) cells, and we review the current knowledge on their biology and possible involvement in MS. Although several studies have evaluated the frequency and functions of iNKT and MAIT cells both in MS patients and in experimental mouse models, contradictory observations have been reported, and it is not clear whether they exert a protective or a pro-inflammatory and harmful role. A better understanding of how immune cells are involved in MS, and of their interactions could be of great interest for the development of new therapeutic strategies.
Zhou, Long-Qiao; Meleshko, Sergey V.
2017-01-01
A linear thermoviscoelastic model for homogeneous, aging materials with memory is established. A system of integro-differential equations is obtained by using two motions (a one-dimensional motion and a shearing motion) for this model. Applying the group analysis method to the system of integro-differential equations, the admitted Lie group is determined. Using this admitted Lie group, invariant and partially invariant solutions are found. The present paper gives a first example of application of partially invariant solutions to integro-differential equations.
First Integrals and Integral Invariants of Relativistic Birkhoffian Systems
Institute of Scientific and Technical Information of China (English)
LUO Shao-Kai
2003-01-01
For a relativistic Birkhoffian system, the first integrals and the construction of integral invariants arestudied. Firstly, the cyclic integrals and the generalized energy integral of the system are found by using the perfectdifferential method. Secondly, the equations of nonsimultaneous variation of the system are established by using therelation between the simultaneous variation and the nonsimultaneous variation. Thirdly, the relation between the firstintegral and the integral invariant of the system is studied, and it is proved that, using a first integral, we can construct anintegral invariant of the system. Finally, the relation between the relativistic Birkhoffian dynamics and the relativisticHamiltonian dynamics is discussed, and the first integrals and the integral invariants of the relativistic Hamiltoniansystem are obtained. Two examples are given to illustrate the application of the results.
Form Invariant Sommerfeld Electrical Conductivity in Generalised d Dimensions
Institute of Scientific and Technical Information of China (English)
Muktish Acharyya
2011-01-01
The Sommerfeld electrical conductivity is calculated in d dimensions following Boltzmann kinetic approach. At T =0, the mathematical form of the electrical conductivity is found to remain invariant in any generalised spatial （d） dimensions.
Modified dispersion relations, inflation and scale-invariance
Bianco, Stefano; Wilson-Ewing, Edward
2016-01-01
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 red-shift these short wavelength modes to cosmological scales in such a way that the scale-invariance is not lost. This can be done by inflation with a sufficiently large Hubble rate, without any requirement for slow roll. We also show that in the case of slow-roll inflation, modes that start in their vacuum quantum state will become nearly scale-invariant when they exit the Hubble radius for any power law modified dispersion relation.
Projections onto Invariant Subspaces of Some Banach Algebras
Institute of Scientific and Technical Information of China (English)
Ali GHAFFARI
2008-01-01
In this paper,among other things,the author studies the weak*-closed left translation invariant complemented subspace of semigroup algebras and group algebras.Also,the author studiesthe relationships between projections and amenability.
Lorentz invariant CPT breaking in the Dirac equation
Fujikawa, Kazuo
2016-01-01
If one modifies the Dirac equation in momentum space to $[\\gamma^{\\mu}p_{\\mu}-m-\\Delta m(\\theta(p_{0})-\\theta(-p_{0})) \\theta(p_{\\mu}^{2})]\\psi(p)=0$, the symmetry of positive and negative energy eigenvalues is lifted by $m\\pm \\Delta m$ for a small $\\Delta m$. The mass degeneracy of the particle and antiparticle is thus lifted in a Lorentz invariant manner since the combinations $\\theta(\\pm p_{0})\\theta(p_{\\mu}^{2})$ with step functions are manifestly Lorentz invariant. We explain an explicit construction of this CPT breaking term in coordinate space, which is Lorentz invariant but non-local at a distance scale of the Planck length. The application of this Lorentz invariant CPT breaking mechanism to the possible mass splitting of the neutrino and antineutrino in the Standard Model is briefly discussed.
A DISCUSSION ABOUT SCALE INVARIANTS FOR TENSOR FUNCTIONS
Institute of Scientific and Technical Information of China (English)
Huang Yongnian; Luo Xiongping; Emily S.C.Ching
2000-01-01
It is found that in some cases the complete and irreducible scale invariants given by Ref.[1]are not independent.There are some implicit functional relations among them.The scale invariants for two different cases are calculated.The first case is an arbitrary second order tensor.The second case includes a symmetric tensor,an antisymmetric tensor and a vector.By using the eigentensor notation it is proved that in the first case there are only six independent scale invariants rather than seven as reported in Ref.[1]and in the second case there are only nine independent scale invariants which are leas than that obtained in Ref.[1].
Invariance entropy for deterministic control systems an introduction
Kawan, Christoph
2013-01-01
This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state space invariant by means of a symbolic coder-controller pair. This concept is essentially equivalent to the notion of topological feedback entropy introduced by Nair, Evans, Mareels and Moran (Topological feedback entropy and nonlinear stabilization. IEEE Trans. Automat. Control 49 (2004), 1585–1597). The book presents the foundations of a theory which aims at finding expressions for invariance entropy in terms of dynamical quantities such as Lyapunov exponents. While both discrete-time and continuous-time systems are treated, the emphasis lies on systems give...
The Scale Invariant Synchrotron Jet of Flat Spectrum Radio Quasars
Indian Academy of Sciences (India)
L. M. Du; J. M. Bai; Z. H. Xie; T. F. Yi; Y. B. Xu; R. Xue; X. H. Wang
2015-06-01
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 fundamental plane, while near-Eddington sources such as FSRQs have not been explicitly studied. The extracted physical properties of synchrotron jet of FSRQs have been shown to be scale invariant using our sample. The results are in good agreement with theoretical expectations of Heinz & Sunyaev (2003). Therefore, the jet synchrotron is shown to be scale independent, regardless of the accretion modes. Results in this article thus lend support to the scale invariant model of the jet synchrotron throughout the mass scale of black hole systems.
Conformal invariance and Hamilton Jacobi theory for dissipative systems
Kiehn, R. M.
1975-01-01
For certain dissipative systems, a comparison can be made between the Hamilton-Jacobi theory and the conformal invariance of action theory. The two concepts are not identical, but the conformal action theory covers the Hamilton-Jacobi theory.
Relationship Between Two Classes of Shape-Invariant Potentials
Institute of Scientific and Technical Information of China (English)
QIAN Shang-Wu; GU Zhi-Yu
2001-01-01
We show that two classes of shape-invariant potentials are interrelated to each other. For all one-dimensional shape-invariant potentials with parameters related by translation, i.e. the first class of shapc-invariant potentials (SIP1),we can find their multi-parameter deformations with q acting as the deformation parameter, i.e. the second class of shape-invariant potentials (SIP2) with parameters related by scaling. In order to get closed solution of SIP2, we consider two infinitesimal intervals, one is close to q= 0 another close to q = 1, and show that in these intervals we can get separately two first-order approximate solutions in closed form, furthermore we prove that all SIP1 can be obtained by the limiting procedures for corresponding SIP2.``
Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
Eldering, Jaap
2012-01-01
We prove a persistence result for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. The bounded geometry of the ambient manifold is a crucial assumption in order to control the uniformity of all estimates throughout the proof.
Invariant approach to CP in unbroken Δ(27
Directory of Open Access Journals (Sweden)
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.
Geometrically Invariant Watermarking Scheme Based on Local Feature Points
Directory of Open Access Journals (Sweden)
Jing Li
2012-06-01
Full Text Available Based on local invariant feature points and cross ratio principle, this paper presents a feature-point-based image watermarking scheme. It is robust to geometric attacks and some signal processes. It extracts local invariant feature points from the image using the improved scale invariant feature transform algorithm. Utilizing these points as vertexes it constructs some quadrilaterals to be as local feature regions. Watermark is inserted these local feature regions repeatedly. In order to get stable local regions it adjusts the number and distribution of extracted feature points. In every chosen local feature region it decides locations to embed watermark bits based on the cross ratio of four collinear points, the cross ratio is invariant to projective transformation. Watermark bits are embedded by quantization modulation, in which the quantization step value is computed with the given PSNR. Experimental results show that the proposed method can strongly fight more geometrical attacks and the compound attacks of geometrical ones.
Kauffman polynomials of some links and invariants of 3-manifolds
Institute of Scientific and Technical Information of China (English)
李起升
2002-01-01
Kauffman bracket polynomials of the so-called generalized tree-like links are studied. An algorithm of Witten type invariants, which was defined by Blanchet and Habegger et al. of more general 3-manifolds is given.
Z2 Invariants of Topological Insulators as Geometric Obstructions
Fiorenza, Domenico; Monaco, Domenico; Panati, Gianluca
2016-05-01
We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to -1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2 d, the obstruction to the existence of such a frame is shown to be encoded in a Z_2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3 d, instead, four Z_2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.
Robust Image Hashing Using Radon Transform and Invariant Features
Directory of Open Access Journals (Sweden)
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.
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 meas
Structure of group invariants of a quasiperiodic flow
Directory of Open Access Journals (Sweden)
Lennard F. Bakker
2004-03-01
Full Text Available It is shown that the multiplier representation of the generalized symmetry group of a quasiperiodic flow induces a semidirect product structure on certain group invariants (including the generalized symmetry group of the flow's smooth conjugacy class.
MINIMAX INVARIANT ESTIMATOR OF CONTINUOUS DISTRIBUTION FUNCTION UNDER LINEX LOSS
Institute of Scientific and Technical Information of China (English)
Jianhui NING; Minyu XIE
2007-01-01
In this paper we consider the problem of estimation of a continuous distribution function under the LINEX loss function.The best invariant estimator is obtained,and proved to be minimax for any sample size n≥1.
Rearrangement invariant optimal range for Hardy type operators
Soria, Javier; Tradacete, Pedro
2013-01-01
We characterize, in the context of rearrangement invariant spaces, the optimal range space for a class of monotone operators related to the Hardy operator. The connection between optimal range and optimal domain for these operators is carefully analyzed.
Discrete Symmetries In Lorentz-Invariant Non-Commutative QED
Morita, K
2003-01-01
It is pointed out that the usual $\\theta$-algebra assumed for non-commuting coordinates is not $P$- and $T$-invariant, unless one {\\it formally} transforms the non-commutativity parameter $\\theta^{\\mu\
Invariant quantities in the scalar-tensor theories of gravitation
Jarv, Laur; Saal, Margus; Vilson, Ott
2014-01-01
We consider the general scalar-tensor gravity without derivative couplings. By rescaling of the metric and reparametrization of the scalar field, the theory can be presented in different conformal frames and parametrizations. In this work we argue, that while due to the freedom to transform the metric and the scalar field, the scalar field itself does not carry a physical meaning (in a generic parametrization), there are functions of the scalar field and its derivatives which remain invariant under the transformations. We put forward a scheme how to construct these invariants, discuss how to formulate the theory in terms of the invariants, and show how the observables like parametrized post-Newtonian parameters and characteristics of the cosmological solutions can be neatly expressed in terms of the invariants. In particular, we describe the scalar field solutions in Friedmann-Lema\\^itre-Robertson-Walker cosmology in Einstein and Jordan frames, and explain their correspondence despite the approximate equation...
Invariant representation for spectral reflectance images and its application
Directory of Open Access Journals (Sweden)
Ibrahim Abdelhameed
2011-01-01
Full Text Available Abstract Spectral images as well as color images observed from object surfaces are much influenced by various illumination conditions such as shading and specular highlight. Several invariant representations were proposed for these conditions using the standard dichromatic reflection model of dielectric materials. However, these representations are inadequate for other materials like metal. This article proposes an invariant representation that is derived from the standard dichromatic reflection model for dielectric and the extended dichromatic reflection model for metal. We show that a normalized surface-spectral reflectance by the minimum reflectance is invariant to highlights, shading, surface geometry, and illumination intensity. Here the illumination spectrum and the spectral sensitivity functions of the imaging system are measured in a separate way. As an application of the proposed invariant representation, a segmentation algorithm based on the proposed representation is presented for effectively segmenting spectral images of natural scenes and bare circuit boards.
Gauge Invariance and Equations of Motion for Closed String Modes
Sathiapalan, B
2014-01-01
We continue earlier discussions on the exact renormalization group and loop variables 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 {\\em including} the physical graviton. The level $(2,\\bar 2)$ massive field equations are used to illustrate the techniques. At this level there are mixed symmetry tensors. Gauge invariant inter...
Dynamics of 3D view invariance in monkey inferotemporal cortex.
Ratan Murty, N Apurva; Arun, Sripati P
2015-04-01
Rotations in depth are challenging for object vision because features can appear, disappear, be stretched or compressed. Yet we easily recognize objects across views. Are the underlying representations view invariant or dependent? This question has been intensely debated in human vision, but the neuronal representations remain poorly understood. Here, we show that for naturalistic objects, neurons in the monkey inferotemporal (IT) cortex undergo a dynamic transition in time, whereby they are initially sensitive to viewpoint and later encode view-invariant object identity. This transition depended on two aspects of object structure: it was strongest when objects foreshortened strongly across views and were similar to each other. View invariance in IT neurons was present even when objects were reduced to silhouettes, suggesting that it can arise through similarity between external contours of objects across views. Our results elucidate the viewpoint debate by showing that view invariance arises dynamically in IT neurons out of a representation that is initially view dependent.
Communication: Fitting potential energy surfaces with fundamental invariant neural network
Shao, Kejie; Chen, Jun; Zhao, Zhiqiang; Zhang, Dong H.
2016-08-01
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 OH3 and CH4 were constructed with FI-NN, with the accuracy confirmed by full-dimensional quantum dynamic scattering and bound state calculations.
Gauge Fixing Invariance and Anti-BRST Symmetry
Varshovi, Amir Abbass
2016-01-01
It is shown that anti-BRST invariance in quantum gauge theories can be considered as the quantized version of the symmetry of classical gauge theories with respect to different gauge fixing mechanisms.
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...
Invariant Quantum Algorithms for Insertion into an Ordered List
Farhi, E; Gutmann, S; Sipser, M; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam; Sipser, Michael
1999-01-01
We consider the problem of inserting one item into a list of N-1 ordered items. We previously showed that no quantum algorithm could solve this problem in fewer than log N/(2 log log N) queries, for N large. We transform the problem into a "translationally invariant" problem and restrict attention to invariant algorithms. We construct the "greedy" invariant algorithm and show numerically that it outperforms the best classical algorithm for various N. We also find invariant algorithms that succeed exactly in fewer queries than is classically possible, and iterating one of them shows that the insertion problem can be solved in fewer than 0.53 log N quantum queries for large N (where log N is the classical lower bound). We don't know whether a o(log N) algorithm exists.
About Shape Identification Methods of Objects Invariant to Projective Transformations
Directory of Open Access Journals (Sweden)
Gostev Ivan M.
2016-01-01
Full Text Available Diffculties concerning the choice of the invariants of the projective transformation groups used for the identification of the shapes of planar objects are illustrated and solutions allowing the derivation of robust identification criteria are discussed.
Permutation Centralizer Algebras and Multi-Matrix Invariants
Mattioli, Paolo
2016-01-01
We introduce a class of permutation centralizer algebras which underly the combinatorics of multi-matrix gauge invariant observables. One family of such non-commutative algebras is parametrised by two integers. Its Wedderburn-Artin decomposition explains the counting of restricted Schur operators, which were introduced in the physics literature to describe open strings attached to giant gravitons and were subsequently used to diagonalize the Gaussian inner product for gauge invariants of 2-matrix models. The structure of the algebra, notably its dimension, its centre and its maximally commuting sub-algebra, is related to Littlewood-Richardson numbers for composing Young diagrams. It gives a precise characterization of the minimal set of charges needed to distinguish arbitrary matrix gauge invariants, which are related to enhanced symmetries in gauge theory. The algebra also gives a star product for matrix invariants. The centre of the algebra allows efficient computation of a sector of multi-matrix correlator...
Exact computation of the n-loop invariants of knots
Garoufalidis, Stavros; Scott, Shane
2015-01-01
The loop invariants of Dimofte-Garoufalidis is a formal power series with arithmetically interesting coefficients that conjecturally appears in the asymptotics of the Kashaev invariant of a knot to all orders in $1/N$. We develop methods implemented in SnapPy that compute the first 6 coefficients of the formal power series of a knot. We give examples that illustrate our method and its results.
Construction of Lie algebras and invariant tensors through abelian semigroups
Energy Technology Data Exchange (ETDEWEB)
Izaurieta, Fernando; RodrIguez, Eduardo; Salgado, Patricio [Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)], E-mail: fizaurie@gmail.com, E-mail: edurodriguez@udec.cl, E-mail: pasalgad@udec.cl
2008-11-01
The Abelian Semigroup Expansion Method for Lie Algebras is briefly explained. Given a Lie Algebra and a discrete abelian semigroup, the method allows us to directly build new Lie Algebras with their corresponding non-trivial invariant tensors. The Method is especially interesting in the context of M-Theory, because it allows us to construct M-Algebra Invariant Chern-Simons/Transgression Lagrangians in d = 11.
On the structure of finitely generated shift-invariant subspaces
Kazarian, K. S.
2016-01-01
A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an element of the finitely generated shift-invariant subspace as a linear combination of Fourier transformations of generators. An estimate for the norms of those coefficients is derived. For the proof a sort of orthogonalization procedure for generators is used wh...
A translation invariant bipolaron in the Holstein model and superconductivity.
Lakhno, Victor
2016-01-01
Large-radius translation invariant (TI) bipolarons are considered in a one-dimensional Holstein molecular chain. Criteria of their stability are obtained. The energy of a translation invariant bipolaron is shown to be lower than that of a bipolaron with broken symmetry. The results obtained are applied to the problem of superconductivity in 1D-systems. It is shown that TI-bipolaron mechanism of Bose-Einstein condensation can support superconductivity even for infinite chain.
Fractal Dimension Invariant Filtering and Its CNN-based Implementation
Xu, Hongteng; Yan, Junchi; Persson, Nils; Lin, Weiyao; Zha, Hongyuan
2016-01-01
Fractal analysis has been widely used in computer vision, especially in texture image processing and texture analysis. The key concept of fractal-based image model is the fractal dimension, which is invariant to bi-Lipschitz transformation of image, and thus capable of representing intrinsic structural information of image robustly. However, the invariance of fractal dimension generally does not hold after filtering, which limits the application of fractal-based image model. In this paper, we...