International Nuclear Information System (INIS)
Mouse monoclonal antibodies directed against human MHC class II-associated p41 invariant chain fragment have been generated. Mice were immunized with human recombinant Ii-isoform p26. For hybridoma production mouse splenocytes and myeloma cells were fused. Hybridoma cells were screened using ELISA and immunoblotting. Three cell lines (42B10, 42G11 and 43C8) were used for production of specific antibodies, which reacted with p41 fragment and did not bind to cathepsins L or S or their proenyzmes. As primary antibody for immunofluorescence staining of lymph node tissue sections clone 2C12 MAb was selected. Specific localization of p41 fragment in certain cells in lymph nodes was observed. (author)
DEFF Research Database (Denmark)
Holst, Peter Johannes; Mandrup Jensen, Camilla Maria; Orskov, Cathrine; Thomsen, Allan Randrup; Christensen, Jan Pravsgaard; Sørensen, Maria Rathmann
2008-01-01
potent and versatile Ag delivery vehicles available. However, the impact of chronic infections like HIV and hepatitis C virus underscore the need for further improvements. In this study, we show that the protective immune response to an adenovirus-encoded vaccine Ag can be accelerated, enhanced......, broadened, and prolonged by tethering of the rAg to the MHC class II-associated invariant chain (Ii). Thus, adenovirus-vectored vaccines expressing lymphocytic choriomeningitis virus (LCMV)-derived glycoprotein linked to Ii increased the CD4+ and CD8+ T cell stimulatory capacity in vitro and in vivo....... Furthermore, mice vaccinated with a single dose of adenovirus-expressing LCMV-derived glycoprotein linked to Ii were protected against lethal virus-induced choriomeningitis, lethal challenge with strains mutated in immunodominant T cell epitopes, and systemic infection with a highly invasive strain. In...
1996-01-01
The invariant chain (Ii) is associated with major histocompatibility complex class II molecules during early stages of their intracellular transport. In an acidic endosomal/lysosomal compartment, it is proteolytically cleaved and removed from class II heterodimers. Participation of aspartic and cysteine proteases has been observed in in vitro degradation of Ii, but the specific enzymes responsible for its in vivo processing are as yet undefined. We have previously isolated a noncovalent compl...
M.M. van Luijn; M.E.D. Chamuleau; J.A. Thompson; S. Ostrand-Rosenberg; T.M. Westers; Y. Souwer; G.J. Ossenkoppele; S.M. Ham; A.A. van de Loosdrecht
2010-01-01
Background Disease recurrence in patients with acute myeloid leukemia may be partially explained by the escape of leukemic blasts from CD4(+) T-cell recognition. The current study investigates the role of aberrant HLA class II antigen presentation on leukemic blasts by determining both the clinical
Conformal classes realizing the Yamabe invariant
Macbeth, Heather
2014-01-01
We give a characterization of conformal classes realizing a compact manifold's Yamabe invariant. This characterization is the analogue of an observation of Nadirashvili for metrics realizing the maximal first eigenvalue, and of Fraser and Schoen for metrics realizing the maximal first Steklov eigenvalue.
Local invariants for a class of mixed states
International Nuclear Information System (INIS)
We investigate the equivalence of quantum states under local unitary transformations. A complete set of invariants under local unitary transformations is presented for a class of mixed states. It is shown that two states in this class are locally equivalent if and only if all these invariants have equal values for them. (orig.)
Invariants for a Class of Nongeneric Three-qubit States
Sun, B Z; Sun, Bao-Zhi; Fei, Shao-Ming
2006-01-01
We investigate the equivalence of quantum states under local unitary transformations. A complete set of invariants under local unitary transformations is presented for a class of non-generic three-qubit mixed states. It is shown that two such states in this class are locally equivalent if and only if all these invariants have equal values for them.
DEFF Research Database (Denmark)
Gustavsen, Marte W; Viken, Marte K; Celius, Elisabeth G;
2014-01-01
Multiple sclerosis (MS) patients have been reported to have different HLA class II allele profiles depending on oligoclonal bands (OCBs) in the cerebrospinal fluid, but HLA class I alleles and killer cell immunoglobulin-like receptor (KIR) ligands have not been studied. We investigated the...... association of HLA alleles and KIR ligands according to OCB status in MS patients (n=3876). Specific KIR ligands were associated with patients when compared to controls (n=3148), supporting a role for NK cells in MS pathogenesis. HLA class I alleles and KIR ligands did not differ between OCB phenotypes, but...... HLA class II associations were convincingly replicated....
Bajoria, Divya; Menon, Thangam
2013-01-01
Introduction: Rheumatic heart disease (RHD) occurs in 30-45% of the patients with rheumatic fever (RF) and it leads to chronic valvular lesions. The human leukocyte antigen (HLA) might confer a susceptibility to RHD. The aim of the present study was to determine the prevalent HLA class II DR/DQ allelic types which were associated with rheumatic heart disease (RHD) in a small group of south Indian patients and to compare them with those in the control subjects.
Invariant tori for a class of nonlinear evolution equations
International Nuclear Information System (INIS)
The paper looks at quite a wide class of nonlinear evolution equations in a Banach space, including the typical boundary value problems for the main wave equations in mathematical physics (the telegraph equation, the equation of a vibrating beam, various equations from the elastic stability and so on). For this class of equations a unified approach to the bifurcation of invariant tori of arbitrary finite dimension is put forward. Namely, the problem of the birth of such tori from the zero equilibrium is investigated under the assumption that in the stability problem for this equilibrium the situation arises close to an infinite-dimensional degeneracy. Bibliography: 28 titles
Basic polynomial invariants, fundamental representations and the Chern class map
Baek, Sanghoon; Zainoulline, Kirill
2011-01-01
Consider a crystallographic root system together with its Weyl group $W$ acting on the weight lattice $M$. Let $Z[M]^W$ and $S^*(M)^W$ be the $W$-invariant subrings of the integral group ring $Z[M]$ and the symmetric algebra $S^*(M)$ respectively. A celebrated theorem of Chevalley says that $Z[M]^W$ is a polynomial ring over $Z$ in classes of fundamental representations $w_1,...,w_n$ and $S^*(M)^{W}$ over rational numbers is a polynomial ring in basic polynomial invariants $q_1,...,q_n$, where $n$ is the rank. In the present paper we establish and investigate the relationship between $w_i$'s and $q_i$'s over the integers.
Buschow, S.I.; Balkom, B.W.M. van; Aalberts, M.; Heck, A.J.R. van; Wauben, M.; Stoorvogel, W.
2010-01-01
Professional antigen-presenting cells secrete major histocompatibility complex class II (MHC II) carrying exosomes with unclear physiological function(s). Exosomes are first generated as the intraluminal vesicles (ILVs) of a specific type of multivesicular body, and are then secreted by fusion of th
Invariants of the harmonic conformal class of an asymptotically flat manifold
Jauregui, Jeffrey L
2010-01-01
Consider an asymptotically flat Riemannian manifold $(M,g)$ of dimension $n \\geq 3$ with nonempty compact boundary. We recall the harmonic conformal class $[g]_h$ of the metric, which consists of all conformal rescalings given by a harmonic function raised to an appropriate power. The geometric significance is that every metric in $[g]_h$ has the same pointwise sign of scalar curvature. For this reason, the harmonic conformal class appears in the study of general relativity, where scalar curvature is related to energy density. Our purpose is to introduce and study invariants of the harmonic conformal class. These invariants are closely related to constrained geometric optimization problems involving hypersurface area-minimizers and the ADM mass. In the final section, we discuss possible applications of the invariants and their relationship with zero area singularities and the positive mass theorem.
Energy Technology Data Exchange (ETDEWEB)
Fink, T.M.; Lichter, P. [Deutsches Krebsforschungszentrum Abt. Organisation komplexer Genome, Heidelberg (Germany); Vaesen, M. [Max-Planck-Institut fuer experimentelle Medizin Abt. Immunchemie, Goettingen (Germany)] [and others
1995-09-01
The putative HLA class II associated proteins PHAPI and PHAPII were purified and cloned on the basis of their ability to bind to the cytoplasmatic domain of the HLA Dr{alpha}-chain. They might be components of the transmembrane signaling pathway that is activated after extracellular binding of ligands during the immune response. Both proteins share extended stretches of highly acidic amino acids in their C-terminal regions that also indicate a nuclear localization. Indeed, PHAPI is likely to be the human homologue of the rat {open_quotes}leucine-rich acidic nuclear protein{close_quotes} (LANP) (83.6% amino acid identity), which was shown to be localized in the nuclei of Purkinje cells. Comparison of the cDNA sequences with entries in the EMBL data library revealed that PHAPII is identical to a protein named SET. The SET gene is located on chromosome 9q34 and was found to be fused to the putative oncogene CAN in one patient with acute undifferentiated leukemia (AUL). 9 refs., 1 fig.
Sevilla, L M; Richter, S S; Miller, J
2001-06-15
MHC class II-restricted antigen presentation requires trafficking of newly synthesized class II-invariant chain complexes from the trans-Golgi network to endosomal, peptide-loading compartments. This transport is mediated by dileucine-like motifs within the cytosolic tail of the invariant chain. Although these signals have been well characterized, the cytosolic proteins that interact with these dileucine signals and mediate Golgi sorting and endosomal transport have not been identified. Recently, an adaptor complex, AP-3, has been identified that interacts with dileucine motifs and mediates endosomal/lysosomal transport in yeast, Drosophila, and mammals. In this report, we have assessed class II-invariant chain trafficking in a strain of mice (mocha) which lacks expression of AP-3. Our studies demonstrate that the lack of AP-3 does not affect the kinetics of invariant chain degradation, the route of class II-invariant chain transport, or the rate and extent of class II-peptide binding as assessed by the generation of SDS-stable dimers. The possible role of other known or unknown adaptor complexes in class II-invariant chain transport is discussed. PMID:11520080
Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
Energy Technology Data Exchange (ETDEWEB)
Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science,1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)
2015-04-27
It is known that Horndeski theories can be transformed to a sub-class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories under the disformal transformation of the metric g{sub μν}→Ω{sup 2}(ϕ)g{sub μν}+Γ(ϕ,X)∇{sub μ}ϕ∇{sub ν}ϕ, where Ω is a function of a scalar field ϕ and Γ is another function depending on both ϕ and X=g{sup μν}∇{sub μ}ϕ∇{sub ν}ϕ. We show that, with the choice of unitary gauge, both curvature and tensor perturbations on the flat isotropic cosmological background are generally invariant under the disformal transformation. By means of the effective field theories encompassing Horndeski and GLPV theories, we obtain the second-order actions of scalar/tensor perturbations and present the relations for physical quantities between the two frames. The invariance of the inflationary power spectra under the disformal transformation is explicitly proved up to next-to-leading order in slow-roll. In particular, we identify the existence of the Einstein frame in which the tensor power spectrum is of the same form as that in General Relativity and derive the condition under which the spectrum of gravitational waves in GLPV theories is red-tilted.
MHC class I-related molecule, MR1, and mucosal-associated invariant T cells.
Franciszkiewicz, Katarzyna; Salou, Marion; Legoux, Francois; Zhou, Qian; Cui, Yue; Bessoles, Stéphanie; Lantz, Olivier
2016-07-01
The MHC-related 1, MR1, molecule presents a new class of microbial antigens (derivatives of the riboflavin [Vitamin B2] biosynthesis pathway) to mucosal-associated invariant T (MAIT) cells. This raises many questions regarding antigens loading and intracellular trafficking of the MR1/ligand complexes. The MR1/MAIT field is also important because MAIT cells are very abundant in humans and their frequency is modified in many infectious and non-infectious diseases. Both MR1 and the invariant TCRα chain expressed by MAIT cells are strikingly conserved among species, indicating important functions. Riboflavin is synthesized by plants and most bacteria and yeasts but not animals, and its precursor derivatives activating MAIT cells are short-lived unless bound to MR1. The recognition of MR1 loaded with these compounds is therefore an exquisite manner to detect invasive bacteria. Herein, we provide an historical perspective of the field before describing the main characteristics of MR1, its ligands, and the few available data regarding its cellular biology. We then summarize the current knowledge of MAIT cell differentiation and discuss the definition of MAIT cells in comparison to related subsets. Finally, we describe the phenotype and effector activities of MAIT cells. PMID:27319347
Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
International Nuclear Information System (INIS)
It is known that Horndeski theories can be transformed to a sub-class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories under the disformal transformation of the metric gμν→Ω2(ϕ)gμν+Γ(ϕ,X)∇μϕ∇νϕ, where Ω is a function of a scalar field ϕ and Γ is another function depending on both ϕ and X=gμν∇μϕ∇νϕ. We show that, with the choice of unitary gauge, both curvature and tensor perturbations on the flat isotropic cosmological background are generally invariant under the disformal transformation. By means of the effective field theories encompassing Horndeski and GLPV theories, we obtain the second-order actions of scalar/tensor perturbations and present the relations for physical quantities between the two frames. The invariance of the inflationary power spectra under the disformal transformation is explicitly proved up to next-to-leading order in slow-roll. In particular, we identify the existence of the Einstein frame in which the tensor power spectrum is of the same form as that in General Relativity and derive the condition under which the spectrum of gravitational waves in GLPV theories is red-tilted
Exposing the specific roles of the invariant chain isoforms in shaping the MHC class II peptidome
Directory of Open Access Journals (Sweden)
Jean-Simon eFortin
2013-12-01
Full Text Available The peptide repertoire (peptidome associated with MHC class II molecules (MHCIIs is influenced by the polymorphic nature of the peptide binding groove but also by cell-intrinsic factors. The invariant chain (Ii chaperones MHCIIs, affecting their folding and trafficking. Recent discoveries relating to Ii functions have provided insights as to how it edits the MHCII peptidome. In humans, the Ii gene encodes four different isoforms for which structure-function analyses have highlighted common properties but also some non-redundant roles. Another layer of complexity arises from the fact that Ii heterotrimerizes, a characteristic that has the potential to affect the maturation of associated MHCIIs in many different ways, depending on the isoform combinations. Here, we emphasize the peptide editing properties of Ii and discuss the impact of the various isoforms on the MHCII peptidome.
Immersion and invariance adaptive control of a class of continuous stirred tank reactors
Institute of Scientific and Technical Information of China (English)
Gaiyan HONG; Xiangbin LIU; Hongye SU
2015-01-01
An immersion and invariance (I&I) manifold based adaptive control algorithm is presented for a class of continuous stirred tank reactors (CSTR) to realize performance-oriented control in this paper. The nonlinear contraction method is combined into the control law design to render the closed-loop CSTR system globally asymptotically stable, firstly. Then, the I&I method is used to form the adaptation law such that the off-the-manifold coordinate (the parameter estimation error) converges to zero using P-monotone property enforced by selecting tuning function in manifold. As a result, the state of the closed-loop CSTR converges to its desired value asymptotically. The simulation is given to illustrate the effectiveness of the presented algorithm.
International Nuclear Information System (INIS)
A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties (through the Lie point symmetry generators) and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ‘multipliers’ associated with the conservation laws with a stronger emphasis on the ‘higher-order’ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers. (general)
Directory of Open Access Journals (Sweden)
Chen Fangfang
2012-09-01
Full Text Available Abstract Background Based on binding of invariant chain (Ii to major histocompatibility complex (MHC class II molecules to form complexes, Ii-segment hybrids, Ii-key structure linking an epitope, or Ii class II-associated invariant chain peptide (CLIP replaced with an epitope were used to increase immune response. It is currently unknown whether the Ii-segment cytosolic and transmembrane domains bind to the MHC non-peptide binding region (PBR and consequently influence immune response. To investigate the potential role of Ii-segments in the immune response via MHC II/peptide complexes, a few hybrids containing Ii-segments and a multiepitope (F306 from Newcastle disease virus fusion protein (F were constructed, and their binding effects on MHC II molecules and specific antibody production were compared using confocal microscopy, immunoprecipitation, western blotting and animal experiments. Results One of the Ii-segment/F306 hybrids, containing ND (Asn–Asp outside the F306 in the Ii-key structure (Ii-key/F306/ND, neither co-localized with MHC II molecules on plasma membrane nor bound to MHC II molecules to form complexes. However, stimulation of mice with the structure produced 4-fold higher antibody titers compared with F306 alone. The two other Ii-segment/F306 hybrids, in which the transmembrane and cytosolic domains of Ii were linked to this structure (Cyt/TM/Ii-key/F306/ND, partially co-localized on plasma membrane with MHC class II molecules and weakly bound MHC II molecules to form complexes. They induced mice to produce approximately 9-fold higher antibody titers compared with F306 alone. Furthermore, an Ii/F306 hybrid (F306 substituting CLIP co-localized well with MHC II molecules on the membrane to form complexes, although it increased antibody titer about 3-fold relative to F306 alone. Conclusions These results suggest that Ii-segments improve specific immune response by binding to the non-PBR on MHC class II molecules and enabling
Gauge invariant classes of feynman diagrams and simplification of quark combinatorics
International Nuclear Information System (INIS)
In theories like SM or MSSM with a complex gauge group structure the complete set of Feynman diagrams contributed to a particular physics process can be splitted to exact gauge invariant subsets. Such a splitting on the gauge invariant subsets is useful for various computations, in particular, to simplify flavour combinatorics in the evaluation of hadronic processes. Talk is based on papers. (author)
Directory of Open Access Journals (Sweden)
Kazuhiro Hikami
2010-12-01
Full Text Available We define a class of Y(sl_{(m|n} Yangian invariant Haldane-Shastry (HS like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials. Using some properties of the super Schur polynomials, we show that the partition functions of this class of spin chains are equivalent to the partition functions of a class of one-dimensional vertex models with appropriately defined energy functions. We also establish a boson-fermion duality relation for the partition functions of this class of supersymmetric HS like spin chains by using their correspondence with one-dimensional vertex models.
Leroux, Louis-Philippe; Nishi, Manami; El-Hage, Sandy; Fox, Barbara A; Bzik, David J; Dzierszinski, Florence S
2015-10-01
Toxoplasma gondii is an obligate intracellular protozoan parasite. This apicomplexan is the causative agent of toxoplasmosis, a leading cause of central nervous system disease in AIDS. It has long been known that T. gondii interferes with major histocompatibility complex class II (MHC-II) antigen presentation to attenuate CD4(+) T cell responses and establish persisting infections. Transcriptional downregulation of MHC-II genes by T. gondii was previously established, but the precise mechanisms inhibiting MHC-II function are currently unknown. Here, we show that, in addition to transcriptional regulation of MHC-II, the parasite modulates the expression of key components of the MHC-II antigen presentation pathway, namely, the MHC-II-associated invariant chain (Ii or CD74) and the peptide editor H2-DM, in professional antigen-presenting cells (pAPCs). Genetic deletion of CD74 restored the ability of infected dendritic cells to present a parasite antigen in the context of MHC-II in vitro. CD74 mRNA and protein levels were, surprisingly, elevated in infected cells, whereas MHC-II and H2-DM expression was inhibited. CD74 accumulated mainly in the endoplasmic reticulum (ER), and this phenotype required live parasites, but not active replication. Finally, we compared the impacts of genetic deletion of CD74 and H2-DM genes on parasite dissemination toward lymphoid organs in mice, as well as activation of CD4(+) T cells and interferon gamma (IFN-γ) levels during acute infection. Cyst burdens and survival during the chronic phase of infection were also evaluated in wild-type and knockout mice. These results highlight the fact that the infection is influenced by multiple levels of parasite manipulation of the MHC-II antigen presentation pathway. PMID:26195549
Solutions by radicals at singular values k_N from new class invariants for N \\equiv 3 mod 8
Broadhurst, David
2008-01-01
For square-free $N\\equiv3$ mod 8 and $N$ coprime to 3, I show how to reduce the singular value $k_N$ to radicals, using a novel pair $[f,g]$ of real numbers that are algebraic integers of the Hilbert class field of $Q(\\sqrt{-N})$. One is a class invariant of modular level 48, with a growth $g=\\alpha(N)\\exp(\\pi\\sqrt{N}/48)+o(1)$, where $\\alpha(N)\\in[-\\sqrt2,\\sqrt2]$ is uniquely determined by the residue of $N$ modulo 64. Hence $g$ is a very economical generator of the class field. For prime $N\\equiv3$ mod 4, I conjecture that the Chowla--Selberg formula provides an algebraic {\\em unit} of the class field and determine its minimal polynomial for the 155 cases with $N<2000$. For N=2317723, with class number $h(-N)=105$, I compute the minimal polynomial of $g$ in 90 milliseconds. Its height is smaller than the {\\em cube} root of the height of the generating polynomial found by the double eta-quotient method of {\\em Pari-GP}. I reduce the complete elliptic integral $K_{2317723}$ to radicals and values of the $\\...
Vaccination against lymphocytic choriomeningitis virus infection in MHC class II-deficient mice
DEFF Research Database (Denmark)
Holst, Peter Johannes; Christensen, Jan Pravsgaard; Thomsen, Allan Randrup
2011-01-01
response could be elicited in MHC class II-deficient mice by vaccination with adenovirus encoding lymphocytic choriomeningitis virus (LCMV) glycoprotein tethered to MHC class II-associated invariant chain. Moreover, the response induced conferred significant cytolytic CD8(+) T cell-mediated protection...
Invariants of the harmonic conformal class of an asymptotically flat manifold
Jauregui, Jeffrey L.
2010-01-01
Consider an asymptotically flat Riemannian manifold $(M,g)$ of dimension $n \\geq 3$ with nonempty compact boundary. We recall the harmonic conformal class $[g]_h$ of the metric, which consists of all conformal rescalings given by a harmonic function raised to an appropriate power. The geometric significance is that every metric in $[g]_h$ has the same pointwise sign of scalar curvature. For this reason, the harmonic conformal class appears in the study of general relativity, where scalar curv...
The p41 isoform of invariant chain is a chaperone for cathepsin L
Lennon-Duménil, Ana-Maria; Roberts, Rebecca A.; Valentijn, Karine; Driessen, Christoph; Overkleeft, Herman S.; Erickson, Ann; Peters, Peter J.; Bikoff, Elizabeth; Ploegh, Hidde L.; Wolf Bryant, Paula
2001-01-01
The p41 splice variant of major histocompatibility complex (MHC) class II-associated invariant chain (Ii) contains a 65 aa segment that binds to the active site of cathepsin L (CatL), a lysosomal cysteine protease involved in MHC class II-restricted antigen presentation. This segment is absent from the predominant form of Ii, p31. Here we document the in vivo significance of the p41–CatL interaction. By biochemical means and electron microscopy, we demonstrate that the levels of active CatL a...
Meyer, Mathieu; Schuett, Carsten; Werner, Elisabeth M.
2013-01-01
An affine invariant point on the class of convex bodies in R^n, endowed with the Hausdorff metric, is a continuous map p which is invariant under one-to-one affine transformations A on R^n, that is, p(A(K))=A(p(K)). We define here the new notion of dual affine point q of an affine invariant point p by the formula q(K^{p(K)})=p(K) for every convex body K, where K^{p(K)} denotes the polar of K with respect to p(K). We investigate which affine invariant points do have a dual point, whether this ...
Donaldson invariants of symplectic manifolds
Sivek, Steven
2013-01-01
We prove that symplectic 4-manifolds with $b_1 = 0$ and $b^+ > 1$ have nonvanishing Donaldson invariants, and that the canonical class is always a basic class. We also characterize in many situations the basic classes of a Lefschetz fibration over the sphere which evaluate maximally on a generic fiber.
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.
Directory of Open Access Journals (Sweden)
Alexandra J Spencer
Full Text Available The orthodox role of the invariant chain (CD74; Ii is in antigen presentation to CD4+ T cells, but enhanced CD8+ T cells responses have been reported after vaccination with vectored viral vaccines encoding a fusion of Ii to the antigen of interest. In this study we assessed whether fusion of the malarial antigen, ME-TRAP, to Ii could increase the vaccine-induced CD8+ T cell response. Following single or heterologous prime-boost vaccination of mice with a recombinant chimpanzee adenovirus vector, ChAd63, or recombinant modified vaccinia virus Ankara (MVA, higher frequencies of antigen-specific CD4+ and CD8+ T cells were observed, with the largest increases observed following a ChAd63-MVA heterologous prime-boost regimen. Studies in non-human primates confirmed the ability of Ii-fusion to augment the T cell response, where a 4-fold increase was maintained up to 11 weeks after the MVA boost. Of the numerous different approaches explored to increase vectored vaccine induced immunogenicity over the years, fusion to the invariant chain showed a consistent enhancement in CD8+ T cell responses across different animal species and may therefore find application in the development of vaccines against human malaria and other diseases where high levels of cell-mediated immunity are required.
Second order invariants and holography
Bonanno, Luca; Luongo, Orlando
2011-01-01
Motivated by recent works on the role of the Holographic principle in cosmology, we relate a class of second order Ricci invariants to the IR cutoff characterizing the holographic Dark Energy density. The choice of second order invariants provides an invariant way to account the problem of causality for the correct cosmological cutoff, since the presence of event horizons is not an \\emph{a priori} assumption. We find that these models work fairly well, by fitting the observational data, through a combined cosmological test with the use of SNeIa, BAO and CMB. This class of models is also able to overcome the fine-tuning and coincidence problems. Finally, to make a comparison with other recent models, we adopt the statistical tests AIC and BIC.
Invariant Solutions for Soil Water Equations
Baikov, V.; Khalique, C.
1999-01-01
We obtain exact solutions for a class of nonlinear partial differential equations which models soil water infiltration and redistribution in a bedded soil profile irrigated by a drip irrigation system. The solutions obtained are invariant under two parameter symmetry groups.
Leroux, Louis-Philippe; Nishi, Manami; El-Hage, Sandy; Fox, Barbara A.; Bzik, David J.; Dzierszinski, Florence S.
2015-01-01
Toxoplasma gondii is an obligate intracellular protozoan parasite. This apicomplexan is the causative agent of toxoplasmosis, a leading cause of central nervous system disease in AIDS. It has long been known that T. gondii interferes with major histocompatibility complex class II (MHC-II) antigen presentation to attenuate CD4+ T cell responses and establish persisting infections. Transcriptional downregulation of MHC-II genes by T. gondii was previously established, but the precise mechanisms...
Finite-type invariants for curves on surfaces
Ito, Noboru
2009-01-01
In this note, we define a notion of finite-type for invariants of curves on surfaces as an analogue of the notion of finite-type for invariants of knots and 3-manifolds (Section 3). We also present a systematic construction for a large family of finite-type invariants SCIn for curves on surfaces (Section 5). Arnold's invariants of plane isotopy classes of plane curves occur as invariants of order 1. Our theory of finite-type invariants of curves on surfaces is developed usin...
Poincare Invariance, Cluster Properties, and Particle Production
Polyzou, W. N.
2002-01-01
A method is presented for constructing a class of Poincare invariant quantum mechanical models of systems of a finite number of degrees of freedom that satisfy cluster separability, the spectral condition, but do not conserve particle number. The class of models includes the relativistic Lee model and relativistic isobar models.
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 is...... 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 with...
Rotational invariance and the Pauli exclusion principle
O'Hara, Paul
2001-01-01
In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This will be referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence...
Complete simultaneous conjugacy invariants in Garside groups
Kalka, Arkadius; Tsaban, Boaz; Vinokur, Gary
2014-01-01
We solve the simultaneous conjugacy problem in Garside groups, by means of an effectively computable invariant. In the one-dimensional case, our invariant generalizes the notion of super summit set of a conjugacy class. As part of our solution, we identify a high-dimensional version of the cyclic sliding operation with a provable convergence rate. The complexity of this solution is a small degree polynomial in the sizes of our generalized super summit sets and the input parameters. Computer e...
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 ...
On logarithmic extensions of local scale-invariance
Henkel, Malte
2010-01-01
The known logarithmic extensions of conformal and Schr\\"odinger-invariance assume translation-invariance in their spatial and temporal coordinates. Therefore, they cannot be applied directly to slow far-from-equilibrium relaxations, where time-translation-invariance no longer holds. Here, the logarithmic extension of ageing-invariance, that is local dynamical scaling without the assumption of time-translation-invariance, is presented. Co-variant two-point functions are derived. Their form is compared to transfer-matrix renormalisation group data for the two-time autoresponse function of the $1D$ critical contact process, which is in the directed percolation universality class.
Geometry-Invariant Resonant Cavities
Liberal, Iñigo; Engheta, Nader
2015-01-01
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modeling to everyday life devices. The eigenfrequencies of conventional cavities are a function of its geometry, and, thus, the size and shape of a resonant cavity is selected in order to operate at a specific frequency. Here, we demonstrate theoretically the existence of geometry-invariant resonant cavities, i.e., resonators whose eigenfrequency is invariant with respect to geometrical deformations. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, which enable decoupling of the time and spatial field variations. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices.
On solvable lattice models and knot invariants
Gepner, D
1993-01-01
Recently, a class of solvable interaction round the face lattice models (IRF) were constructed for an arbitrary rational conformal field theory (RCFT) and an arbitrary field in it. The Boltzmann weights of the lattice models are related in the extreme ultra violet limit to the braiding matrices of the rational conformal field theory. In this note we use these new lattice models to construct a link invariant for any such pair of an RCFT and a field in it. Using the properties of RCFT and the IRF lattice models, we prove that the invariants so constructed always obey the Markov properties, and thus are true link invariants. Further, all the known link invariants, such as the Jones, HOMFLY and Kauffman polynomials arise in this way, along with giving a host of new invariants, and thus also a unified approach to link polynomials. It is speculated that all link invariants arise from some RCFT, and thus the problem of classifying link and knot invariants is equivalent to that of classifying two dimensional conforma...
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...
Invariant f-structures in generalized Hermitian geometry
Balashchenko, Vitaly V.
2006-01-01
We collect the recent results on invariant f-structures in generalized Hermitian geometry. Here the canonical f-structures on homogeneous k-symmetric spaces play a remarkable role. Specifically, these structures provide a wealth of invariant examples for the classes of nearly Kähler f-structures, Hermitian f-structures and some others. Finally, we consider all invariant f-structures on the complex flag manifold SU(3)/Tmax and describe them in the sense of generalized Hermitian ...
Conformal Invariance of Graphene Sheets
Giordanelli, I.; Posé, N.; Mendoza, M.; Herrmann, H. J.
2016-01-01
Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent 0.72 ± 0.01. Here, we show that, independent of the temperature, the iso-height lines at the percolation threshold have a well-defined fractal dimension and are conformally invariant, sharing the same statistical properties as Schramm-Loewner evolution (SLEκ) curves with κ = 2.24 ± 0.07. Interestingly, iso-height lines of other rough surfaces are not necessarily conformally invariant even if they have the same Hurst exponent, e.g. random Gaussian surfaces. We have found that the distribution of the modulus of the Fourier coefficients plays an important role on this property. Our results not only introduce a new universality class and place the study of suspended graphene membranes within the theory of critical phenomena, but also provide hints on the long-standing question about the origin of conformal invariance in iso-height lines of rough surfaces. PMID:26961723
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.
Second-Order Invariants and Holography
Luongo, Orlando; Bonanno, Luca; Iannone, Gerardo
2012-12-01
Motivated by recent works on the role of the holographic principle in cosmology, we relate a class of second-order Ricci invariants to the IR cutoff characterizing the holographic dark energy density. The choice of second-order invariants provides an invariant way to account the problem of causality for the correct cosmological cutoff, since the presence of event horizons is not an a priori assumption. We find that these models work fairly well, by fitting the observational data, through a combined cosmological test with the use of SNeIa, BAO and CMB. This class of models is also able to overcome the fine-tuning and coincidence problems. Finally, to make a comparison with other recent models, we adopt the statistical tests AIC and BIC.
Attractiveness of Invariant Manifolds
Pei, Lijun
2011-01-01
In this paper an operable, universal and simple theory on the attractiveness of the invariant manifolds is first obtained. It is motivated by the Lyapunov direct method. It means that for any point $\\overrightarrow{x}$ in the invariant manifold $M$, $n(\\overrightarrow{x})$ is the normal passing by $\\overrightarrow{x}$, and $\\forall \\overrightarrow{x^{'}} \\in n(\\overrightarrow{x})$, if the tangent $f(\\overrightarrow{x^{'}})$ of the orbits of the dynamical system intersects at obtuse (sharp) angle with the normal $n(\\overrightarrow{x})$, or the inner product of the normal vector $\\overrightarrow{n}(\\overrightarrow{x})$ and tangent vector $\\overrightarrow{f}(\\overrightarrow{x^{'}})$ is negative (positive), i.e., $\\overrightarrow{f}(\\overrightarrow{x^{'}}). \\overrightarrow{n}(\\overrightarrow{x}) )0$, then the invariant manifold $M$ is attractive (repulsive). Some illustrative examples of the invariant manifolds, such as equilibria, periodic solution, stable and unstable manifolds, other invariant manifold are pre...
Conformal invariant D-dimensional field theory
International Nuclear Information System (INIS)
Conformation invariant quantum field theory is especially interesting by the fact that the high symmetry imposes very strict limitations on its structure and one can try to find exact solutions for very wide classes of field models. In this paper, the authors consider field theory in D-dimensional Euclidean space and describe the method to find it's exact solution
An almost-integral universal Vassiliev invariant of knots
Willerton, Simon
2001-01-01
A `total Chern class' invariant of knots is defined. This is a universal Vassiliev invariant which is integral `on the level of Lie algebras' but it is not expressible as an integer sum of diagrams. The construction is motivated by similarities between the Kontsevich integral and the topological Chern character.
Invariant see-saw models and sequential dominance
King, S F
2006-01-01
We propose an invariant see-saw (ISS) approach to model building, based on the observation that see-saw models of neutrino mass and mixing fall into basis invariant classes labelled by the Casas-Ibarra $R$-matrix, which we prove to be invariant not only under basis transformations but also non-unitary right-handed neutrino transformations $S$. According to the ISS approach, given any see-saw model in some particular basis one may determine the invariant $R$ matrix and hence the invariant class to which that model belongs. The formulation of see-saw models in terms of invariant classes puts them on a firmer theoretical footing, and allows different see-saw models in the same class to be related more easily, while their relation to the $R$-matrix makes them more easily identifiable in phenomenological studies. We also present an ISS mass formula which may be useful in model building. To illustrate the ISS approach we show that sequential dominance (SD) models form basis invariant classes in which the $R$-matrix...
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
A generalized Jaynes-Cummings Hamiltonian and supersymmetric shape invariance
International Nuclear Information System (INIS)
A class of shape-invariant bound-state problems which represent two-level systems are introduced. It is shown that the coupled-channel Hamiltonians obtained correspond to the generalization of the Jaynes-Cummings Hamiltonian. (author)
A scale invariant covariance structure on jet space
DEFF Research Database (Denmark)
Pedersen, Kim Steenstrup; Loog, Marco; Markussen, Bo
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...
Vacuum Plane Waves; Cartan Invariants and physical interpretation
Coley, Alan; Milson, Robert
2012-01-01
As an application of the Cartan invariants obtained using the Karlhede algorithm, we study a simple subclass of the PP-wave spacetimes, the gravitational plane waves. We provide an invariant classification of these spacetimes and then study a few notable subcases: the linearly polarized plane waves, the weak-field circularly polarized waves, and another class of plane waves found by imposing conditions on the set of invariants. As we study these spacetimes we relate the invariant structure (i.e., Cartan scalars) to the physical description of these spacetimes using the geodesic deviation equations relative to timelike geodesic observers.
Vacuum plane waves: Cartan invariants and physical interpretation
Coley, A.; McNutt, D.; Milson, R.
2012-12-01
As an application of the Cartan invariants obtained using the Karlhede algorithm, we study a simple subclass of the PP-wave spacetimes, the gravitational plane waves. We provide an invariant classification of these spacetimes and then study a few notable subcases: the linearly polarized plane waves, the weak-field circularly polarized waves, and another class of plane waves found by imposing conditions on the set of invariants. As we study these spacetimes we relate the invariant structure (i.e., Cartan scalars) to the physical description of these spacetimes using the geodesic deviation equations relative to timelike geodesic observers.
Vacuum plane waves: Cartan invariants and physical interpretation
International Nuclear Information System (INIS)
As an application of the Cartan invariants obtained using the Karlhede algorithm, we study a simple subclass of the PP-wave spacetimes, the gravitational plane waves. We provide an invariant classification of these spacetimes and then study a few notable subcases: the linearly polarized plane waves, the weak-field circularly polarized waves, and another class of plane waves found by imposing conditions on the set of invariants. As we study these spacetimes we relate the invariant structure (i.e., Cartan scalars) to the physical description of these spacetimes using the geodesic deviation equations relative to timelike geodesic observers. (paper)
Institute of Scientific and Technical Information of China (English)
桑波
2013-01-01
对于一类具有一对共轭复不变直线和中心-焦点型奇点的三次系统,证明它以原点为中心的充要条件是其前五阶焦点量全为零.此中心条件是通过不变代数曲线构造积分因子或对称原理得以证明.%A class of cubic systems with a pair of invariant conjugate imaginary straight lines and a center-focus type singular point,is proved to have a center at the origin if and only if the first five focal values vanish. The presence of a center at the origin is proved by constructing integrating factor formed from invariant algebraic curves or by symmetry principle.
Relativistic gauge invariant potentials
International Nuclear Information System (INIS)
A global method characterizing the invariant connections on an abelian principal bundle under a group of transformations is applied in order to get gauge invariant electromagnetic (elm.) potentials in a systematic way. So, we have classified all the elm. gauge invariant potentials under the Poincare subgroups of dimensions 4, 5, and 6, up to conjugation. It is paid attention in particular to the situation where these subgroups do not act transitively on the space-time manifold. We have used the same procedure for some galilean subgroups to get nonrelativistic potentials and study the way they are related to their relativistic partners by means of contractions. Some conformal gauge invariant potentials have also been derived and considered when they are seen as consequence of an enlargement of the Poincare symmetries. (orig.)
Scale-invariant geometric random graphs
Xie, Zheng; Rogers, Tim
2016-03-01
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 influence zones that depend on node position in space and time, mimicking the heterogeneity and increased specialization found in growing networks. Through calculations and numerical simulations we explore the consequences of scale invariance for geometric random 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 behavior. These properties are similar to those of empirically observed web graphs.
Reparametrization invariance and the Schroedinger equation
International Nuclear Information System (INIS)
A time-dependent Schroedinger equation for systems invariant under the reparametrization of time is considered. We develop the two-stage procedure of construction such systems from a given initial ones, which are not invariant under the time reparametrization. One of the first-class constraints of the systems in such description becomes the time-dependent Schroedinger equation. The procedure is applicable in the supersymmetric theories as well. The n = 2 supersymmetric quantum mechanics is coupled to world-line supergravity, and the local supersymmetric action is constructed leading to the square root representation of the time-dependent Schroedinger equation
On Invariant Structures of Black Hole Charges
Ferrara, Sergio(Physics Department, Theory Unit, CERN, Geneva 23, CH, 1211, Switzerland); Marrani, Alessio; Yeranyan, Armen
2011-01-01
We study "minimal degree" complete bases of duality- and "horizontal"- invariant homogeneous polynomials in the flux representation of two-centered black hole solutions in two classes of D=4 Einstein supergravity models with symmetric vector multiplets' scalar manifolds. Both classes exhibit an SL(2,R) "horizontal" symmetry. The first class encompasses N=2 and N=4 matter-coupled theories, with semi-simple U-duality given by SL(2,R) x SO(m,n); the analysis is carried out in the so-called Calab...
International Nuclear Information System (INIS)
We show there are at least 28 distinct true stochastic local operations and classical communication (SLOCC) entanglement classes for four qubits by means of SLOCC invariant and semi-invariants and derive the number of degenerate SLOCC classes for n qubits
Invariant measures for subshifts arising from substitutions of some primitive components
Hama, Masaki
2010-01-01
The class of substitutions of some primitive components is introduced. A bilateral subshift arising from a substitution of some primitive components is decomposed into pairwise disjoint, locally compact, shift-invariant sets, on each of which an invariant Radon measure is unique up to scaling. It is completely characterized in terms of eigenvalues of an incidence matrix when the unique invariant measure is finite.
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.
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.)
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....
NIMET PANCAROGLU; FATIH NURAY
2013-01-01
In this paper, we define invariant convergence, lacunary invariant convergence, invariant statistical convergence, lacunary invariant statistical convergence for sequences of sets. We investigate some relations between lacunary invariant statistical convergence and invariant statistical convergence for sequences of sets.
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.
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.
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.
Illumination Invariant Unsupervised Segmenter
Czech Academy of Sciences Publication Activity Database
Haindl, Michal; Mikeš, Stanislav; Vácha, Pavel
Los Alamitos : IEEE, 2009, s. 4025-4028. ISBN 978-1-4244-5655-0. ISSN 1522-4880. [ICIP 2009. Cairo (EG), 07.11.2009-11.11.2009] R&D Projects: GA MŠk 1M0572; GA ČR GA102/08/0593 Grant ostatní: GA MŠk(CZ) 2C06019 Institutional research plan: CEZ:AV0Z10750506 Keywords : unsupervised image segmentation * Illumination Invariants Subject RIV: BD - Theory of Information http://library.utia.cas.cz/separaty/2009/RO/haindl-illumination invariant unsupervised segmenter.pdf
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.
Kameko, Masaki
2012-01-01
For any odd prime $p$, we prove that the induced homomorphism from the mod $p$ cohomology of the classifying space of a compact simply-connected simple connected Lie group to the Weyl group invariants of the mod $p$ cohomology of the classifying space of its maximal torus is an epimorphism except for the case $p=3$, $G=E_8$.
Relativistically invariant quantum information
Bartlett, Stephen D.; Terno, Daniel R.
2004-01-01
We show that quantum information can be encoded into entangled states of multiple indistinguishable particles in such a way that any inertial observer can prepare, manipulate, or measure the encoded state independent of their Lorentz reference frame. Such relativistically invariant quantum information is free of the difficulties associated with encoding into spin or other degrees of freedom in a relativistic context.
Modular invariant gaugino condensation
International Nuclear Information System (INIS)
The construction of effective supergravity lagrangians for gaugino condensation is reviewed and recent results are presented that are consistent with modular invariance and yield a positive definite potential of the noscale type. Possible implications for phenomenology are briefly discussed. 29 refs
Wetterich, C
2016-01-01
We propose a gauge invariant flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations, corresponding to a particular gauge fixing. The freedom in the precise choice of the macroscopic field can be exploited in order to keep the flow equation simple.
Galilei invariant molecular dynamics
International Nuclear Information System (INIS)
We construct a C*-dynamical model for a chemical reaction. Galilei invariance of our nonrelativistic model is demonstrated by defining it directly on a Galilean space-time fibrebundle with C*-algebra valued fibre, i.e. without reference to any coordinate system. The existence of equilibrium states in this model is established and some of their properties are discussed. (orig.)
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.
Modifications of Paroemia Invariants
Directory of Open Access Journals (Sweden)
Taliya F. Pecherskikh
2013-01-01
Full Text Available The phenomenon of modifications of paroemia invariants proves that language constantly changes and develops. The realization of communication need through the new evocative forms of expression is generality of the opposite linguistic phenomena of occasional variants of paroemia, aimed at the establishment of equilibrium in phraseology.
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...
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.
Orientation invariant features for multiclass object recognition
Villamizar, Michael; Sanfeliu, Alberto; Andrade-Cetto, J.
2006-01-01
We present a framework for object recognition based on simple scale and orientation invariant local features that when combined with a hierarchical multiclass boosting mechanism produce robust classifiers for a limited number of object classes in cluttered backgrounds. The system extracts the most relevant features from a set of training samples and builds a hierarchical structure of them. By focusing on those features common to all trained objects, and also searching for those features parti...
Branicki, M.; Wiggins, S
2009-01-01
We present a computational method for determining the geometry of a class of three-dimensional invariant manifolds in non-autonomous (aperiodically time-dependent) dynamical systems. The presented approach can be also applied to analyse the geometry of 3D invariant manifolds in three-dimensional, time-dependent fluid flows. The invariance property of such manifolds requires that, at any fixed time, they are given by surfaces in R3. We focus on a class of manifolds whose instantaneous geometry...
The Structure of Differential Invariants and Differential Cut Elimination
Platzer, André
2011-01-01
The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more scalable verification. Search procedures for these proof certificates are still rather ad-hoc, though, because the problem structure is only understood poorly. We investigate differential invariants, which can be checked for invariance along a differential equation just by using their differential structure and without having to solve the differential equation. We study the structural properties of differential invariants. To analyze trade-offs for proof search complexity, we identify more than a dozen relations between several classes of differential invariants and compare their deductive power. As our main results, we analyze the deductive power of differential cuts and the deductive power of differential invariants with auxiliary differential variables. We refute the differen...
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...
Invariant types in NIP theories
Simon, Pierre
2014-01-01
We study invariant types in NIP theories. Amongst other things: we prove a definable version of the (p,q)-theorem in theories of small or medium directionality; we construct a canonical retraction from the space of M-invariant types to that of M-finitely satisfiable types; we show some amalgamation results for invariant types and list a number of open questions.
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...
Conformal invariance in supergravity
International Nuclear Information System (INIS)
In this thesis the author explains the role of conformal invariance in supergravity. He presents the complete structure of extended conformal supergravity for N <= 4. The outline of this work is as follows. In chapter 2 he briefly summarizes the essential properties of supersymmetry and supergravity and indicates the use of conformal invariance in supergravity. The idea that the introduction of additional symmetry transformations can make clear the structure of a field theory is not reserved to supergravity only. By means of some simple examples it is shown in chapter 3 how one can always introduce additional gauge transformations in a theory of massive vector fields. Moreover it is shown how the gauge invariant formulation sometimes explains the quantum mechanical properties of the theory. In chapter 4 the author defines the conformal transformations and summarizes their main properties. He explains how these conformal transformations can be used to analyse the structure of gravity. The supersymmetric extension of these results is discussed in chapter 5. Here he describes as an example how N=1 supergravity can be reformulated in a conformally-invariant way. He also shows that beyond N=1 the gauge fields of the superconformal symmetries do not constitute an off-shell field representation of extended conformal supergravity. Therefore, in chapter 6, a systematic method to construct the off-shell formulation of all extended conformal supergravity theories with N <= 4 is developed. As an example he uses this method to construct N=1 conformal supergravity. Finally, in chapter 7 N=4 conformal supergravity is discussed. (Auth.)
Scale-Invariant Rotating Black Holes in Quadratic Gravity
Directory of Open Access Journals (Sweden)
Guido Cognola
2015-07-01
Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.
Rotational invariance and the spin-statistics theorem
O'Hara, Paul
2003-01-01
In this article the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This is referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence of th...
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.
Cheng, Miranda C N; Harrison, Sarah M; Kachru, Shamit
2015-01-01
In this note, we describe a connection between the enumerative geometry of curves in K3 surfaces and the chiral ring of an auxiliary superconformal field theory. We consider the invariants calculated by Yau--Zaslow (capturing the Euler characters of the moduli spaces of D2-branes on curves of given genus), together with their refinements to carry additional quantum numbers by Katz--Klemm--Vafa (KKV), and Katz--Klemm--Pandharipande (KKP). We show that these invariants can be reproduced by studying the Ramond ground states of an auxiliary chiral superconformal field theory which has recently been observed to give rise to mock modular moonshine for a variety of sporadic simple groups that are subgroups of Conway's group. We also study equivariant versions of these invariants. A K3 sigma model is specified by a choice of 4-plane in the K3 D-brane charge lattice. Symmetries of K3 sigma models are naturally identified with 4-plane preserving subgroups of the Conway group, according to the work of Gaberdiel--Hoheneg...
A classical theory of continuous spin and hidden gauge invariance
International Nuclear Information System (INIS)
We present a classical higher derivative point particle theory whose quantization gives Wigner's continuous spin representation of the Poincare group. Although the theory is not reparameterization invariant in the usual sense, it does possess a hidden gauge invariance that provides a non-local representation of the reparameterization group. The Hamiltonian of the theory does not vanish and its value is the continuous spin parameter. The theory presented here represents the simplest example of a wide class of higher derivative theories possessing a hidden gauge invariance
A classical theory of continuous spin and hidden gauge invariance
Energy Technology Data Exchange (ETDEWEB)
Zoller, D.
1991-01-01
We present a classical higher derivative point particle theory whose quantization gives Wigner's continuous spin representation of the Poincare group. Although the theory is not reparameterization invariant in the usual sense, it does possess a hidden gauge invariance that provides a non-local representation of the reparameterization group. The Hamiltonian of the theory does not vanish and its value is the continuous spin parameter. The theory presented here represents the simplest example of a wide class of higher derivative theories possessing a hidden gauge invariance.
A classical theory of continuous spin and hidden gauge invariance
Energy Technology Data Exchange (ETDEWEB)
Zoller, D.
1991-12-31
We present a classical higher derivative point particle theory whose quantization gives Wigner`s continuous spin representation of the Poincare group. Although the theory is not reparameterization invariant in the usual sense, it does possess a hidden gauge invariance that provides a non-local representation of the reparameterization group. The Hamiltonian of the theory does not vanish and its value is the continuous spin parameter. The theory presented here represents the simplest example of a wide class of higher derivative theories possessing a hidden gauge invariance.
Invariant f-structures in the generalized Hermitian geometry
Balashchenko, Vitaly V.
2005-01-01
We collect the recent results on invariant f-structures in the generalized Hermitian geometry. Here the canonical f-structures on homogeneous k-symmetric spaces play a remarkable role. Specifically, these structures provide a wealth of invariant examples for the classes of nearly Kaehler f-structures, Hermitian f-structures and some others. Finally, we consider all invariant f-structures on the complex flag manifold SU(3)/T_{max} and describe them in the sense of generalized Hermitian geometr...
Field transformations, collective coordinates and BRST invariance
International Nuclear Information System (INIS)
A very large class of general field transformations can be viewed as a field theory generalization of the method of collective coordinates. The introduction of new variables induces a gauge invariance in the transformed theory, and the freedom left in gauge fixing this new invariance can be used to find equivalent formulations of the same theory. First the Batalin-Fradkin-Vilkovisky formalism is applied to the Hamiltonian formulation of physical systems that can be described in terms of collective coordinates. We then show how this type of collective coordinate scheme can be generalized to field transformations, and discuss the War Identities of the associated BRST invariance. For Yang-Mills theory a connection to topological field theory and the background field method is explained in detail. In general the resulting BRST invariance we find hidden in any quantum field theory can be viewed as a consequence of our freedom in choosing a basis of coordinates φ(χ) in the action S[φ]. (orig.)
Rotation invariant features for wear particle classification
Arof, Hamzah; Deravi, Farzin
1997-09-01
This paper investigates the ability of a set of rotation invariant features to classify images of wear particles found in used lubricating oil of machinery. The rotation invariant attribute of the features is derived from the property of the magnitudes of Fourier transform coefficients that do not change with spatial shift of the input elements. By analyzing individual circular neighborhoods centered at every pixel in an image, local and global texture characteristics of an image can be described. A number of input sequences are formed by the intensities of pixels on concentric rings of various radii measured from the center of each neighborhood. Fourier transforming the sequences would generate coefficients whose magnitudes are invariant to rotation. Rotation invariant features extracted from these coefficients were utilized to classify wear particle images that were obtained from a number of different particles captured at different orientations. In an experiment involving images of 6 classes, the circular neighborhood features obtained a 91% recognition rate which compares favorably to a 76% rate achieved by features of a 6 by 6 co-occurrence matrix.
Invariant operators of inhomogeneous groups
International Nuclear Information System (INIS)
The problems concerning the invariant operators of the W(p, q) Weyl group of arbitrary dimension are considered. The Weyl group relative invariants, which do not contain the dilatation operators and which are the absolute invariants of the ISO (p, q) group, are searched for. The invariant operators of the Weyl group are represented in the form of the ratio of the Cazimir operators of the inhomogeneous pseudoorthogonal subgroup. It is shown that all the invariant operators of the W(p, q) Weyl group are rational and their number is [p+q-1/2
Thinning Invariant Partition Structures
Starr, Shannon
2011-01-01
A partition structure is a random point process on $[0,1]$ whose points sum to 1, almost surely. In the case that there are infinitely many points to begin with, we consider a thinning action by: first, removing points independently, such that each point survives with probability $p>0$; and, secondly, rescaling the remaining points by an overall factor to normalize the sum again to 1. We prove that the partition structures which are "thinning divisible" for a sequence of $p$'s converging to 0 are mixtures of the Poisson-Kingman partition structures. We also consider the property of being "thinning invariant" for all $p \\in (0,1)$.
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.
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.
Natural inflation with hidden scale invariance
Barrie, Neil D.; Kobakhidze, Archil; Liang, Shelley
2016-05-01
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: 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.
Tractors, mass, and Weyl invariance
International Nuclear Information System (INIS)
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
On obtaining strictly invariant Lagrangians from gauge-invariant Lagrangians
International Nuclear Information System (INIS)
Lagrangian dynamical systems are considered on tangent bundles of differentiable manifolds whose Lagrangian functions are gauge invariant under the action of a Lie group on the base manifold. Necessary and sufficient conditions are then obtained for finding a function on the base manifold whose time derivative, if added to the gauge-invariant Lagrangian, yields a strictly invariant one. The problem is transported from the tangent bundle also to the cotangent bundle
On the disformal invariance of the Dirac equation
Bittencourt, Eduardo; Lobo, Iarley P.; Carvalho, Gabriel G.
2015-09-01
We analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field acting on the metric tensor. Using the Weyl-Cartan formalism, we construct a large class of disformal maps between different metric tensors, respecting the order of differentiability of the Dirac operator and satisfying the Clifford algebra in both metrics. We split the analysis in some cases according to the spinor mass and the norm of the Dirac current, exhibiting sufficient conditions to find classes of solutions which keep the Dirac operator invariant under the action of the disformal group.
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 $I_U$...
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...
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......-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...
Polynomial invariants of quantum codes
Rains, E M
1997-01-01
The weight enumerators (quant-ph/9610040) of a quantum code are quite powerful tools for exploring its structure. As the weight enumerators are quadratic invariants of the code, this suggests the consideration of higher-degree polynomial invariants. We show that the space of degree k invariants of a code of length n is spanned by a set of basic invariants in one-to-one correspondence with S_k^n. We then present a number of equations and inequalities in these invariants; in particular, we give a higher-order generalization of the shadow enumerator of a code, and prove that its coefficients are nonnegative. We also prove that the quartic invariants of a ((4,4,2)) are uniquely determined, an important step in a proof that any ((4,4,2)) is additive ([2]).
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...
Factorization invariants in numerical monoids
O'Neill, Christopher; Pelayo, Roberto
2015-01-01
Nonunique factorization in commutative monoids is often studied using factorization invariants, which assign to each monoid element a quantity determined by the factorization structure. For numerical monoids (co-finite, additive submonoids of the natural numbers), several factorization invariants have received much attention in the recent literature. In this survey article, we give an overview of the length set, elasticity, delta set, $\\omega$-primality, and catenary degree invariants in the ...
Invariants and Likelihood Ratio Statistics
McCullagh, P.; Cox, D. R.
1986-01-01
Because the likelihood ratio statistic is invariant under reparameterization, it is possible to make a large-sample expansion of the statistic itself and of its expectation in terms of invariants. In particular, the Bartlett adjustment factor can be expressed in terms of invariant combinations of cumulants of the first two log-likelihood derivatives. Such expansions are given, first for a scalar parameter and then for vector parameters. Geometrical interpretation is given where possible and s...
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.
Topological invariants in magnetic hydrodynaics
International Nuclear Information System (INIS)
A definition of force line reconnection is proposed within the framework of the ideal hydrodynamics (Rem > 1). It detailizes some previous results. On the basis of the definition it is proved that the asymptotic Hopf invariant is conserved within a time interval τ which is much smaller than the skin (diffusion) time τd. Generally speaking there are no other invariants characterizing a magnetic field configuration (in simply-connected domains). For smooth flow of an ideally conducting fluid (Rem=∞) a method is proposed for determining the linked force line invariants which differ from the Hopf invariant
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...
Conformal Invariant Teleparallel Cosmology
Momeni, Davood
2014-01-01
Teleparallel gravities revisited under conformal transformations. We find several kinds of the Lagrangians, all invariant under conformal transformation. Motivated by observational data,we investigate FRW cosmological solutions in the vacuum. To include the matter fields,we mention that we have few possibilities for our matter Lagrangian to respect the conformal symmetry. FRW equations,have been derived in terms of the effective energy and pressure components. In vacuum we find an exact solution for Hubble parameter which is compatible with the observational data but it is valid only in the range of $z\\ge 0.07$. Scalar torsion models in which we have the extra scalar field is examined under FRW spacetime. We introduce the potential term $\\frac{1}{4!}\\mu\\phi^4$ as the minimal self interaction with conformal symmetry.
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...
Invariants of Lagrangian surfaces
Yau, Mei-Lin
2004-01-01
We define a nonnegative integer $\\la(L,L_0;\\phi)$ for a pair of diffeomorphic closed Lagrangian surfaces $L_0,L$ embedded in a symplectic 4-manifold $(M,\\w)$ and a diffeomorphism $\\phi\\in\\Diff^+(M)$ satisfying $\\phi(L_0)=L$. We prove that if there exists $\\phi\\in\\Diff^+_o(M)$ with $\\phi(L_0)=L$ and $\\la(L,L_0;\\phi)=0$, then $L_0,L$ are symplectomorphic. We also define a second invariant $n(L_1,L_0;[L_t])=n(L_1,L_0,[\\phi_t])$ for a smooth isotopy $L_t=\\phi_t(L_0)$ between two Lagrangian surfac...
The axion mass in modular invariant supergravity
International Nuclear Information System (INIS)
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)
Structure of BRS-invariant local functionals
International Nuclear Information System (INIS)
For a large class of gauge theories a nilpotent BRS-operator s is constructed and its cohomology in the space of local functionals of the off-shell fields is shown to be isomorphic to the cohomology of s=s+d on functions f(C,T) of tensor fields T and of variables C which are constructed of the ghosts and the connection forms. The result allows general statements about the structure of invariant classical actions and anomaly cadidates whose BRS-variation vanishes off-shell. The assumptions under which the result holds are thoroughly discussed. (orig.)
International Nuclear Information System (INIS)
Let ZLMO be the 3-manifold invariant of [LMO]. It is shown that ZLMO(M) = 1, if the first Betti number of M, b1 (M), is greater than 3. If b1 (M) = 3, then ZLMO (M) is completely determined by the cohomology ring of M. A relation of ZLMO with the Rozansky-Witten invariants ZXRW[M] is established at a physical level of rigour. We show that ZXRW[M] satisfies appropriate connected sum properties suggesting that the generalized Casson invariant ought to be computable from the LMO invariant. (author)
On the invariance properties of the Klein–Gordon equation with external electromagnetic ﬁeld
Indian Academy of Sciences (India)
N D Sen Gupta
2003-09-01
Here we attempt to ﬁnd the nature of the external electromagnetic ﬁeld such that the KG equation with external electromagnetic ﬁeld is invariant. Lie’s extended group method is applied to obtain the class of external electromagnetic ﬁeld which admits the invariance of the KG equation. Though, the ﬁeld potential only explicitly appears in the equation, the constraints for the invariance are only on the electromagnetic ﬁeld.
Remarks on mass and angular momenta for U(1)2-invariant initial data
Alaee, Aghil; Kunduri, Hari K.
2016-03-01
We extend Brill's positive mass theorem to a large class of asymptotically flat, maximal, U(1)2-invariant initial data sets on simply connected four dimensional manifolds Σ. Moreover, we extend the local mass angular momenta inequality result [A. Alaee and H. K. Kunduri, Classical Quantum Gravity 32(16), 165020 (2015)] for U(1)2 invariant black holes to the case with nonzero stress energy tensor with positive matter density and energy-momentum current invariant under the above symmetries.
Remarks on mass and angular momenta for $U(1)^2$-invariant initial data
Alaee, Aghil
2015-01-01
We extend Brill's positive mass theorem to a large class of asymptotically flat, maximal, $U(1)^2$-invariant initial data sets on simply connected four dimensional manifolds $\\Sigma$. Moreover, we extend the local mass angular momenta inequality result Ref [1] for $U(1)^2$ invariant black holes to the case with nonzero stress energy tensor with positive matter density and energy-momentum current invariant under the above symmetries.
New texture signatures and their use in rotation invariant texture classification
Zhang, Jianguo; Tan, Tieniu
2002-01-01
In this paper, we present a theoretically and computationally simple but efficient approach for rotation invariant texture classification. This method is based on new texture signatures extracted from spectrum. Rotation invariant texture features are obtained based on the extension of the derived signatures. The features are tested with 1000 randomly rotated samples of 20 Brodatz texture classes. Comparative study results show that our method is highly efficient in rotation invariant texture ...
International Nuclear Information System (INIS)
It is a recent observation that entanglement classification for qubits is closely related to stochastic local operations and classical communication (SLOCC) invariants. Verstraete et al.[Phys. Rev. A 65 (2002) 052112] showed that for pure states of four qubits there are nine different degenerate SLOCC entanglement classes. Li et al.[Phys. Rev. A 76 (2007) 052311] showed that there are at feast 28 distinct true SLOCC entanglement classes for four qubits by means of the SLOCC invariant and semi-invariant. We give 16 different entanglement classes for four qubits by means of basic SLOCC invariants. (general)
Chiral Invariance of Massive Fermions
Das, A.(University of Arizona, Tucson, AZ, 85721, USA); Hott, M
1994-01-01
We show that a massive fermion theory, while not invariant under the conventional chiral transformation, is invariant under a $m$-deformed chiral transformation. These transformations and the associated conserved charges are nonlocal but reduce to the usual transformations and charges when $m=0$. The $m$-deformed charges commute with helicity and satisfy the conventional chiral algebra.
Reducing Lookups for Invariant Checking
DEFF Research Database (Denmark)
Thomsen, Jakob Grauenkjær; Clausen, Christian; Andersen, Kristoffer Just;
2013-01-01
satisfied. We present a formal model of this scenario, based on a simple query language for the expression of invariants that covers the core of a realistic query language. We present an algorithm which simplifies a representation of the invariant, along with a mechanically verified proof of correctness. We...
Gluing formulae for Donaldson invariants for connected sums along surfaces
Muñoz, V
1997-01-01
We solve a conjecture of Morgan and Szabo (Embedded genus 2 surfaces in four-manifolds, Preprint) about the relationship of the basic classes of two four-manifolds $X_i$ of simple type with $b_1=0$, $b^+>1$, such that there are embedded Riemann surfaces of genus $g \\geq 2$ and self-intersection zero (and representing odd homology classes) with the basic classes of the manifold X which appears as a connected sum along the surfaces (supposing this latter one is of simple type). This is also expressed as constraints in the basic classes of X. The result is in accordance with the results on Seiberg-Witten invariants (Morgan, Szabo and Taubes, A product formula for the Seiberg-Witten invariants and the generalized Thom conjecture).
Multilocal invariants for the classical groups
Directory of Open Access Journals (Sweden)
Paul F. Dhooghe
2003-01-01
Full Text Available Multilocal higher-order invariants, which are higher-order invariants defined at distinct points of representation space, for the classical groups are derived in a systematic way. The basic invariants for the classical groups are the well-known polynomial or rational invariants as derived from the Capelli identities. Higher-order invariants are then constructed from the former ones by means of total derivatives. At each order, it appears that the invariants obtained in this way do not generate all invariants. The necessary additional invariants are constructed from the invariant polynomials on the Lie algebra of the Lie transformation groups.
Fayngold, Moses
2010-01-01
A careful look at an allegedly well-known century-old concept reveals interesting aspects in it that have generally avoided recognition in literature. There are four different kinds of physical observables known or proclaimed as relativistic invariants under space-time rotations. Only observables in the first three categories are authentic invariants, whereas the single "invariant" - proper length - in the fourth category is actually not an invariant. The proper length has little is anything to do with proper distance which is a true invariant. On the other hand, proper distance, proper time, and rest mass have more in common than usually recognized, and particularly, mass - time analogy opens another view of the twin paradox.
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
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...... 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...
Energy Technology Data Exchange (ETDEWEB)
Fakhri, H
2003-02-24
A wide range of 1D shape invariant potentials lie in two different classes. In either of these classes the quantum states are distinguished by both of the main and the secondary quantum numbers n and m. We show that quantum states of the first and of the second classes represent shape invariance with respect to n and m, respectively. We also analyze the relationship between these two classes with Lie algebra sl(2,c)
Fakhri, H.
2003-02-01
A wide range of 1D shape invariant potentials lie in two different classes. In either of these classes the quantum states are distinguished by both of the main and the secondary quantum numbers n and m. We show that quantum states of the first and of the second classes represent shape invariance with respect to n and m, respectively. We also analyze the relationship between these two classes with Lie algebra sl(2, c).
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
DU and UD-invariants of unitary groups
International Nuclear Information System (INIS)
Four distint ways of obtaining the eigenvalues of unitary groups, in any irreducible representation, are presented. The invariants are defined according to two different contraction conventions. Their eigenvalue can be given in terms of two classes of special partial hooks associated with the young diagram characterizing the irreducible representation considered
Notes on Group Invariants and Positivity of Density Matrices and Superoperators
Byrd, M S; Byrd, Mark S.; Khaneja, Navin
2003-01-01
In this paper, we construct a distinguished class of unitary invariants, the Casimir invariants, in terms of the generalized coherence vector representation of the density operator. Using a tensor product basis, we show how to extract local information about the density operator and the n-positivity of maps from density operators to density operators (superoperators). We then discuss some applications and implications.
α∗-cohomology, and classification of translation-invariant non-commutative quantum field theories
Varshovi, Amir Abbass
2014-09-01
Translation-invariant ⋆ products are studied in the setting of α∗-cohomology. It is explicitly shown that all quantum behaviors including Green's functions and the scattering matrix of translation-invariant non-commutative quantum field theories are thoroughly characterized by α∗-cohomology classes of the star products.
Measurements of Narrow Mg II Associated Absorption Doublets with Two Observations
Indian Academy of Sciences (India)
Zhi-Fu Chen; Cai-Juan Pan; Guo-Qiang Li; Wei-Rong Huang; Mu-Sheng Li
2013-12-01
The measurement of the variations of absorption lines over time is a good method to study the physical conditions of absorbers. In this paper, we measure the variations of the line strength of 36 narrow Mg II2796, 2803 associated absorption doublets, which are imprinted on 31 quasar spectra with two observations of the Sloan Digital Sky Survey (SDSS). The timescales of these quasar span 1.1–5.5 years at the quasar rest-frame. On these timescales, we find that these narrow Mg II associated absorption doublets are stable, with no one 2796 line showing strength variation beyond 2 times error (2).
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. PMID:26428557
Invariants of Toric Seiberg Duality
Hanany, Amihay; Jejjala, Vishnu; Pasukonis, Jurgis; Ramgoolam, Sanjaye; Rodriguez-Gomez, Diego
2011-01-01
Three-branes at a given toric Calabi-Yau singularity lead to different phases of the conformal field theory related by toric (Seiberg) duality. Using the dimer model/brane tiling description in terms of bipartite graphs on a torus, we find a new invariant under Seiberg duality, namely the Klein j-invariant of the complex structure parameter in the distinguished isoradial embedding of the dimer, determined by the physical R-charges. Additional number theoretic invariants are described in terms of the algebraic number field of the R-charges. We also give a new compact description of the a-maximization procedure by introducing a generalized incidence matrix.
Invariants for Normal Completely Positive Maps on the Hyperfinite $II_1$ Factor
Indian Academy of Sciences (India)
Debashish Goswami; Lingaraj Sahu
2006-11-01
We investigate certain classes of normal completely positive (CP) maps on the hyperfinite $II_1$ factor $\\mathcal{A}$. Using the representation theory of a suitable irrational rotation algebra, we propose some computable invariants for such CP maps.
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.
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.
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.
Moment Invariants for Object Recognition
Czech Academy of Sciences Publication Activity Database
Flusser, Jan
Boca Raton: Wiley&Sons, 2015. ISBN 9780471346081 Institutional support: RVO:67985556 Keywords : invariants * object recognition * moments Subject RIV: JC - Computer Hardware ; Software http://library.utia.cas.cz/separaty/2015/ZOI/flusser-0442976.pdf
Invariant measures in brain dynamics
International Nuclear Information System (INIS)
This note concerns brain activity at the level of neural ensembles and uses ideas from ergodic dynamical systems to model and characterize chaotic patterns among these ensembles during conscious mental activity. Central to our model is the definition of a space of neural ensembles and the assumption of discrete time ensemble dynamics. We argue that continuous invariant measures draw the attention of deeper brain processes, engendering emergent properties such as consciousness. Invariant measures supported on a finite set of ensembles reflect periodic behavior, whereas the existence of continuous invariant measures reflect the dynamics of nonrepeating ensemble patterns that elicit the interest of deeper mental processes. We shall consider two different ways to achieve continuous invariant measures on the space of neural ensembles: (1) via quantum jitters, and (2) via sensory input accompanied by inner thought processes which engender a 'folding' property on the space of ensembles
Object recognition by implicit invariants
Czech Academy of Sciences Publication Activity Database
Flusser, Jan; Kautsky, J.; Šroubek, Filip
2007-01-01
Roč. 2007, č. 4673 (2007), s. 856-863. ISSN 0302-9743. [Computer Analysis of Images and Patterns. Vienna, 27.08.2007-29.08.2007] R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : Invariants * implicit invariants * moments * orthogonal polynomials * nonlinear object deformation Subject RIV: JD - Computer Applications, Robotics Impact factor: 0.402, year: 2005 http:// staff .utia.cas.cz/sroubekf/papers/CAIP_07.pdf
Current forms and gauge invariance
International Nuclear Information System (INIS)
Let C be the bundle of connections of a principal G-bundle π:P → M, and let V be the vector bundle associated with P by a linear representation G → GL(V) on a finite-dimensional vector space V. The Lagrangians on J1(C x MV) whose current form is gauge invariant, are described and the gauge-invariant Lagrangians on J1(V) are classified
Gauge invariance and lattice monopoles
International Nuclear Information System (INIS)
The number and the location of monopoles in Lattice configurations depend on the choice of the gauge, in contrast to the obvious requirement that monopoles, as physical objects, have a gauge-invariant status. It is proved, starting from non-abelian Bianchi identities, that monopoles are indeed gauge-invariant: the technique used to detect them has instead an efficiency which depends on the choice of the abelian projection, in a known and well understood way.
Classification of Simple Current Invariants
Gato-Rivera, Beatriz
1991-01-01
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.)
Modern Tests of Lorentz Invariance
Directory of Open Access Journals (Sweden)
Mattingly David
2005-09-01
Full Text Available Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.
Gauge Invariants and Correlators in Flavoured Quiver Gauge Theories
Mattioli, Paolo
2016-01-01
In this paper we study the construction of holomorphic gauge invariant operators for general quiver gauge theories with flavour symmetries. Using a characterisation of the gauge invariants in terms of equivalence classes generated by permutation actions, along with representation theory results in symmetric groups and unitary groups, we give a diagonal basis for the 2-point functions of holomorphic and anti-holomorphic operators. This involves a generalisation of the previously constructed Quiver Restricted Schur operators to the flavoured case. The 3-point functions are derived and shown to be given in terms of networks of symmetric group branching coefficients. The networks are constructed through cutting and gluing operations on the quivers.
Invariant sets for discontinuous parabolic area-preserving torus maps
Ashwin, P; Nishikawa, T; Zyczkowski, K; Ashwin, Peter; Fu, Xin-Chu; Nishikawa, Takashi; Zyczkowski, Karol
1999-01-01
We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in both components. We show that within this two parameter family of maps, the set of noninvertible maps is open and dense. For certain cases (where the entries in the matrix are rational) we show that the maximal invariant set has positive Lebesgue measure and give bounds on the measure. For certain examples we find expressions for the measure of the invariant set.
On Quasiperiodic Space Tilings, Inflation and Dehn Invariants
Ogievetsky, Oleg; Papadopolos, Zorka
1999-01-01
We introduce Dehn invariants as a useful tool in the study of the inflation of quasiperiodic space tilings. The tilings by ``golden tetrahedra'' are considered. We discuss how the Dehn invariants can be applied to the study of inflation properties of the six golden tetrahedra. We also use geometry of the faces of the golden tetrahedra to analyze their inflation properties. We give the inflation rules for decorated Mosseri-Sadoc tiles in the projection class of tilings ${\\cal T}^{(MS)}$. The D...
On the disformal invariance of the Dirac equation
Bittencourt, Eduardo; Carvalho, Gabriel G
2015-01-01
In this paper we analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field. Using the Weyl-Cartan formalism, we construct a large class of disformal maps between different metric tensors, respecting the order of differentiability of the Dirac operator and satisfying the Clifford algebra in both metrics. Then, we have shown that there is a subclass of solutions of the Dirac equation, provided by Inomata's condition, which keeps the Dirac operator invariant under the action of the disformal group.
How is Lorentz Invariance encoded in the Hamiltonian?
Kajuri, Nirmalya
2016-01-01
One of the disadvantages of the Hamiltonian formulation is that Lorentz invariance is not manifest in the former. Given a Hamiltonian, there is no simple way to check whether it is relativistic or not. One would either have to solve for the equations of motion or calculate the Poisson Brackets of the Noether charges to perform such a check. In this paper we show that, for a class of Hamiltonians, it is possible to check Lorentz invariance directly from the Hamiltonian. Our work is particularly useful for theories where the other methods may not be readily available.
Hidden scale invariance of metals
Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.; Pedersen, Ulf R.
2015-11-01
Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general "hidden" scale invariance of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Grüneisen parameter, are in good agreement with experimental values for the 16 elements where reliable data were available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant inverse power-law (IPL) pair interactions. However, crystal packings of several transition metals (V, Cr, Mn, Fe, Nb, Mo, Ta, W, and Hg), most post-transition metals (Ga, In, Sn, and Tl), and the metalloids Si and Ge cannot be explained by the IPL assumption. The virial-energy correlation coefficients of iron and phosphorous are shown to increase at elevated pressures. Finally, we discuss how scale invariance explains the Grüneisen equation of state and a number of well-known empirical melting and freezing rules.
On Invariant Structures of Black Hole Charges
Ferrara, Sergio; Yeranyan, Armen
2012-01-01
We study "minimal degree" complete bases of duality- and "horizontal"- invariant homogeneous polynomials in the flux representation of two-centered black hole solutions in two classes of D=4 Einstein supergravity models with symmetric vector multiplets' scalar manifolds. Both classes exhibit an SL(2,R) "horizontal" symmetry. The first class encompasses N=2 and N=4 matter-coupled theories, with semi-simple U-duality given by SL(2,R) x SO(m,n); the analysis is carried out in the so-called Calabi-Vesentini symplectic frame (exhibiting maximal manifest covariance) and until order six in the fluxes included. The second class, exhibiting a non-trivial "horizontal" stabilizer SO(2), includes N=2 minimally coupled and N=3 matter coupled theories, with U-duality given by the pseudo-unitary group U(r,s) (related to complex flux representations). Finally, we comment on the formulation of special Kaehler geometry in terms of "generalized" groups of type E7.
Topological invariants of edge states for periodic two-dimensional models
Avila, Julio Cesar; Villegas-Blas, Carlos
2012-01-01
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define topological invariants by considering the associated Bott-Maslov indices which can be easily calculated numerically. For time-reversal symmetric systems in the symplectic universality class this leads to a Z_2-invariant for the edge states. It is shown that the edge state invariants are related to Chern numbers of the bulk systems and also to (spin) edge currents, in the spirit of the theory of topological insulators.
On the motivic Donaldson-Thomas invariants of quivers with potentials
Mozgovoy, Sergey
2011-01-01
We study motivic Donaldson-Thomas invariants for a class of quivers with potentials using the strategy of Behrend, Bryan, and Szendroi. This class includes quivers with potentials arising from consistent brane tilings and quivers with zero potential. Our construction is an alternative to the constructions of Kontsevich and Soibelman. We construct an integration map from the equivariant Hall algebra to the quantum torus and show that our motivic Donaldson-Thomas invariants are images of the natural elements in the equivariant Hall algebra. We show that the inegration map is an algebra homomorphism and use this fact to prove the Harder-Narasimhan relation for the motivic Donaldson-Thomas invariants.
Topological Invariants of Edge States for Periodic Two-Dimensional Models
Energy Technology Data Exchange (ETDEWEB)
Avila, Julio Cesar; Schulz-Baldes, Hermann, E-mail: schuba@mi.uni-erlangen.de; Villegas-Blas, Carlos [Instituto de Matematicas, UNAM (Mexico)
2013-06-15
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define topological invariants by considering the associated Bott-Maslov indices which can be easily calculated numerically. For time-reversal symmetric systems in the symplectic universality class this leads to a Z{sub 2} -invariant for the edge states. It is shown that the edge state invariants are related to Chern numbers of the bulk systems and also to (spin) edge currents, in the spirit of the theory of topological insulators.
Manifestly gauge invariant discretizations of the Schrödinger equation
International Nuclear Information System (INIS)
Grid-based discretizations of the time dependent Schrödinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done using generalizations of ideas used in classical lattice gauge theory, and the process defined is applicable to a large class of discretized differential operators. In particular, popular discretizations such as pseudospectral discretizations using the fast Fourier transform can be transformed to gauge invariant schemes. Also generic gauge invariant versions of generic time integration methods are considered, enabling completely gauge invariant calculations of the time dependent Schrödinger equation. Numerical examples illuminating the differences between a gauge invariant discretization and conventional discretization procedures are also presented. -- Highlights: ► We investigate the Schrödinger equation coupled to an external magnetic field. ► Any grid-based discretization is made trivially gauge invariant. ► An extension of classical lattice gauge theory.
Renormalization group invariants in supersymmetric theories: one- and two-loop results
Beenakker, Wim; Kleiss, Ronald; Verheyen, Rob
2015-01-01
We stress the potential usefulness of renormalization group invariants. Especially particular combinations thereof could for instance be used as probes into patterns of supersymmetry breaking in the MSSM at inaccessibly high energies. We search for these renormalization group invariants in two systematic ways: on the one hand by making use of symmetry arguments and on the other by means of a completely automated exhaustive search through a large class of candidate invariants. At the one-loop level, we find all known invariants for the MSSM and in fact several more, and extend our results to the more constrained pMSSM and dMSSM, leading to even more invariants. Extending our search to the two-loop level we find that the number of invariants is considerably reduced.
Rotation invariant moments and transforms for geometrically invariant image watermarking
Singh, Chandan; Ranade, Sukhjeet K.
2013-01-01
We present invariant image watermarking based on a recently introduced set of polar harmonic transforms and angular radial transforms and their comparative analysis with state-of-art approaches based on Zernike moments and pseudo-Zernike moments (ZMs/PZMs). Similar to ZMs/PZMs, these transforms provide rotation invariance and resilience to noise while mitigating inherent limitations like numerical instability and computational cost at high order of moments. These characteristics motivate us to design invariant transform-based invariant image watermarking schemes that can withstand various intentional or unintentional attacks, handle large bitcarriers, and work in a limited computing environment. A comparative performance evaluation of watermarking systems regarding critical parameters like visual imperceptibility, embedding capacity, and watermark robustness against geometric transformations, common signal processing distortions, and Stirmark attacks is performed along with the empirical analysis of various inherent properties of transforms and moments such as magnitude invariance, reconstruction capabilities, and computational complexity to investigate relationships between the performance of watermarking schemes and inherent properties of transforms.
Local Unitary Invariants for Multipartite Quantum Systems
Wang, Jing; Li, Ming; Fei, Shao-Ming; Li-Jost, Xianqing
2014-01-01
We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples are given to compute such invariant in detail. It is shown that these invariants can be used to detect the local unitary equivalence of degenerated quantum states.
Weyl invariance with a nontrivial mass scale
Alvarez, Enrique
2016-01-01
A theory with a mass scale and yet Weyl invariant is presented. The theory is not invariant under all diffeomorphisms but only under transverse ones. This is the reason why Weyl invariance does not imply scale invariance in a free falling frame. Physical implications of this framework are discussed.
Lectures on Gromov invariants for symplectic 4-manifolds
McDuff, D
1996-01-01
These are notes of lectures given at the NATO Summer School, Montreal 1995. Taubes's recent spectacular work setting up a correspondence between $J$-holo\\-morphic curves in symplectic $4$-manifolds and solutions of the Seiberg-Witten equations counts $J$-holomor\\-phic curves in a somewhat new way. The \\lq\\lq standard" theory concerns itself with moduli spaces of connected curves, and gives rise to Gromov-Witten invariants. However, Taubes's curves arise as zero sets of sections and so need not be connected. These notes are in the main expository. We first discuss the invariants as Taubes defined them, and then discuss some alternatives, showing, for example, a way of dealing with multiply-covered exceptional spheres. We also calculate some examples, in particular finding the Gromov invariant of the fiber class of an elliptic surface by counting $J$-holomorphic curves, rather than going via Seiberg--Witten theory.
Early Universe Cosmology, Effective Supergravity, and Invariants of Algebraic Forms
Sinha, Kuver
2015-01-01
The presence of light scalars can have profound effects on early universe cosmology, influencing its thermal history as well as paradigms like inflation and baryogenesis. Effective supergravity provides a framework to make quantifiable, model-independent studies of these effects. The Riemanian curvature of the Kahler manifold spanned by scalars belonging to chiral superfields, evaluated along supersymmetry breaking directions, provides an order parameter (in the sense that it must necessarily take certain values) for phenomena as diverse as slow roll modular inflation, non-thermal cosmological histories, and the viability of Affleck-Dine baryogenesis. Within certain classes of UV completions, the order parameter for theories with $n$ scalar moduli is conjectured to be related to invariants of $n$-ary cubic forms (for example, for models with three moduli, the order parameter is given by the ring of invariants spanned by the Aronhold invariants). Within these completions, and under the caveats spelled out, thi...
Time-reparametrization-invariant dynamics of a relativistic string
International Nuclear Information System (INIS)
The time-reparametrization-invariant dynamics of a relativistic string is studied in the Dirac generalized Hamiltonian theory by resolving the first class constraints. The reparametrization-invariant evolution parameter is identified with the time-like coordinate of the 'center of mass' of a string which is separated from local degrees of freedom by transformation conserving the group of diffeomorphisms of the generalized Hamiltonian formulation and the Poincare covariance of local constraints. To identify the 'center of mass' time-like coordinate with the invariant proper time (measured by an observer in the comoving frame of reference), we apply the Levi-Civita-Shanmugadhasan canonical transformations which convert the global (mass-shell) constraint into a new momentum, so that the corresponding gauge is not needed for the Hamiltonian reduction. The resolving of local constraints leads to an equivalent unconstrained system in the reduced phase space with the Roehrlich-type Hamiltonian of evolution with respect to the proper time
Geometric invariance of mass-like asymptotic invariants
Michel, Benoît
2010-01-01
We study coordinate-invariance of some asymptotic invariants such as the ADM mass or the Chru\\'sciel-Herzlich momentum, given by an integral over a "boundary at infinity". When changing the coordinates at infinity, some terms in the change of integrand do not decay fast enough to have a vanishing integral at infinity; but they may be gathered in a divergence, thus having vanishing integral over any closed hypersurface. This fact could only be checked after direct calculation (and was called a...
Inflationary quasi-scale invariant attractors
Rinaldi, Massimiliano; Zerbini, Sergio; Venturi, Giovanni
2016-01-01
In a series of papers Kallosh, Linde, and collaborators have provided a unified description of single-field inflation with several types of potentials, ranging from power law to supergravity, in terms of just one parameter $\\alpha$. These so-called $\\alpha$-attractors predict a spectral index $n_{s}$ and a tensor-to-scalar ratio $r$, which are fully compatible with the latest Planck data. The only common feature of all $\\alpha$-attractors is the analyticity of the scalar potential in the non-canonical Einstein frame. In this paper we explore the case of non-analytic potentials and we find that they lead to a class of attractors characterized by quasi-scale invariance in the Jordan frame. In the canonical Einstein frame they all converge to a model with a linear potential and a universal relation between $r$ and $n_{s}$ that can fit the observational data. We show that the breaking of exact, classical, scale invariance in the Jordan frame can be attributed to one-loop corrections, in line with previous results...
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.
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.
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...
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.
Gauge invariance in simple mechanical systems
International Nuclear Information System (INIS)
This article discusses and explains the Hamiltonian formulation for a class of simple gauge invariant mechanical systems consisting of point masses and idealized rods. The study of these models may be helpful to advanced undergraduate or graduate students in theoretical physics to understand, in a familiar context, some concepts relevant to the study of classical and quantum field theories. We use a geometric approach to derive the Hamiltonian formulation for the model considered in the paper: four equal masses connected by six ideal rods. We obtain and discuss the meaning of several important elements, in particular, the constraints and the Hamiltonian vector fields that define the dynamics of the system, the constraint manifold, gauge symmetries, gauge orbits, gauge fixing, and the reduced phase space. (papers)
Trace Invariance for Quaternion Matrices
Directory of Open Access Journals (Sweden)
Ralph John de la Cruz
2015-12-01
Full Text Available Let F be a f ield. It is a classical result in linear algebra that for each A, P ϵ Mn (F such that P is nonsingular, tr A = tr (PAP-1. We show in this paper that the preceding property does not hold true if F is the division ring of real quaternions. We show that the only quaternion matrices that have their trace invariant under unitary similarity are Hermitian matrices, and that the only matrices that have their trace invariant under similarity are real scalar matrices.
Instanton counting and Donaldson invariants
International Nuclear Information System (INIS)
For a smooth projective toric surface we determine the Donaldson invariants and their wall-crossing in terms of the Nekrasov partition function. Using the solution of the Nekrasov conjecture and its refinement , we apply this result to give a generating function for the wall-crossing of Donaldson invariants of good walls of simply connected projective surfaces with b+ = 1 in terms of modular forms. This formula was proved earlier in more generally for simply connected 4-manifolds with b+ = 1, assuming the Kotschick- Morgan conjecture and it was also derived by physical arguments. (author)
Trace Invariance for Quaternion Matrices
Ralph John de la Cruz
2015-01-01
Let F be a f ield. It is a classical result in linear algebra that for each A, P ϵ Mn (F) such that P is nonsingular, tr A = tr (PAP-1). We show in this paper that the preceding property does not hold true if F is the division ring of real quaternions. We show that the only quaternion matrices that have their trace invariant under unitary similarity are Hermitian matrices, and that the only matrices that have their trace invariant under similarity are real scalar matrices.
Leptogenesis and a Jarlskog Invariant
Davidson, Sacha; Davidson, Sacha; Kitano, Ryuichiro
2004-01-01
The relation between low energy CP violating phases, and the CP asymmetry of leptogenesis, $\\epsilon$, is investigated. Although it is known that in general those are independent, there may be a relation when a model is specified. We construct a Jarlskog invariant which is proportional to $\\epsilon$ if the right-handed neutrino masses are hierarchical. Since the invariant can be expressed in terms of left-handed neutrino parameters--some measurable, and some not--it is useful in identifying the limits in which $\\epsilon$ is related to MNS phases.
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.
Duality and scale invariant magnetic fields from bouncing universes
Chowdhury, Debika; Jain, Rajeev Kumar
2016-01-01
Recently, we had numerically shown that, for a non-minimal coupling that is a simple power of the scale factor, scale invariant magnetic fields arise in a class of bouncing universes. In this work, we {\\it analytically}\\/ evaluate the spectrum of magnetic and electric fields generated in a sub-class of such models. We illustrate that, for cosmological scales which have wavenumbers much smaller than the wavenumber associated with the bounce, the shape of the spectrum is preserved across the bounce. Using the analytic solutions obtained, we also illustrate that the problem of backreaction is severe at the bounce. Finally, we show that the power spectrum of the magnetic field remains invariant under a two parameter family of transformations of the non-minimal coupling function.
Permutations and the combinatorics of gauge invariants for general N
Ramgoolam, Sanjaye
2016-01-01
Group algebras of permutations have proved highly useful in solving a number of problems in large N gauge theories. I review the use of permutations in classifying gauge invariants in one-matrix and multi-matrix models and computing their correlators. These methods are also applicable to tensor models and have revealed a link between tensor models and the counting of branched covers. The key idea is to parametrize $U(N)$ gauge invariants using permutations, subject to equivalences. Correlators are related to group theoretic properties of these equivalence classes. Fourier transformation on symmetric groups by means of representation theory offers nice bases of functions on these equivalence classes. This has applications in AdS/CFT in identifying CFT duals of giant gravitons and their perturbations. It has also lead to general results on quiver gauge theory correlators, uncovering links to two dimensional topological field theory and the combinatorics of trace monoids.
International Nuclear Information System (INIS)
A momentum-resonance ansatz of Lewis and Leach was used to study exact invariants for time-dependent, one-dimensional potentials. This ansatz provides a framework for finding invariants admitted by a larger class of time-dependent potentials that was known previously. For a potential that admits an exact invariant in this resonance form, we have shown how to construct the invariant as a functional of the potential in terms of the solution of a definite linear algebraic system of equations. We have found a necessary and sufficient condition on the potential for the existence of an invariant with a given number of resonances. There exist more potentials that admit invariants with two resonances than were previously known and we have found an example in parametric form of such a potential. We have also found examples of potentials that admit invariants with three resonances
Scale-invariant power spectra from a Weyl-invariant scalar-tensor theory
Energy Technology Data Exchange (ETDEWEB)
Myung, Yun Soo [Inje University, Institute of Basic Sciences and Department of Computer Simulation, Gimhae (Korea, Republic of); Park, Young-Jai [Sogang University, Department of Physics, Seoul (Korea, Republic of)
2016-02-15
We obtain scale-invariant scalar and tensor power spectra from a Weyl-invariant scalar-tensor theory in de Sitter spacetime. This implies that the Weyl invariance guarantees the implementation of the scale invariance of the power spectrum in de Sitter spacetime. We establish a deep connection between the Weyl invariance of the action and the scale invariance of the power spectrum in de Sitter spacetime. (orig.)
Identity from classical invariant theory
International Nuclear Information System (INIS)
A simple derivation is given of a well-known relation involving the so-called Cayley Operator of classical invariant theory. The proof is induction-free and independent of Capelli's identity; it makes use only of a known-theorem in the theory of determinants and some elementary combinatorics
Supersymmetric gauge invariant interaction revisited
International Nuclear Information System (INIS)
A supersymmetric Lagrangian invariant under local U(1) gauge transformations is written in terms of a non-chiral superfield which substitute the usual vector supermultiplet together with chiral and anti-chiral superfields. The Euler equations allow us to obtain the off-shell version of the usual Lagrangian for supersymmetric quantum-electrodynamics (SQED). (Author)
Geng, C. Q.; Geng, Lei
2005-01-01
We first briefly review tests on CPT invariance based on the consequences of the CPT theorem and then present some possible CPT tests due to exotic models in which some of the CPT conditions are lost, such as those without hermiticity.
Translation-invariant noncommutative renormalization
Tanasa, Adrian
2010-01-01
We review here the construction of a translation-invariant scalar model which was proved to be renormalizable on Moyal space. Some general considerations on non-local renormalizability are given. Finally, we present perspectives for generalizing these quantum field theoretical techniques to group field theory, a new setting for quantum gravity.
Lorentz invariance and gauge equivariance
International Nuclear Information System (INIS)
Trying to place Lorentz and gauge transformations on the same foundation, it turns out that the first one generates invariance, the second one equivariance, at least for the abelian case. This similarity is not a hypothesis but is supported by and a consequence of the path integral formalism in quantum field theory.
Invariants in Supersymmetric Classical Mechanics
Alonso Izquierdo, Alberto; González León, Miguel Ángel; Mateos Guilarte, Juan
2000-01-01
[EN] The bosonic second invariant of SuperLiouville models in supersymmetric classical mechanics is described. [ES] El segundo campo cuántico de bosones invariante del modelo SuperLiouville es descrito en la mecanica clasica supersimétrica.
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...
A Many Particle Adiabatic Invariant
DEFF Research Database (Denmark)
Hjorth, Poul G.
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 in...
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.
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.
Pairing interaction and Galilei invariance
International Nuclear Information System (INIS)
The relation between Galilei invariance and the energy weighted sum rule for a mass dipole operator is discussed using a monopole pairing interaction. It is found that the energy weighted sum rule for the mass dipole operator changes as much as 18% in medium and heavy nuclei. copyright 1997 The American Physical Society
Scale Invariance, Bounded Rationality and Non-Equilibrium Economics
Vazquez, Samuel E.
2009-01-01
We study a class of heterogeneous agent-based models which are based on a basic set of principles, and the most fundamental operations of an economic system: trade and product transformations. A basic guiding principle is scale invariance, which means that the dynamics of the economy should not depend on the units used to measure the different products. We develop the idea of a "near-equilibrium" expansion which allow us to study the dynamics of fluctuations around economic equilibrium. This ...
Electromagnetic field and the theory of conformal and biholomorphic invariants
International Nuclear Information System (INIS)
This paper contains sections on: 1. Conformal invariance and variational principles in electrodynamics. 2. The principles of Dirichlet and Thomson as a physical motivation for the methods of conformal capacities and extremal lengths. 3. Extension to pseudoriemannian manifolds. 4. Extension to hermitian manifolds. 5. An extension of Schwarz's lemma for hermitian manifolds and its physical significance. 6. Variation of ''complex'' capacities within the admissible class of plurisubharmonic functions. The author concentrates on motivations and interpretations connected with the electromagnetic field. (author)
Deligne-Beilinson Cohomology and Abelian Link Invariants
Directory of Open Access Journals (Sweden)
Enore Guadagnini
2008-11-01
Full Text Available For the Abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and we derive the main properties of the observables in a generic closed orientable 3-manifold. We present an explicit path-integral non-perturbative computation of the Chern-Simons link invariants in the case of the torsion-free 3-manifolds S^3, S^1 × S^2 and S^1 × Σ_g.
Donaldson invariants for connected sums along surfaces of genus 2
Muñoz, V
1997-01-01
We relate the Donaldson invariants of two four-manifolds $X_i$ with embedded Riemann surfaces of genus 2 and self-intersection zero with the invariants of the manifold X which appears as a connected sum along the surfaces. When the original manifolds are of simple type with $b_1=0$ and $b^+>1$, X is of simple type with $b_1=0$ and $b^+>1$ as well, and the relationship between the invariants is expressed as constraints in the basic classes for X. Also we give some applications. For instance, if $X_i$ have both $b_1=0$ then X is of simple type with $b_1=0$, $b^+>1$, and has no basic classes evaluating zero on the Riemann surface. Finally, we prove that any four-manifold with $b^+>1$ and with an embedded surface of genus 2, self-intersection zero and representing an odd homology class, is of finite type of second order.
Commutative n-ary superalgebras with an invariant skew-symmetric form
Vishnyakova, E. G.
2015-12-01
We study n-ary commutative superalgebras and L∞-algebras that possess a skew-symmetric invariant form, using the derived bracket formalism. This class of superalgebras includes for instance Lie algebras and their n-ary generalizations, commutative associative and Jordan algebras with an invariant form. We give a classification of anti-commutative m-dimensional (m - 3) -ary algebras with an invariant form, and a classification of real simple m-dimensional Lie (m - 3) -algebras with a positive definite invariant form up to isometry. Furthermore, we develop the Hodge Theory for L∞-algebras with a symmetric invariant form, and we describe quasi-Frobenius structures on skew-symmetric n-ary algebras.
Complete classification of simple current modular invariants for RCFT's with a center (Zp)k
International Nuclear Information System (INIS)
Simple currents have been used previously to construct various examples of modular invariant partition functions for given rational conformal field theories. In this paper we present for a large class of such theories (namely those with a center that decomposes into factors Zp, p prime) the complete set of modular invariants that can be obtained with simple currents. In addition to the fusion rule automorphisms classified previously for any center, this includes all possible left-right combinations of all possible extensions of the chiral algebra that can be obtained with simple currents, for all possible current-current monodromies. Formulas for the number of invariants of each kind are derived. Although the number of invariants in each of these subsets depends on the current-current monodromies, the total number of invariants depends rather surprisingly only on p and the number of Zp factors. (orig.)
Complete classification of simple current modular invariants for RCFT's with a center (Z p ) k
Gato-Rivera, B.; Schellekens, A. N.
1992-03-01
Simple currents have been used previously to construct various examples of modular invariant partition functions for given rational conformal field theories. In this paper we present for a large class of such theories (namely those with a center that decomposes into factors Z p , p prime) the complete set of modular invariants that can be obtained with simple currents. In addition to the fusion rule automorphisms classified previously for any center, this includes all possible left-right combinations of all possible extensions of the chiral algebra that can be obtained with simple currents, for all possible current-current monodromies. Formulas for the number of invariants of each kind are derived. Although the number of invariants in each of these subsets depends on the current-current monodromies, the total number of invariants depends rather surprisingly only on p and the number of Z p factors.
On the use of K\\"ulshammer type invariants in representation theory
Zimmermann, Alexander
2010-01-01
Since 2005 a new powerful invariant of an algebra emerged using earlier work of Horv\\'ath, H\\'ethelyi, K\\"ulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the centre of a finite dimensional algebra over a field of finite characteristic. It was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modified version of it an invariant under stable equivalences of Morita type. The invariant was used in various contexts to distinguish derived and stable equivalence classes of pairs of algebras in very subtle situations. Generalisations to non symmetric algebras and to higher Hochschild (co-)homology was given. This article surveys the results and gives some of the constructions in more detail.
Gauge-invariant cosmological density perturbations
International Nuclear Information System (INIS)
Gauge-invariant formulation of cosmological density perturbation theory is reviewed with special emphasis on its geometrical aspects. Then the gauge-invariant measure of the magnitude of a given perturbation is presented. (author)
Gauge-invariant extensions of the Proca model in a noncommutative space-time
Abreu, Everton M C; Fernandes, Rafael L; Mendes, Albert C R
2016-01-01
The gauge invariance analysis of theories described in noncommutative (NC) space-times can lead us to interesting results since noncommutativity is one of the possible paths to investigate quantum effects in classical theories such as general relativity, for example. This theoretical possibility has motivated us to analyze the gauge invariance of the NC version of the Proca model, which is a second-class system, in Dirac's classification, since its classical formulation (commutative space-time) has its gauge invariance broken thanks to the mass term. To obtain such gauge invariant model, we have used the gauge unfixing method to construct a first-class NC version of the Proca model. We have also questioned if the gauge symmetries of NC theories, are affected necessarily or not by the NC parameter. In this way, we have calculated its respective symmetries in a standard way via Poisson brackets.
Baryogenesis in a CP invariant theory
Hook, Anson
2015-01-01
We consider baryogenesis in a model which has a CP invariant Lagrangian, CP invariant initial conditions and does not spontaneously break CP at any of the minima. We utilize the fact that tunneling processes between CP invariant minima can break CP to implement baryogenesis. CP invariance requires the presence of two tunneling processes with opposite CP breaking phases and equal probability of occurring. In order for the entire visible universe to see the same CP violating phase, we consider ...
Energy balance invariance for interacting particle systems
Yavari, Arash; Marsden, Jerrold E.
2009-01-01
This paper studies the principle of invariance of balance of energy and its consequences for a system of interacting particles under groups of transformations. Balance of energy and its invariance is first examined in Euclidean space. Unlike the case of continuous media, it is shown that conservation and balance laws do not follow from the assumption of invariance of balance of energy under time-dependent isometries of the ambient space. However, the postulate of invariance of balance of ener...
A functional LMO invariant for Lagrangian cobordisms
DEFF Research Database (Denmark)
Cheptea, Dorin; Habiro, Kazuo; Massuyeau, Gwénaël
2008-01-01
Jacobi diagrams. We prove some properties of this functorial LMO invariant, including its universality among rational finite-type invariants of Lagrangian cobordisms. Finally, we apply the LMO functor to the study of homology cylinders from the point of view of their finite-type invariants....
On Link Invariants and Topological String Amplitudes
Ramadevi, P; Sarkar, Tapobrata
2001-01-01
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. From the multi-component link invariants in SU(N) Chern-Simons theory, we suggest a form for the new polynomial invariants.
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.
Gauge invariance and holographic renormalization
Directory of Open Access Journals (Sweden)
Keun-Young Kim
2015-10-01
Full Text Available We study the gauge invariance of physical observables in holographic theories under the local diffeomorphism. We find that gauge invariance is intimately related to the holographic renormalization: the local counter terms defined in the boundary cancel most of gauge dependences of the on-shell action as well as the divergences. There is a mismatch in the degrees of freedom between the bulk theory and the boundary one. We resolve this problem by noticing that there is a residual gauge symmetry (RGS. By extending the RGS such that it satisfies infalling boundary condition at the horizon, we can understand the problem in the context of general holographic embedding of a global symmetry at the boundary into the local gauge symmetry in the bulk.
Relativistically invariant photonic wave packets
Bradler, Kamil
2009-01-01
We present a photonic wave packet construction which is immune against the decoherence effects induced by the action of the Lorentz group. The amplitudes of a pure quantum state representing the wave packet remain invariant irrespective of the reference frame into which the wave packet has been transformed. Transmitted information is encoded in the helicity degrees of freedom of two correlated momentum modes. The helicity encoding is considered to be particularly suitable for free-space communication. The integral part of the story is information retrieval on the receiver's side. We employed probably the simplest possible helicity (polarization) projection measurement originally studied by Peres and Terno. Remarkably, the same conditions ensuring the invariance of the wave packet also guarantee perfect distinguishability in the process of measuring the helicity.
Anisotropic invariance in minisuperspace models
Chagoya, Javier; Sabido, Miguel
2016-06-01
In this paper we introduce invariance under anisotropic transformations to cosmology. This invariance is one of the key ingredients of the theory of quantum gravity at a Lifshitz point put forward by Hořava. We find that this new symmetry in the minisuperspace introduces characteristics to the model that can be relevant in the ultraviolet regime. For example, by canonical quantization we find a Schrödinger-type equation which avoids the problem of frozen time in quantum cosmology. For simple cases we obtain solutions to this quantum equation in a Kantowski–Sachs (KS) minisuperspace. At the classical level, we study KS and Friedmann–Robertson–Walker cosmologies, obtaining modifications to the solutions of general relativity that can be relevant in the early Universe.
Blur Invariants and Projection Operators
Czech Academy of Sciences Publication Activity Database
Flusser, Jan; Suk, Tomáš; Boldyš, Jiří; Zitová, Barbara
Indbruck: ACTA Press, 2013 - (Linsen, L.; Kampel, M.), s. 305-312. (Computer Graphics and Imaging. 798). ISBN 978-0-88986-944-8. [Signal Processing , Pattern Recognition and Applications (SPPRA 2013). Insbruck (AT), 12.02.2013-14.02.2013] R&D Projects: GA ČR GAP103/11/1552 Keywords : image recognition * Fourier transform * projection operators * invariants Subject RIV: JD - Computer Applications, Robotics
A reparametrization invariant surface ordering
Gustavsson, Andreas
2005-01-01
We introduce a notion of a non-Abelian loop gauge field defined on points in loop space. For this purpose we first find an infinite-dimensional tensor product representation of the Lie algebra which is particularly suited for fields on loop space. We define the non-Abelian Wilson surface as a `time' ordered exponential in terms of this loop gauge field and show that it is reparametrization invariant.
Molecular invariants: atomic group valence
International Nuclear Information System (INIS)
Molecular invariants may be deduced in a very compact way through Grassman algebra. In this work, a generalized valence is defined for an atomic group; it reduces to the Known expressions for the case of an atom in a molecule. It is the same of the correlations between the fluctions of the atomic charges qc and qd (C belongs to the group and D does not) around their average values. Numerical results agree with chemical expectation. (author)
Gauge Invariance in Classical Electrodynamics
Engelhardt, W
2005-01-01
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from the field equations we obtain, however, contradicting solutions. We conclude that the tacit assumption of uniqueness is not justified. The reason for this failure is traced back to the inhomogeneous wave equations which connect the propagating fields and their sources at the same time.
Learning Local Invariant Mahalanobis Distances
Fetaya, Ethan; Ullman, Shimon
2015-01-01
For many tasks and data types, there are natural transformations to which the data should be invariant or insensitive. For instance, in visual recognition, natural images should be insensitive to rotation and translation. This requirement and its implications have been important in many machine learning applications, and tolerance for image transformations was primarily achieved by using robust feature vectors. In this paper we propose a novel and computationally efficient way to learn a loca...
SCALe-invariant Integral Surfaces
Zanni, C.; A. Bernhardt; Quiblier, M.; Cani, M.-P.
2013-01-01
Extraction of skeletons from solid shapes has attracted quite a lot of attention, but less attention was paid so far to the reverse operation: generating smooth surfaces from skeletons and local radius information. Convolution surfaces, i.e. implicit surfaces generated by integrating a smoothing kernel along a skeleton, were developed to do so. However, they failed to reconstruct prescribed radii and were unable to model large shapes with fine details. This work introduces SCALe-invariant Int...
Time Invariant Surface Roughness Evolution during Atmospheric Pressure Thin Film Depositions
Thomas Merkh; Robert Spivey; Toh Ming Lu
2016-01-01
The evolution of thin film morphology during atmospheric pressure deposition has been studied utilizing Monte Carlo methods. Time invariant root-mean-squared roughness and local roughness morphology were both observed when employing a novel simulation parameter, modeling the effect of the experimental high pressure condition. This growth regime, where the surface roughness remains invariant after reaching a critical value, has not been classified by any existing universality class. An anti-sh...
Mutually Quadratically Invariant Information Structures in Two-Team Stochastic Dynamic Games
Colombino, Marcello; Smith, Roy S; Summers, Tyler H.
2016-01-01
We formulate a two-team linear quadratic stochas- tic dynamic game featuring two opposing teams each with decentralized information structures. We introduce the concept of mutual quadratic invariance (MQI), which, analogously to quadratic invariance in (single team) decentralized control, defines a class of interacting information structures for the two teams under which optimal linear feedback control strate- gies are easy to compute. We show that, for zero-sum two- team dynamic games, struc...
Helicity is the only integral invariant of volume-preserving transformations
Enciso, Alberto; Peralta-Salas, Daniel; de Lizaur, Francisco Torres
2016-01-01
We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional $\\mathcal I$ 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 $\\mathcal I$ is invariant under arbitrary volume-preserving diffeomorphisms if and only if it is a function of the helicity.
Tests of Non-Equivalence among Absolutely Nonsingular Tensors through Geometric Invariants
Sakata, Toshio; Maehra, Kazumitsu; Sasaki, Takeshi; Sumi, Toshio; MIYAZAKI, Mitsuhiro; Watanabe, Yoshitaka
2010-01-01
4x4x3 absolutely nonsingular tensors are characterized by their determinant polynomial. Non-quivalence among absolutely nonsingular tensors with respect to a class of linear transformations, which do not chage the tensor rank,is studied. It is shown theoretically that affine geometric invariants of the constant surface of a determinant polynomial is useful to discriminate non-equivalence among absolutely nonsingular tensors. Also numerical caluculations are presented and these invariants are ...
Screen Conformal Invariant Light-like Hypersurfaces of Indefinite Sasakian Space Forms
Massamba, F.
2012-01-01
In this paper, we investigate a class of screen conformal invariant lightlike hypersurfaces of an indefinite Sasakian manifold. The geometric configuration of such hypersurfaces is established. We prove that its geometry is closely related to the one of leaves of its conformal screen distributions. We also prove that, in any leaf of a conformal screen distribution of an invariant lightlike hypersurface of an indefinite Sasakian space form, the parallelism and semiparallelism...
On the Iwasawa invariants of a link in the 3-sphere
Kadokami, Teruhisa
2012-01-01
Based on the analogy between knots and primes, J. Hillman, D. Matei and M. Morishita defined the Iwasawa invariants for sequences of cyclic covers of links with an analogue of Iwasawa's class number formula of number fields. In this paper, we consider the existence of covers of links with prescribed Iwasawa invariants, discussing analogies in number theory. We also propose and consider a problem analogous to Greenberg's conjecture.
Invariants and structures of the homology cobordism group of homology cylinders
Song, Minkyoung
2015-01-01
The homology cobordism group of homology cylinders is a generalization of the mapping class group and the string link concordance group. We study this group and its filtrations by subgroups by developing new homomorphisms. First, we define extended Milnor invariants by combining the ideas of Milnor's link invariants and Johnson homomorphisms. They give rise to a descending filtration of the homology cobordism group of homology cylinders. We show that each successive quotient of the filtration...
Finite type invariants and fatgraphs
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Bene, Alex; Meilhan, Jean-Baptiste Odet Thierry;
2010-01-01
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......We define an invariant G(M) of pairs M,G , where M is a 3-manifold obtained by surgery on some framed link in the cylinder Σ×I , Σ is a connected surface with at least one boundary component, and G is a fatgraph spine of Σ. In effect, G is the composition with the ιn maps of Le–Murakami–Ohtsuki of...... 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...
Institute of Scientific and Technical Information of China (English)
HUANG Bo-Wen; GU Zhi-Yu; QIAN Shang-Wu
2005-01-01
This article puts forward a general shape invariant potential, which includes the translational shape invariant potential and scaling shape invariant potential as two particular cases, and derives the set of linear differential equations for obtaining general solutions of the generalized shape invariance condition.
Quantum moment maps and invariants for G-invariant star products
Hamachi, Kentaro
2002-01-01
We study a quantum moment map and propose an invariant for $G$-invariant star products on a $G$-transitive symplectic manifold. We start by describing a new method to construct a quantum moment map for $G$-invariant star products of Fedosov type. We use it to obtain an invariant that is invariant under $G$-equivalence. In the last section we give two simple examples of such invariants, which involve non-classical terms and provide new insights into the classification of $G$-invariant star pro...
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.
Replication invariance on NTU games
Emilio Calvo; Iñaki Garci´a; Zarzuelo, José M.
2001-01-01
Two concepts of replication (conflictual and non-conflictual) are extended from the class of pure bargaining games to the class of NTU games. The behavior of the Harsanyi, Shapley NTU, Egalitarian and Maschler-Owen solutions of the replica games is compared with that of the Nash and Egalitarian solutions in pure bargaining games.
Scale invariance and renormalization group
International Nuclear Information System (INIS)
Scale invariance enabled the understanding of cooperative phenomena and the study of elementary interactions, such as phase transition phenomena, the Curie critical temperature and spin rearrangement in crystals. The renormalization group method, due to K. Wilson in 1971, allowed for the study of collective phenomena, using an iterative process from smaller scales to larger scales, leading to universal properties and the description of matter state transitions or long polymer behaviour; it also enabled to reconsider the quantum electrodynamic theory and its relations to time and distance scales
Invariants of quadratic differential forms
Wright, Joseph Edmund
2013-01-01
This classic monograph by a mathematician affiliated with Trinity College, Cambridge, offers a brief account of the invariant theory connected with a single quadratic differential form. Suitable for advanced undergraduates and graduate students of mathematics, it avoids unnecessary analysis and offers an accessible view of the field for readers unfamiliar with the subject.A historical overview is followed by considerations of the methods of Christoffel and Lie as well as Maschke's symbolic method and explorations of geometrical and dynamical methods. The final chapter on applications, which d
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.
Quantum Weyl Invariance and Cosmology
Dabholkar, Atish
2015-01-01
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.
Scale-invariance as the origin of dark radiation?
Energy Technology Data Exchange (ETDEWEB)
Gorbunov, Dmitry, E-mail: gorby@ms2.inr.ac.ru [Institute for Nuclear Research of Russian Academy of Sciences, 117312 Moscow (Russian Federation); Moscow Institute of Physics and Technology, 141700 Dolgoprudny (Russian Federation); Tokareva, Anna [Institute for Nuclear Research of Russian Academy of Sciences, 117312 Moscow (Russian Federation); Faculty of Physics of Moscow State University, 119991 Moscow (Russian Federation)
2014-12-12
Recent cosmological data favor R{sup 2}-inflation and some amount of non-standard dark radiation in the Universe. We show that a framework of high energy scale invariance can explain these data. The spontaneous breaking of this symmetry provides gravity with the Planck mass and particle physics with the electroweak scale. We found that the corresponding massless Nambu–Goldstone bosons – dilatons – are produced at reheating by the inflaton decay right at the amount needed to explain primordial abundances of light chemical elements and anisotropy of the cosmic microwave background. Then we extended the discussion on the interplay with Higgs-inflation and on general class of inflationary models where dilatons are allowed and may form the dark radiation. As a result we put a lower limit on the reheating temperature in a general scale invariant model of inflation.
Yang–Baxter invariance of the Nappi–Witten model
Directory of Open Access Journals (Sweden)
Hideki Kyono
2016-04-01
Full Text Available We study Yang–Baxter deformations of the Nappi–Witten model with a prescription invented by Delduc, Magro and Vicedo. The deformations are specified by skew-symmetric classical r-matrices satisfying (modified classical Yang–Baxter equations. We show that the sigma-model metric is invariant under arbitrary deformations (while the coefficient of B-field is changed by utilizing the most general classical r-matrix. Furthermore, the coefficient of B-field is determined to be the original value from the requirement that the one-loop β-function should vanish. After all, the Nappi–Witten model is the unique conformal theory within the class of the Yang–Baxter deformations preserving the conformal invariance.
Projectively related metrics, Weyl nullity, and metric projectively invariant equations
Gover, A Rod
2015-01-01
A metric projective structure is a manifold equipped with the unparametrised geodesics of some pseudo-Riemannian metric. We make acomprehensive treatment of such structures in the case that there is a projective Weyl curvature nullity condition. The analysis is simplified by a fundamental and canonical 2-tensor invariant that we discover. It leads to a new canonical tractor connection for these geometries which is defined on a rank $(n+1)$-bundle. We show this connection is linked to the metrisability equations that govern the existence of metrics compatible with the structure. The fundamental 2-tensor also leads to a new class of invariant linear differential operators that are canonically associated to these geometries; included is a third equation studied by Gallot et al. We apply the results to study the metrisability equation, in the nullity setting described. We obtain strong local and global results on the nature of solutions and also on the nature of the geometries admitting such solutions, obtaining ...
Completed Local Ternary Pattern for Rotation Invariant Texture Classification
Directory of Open Access Journals (Sweden)
Taha H. Rassem
2014-01-01
Full Text Available Despite the fact that the two texture descriptors, the completed modeling of Local Binary Pattern (CLBP and the Completed Local Binary Count (CLBC, have achieved a remarkable accuracy for invariant rotation texture classification, they inherit some Local Binary Pattern (LBP drawbacks. The LBP is sensitive to noise, and different patterns of LBP may be classified into the same class that reduces its discriminating property. Although, the Local Ternary Pattern (LTP is proposed to be more robust to noise than LBP, however, the latter’s weakness may appear with the LTP as well as with LBP. In this paper, a novel completed modeling of the Local Ternary Pattern (LTP operator is proposed to overcome both LBP drawbacks, and an associated completed Local Ternary Pattern (CLTP scheme is developed for rotation invariant texture classification. The experimental results using four different texture databases show that the proposed CLTP achieved an impressive classification accuracy as compared to the CLBP and CLBC descriptors.
Levels of complexity in scale-invariant neural signals
Ivanov, Plamen Ch.; Ma, Qianli D. Y.; Bartsch, Ronny P.
2012-02-01
Many physiological systems exhibit complex scale-invariant and nonlinear features characterized long-range power-law correlations, indicating a possibly common control mechanism. It has been suggested that dynamical processes, influenced by inputs and feedback on multiple time scales, may be sufficient to give rise to this complexity. Two examples of physiologic signals that are the output of hierarchical multiscale physiologic systems under neural control are the human heartbeat and human gait. We show that while both cardiac interbeat interval and gait interstride interval time series under healthy conditions have comparable scale-invariant behavior, they still belong to different complexity classes. We compare results from empirical findings and stochastic feedback modeling approaches to cardiac and locomotor dynamics, which provide new insights into the multicomponent neural mechanisms regulating these complex systems.
Invariant currents in lossy acoustic waveguides with complete local symmetry
Kalozoumis, P A; Diakonos, F K; Theocharis, G; Schmelcher, P
2015-01-01
We implement the concept of complete local symmetry in lossy acoustic waveguides. Despite the presence of losses, the existence of a spatially invariant current is shown theoretically and observed experimentally. We demonstrate how this invariant current leads to the generalization of the Bloch and parity theorems for lossy systems defining a mapping of the pressure field between symmetry related spatial domains. Using experimental data we verify this mapping with remarkable accuracy. For the performed experiment we employ a construction technique based on local symmetries which allows the design of setups with prescribed perfect transmission resonances in the lossless case. Our results reveal the fundamental role of symmetries in restricted spatial domains and clearly indicate that completely locally symmetric devices constitute a promising class of setups, regarding the manipulation of wave propagation.
Tensor network methods for invariant theory
International Nuclear Information System (INIS)
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical approach provides an alternative to the polynomial equations that describe invariants, which often contain a large number of terms with coefficients raised to high powers. This approach also enables one to use known methods from tensor network theory (such as the matrix product state (MPS) factorization) when studying polynomial invariants. As our main example, we consider invariants of MPSs. We generate a family of tensor contractions resulting in a complete set of local unitary invariants that can be used to express the Rényi entropies. We find that the graphical approach to representing invariants can provide structural insight into the invariants being contracted, as well as an alternative, and sometimes much simpler, means to study polynomial invariants of quantum states. In addition, many tensor network methods, such as MPSs, contain excellent tools that can be applied in the study of invariants. (paper)
Fundamental Solution via Invariant Approach for a Brain Tumor Model and its Extensions
Johnpillai, Andrew G.; Mahomed, Fazal M.; Abbasbandy, Saeid
2014-12-01
We firstly show how one can use the invariant criteria for a scalar linear (1+1) parabolic partial differential equations to perform reduction under equivalence transformations to the first Lie canonical form for a class of brain tumor models. Fundamental solution for the underlying class of models via these transformations is thereby found by making use of the well-known fundamental solution of the classical heat equation. The closed-form solution of the Cauchy initial value problem of the model equations is then obtained as well. We also demonstrate the utility of the invariant method for the extended form of the class of brain tumor models and find in a simple and elegant way the possible forms of the arbitrary functions appearing in the extended class of partial differential equations. We also derive the equivalence transformations which completely classify the underlying extended class of partial differential equations into the Lie canonical forms. Examples are provided as illustration of the results.
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.
Exceptional Lie Algebra $E_{7(-25)}$ (Multiplets and Invariant Differential Operators)
Dobrev, V K
2008-01-01
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional algebra $E_{7(-25)}$. Our choice of this particular algebra is motivated by the fact that it belongs to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of $n$-dimensional Minkowski space-time. This class of algebras is identified and summarized in a table. Another motivation is related to the AdS/CFT correspondence. We give the multiplets of indecomposable elementary representations, including the necessary data for all relevant invariant differential operators.
Dualities and geometrical invariants for static and spherically symmetric spacetimes
Seidel, Paola Terezinha; Cabral, Luís Antonio
2016-04-01
In this work, we consider spinless particles in curved spacetime and symmetries related to extended isometries. We search for solutions of a generalized Killing equation whose structure entails a general class of Killing tensors. The conserved quantities along particle’s geodesic are associated with a dual description of the spacetime metric. In the Hamiltonian formalism, some conserved quantities generate a dual description of the metric. The Killing tensors belonging to the conserved objects imply in a nontrivial class of dual metrics even for a Schwarzschild metric in the original spacetime. From these metrics, we construct geometrical invariants for classes of dual spacetimes to explore their singularity structure. A nontrivial singularity behavior is obtained in the dual sector.
Equivalent topological invariants of topological insulators
Energy Technology Data Exchange (ETDEWEB)
Wang Zhong [Department of Modern Physics, University of Science and Technology of China, Hefei, 230026 (China); Qi Xiaoliang; Zhang Shoucheng, E-mail: sczhang@stanford.ed [Department of Physics, Stanford University, Stanford, CA 94305 (United States)
2010-06-15
A time-reversal (TR) invariant topological insulator can be generally defined by the effective topological field theory with a quantized {theta} coefficient, which can only take values of 0 or {pi}. This theory is generally valid for an arbitrarily interacting system and the quantization of the {theta} invariant can be directly measured experimentally. Reduced to the case of a non-interacting system, the {theta} invariant can be expressed as an integral over the entire three-dimensional Brillouin zone. Alternatively, non-interacting insulators can be classified by topological invariants defined over discrete TR invariant momenta. In this paper, we show the complete equivalence between the integral and the discrete invariants of the topological insulator.
Equivalent topological invariants of topological insulators
Wang, Zhong; Qi, Xiao-Liang; Zhang, Shou-Cheng
2009-01-01
A time-reversal invariant topological insulator can be generally defined by the effective topological field theory with a quantized \\theta coefficient, which can only take values of 0 or \\pi. This theory is generally valid for an arbitrarily interacting system and the quantization of the \\theta invariant can be directly measured experimentally. Reduced to the case of a non-interacting system, the \\theta invariant can be expressed as an integral over the entire three dimensional Brillouin zone...
Knot invariants and higher representation theory
Webster, Ben
2013-01-01
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. Our technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimens...
Light Speed Invariance is a Remarkable Illusion
Gift, Stephan J. G.
2007-01-01
Though many experiments appear to have confirmed the light speed invariance postulate of special relativity theory, this postulate is actually unverified. This paper resolves this issue by first showing the manner in which an illusion of light speed invariance occurs in two-way light speed measurement in the framework of a semi-classical absolute space theory. It then demonstrates a measurable variation of the one-way speed of light, which directly invalidates the invariance postulate and con...
On factorization invariants and Hilbert functions
O'Neill, Christopher
2015-01-01
Nonunique factorization in commutative semigroups is often studied using factorization invariants, which assign to each semigroup element a quantity determined by the factorization structure. For numerical semigroups (additive subsemigroups of the natural numbers), several factorization invariants are known to admit predictable behavior for sufficiently large semigroup elements. In particular, the catenary degree and delta set invariants are both eventually periodic, and the omega-primality i...
On a Class Almost Contact Manifolds with Norden Metric
Teofilova, Marta
2011-01-01
Certain curvature properties and scalar invariants of the manifolds belonging to one of the main classes almost contact manifolds with Norden metric are considered. An example illustrating the obtained results is given and studied.
Wilson loop invariants from WN conformal blocks
Alekseev, Oleg; Novaes, Fábio
2015-12-01
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.
Baryogenesis in a CP invariant theory
Hook, Anson
2015-01-01
We consider baryogenesis in a model which has a CP invariant Lagrangian, CP invariant initial conditions and does not spontaneously break CP at any of the minima. We utilize the fact that tunneling processes between CP invariant minima can break CP to implement baryogenesis. CP invariance requires the presence of two tunneling processes with opposite CP breaking phases and equal probability of occurring. In order for the entire visible universe to see the same CP violating phase, we consider a model where the field doing the tunneling is the inflaton.
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.
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.
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.
Controller Synthesis for Robust Invariance of Polynomial Dynamical Systems using Linear Programming
Sassi, Mohamed Amin Ben
2011-01-01
In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances and with input constraints. More precisely, we aim at synthesizing at the same time a controller and an invariant set for the controlled system under all admissible disturbances. We propose a computational method to solve this problem. Given a candidate polyhedral invariant, we show that controller synthesis can be formulated as an optimization problem involving polynomial cost functions over bounded polytopes for which effective linear programming relaxations can be obtained. Then, we propose an iterative approach to compute the controller and the polyhedral invariant at once. Each iteration of the approach mainly consists in solving two linear programs (one for the controller and one for the invariant) and is thus computationally tractable. Finally, we show with several examples the usefulness of our method in applications.
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.
Introduction to Vassiliev Knot Invariants
Chmutov, S; Mostovoy, J
2011-01-01
This book is a detailed introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. It is intended to serve both as a textbook for readers with no or little background in this area, and as a guide to some of the more advanced material. Our aim is to lead the reader to understanding by means of pictures and calculations, and for this reason we often prefer to convey the idea of the proof on an instructive example rather than give a complete argument. While we have made an effort to make the text reasonably self-contained, an advanced reader is sometimes referred to the original papers for the technical details of the proofs.
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...
Uniform distribution of Hasse invariants
Directory of Open Access Journals (Sweden)
R. A. Mollin
1985-03-01
Full Text Available I. Schur's study of simple algebras around the turn of the century, and subsequent investigations by R. Brauer, E. Witt and others, were later reformulated in terms of what is now called the Schur subgroup of the Brauer group. During the last twenty years this group has generated substantial interest and numerous palatable results have ensued. Among these is the discovery that elements of the Schur group satisfy uniform distribution of Hasse invariants. It is the purpose of this paper to continue an investigation of the latter concept and to highlight certain applications of these results, not only to the Schur group, but also to embeddings of simple algebras and extensions of automorphisms, among others.
Higher-genus Gromov-Witten invariants as genus 0 invariants of symmetric products
Costello, Kevin
2003-01-01
I prove a formula expressing the descendent genus g Gromov-Witten invariants of a projective variety X in terms of genus 0 invariants of its symmetric product stack S^{g+1}(X). When X is a point, the latter are structure constants of the symmetric group, and we obtain a new way of calculating the Gromov-Witten invariants of a point.
Directory of Open Access Journals (Sweden)
Tina Zavašnik-Bergant
Full Text Available Dendritic cells (DC play a pivotal role as antigen presenting cells (APC and their maturation is crucial for effectively eliciting an antigen-specific immune response. The p41 splice variant of MHC class II-associated chaperone, called invariant chain p41 Ii, contains an amino acid sequence, the p41 fragment, which is a thyropin-type inhibitor of proteolytic enzymes. The effects of exogenous p41 fragment and related thyropin inhibitors acting on human immune cells have not been reported yet. In this study we demonstrate that exogenous p41 fragment can enter the endocytic pathway of targeted human immature DC. Internalized p41 fragment has contributed to the total amount of the immunogold labelled p41 Ii-specific epitope, as quantified by transmission electron microscopy, in particular in late endocytic compartments with multivesicular morphology where antigen processing and binding to MHC II take place. In cell lysates of treated immature DC, diminished enzymatic activity of cysteine proteases has been confirmed. Internalized exogenous p41 fragment did not affect the perinuclear clustering of acidic cathepsin S-positive vesicles typical of mature DC. p41 fragment is shown to interfere with the nuclear translocation of NF-κB p65 subunit in LPS-stimulated DC. p41 fragment is also shown to reduce the secretion of interleukin-12 (IL-12/p70 during the subsequent maturation of treated DC. The inhibition of proteolytic activity of lysosomal cysteine proteases in immature DC and the diminished capability of DC to produce IL-12 upon their subsequent maturation support the immunomodulatory potential of the examined thyropin from p41 Ii.
Invariant effective actions, cohomology of homogeneous spaces and anomalies
Energy Technology Data Exchange (ETDEWEB)
D`Hoker, E. [California Univ., Los Angeles, CA (United States). Dept. of Physics
1995-10-02
We construct the most general local effective actions for Goldstone boson fields associated with spontaneous symmetry breakdown from a group G to a subgroup H. In a preceding paper, it was shown that any G-invariant term in the action, which results from a non-invariant Lagrangian density, corresponds to a non-trivial generator of the de Rham cohomology classes of G/H. Here, we present an explicit construction of all the generators of this cohomology for any coset space G/H and compact, connected group G. Generators contributing to actions in 4-dimensional space-time arise either as products of generators of lower degree such as the Goldstone-Wilczek current, or are of the Wess-Zumino-Witten type. The latter arise if and only if G has a non-zero G-invariant symmetric d-symbol, which vanishes when restricted to the subgroup H, i.e. when G has anomalous representations in which H is embedded in an anomaly free way. Coupling of additional gauge fields leads to actions whose gauge variation coincides with the chiral anomaly, which is carried here by Goldstone boson fields at tree level. Generators contributing to actions in 3-dimensional space-time arise as Chern-Simons terms evaluated on connections that are composites of the Goldstone field. (orig.).
Invariant effective actions, cohomology of homogeneous spaces and anomalies
International Nuclear Information System (INIS)
We construct the most general local effective actions for Goldstone boson fields associated with spontaneous symmetry breakdown from a group G to a subgroup H. In a preceding paper, it was shown that any G-invariant term in the action, which results from a non-invariant Lagrangian density, corresponds to a non-trivial generator of the de Rham cohomology classes of G/H. Here, we present an explicit construction of all the generators of this cohomology for any coset space G/H and compact, connected group G. Generators contributing to actions in 4-dimensional space-time arise either as products of generators of lower degree such as the Goldstone-Wilczek current, or are of the Wess-Zumino-Witten type. The latter arise if and only if G has a non-zero G-invariant symmetric d-symbol, which vanishes when restricted to the subgroup H, i.e. when G has anomalous representations in which H is embedded in an anomaly free way. Coupling of additional gauge fields leads to actions whose gauge variation coincides with the chiral anomaly, which is carried here by Goldstone boson fields at tree level. Generators contributing to actions in 3-dimensional space-time arise as Chern-Simons terms evaluated on connections that are composites of the Goldstone field. (orig.)
Invariant sets near singularities of holomorphic foliations
Camacho, César; Rosas, Rudy
2013-01-01
Consider a complex one dimensional foliation on a complex surface near a singularity $p$. If $\\mathcal{I}$ is a closed invariant set containing the singularity $p$, then $\\mathcal{I}$ contains either a separatrix at $p$ or an invariant real three dimensional manifold singular at $p$.
Uniqueness in ergodic decomposition of invariant probabilities
Zimmermann, Dieter
1992-01-01
We show that for any set of transition probabilities on a common measurable space and any invariant probability, there is at most one representing measure on the set of extremal, invariant probabilities with the $\\sigma$-algebra generated by the evaluations. The proof uses nonstandard analysis.
A rephasing invariant study of neutrino mixing
Chiu, S H
2015-01-01
We derive a set of renormalization group equations (RGE) for Dirac neutrinos using a rephasing invariant parametrization. The symmetric properties of these equations under flavor permutation facilitate the derivation of some exact and approximate RGE invariants. Even though the complete analytical solutions for the RGE are unavailable, we provide a numerical example that illustrate the evolution of the neutrino mixing parameters.
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.
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...
Synthesizing Chaotic Maps with Prescribed Invariant Densities
Rogers, Alan; Shorten, Robert; Heffernan, Daniel M.
2004-01-01
The Inverse Frobenius-Perron problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this note, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized.
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 ...
Transverse invariant higher-spin fields
Energy Technology Data Exchange (ETDEWEB)
Skvortsov, E.D. [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute, Leninsky prospect 53, 119991 Moscow (Russian Federation)], E-mail: eugene.skvortsov@gmail.com; Vasiliev, M.A. [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute, Leninsky prospect 53, 119991 Moscow (Russian Federation)], E-mail: vasiliev@lpi.ru
2008-06-26
It is shown that a symmetric massless bosonic higher-spin field can be described by a traceless tensor field with reduced (transverse) gauge invariance. The Hamiltonian analysis of the transverse gauge invariant higher-spin models is used to control a number of degrees of freedom.
Stability of (A,B)-invariant subspaces
Peña Carrera, Marta; Puerta Coll, Xavier; Puerta Sales, Ferran
2005-01-01
Given a pair of matrices (A;B) we study the stability of their invariant subspaces from the geometry of the manifold of quadruples (A;B; S; F) where S is an (A;B)-invariant subspace and F is such that (A + BF)S ½ S. In particular, we derive a su±cient computable condition of stability.
Rational Invariants of the Generalized Classical Groups
Institute of Scientific and Technical Information of China (English)
NAN JI-ZHU; ZHAO JING
2011-01-01
In this paper, we give transcendence bases of the rational invariants fields of the generalized classical groups and their subgroups B, N and T, and we also compute the orders of them. Furthermore, we give explicit generators for the rational invariants fields of the Borel subgroup and the Neron-Severi subgroup of the general linear group.
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.
Geometric invariance of compressible turbulent boundary layers
Bi, Wei-Tao; Wu, Bin; She, Zhen-Su; Hussain, Fazle
2015-11-01
A symmetry based approach is applied to analyze the mean velocity and temperature fields of compressible, flat plate turbulent boundary layers (CTBL). A Reynolds stress length scale and a turbulent heat flux length scale are identified to possess the same defect scaling law in the CTBL bulk, which is solely owing to the constraint of the wall to the geometry of the wall-attached eddies, but invariant to compressibility and wall heat transfer. This invariance is called the geometric invariance of CTBL eddies and is likely the origin of the Mach number invariance of Morkovin's hypothesis, as well as the similarity of energy and momentum transports. A closure for the turbulent transport by using the invariant lengths is attainted to predict the mean velocity and temperature profiles in the CTBL bulk- superior to the van Driest transformation and the Reynolds analogy based relations for its sound physics and higher accuracy. Additionally, our approach offers a new understanding of turbulent Prandtl number.
Optimal demand for contingent claims when agents have law invariant utilities
Carlier, Guillaume; Dana, Rose-Anne
2011-01-01
International audience We consider a class of law invariant utilities which contains the Rank Dependent Expected Utility (RDU) and the cumulative prospect theory (CPT). We show that the computation of demand for a contingent claim when utilities are within that class, although not as simple as in the Expected Utility (EU) case, is still tractable. Specific attention is given to the RDU and to the CPT cases. Numerous examples are fully solved.
Spectral and scattering theory for translation invariant models in quantum field theory
DEFF Research Database (Denmark)
Rasmussen, Morten Grud
This thesis is concerned with a large class of massive translation invariant models in quantum field theory, including the Nelson model and the Fröhlich polaron. The models in the class describe a matter particle, e.g. a nucleon or an electron, linearly coupled to a second quantised massive scalar...... spectrum is proven to hold globally and scattering theory of the model is studied using time-dependent methods, of which the main result is asymptotic completeness....
Invariant classification of second-order conformally flat superintegrable systems
International Nuclear Information System (INIS)
In this paper we continue the work of Kalnins et al in classifying all second-order conformally-superintegrable (Laplace-type) systems over conformally flat spaces, using tools from algebraic geometry and classical invariant theory. The results obtained show, through Stäckel equivalence, that the list of known nondegenerate superintegrable systems over three-dimensional conformally flat spaces is complete. In particular, a seven-dimensional manifold is determined such that each point corresponds to a conformal class of superintegrable systems. This manifold is foliated by the nonlinear action of the conformal group in three dimensions. Two systems lie in the same conformal class if and only if they lie in the same leaf of the foliation. This foliation is explicitly described using algebraic varieties formed from representations of the conformal group. The proof of these results rely heavily on Gröbner basis calculations using the computer algebra software packages Maple and Singular. (paper)
Performance prediction using EEG and trial-invariant characteristic signals.
Varnavas, Andreas; Petrou, Maria
2008-01-01
One of the most important parts of all applications trying to discriminate between a person's different mental tasks using their recorded EEG data is the process of feature construction. A common practice for this is to exploit an apriori knowledge about the nature of the mental processes of interest and their impact on the EEG signals. However, the use of features constructed in this way is restricted to applications concerning the corresponding mental processes. We present here a novel method for EEG data classification which is very general as it makes no assumptions about the nature of the EEG signals. It is based on the construction of a characteristic signal for each class which remains as invariant as possible over the trials belonging to that class. We use the proposed method in combination with a novel method for channel selection in an oddball experiment to predict a person's quick or late response. PMID:19163241
Conformal invariant two particle processes
International Nuclear Information System (INIS)
For the conformal group (essentially the SO2(n,2)group) in n-dimensional Minkowsi-space homogeneous spaces are studied which can be interpreted as 2-particle configuration spaces, and 2-particle representations are induced (both participants are spin 0 particles). The eigensolutions of the Casimir-operator in momentum space are Clebsch-Gordan coefficients in momentum basis. The separation of a complete set of comuting operators from the Casimir eigenvalue equations results in all cases in differential equations with 2 variables (a direct consequence of the rank 2 of the homogen spaces), which can be classified as 'generalized hypergeometric differential operators in 2 variables' (this type, as the author supposes, has not been delt with in the literature so far). In the second part the classical conform invariant (relativistic) 2-particle problem, corresponding to the common quantum mechanical (or quantum field theoretical) problem, is presented and solved completely. It is shown for example that for participant momentums (reasonable in the classic sens) on the forward - or on the zero cone only scattering and no bound states are found. (orig./WBU)
Institute of Scientific and Technical Information of China (English)
A H Bokhari; F D Zaman; K Fakhar; A H Kara
2011-01-01
@@ First,we studied the invariance properties of the Kadomstev-Petviashvili equation with power law nonlinearity.Then,we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the equation.The point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved flows.%First, we studied the invariance properties of the Kadomstev-Petviashvili equation with power law nonlinearity. Then, we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the equation. The point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved Bows.
Generating Bell states in invariant stratification spin networks
International Nuclear Information System (INIS)
In this paper, we study the generation of Bell states between distant vertices in a permanently coupled quantum spin network, interacting via invariant stratification graphs. To begin with we establish a class of upper bounds over the achievable entanglement between the reference site and various vertices. We observe that the maximum of these upper bounds is one e-bit. We conclude that the reference site can generate a Bell state with a vertex if the corresponding upper bound of the vertex is one e-bit. Thus for generation of a Bell state this upper bound must be saturated. Taking this into account, we obtain the characteristic constraint of the proper graphs. We introduce a special class of antipodal invariant stratification graphs, which is called reflective, whereas the antipode vertex obeys the characteristic constraint. We also show that the antipodal association scheme graphs are reflective so Bell states can be generated between the antipodal vertices. Moreover, we observe that in such graphs the proper Hamiltonian that enables the creation of a Bell state is the Heisenberg interaction between vertex pairs
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.
Gromov-Witten invariants and localization
Morrison, David R
2016-01-01
We give a pedagogical review of the computation of Gromov-Witten invariants via localization in 2D gauged linear sigma models. We explain the relationship between the two-sphere partition function of the theory and the Kahler potential on the conformal manifold. We show how the Kahler potential can be assembled from classical, perturbative, and non-perturbative contributions, and explain how the non-perturbative contributions are related to the Gromov-Witten invariants of the corresponding Calabi-Yau manifold. We then explain how localization enables efficient calculation of the two-sphere partition function and, ultimately, the Gromov-Witten invariants themselves.
On Metrizability of Invariant Affine Connections
Tanaka, Erico
2011-01-01
The metrizability problem for a symmetric affine connection on a manifold, invariant with respect to a group of diffeomorphisms G, is considered. We say that the connection is G-metrizable, if it is expressible as the Levi-Civita connection of a G-invariant metric field. In this paper we analyze the G-metrizability equations for the rotation group G = SO(3), acting canonically on three- and four-dimensional Euclidean spaces. We show that the property of the connection to be SO(3)-invariant allows us to find complete explicit description of all solutions of the SO(3)-metrizability equations.
Invariants of the local Clifford group
International Nuclear Information System (INIS)
We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct bases for these vector spaces for each degree, thereby obtaining a generating set of polynomial invariants. Our approach is based on the description of Clifford operators in terms of linear operations over GF(2). Such a study of polynomial invariants of the local Clifford group is mainly of importance in quantum coding theory, in particular in the classification of binary quantum codes. Some applications in entanglement theory and quantum computing are briefly discussed as well
Comment on ``Pairing interaction and Galilei invariance''
Arias, J. M.; Gallardo, M.; Gómez-Camacho, J.
1999-05-01
A recent article by Dussel, Sofia, and Tonina studies the relation between Galilei invariance and dipole energy weighted sum rule (EWSR). The authors find that the pairing interaction, which is neither Galilei nor Lorentz invariant, produces big changes in the EWSR and in effective masses of the nucleons. They argue that these effects of the pairing force could be realistic. In this Comment we stress the validity of Galilei invariance to a very good approximation in this context of low-energy nuclear physics and show that the effective masses and the observed change in the EWSR for the electric dipole operator relative to its classical value are compatible with this symmetry.
International Nuclear Information System (INIS)
The Bureau of Reclamation (Reclamation) is proposing to modify or install additional transmission facilities between the Hoover Dam hydroelectric plant and the Western Area Power Authority substation near Boulder City, Nevada. Reclamation has completed cultural resource investigations to identify historic or prehistoric resources in the project area that might be affected during construction of the transmission line. Four possible transmission corridors approximately 50 feet wide and between 9.5 and 11.5 miles long were investigated. The proposed transmission lines either parallel or replace existing transmission lines. The corridors generally have undergone significant disturbance from past transmission line construction. A Class II sampling survey covering approximately 242 acres was conducted. Access or construction roads have not been identified and surveys of these areas will have to be completed in the future. No historic or prehistoric archeological sites were encountered within the four corridor right-of-ways. It is believed that the probability for prehistoric sites is very low. Four historic period sites were recorded that are outside, but near, the proposed corridor. These sites are not individually eligible for the National Register of Historic Places, but may be associated with the construction of Hoover Dam and contribute to a historic district or multiple property resource area focusing on the dam and its construction
Energy Technology Data Exchange (ETDEWEB)
Varshovi, Amir Abbass [School of Mathematics, Institute for Research in Fundamental Sciences (IPM) and School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran (Iran, Islamic Republic of)
2013-07-15
The theory of α*-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an algebraic classification of translation-invariant non-commutative structures and shows that any general translation-invariant non-commutative quantum field theory is physically equivalent to a Groenewold-Moyal non-commutative quantum field theory.
International Nuclear Information System (INIS)
First, we studied the invariance properties of the Kadomstev—Petviashvili equation with power law nonlinearity. Then, we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the equation. The point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved flows. (general)
Varshovi, Amir Abbass
2013-07-01
The theory of α*-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an algebraic classification of translation-invariant non-commutative structures and shows that any general translation-invariant non-commutative quantum field theory is physically equivalent to a Groenewold-Moyal non-commutative quantum field theory.
International Nuclear Information System (INIS)
The theory of α*-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an algebraic classification of translation-invariant non-commutative structures and shows that any general translation-invariant non-commutative quantum field theory is physically equivalent to a Groenewold-Moyal non-commutative quantum field theory
On invariant measures of nonlinear Markov processes
Directory of Open Access Journals (Sweden)
N. U. Ahmed
1993-01-01
Full Text Available We consider a nonlinear (in the sense of McKean Markov process described by a stochastic differential equations in Rd. We prove the existence and uniqueness of invariant measures of such process.
Invariant Spectral Hashing of Image Saliency Graph
Taquet, Maxime; De Vleeschouwer, Christophe; Macq, Benoit
2010-01-01
Image hashing is the process of associating a short vector of bits to an image. The resulting summaries are useful in many applications including image indexing, image authentication and pattern recognition. These hashes need to be invariant under transformations of the image that result in similar visual content, but should drastically differ for conceptually distinct contents. This paper proposes an image hashing method that is invariant under rotation, scaling and translation of the image. The gist of our approach relies on the geometric characterization of salient point distribution in the image. This is achieved by the definition of a "saliency graph" connecting these points jointly with an image intensity function on the graph nodes. An invariant hash is then obtained by considering the spectrum of this function in the eigenvector basis of the Laplacian graph, that is, its graph Fourier transform. Interestingly, this spectrum is invariant under any relabeling of the graph nodes. The graph reveals geomet...
Kinematical bound in asymptotically translationally invariant spacetimes
Shiromizu, T; Tomizawa, S; Shiromizu, Tetsuya; Ida, Daisuke; Tomizawa, Shinya
2004-01-01
We present positive energy theorems in asymptotically translationally invariant spacetimes which can be applicable to black strings and charged branes. We also address the bound property of the tension and charge of branes.
Fourier tranform in exponential rearrangement invariant spaces
Ostrovsky, E.; Sirota, L.
2004-01-01
In this article we investigate the Fourier series and transforms for the functions defined on the $ [0, 2 \\pi]^ d $ or $ R^d $ and belonging to the exponential Orlicz and some other rearrangement invariant (r.i.) spaces.
On link invariants and topological string amplitudes
International Nuclear Information System (INIS)
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
Conformal Invariance in Classical Field Theory
Grigore, D. R.
1993-01-01
A geometric generalization of first-order Lagrangian formalism is used to analyse a conformal field theory for an arbitrary primary field. We require that global conformal transformations are Noetherian symmetries and we prove that the action functional can be taken strictly invariant with respect to these transformations. In other words, there does not exists a "Chern-Simons" type Lagrangian for a conformally invariant Lagrangian theory.
Gauge Invariant Monopoles in SU(2) Gluodynamics
Gubarev, F V
2002-01-01
We introduce a gauge invariant topological definition of monopole charge in pure SU(2) gluodynamics. The non-trivial topology is provided by hedgehog configurations of the non-Abelian field strength tensor on the two-sphere surrounding the monopole. It is shown that this definition can be formulated entirely in terms of Wilson loops which makes the gauge invariance manifest. Moreover, it counts correctly the monopole charge in case of spontaneously broken gauge symmetry and of pure Abelian gauge fields.
Conformal Invariance of Black Hole Temperature
Jacobson, Ted; Kang, Gungwon
1993-01-01
It is shown that the surface gravity and temperature of a stationary black hole are invariant under conformal transformations of the metric that are the identity at infinity. More precisely, we find a conformal invariant definition of the surface gravity of a conformal Killing horizon that agrees with the usual definition(s) for a true Killing horizon and is proportional to the temperature as defined by Hawking radiation. This result is reconciled with the intimate relation between the trace ...
A Homeomorphism Invariant for Substitution Tiling Spaces
Ormes, Nic; Radin, Charles; Sadun, Lorenzo
2000-01-01
We derive a homeomorphism invariant for those tiling spaces which are made by rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in infinitely many orientations. The invariant is a quotient of Cech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like tiling spaces. We also introduce a module structure on cohomology which is very convenient as well as ...
Invariant and type inference for matrices
Henzinger, Thomas A.; Hottelier, Thibaud; Kovács, Laura; Voronkov, Andrei
2010-01-01
Wepresentalooppropertygenerationmethodforloopsiteratingover multi-dimensional arrays. When used on matrices, our method is able to infer their shapes (also called types), such as upper-triangular, diagonal, etc. To gen- erate loop properties, we first transform a nested loop iterating over a multi- dimensional array into an equivalent collection of unnested loops. Then, we in- fer quantified loop invariants for each unnested loop using a generalization of a recurrence-based invariant generati...
Computer calculation of Witten's 3-manifold invariant
International Nuclear Information System (INIS)
Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant. (orig.)
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 adiabatic invariant in generalized Galileon theories
Ema, Yohei; Jinno, Ryusuke; 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 us...
Computer calculation of Witten's 3-manifold invariant
Freed, Daniel S.; Gompf, Robert E.
1991-10-01
Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant.
The invariator principle in convex geometry
DEFF Research Database (Denmark)
Thórisdóttir, Ólöf; Kiderlen, Markus
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, w...... functions and derive several, more explicit representations of these functions. In particular, we use Morse theory to write the measurement functions in terms of critical values of the sectioned object. This is very useful for surface area estimation....
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.
Invariant Spectral Hashing of Image Saliency Graph
Taquet, Maxime; Jacques, Laurent; De Vleeschouwer, Christophe; Macq, Benoît
2010-01-01
Image hashing is the process of associating a short vector of bits to an image. The resulting summaries are useful in many applications including image indexing, image authentication and pattern recognition. These hashes need to be invariant under transformations of the image that result in similar visual content, but should drastically differ for conceptually distinct contents. This paper proposes an image hashing method that is invariant under rotation, scaling and translation of the image....
The Fundamental Theorem of Vassiliev Invariants
Bar-Natan, Dror; STOIMENOW, Alexander
1997-01-01
The "fundamental theorem of Vassiliev invariants" says that every weight system can be integrated to a knot invariant. We discuss four different approaches to the proof of this theorem: a topological/combinatorial approach following M. Hutchings, a geometrical approach following Kontsevich, an algebraic approach following Drinfel'd's theory of associators, and a physical approach coming from the Chern-Simons quantum field theory. Each of these approaches is unsatisfactory in one way or anothe...
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.
The invariance assumption in process-dissociation models: an evaluation across three domains.
Klauer, Karl Christoph; Dittrich, Kerstin; Scholtes, Christine; Voss, Andreas
2015-02-01
The class of process-dissociation models, a subset of the class of multinomial processing-tree models, is one of the best understood classes of models used in experimental psychology. A number of prominent debates have addressed fundamental assumptions of process-dissociation models, leading, in many cases, to conceptual clarifications and extended models that address identified issues. One issue that has so far defied empirical clarification is how to evaluate the invariance assumption for the dominant process. Violations of the invariance assumption have, however, the potential to bias conventional process-dissociation analyses in different ways, and they can cause misleading theoretical interpretations and conclusions. Based on recent advances in multinomial modeling, we propose new approaches to examine the invariance assumption empirically and apply them in 6 studies to 3 prominent fields of application of process-dissociation models: to the Stroop task, to the interplay of recollection and habit in cued recall, and to the study of racial bias in the weapon task. In each of these content domains, the invariance assumption is found to be violated to a considerable extent. PMID:25528668
Cognitive Invariants of Geographic Event Conceptualization: What Matters and What Refines?
Klippel, Alexander; Li, Rui; Hardisty, Frank; Weaver, Chris
Behavioral experiments addressing the conceptualization of geographic events are few and far between. Our research seeks to address this deficiency by developing an experimental framework on the conceptualization of movement patterns. In this paper, we report on a critical experiment that is designed to shed light on the question of cognitively salient invariants in such conceptualization. Invariants have been identified as being critical to human information processing, particularly for the processing of dynamic information. In our experiment, we systematically address cognitive invariants of one class of geographic events: single entity movement patterns. To this end, we designed 72 animated icons that depict the movement patterns of hurricanes around two invariants: size difference and topological equivalence class movement patterns endpoints. While the endpoint hypothesis, put forth by Regier (2007), claims a particular focus of human cognition to ending relations of events, other research suggests that simplicity principles guide categorization and, additionally, that static information is easier to process than dynamic information. Our experiments show a clear picture: Size matters. Nonetheless, we also find categorization behaviors consistent with experiments in both the spatial and temporal domain, namely that topology refines these behaviors and that topological equivalence classes are categorized consistently. These results are critical steppingstones in validating spatial formalism from a cognitive perspective and cognitively grounding work on ontologies.
Van der Waerden invariant and Wigner coefficients for some compact groups
International Nuclear Information System (INIS)
A simple approach is developed for obtaining the general van der Waerden invariant for SU(n). The solution is symmetric within a phase factor and is expressed in terms of elementary scalars. The results are useful for evaluating the general Wigner coefficient or Clebsch-Gordan coefficient. The internal and the external labelling problems are simultaneously solved by exploiting Speiser's theorem. The SU(5) and O(5) van der Waerden invariants are explicitly worked out; and the general O(5) is contained in SU(2) x SU(2) Wigner coefficient is evaluated as well as certain simple classes of O(5) is contained in SU(2) x U(1) Wigner coefficients. (author)
Page, Don N.
2008-01-01
VSI (`vanishing scalar invariant') spacetimes have zero values for all total scalar contractions of all polynomials in the Riemann tensor and its covariant derivatives. However, there are other ways of concocting local scalar invariants (nonpolynomial) from the Riemann tensor that need not vanish even in VSI spacetimes, such as Cartan invariants. Simple examples are given that reduce to the squared amplitude for a linearized monochromatic plane gravitational wave. These nonpolynomial local sc...
On gauge-invariant and phase-invariant spinor analysis. II
Buchdahl, H. A.
1992-01-01
Granted customary definitions, the operations of juggling indices and covariant differentiation do not commute with one another in a Weyl space. The same noncommutativity obtains in the spinor calculus of Infeld and van der Waerden. Gauge-invariant and phase-invariant calculations therefore tend to be rather cumbersome. Here, a modification of the definition of covariant derivative leads immediately to a manifestly gauge-invariant and phase-invariant version of Weyl-Cartan space and of the two-spinor calculus associated with it in which the metric tensor and the metric spinor are both covariant constant.
Basis invariant conditions for supersymmetry in the two-Higgs-doublet model
International Nuclear Information System (INIS)
The minimal supersymmetric standard model involves a rather restrictive Higgs potential with two Higgs fields. Recently, the full set of classes of symmetries allowed in the most general two-Higgs-doublet model was identified; these classes do not include the supersymmetric limit as a particular class. Thus, a physically meaningful definition of the supersymmetric limit must involve the interaction of the Higgs sector with other sectors of the theory. Here we show how one can construct basis invariant probes of supersymmetry involving both the Higgs sector and the gaugino-Higgsino-Higgs interactions.
A new class of generalized Fibonacci unimodal maps
International Nuclear Information System (INIS)
We study a class of unimodal maps with generalized Fibonacci combinatorics in terms of generalized renormalization. This class is different from the ‘Fibonacci-like’ one considered by Bruin. It is proved that the map has no absolutely continuous invariant probability measure, provided that the critical order is large enough. (paper)
PROC LCA: A SAS Procedure for Latent Class Analysis
Lanza, Stephanie T.; Collins, Linda M.; Lemmon, David R.; Schafer, Joseph L.
2007-01-01
Latent class analysis (LCA) is a statistical method used to identify a set of discrete, mutually exclusive latent classes of individuals based on their responses to a set of observed categorical variables. In multiple-group LCA, both the measurement part and structural part of the model can vary across groups, and measurement invariance across…
On the statistics of magnetotelluric rotational invariants
Chave, Alan D.
2014-01-01
The statistical properties of the Swift skew, the phase-sensitive skew and the WAL invariants I1-I7 and Q are examined through analytic derivation of their probability density functions and/or simulation based on a Gaussian model for the magnetotelluric response tensor. The WAL invariants I1-I2 are shown to be distributed as a folded Gaussian, and are statistically well behaved in the sense that all of their moments are defined. The probability density functions for Swift skew, phase-sensitive skew and the WAL invariants I3-I4, I7 and Q are derived analytically or by simulation, and are shown to have no moments of order 2 or more. Since their support is semi-infinite or infinite, they cannot be represented trigonometrically, and hence are inconsistent with a Mohr circle interpretation. By contrast, the WAL invariants I5-I6 are supported on [ - 1, 1], and are inferred to have a beta distribution based on analysis and simulation. Estimation of rotational invariants from data is described using two approaches: as the ratio of magnetotelluric responses that are themselves averages, and as averages of section-by-section estimates of the invariant. Confidence intervals on the former utilize either Fieller's theorem, which is preferred because it is capable of yielding semi-infinite or infinite confidence intervals, or the less accurate delta method. Because section-by-section averages of most of the rotational invariants are drawn from distributions with infinite variance, the classical central limit theorem does not pertain. Instead, their averaging is accomplished using the median in place of the mean for location and an order statistic model to bound the confidence interval of the median. An example using real data demonstrates that the ratio of averages approach has serious systematic bias issues that render the result physically inconsistent, while the average of ratios result is a smooth, physically interpretable function of period, and is the preferred approach.
Invariant object recognition based on extended fragments.
Bart, Evgeniy; Hegdé, Jay
2012-01-01
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. PMID:22936910
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.
Huang, Xin; Kushekhar, Kushi; Nolte, Ilja; Kooistra, Wierd; Visser, Lydia; Bouwman, Ilby; Kouprie, Niels; van Imhoff, Gustaaf; Olver, Bianca; Houlston, Richard S.; Poppema, Sibrand; Diepstra, Arjan; Hepkema, Bouke; van den Berg, Anke; Veenstra, R.
2011-01-01
The pathogenesis of classical Hodgkin lymphoma (cHL) involves environmental and genetic factors. To explore the role of the human leukocyte antigen (HLA) genes, we performed a case-control genotyping study in 338 Dutch cHL patients and more than 5000 controls using a PCR-based sequence-specific olig
Energy Technology Data Exchange (ETDEWEB)
Jacob, C.O.; Fronek, Z.; Koo, M.; McDevitt, H.O. (Stanford Univ. School of Medicine, CA (USA)); Lewis, G.C. (Genentech Inc., San Francisco, CA (USA)); Hansen, J.A. (Fred Hutchinson Cancer Research Center, Seattle, WA (USA))
1990-02-01
The authors report on the production of tumor necrosis factor (TNF)-{alpha} and TNF-{beta} by mitogen-activated peripheral blood lymphocytes or enriched monocyte subpopulations from human leukocyte antigen (HLA)-typed healthy subjects. The results indicate that HLA-DR2- and DQw1-positive donors frequently exhibit low production of TNF-{alpha}, whereas DR3- and DR4-positive subjects show high levels of TNF-{alpha} production. No correlation between TNF-{alpha} levels and HLA-A, -B, and -C genotype was found. The relevance of this quantitative polymorphism to the genetic predisposition to lupus nephritis in systemic lupus erythematosus (SLE) patients was investigated. DR2, DQw1-positive SLE patients show low levels of TNF-{alpha} inducibility; this genotype is also associated with an increased incidence of lupus nephritis. DR3-positive SLE patients, on the other hand, are not predisposed to nephritis, and these patients have high TNF-{alpha} production. DR4 haplotype is associated with high TNF-{alpha} inducibility and is negatively correlated with lupus nephritis. These data may help explain the strong association between HLA-DR2, DQw1 in SLE patients and their susceptibility to nephritis.
Testing strong factorial invariance using three-level structural equation modeling
Directory of Open Access Journals (Sweden)
SuzanneJak
2014-07-01
Full Text Available Within structural equation modeling, the most prevalent model to investigate measurement bias is the multigroup model. Equal factor loadings and intercepts across groups in a multigroup model represent strong factorial invariance (absence of measurement bias across groups. Although this approach is possible in principle, it is hardly practical when the number of groups is large or when the group size is relatively small. Jak, Oort and Dolan (2013 showed how strong factorial invariance across large numbers of groups can be tested in a multilevel structural equation modeling framework, by treating group as a random instead of a fixed variable. In the present study, this model is extended for use with three-level data. The proposed method is illustrated with an investigation of strong factorial invariance across 156 school classes and 50 schools in a Dutch dyscalculia test, using three-level structural equation modeling.
Testing strong factorial invariance using three-level structural equation modeling.
Jak, Suzanne
2014-01-01
Within structural equation modeling, the most prevalent model to investigate measurement bias is the multigroup model. Equal factor loadings and intercepts across groups in a multigroup model represent strong factorial invariance (absence of measurement bias) across groups. Although this approach is possible in principle, it is hardly practical when the number of groups is large or when the group size is relatively small. Jak et al. (2013) showed how strong factorial invariance across large numbers of groups can be tested in a multilevel structural equation modeling framework, by treating group as a random instead of a fixed variable. In the present study, this model is extended for use with three-level data. The proposed method is illustrated with an investigation of strong factorial invariance across 156 school classes and 50 schools in a Dutch dyscalculia test, using three-level structural equation modeling. PMID:25120499
Local energy-momentum conservation in scalar-tensor-like gravity with generic curvature invariants
Tian, David Wenjie
2016-08-01
For a large class of scalar-tensor-like gravity whose action contains nonminimal couplings between a scalar field φ (x^α ) and generic curvature invariants R beyond the Ricci scalar R=R^α _{α }, we prove the covariant invariance of its field equation and confirm/prove the local energy-momentum conservation. These φ (x^α )- R coupling terms break the symmetry of diffeomorphism invariance under an active transformation, which implies that the solutions to the field equation should satisfy the consistency condition R ≡ 0 when φ (x^α ) is nondynamical and massless. Following this fact and based on the accelerated expansion of the observable Universe, we propose a primary test to check the viability of the modified gravity to be an effective dark energy, and a simplest example passing the test is the "Weyl/conformal dark energy".
Bulk and boundary invariants for complex topological insulators from K-theory to physics
Prodan, Emil
2016-01-01
This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields. The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to use analysis tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connect...
Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis
Ghilardi, Silvio
2010-01-01
The safety of infinite state systems can be checked by a backward reachability procedure. For certain classes of systems, it is possible to prove the termination of the procedure and hence conclude the decidability of the safety problem. Although backward reachability is property-directed, it can unnecessarily explore (large) portions of the state space of a system which are not required to verify the safety property under consideration. To avoid this, invariants can be used to dramatically prune the search space. Indeed, the problem is to guess such appropriate invariants. In this paper, we present a fully declarative and symbolic approach to the mechanization of backward reachability of infinite state systems manipulating arrays by Satisfiability Modulo Theories solving. Theories are used to specify the topology and the data manipulated by the system. We identify sufficient conditions on the theories to ensure the termination of backward reachability and we show the completeness of a method for invariant sy...
Conformal Invariance of Iso-height Lines in two-dimensional KPZ Surface
Saberi, A A; Fazeli, S M; Tabar, M R Rahimi; Rouhani, S
2008-01-01
The statistics of the iso-height lines in (2+1)-dimensional Kardar-Parisi-Zhang (KPZ) model is shown to be conformal invariant and equivalent to those of self-avoiding random walks. This leads to a rich variety of new exact analytical results for the KPZ dynamics. We present direct evidence that the iso-height lines can be described by the family of conformal invariant curves called Schramm-Loewner evolution (or $SLE_\\kappa$) with diffusivity $\\kappa=8/3$. It is shown that the absence of the non-linear term in the KPZ equation will change the diffusivity $\\kappa$ from 8/3 to 4, indicating that the iso-height lines of the Edwards-Wilkinson (EW) surface are also conformally invariant, and belong to the universality class of the domain walls in the O(2) spin model.
Conformal invariance of isoheight lines in a two-dimensional Kardar-Parisi-Zhang surface.
Saberi, A A; Niry, M D; Fazeli, S M; Rahimi Tabar, M R; Rouhani, S
2008-05-01
The statistics of isoheight lines in the (2+1) -dimensional Kardar-Parisi-Zhang (KPZ) model is shown to be conformally invariant and equivalent to those of self-avoiding random walks. This leads to a rich variety of exact analytical results for the KPZ dynamics. We present direct evidence that the isoheight lines can be described by the family of conformally invariant curves called Schramm-Loewner evolution (or SLE_{kappa} ) with diffusivity kappa=8/3 . It is shown that the absence of the nonlinear term in the KPZ equation will change the diffusivity kappa from 8/3 to 4, indicating that the isoheight lines of the Edwards-Wilkinson surface are also conformally invariant and belong to the universality class of domain walls in the O(2) spin model. PMID:18643079
Invariance properties of the Dirac equation with external electro-magnetic ﬁeld
Indian Academy of Sciences (India)
N D Sen Gupta
2003-01-01
In this paper, we attempt to obtain the nature of the external ﬁeld such that the Dirac equation with external electro-magnetic ﬁeld is invariant. The Poincar´e group, which is the maximal symmetry group for ﬁeld free case, is constrained by the presence of the external ﬁeld. Introducing inﬁnitesimal transformation of x andψ, we apply Lie’s extended group method to obtain the class of external ﬁeld which admit of the invariance of the equation. It is important to note that the constraints for the existence of invariance are explicity on the electric and magnetic ﬁeld, though only potentials explicity appears in the equation.
U(N) Framed Links, Three-Manifold Invariants, and Topological Strings
Borhade, P; Sarkar, Tapan K; Borhade, Pravina; Sarkar, Tapobrata
2004-01-01
Three-manifolds can be obtained through surgery of framed links in $S^3$. We study the meaning of surgery procedures in the context of topological strings. We obtain U(N) three-manifold invariants from U(N) framed link invariants in Chern-Simons theory on $S^3$. These three-manifold invariants are proportional to the trivial connection contribution to the Chern-Simons partition function on the respective three-manifolds. Using the topological string duality conjecture, we show that the large $N$ expansion of U(N) Chern-Simons free energies on three-manifolds, obtained from some class of framed links, have a closed string expansion. These expansions resemble the closed string $A$-model partition functions on Calabi-Yau manifolds with one Kahler parameter. We also determine Gopakumar-Vafa integer coefficients and Gromov-Witten rational coefficients corresponding to Chern-Simons free energies on some three-manifolds.
U(N) framed links, three-manifold invariants, and topological strings
International Nuclear Information System (INIS)
Three-manifolds can be obtained through surgery of framed links in S3. We study the meaning of surgery procedures in the context of topological strings. We obtain U(N) three-manifold invariants from U(N) framed link invariants in Chern-Simons theory on S3. These three-manifold invariants are proportional to the Chern-Simons partition function on the respective three-manifolds. Using the topological string duality conjecture, we show that the large N expansion of U(N) Chern-Simons free energies on three-manifolds, obtained from some class of framed links, have a closed string expansion. These expansions resemble the closed string A-model partition functions on Calabi-Yau manifolds with one Kahler parameter. We also determine Gopakumar-Vafa integer coefficients and Gromov-Witten rational coefficients corresponding to Chern-Simons free energies on some three-manifolds
Class size versus class composition
DEFF Research Database (Denmark)
Jones, Sam
Raising schooling quality in low-income countries is a pressing challenge. Substantial research has considered the impact of cutting class sizes on skills acquisition. Considerably less attention has been given to the extent to which peer effects, which refer to class composition, also may affect...
Asymptotic distribution of the most powerful invariant test for invariant families
Arcones, Miguel A.
2009-01-01
We obtain the limit distribution of the test statistic of the most powerful invariant test for location families of densities. As an application, we obtain the consistency of this test. From these results similar results are obtained for the test statistic of the most powerful invariant test for scale families.
Buchstaber numbers and classical invariants of simplicial complexes
Ayzenberg, Anton
2014-01-01
Buchstaber invariant is a numerical characteristic of a simplicial complex, arising from torus actions on moment-angle complexes. In the paper we study the relation between Buchstaber invariants and classical invariants of simplicial complexes such as bigraded Betti numbers and chromatic invariants. The following two statements are proved. (1) There exists a simplicial complex U with different real and ordinary Buchstaber invariants. (2) There exist two simplicial complexes with equal bigrade...
A Unified Framework for Verification Techniques for Object Invariants
Drossopoulou, Sophia; Francalanza, Adrian; Müller, P; Summers, Alexander J.
2008-01-01
Object invariants define the consistency of objects. They have subtle semantics, mainly because of call-backs, multi-object invariants, and subclassing. Several verification techniques for object invariants have been proposed. It is difficult to compare these techniques, and to ascertain their soundness, because of their differences in restrictions on programs and invariants, in the use of advanced type systems (e.g., ownership types), in the meaning of invariants, and in...
Cascaded linear shift-invariant processors in optical pattern recognition.
Reed, S; Coupland, J
2001-08-10
We study a cascade of linear shift-invariant processing modules (correlators), each augmented with a nonlinear threshold as a means to increase the performance of high-speed optical pattern recognition. This configuration is a special class of multilayer, feed-forward neural networks and has been proposed in the literature as a relatively fast best-guess classifier. However, it seems that, although cascaded correlation has been proposed in a number of specific pattern recognition problems, the importance of the configuration has been largely overlooked. We prove that the cascaded architecture is the exact structure that must be adopted if a multilayer feed-forward neural network is trained to produce a shift-invariant output. In contrast with more generalized multilayer networks, the approach is easily implemented in practice with optical techniques and is therefore ideally suited to the high-speed analysis of large images. We have trained a digital model of the system using a modified backpropagation algorithm with optimization using simulated annealing techniques. The resulting cascade has been applied to a defect recognition problem in the canning industry as a benchmark for comparison against a standard linear correlation filter, the minimum average correlation energy (MACE) filter. We show that the nonlinear performance of the cascade is a significant improvement over that of the linear MACE filter in this case. PMID:18360417
Conformal Laplace superintegrable systems in 2D: polynomial invariant subspaces
Escobar-Ruiz, M. A.; Miller, Willard, Jr.
2016-07-01
2nd-order conformal superintegrable systems in n dimensions are Laplace equations on a manifold with an added scalar potential and 2n-1 independent 2nd order conformal symmetry operators. They encode all the information about Helmholtz (eigenvalue) superintegrable systems in an efficient manner: there is a 1-1 correspondence between Laplace superintegrable systems and Stäckel equivalence classes of Helmholtz superintegrable systems. In this paper we focus on superintegrable systems in two-dimensions, n = 2, where there are 44 Helmholtz systems, corresponding to 12 Laplace systems. For each Laplace equation we determine the possible two-variate polynomial subspaces that are invariant under the action of the Laplace operator, thus leading to families of polynomial eigenfunctions. We also study the behavior of the polynomial invariant subspaces under a Stäckel transform. The principal new results are the details of the polynomial variables and the conditions on parameters of the potential corresponding to polynomial solutions. The hidden gl 3-algebraic structure is exhibited for the exact and quasi-exact systems. For physically meaningful solutions, the orthogonality properties and normalizability of the polynomials are presented as well. Finally, for all Helmholtz superintegrable solvable systems we give a unified construction of one-dimensional (1D) and two-dimensional (2D) quasi-exactly solvable potentials possessing polynomial solutions, and a construction of new 2D PT-symmetric potentials is established.
DEFF Research Database (Denmark)
Rijkhoff, Jan
2007-01-01
This article provides an overview of recent literature and research on word classes, focusing in particular on typological approaches to word classification. The cross-linguistic classification of word class systems (or parts-of-speech systems) presented in this article is based on statements found...... in grammatical descriptions of some 50 languages, which together constitute a representative sample of the world’s languages (Hengeveld et al. 2004: 529). It appears that there are both quantitative and qualitative differences between word class systems of individual languages. Whereas some languages...... employ a parts-of-speech system that includes the categories Verb, Noun, Adjective and Adverb, other languages may use only a subset of these four lexical categories. Furthermore, quite a few languages have a major word class whose members cannot be classified in terms of the categories Verb – Noun...
Hidden Scale Invariance in Condensed Matter
DEFF Research Database (Denmark)
Dyre, J. C.
2014-01-01
Recent developments show that many liquids and solids have an approximate “hidden” scale invariance that implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics in properly reduced units are invariant to a good approximation. This...... (hydrogen bonds or covalent bonds) or strong Coulomb forces generally do not exhibit hidden scale invariance. The article reviews the theory behind this picture of condensed matter and the evidence for it coming from computer simulations and experiments...... means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. Liquids and solids with isomorphs include most or all van der Waals bonded systems and metals, as well as weakly ionic or dipolar systems. On the other hand, systems with directional bonding...
Rainbow gravity and scale-invariant fluctuations
Amelino-Camelia, Giovanni; Arzano, Michele; Gubitosi, Giulia; Magueijo, João
2013-08-01
We reexamine 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 behavior of gravity under the phenomenon of dimensional reduction.
Thermodynamics and time-directional invariance
Klimenko, A Y
2012-01-01
Time directions are not invariant in conventional thermodynamics. We broadly follow ideas of Ludwig Boltzmann and investigate implications of postulating time-directional invariance in thermodynamics. In this investigation, we require that thermodynamic descriptions are not changed under time reversal accompanied by replacement of matter by antimatter (i.e. CPT-invariant thermodynamics). The matter and antimatter are defined as thermodynamic concepts without detailing their physical structure. Our analysis stays within the limits of conceptual thermodynamics and leads to effective negative temperatures, to thermodynamic restrictions on time travel and to inherent antagonism of matter and antimatter. This antagonism is purely thermodynamic; it explains the difficulty in achieving thermodynamic equilibrium between matter and antimatter and does not postulate their mutual annihilation on contact. We believe that the conclusions of this work can be of interest not only for people researching or teaching thermodyn...
Manifestly diffeomorphism invariant classical Exact Renormalization Group
Morris, Tim R
2016-01-01
We construct a manifestly diffeomorphism invariant Wilsonian (Exact) Renormalization Group for classical gravity, and begin the construction for quantum gravity. We demonstrate that the effective action can be computed without gauge fixing the diffeomorphism invariance, and also without introducing a background space-time. We compute classical contributions both within a background-independent framework and by perturbing around a fixed background, and verify that the results are equivalent. We derive the exact Ward identities for actions and kernels and verify consistency. We formulate two forms of the flow equation corresponding to the two choices of classical fixed-point: the Gaussian fixed point, and the scale invariant interacting fixed point using curvature-squared terms. We suggest how this programme may completed to a fully quantum construction.
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.
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.
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.
Manifestly diffeomorphism invariant classical Exact Renormalization Group
Morris, Tim R.; Preston, Anthony W. H.
2016-06-01
We construct a manifestly diffeomorphism invariant Wilsonian (Exact) Renor-malization Group for classical gravity, and begin the construction for quantum gravity. We demonstrate that the effective action can be computed without gauge fixing the diffeo-morphism invariance, and also without introducing a background space-time. We compute classical contributions both within a background-independent framework and by perturbing around a fixed background, and verify that the results are equivalent. We derive the exact Ward identities for actions and kernels and verify consistency. We formulate two forms of the flow equation corresponding to the two choices of classical fixed-point: the Gaussian fixed point, and the scale invariant interacting fixed point using curvature-squared terms. We suggest how this programme may completed to a fully quantum construction.
Gauge-Invariant Formulation of Circular Dichroism.
Raimbault, Nathaniel; de Boeij, Paul L; Romaniello, Pina; Berger, J A
2016-07-12
Standard formulations of magnetic response properties, such as circular dichroism spectra, are plagued by gauge dependencies, which can lead to unphysical results. In this work, we present a general gauge-invariant and numerically efficient approach for the calculation of circular dichroism spectra from the current density. First we show that in this formulation the optical rotation tensor, the response function from which circular dichroism spectra can be obtained, is independent of the origin of the coordinate system. We then demonstrate that its trace is independent of the gauge origin of the vector potential. We also show how gauge invariance can be retained in practical calculations with finite basis sets. As an example, we explain how our method can be applied to time-dependent current-density-functional theory. Finally, we report gauge-invariant circular dichroism spectra obtained using the adiabatic local-density approximation. The circular dichroism spectra we thus obtain are in good agreement with experiment. PMID:27295541
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.
International Nuclear Information System (INIS)
In this paper advected invariants and conservation laws in ideal magnetohydrodynamics (MHD) and gas dynamics are obtained using Lie dragging techniques. There are different classes of invariants that are advected or Lie dragged with the flow. Simple examples are the advection of the entropy S (a 0-form), and the conservation of magnetic flux (an invariant 2-form advected with the flow). The magnetic flux conservation law is equivalent to Faraday's equation. The gauge condition for the magnetic helicity to be advected with the flow is determined. Different variants of the helicity in ideal fluid dynamics and MHD including: fluid helicity, cross helicity and magnetic helicity are investigated. The fluid helicity conservation law and the cross-helicity conservation law in MHD are derived for the case of a barotropic gas. If the magnetic field lies in the constant entropy surface, then the gas pressure can depend on both the entropy and the density. In these cases the conservation laws are local conservation laws. For non-barotropic gases, we obtain nonlocal conservation laws for fluid helicity and cross helicity by using Clebsch variables. These nonlocal conservation laws are the main new results of the paper. Ertel's theorem and potential vorticity, the Hollman invariant, and the Godbillon–Vey invariant for special flows for which the magnetic helicity is zero are also discussed. (paper)
Disambiguating Seesaw Models using Invariant Mass Variables at Hadron Colliders
Dev, P S Bhupal; Mohapatra, Rabindra N
2015-01-01
We propose ways to distinguish between different mechanisms behind the collider signals of TeV-scale seesaw models for neutrino masses using kinematic endpoints of invariant mass variables. We particularly focus on two classes of such models widely discussed in literature: (i) Standard Model extended by the addition of singlet neutrinos and (ii) Left-Right Symmetric Models. Relevant scenarios involving the same "smoking-gun" collider signature of dilepton plus dijet with no missing transverse energy differ from one another by their event topology, resulting in distinctive relationships among the kinematic endpoints to be used for discerning them at hadron colliders. These kinematic endpoints are readily translated to the mass parameters of the on-shell particles through simple analytic expressions which can be used for measuring the masses of the new particles. A Monte Carlo simulation with detector effects is conducted to test the viability of the proposed strategy in a realistic environment. Finally, we dis...
Contrast/offset-invariant generic low-order MGRF models of uniform textures
Liu, Ni; Gimel'farb, Georgy; Delmas, Patrice; Chan, Yuk Hin
2013-10-01
Statistical properties of many textured objects on digital biomedical images are often nearly translation-invariant, except for sizeable spatially-variant perceptive (contrast and offset) deviations due to different imaging conditions and/or contrast agents. To make widely-used translation-invariant Markov-Gibbs random field (MGRF) models of uniform textures more suitable for biomedical objects, we introduce, in the context of semi-supervised texture recognition, a new class of generic low-order MGRFs. These models account for ordinal relations between signals, rather than signal magnitudes, and therefore are invariant also to arbitrary perceptive signal deviations. Since the numbers of the possible ordinal relations are considerably smaller, than of signal co-occurrences, our earlier fast framework for learning generic 2nd-order MGRFs with multiple translation-invariant pixel/voxel interactions is easily extended up to the 4th-or even higher-order ordinal models. To explore the class introduced, the learned generic 3rd-order ordinal and 2nd-order co-occurrence-based and ordinal MGRFs are experimentally compared on the popular OUTEX and Brodatz databases of realistic natural textures. The experiments have shown that the ordinal 3rd-order model not only has as good descriptive abilities as the conventional co-occurrence-based 2nd-order one, but also is both simpler and considerably more robust to the perceptive deviations.
Invariants of contact structures from open books
Etnyre , John B.; Ozbagci, Burak
2006-01-01
In this note we define three invariants of contact structures in terms of open books supporting the contact structures. These invariants are the support genus (which is the minimal genus of a page of a supporting open book for the contact structure), the binding number (which is the minimal number of binding components of a supporting open book for the contact structure with minimal genus pages) and the norm (which is minus the maximal Euler characteristic of a page of a supporting open book).
Hidden BRS invariance in classical mechanics
International Nuclear Information System (INIS)
We give in this paper a path integral formulation of classical mechanics. We do so by writing down the associated classical-generating functional. This functional exhibits an unexpected BRS-like and antiBRS-like invariance. This invariance allows for a simple expression, in term of superfields, of this generating functional. Associated to the BRS and antiBRS charges there is also a ghost charge whose conservation turns out to be nothing else than the well-known theorem of classical mechanics. (orig.)
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
Perturbative string theory in BRST invariant formalism
International Nuclear Information System (INIS)
In this talk we present a constructive and very explicit way of calculating multiloop amplitudes in string theories. The main ingredients are the BRST invariant N String Vertex and the BRST invariant twisted propagator. This approach naturally leads to the Schottky parametrization of moduli space in terms of multipliers and fixed points of the g projective transformations which characterize a Riemann surface of genus g. The complete expression (including measure) of the multiloop corrections to the N String Vertex for the bosonic string is exhibited. (orig.)
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
On black hole spectroscopy via adiabatic invariance
Energy Technology Data Exchange (ETDEWEB)
Jiang Qingquan, E-mail: qqjiangphys@yeah.net [College of Physics and Electronic Information, China West Normal University, Nanchong, Sichuan 637002 (China); Han Yan [College of Mathematic and Information, China West Normal University, Nanchong, Sichuan 637002 (China)
2012-12-05
In this Letter, we obtain the black hole spectroscopy by combining the black hole property of adiabaticity and the oscillating velocity of the black hole horizon. This velocity is obtained in the tunneling framework. In particular, we declare, if requiring canonical invariance, the adiabatic invariant quantity should be of the covariant form I{sub adia}= Contour-Integral p{sub i}dq{sub i}. Using it, the horizon area of a Schwarzschild black hole is quantized independently of the choice of coordinates, with an equally spaced spectroscopy always given by {Delta}A=8{pi}l{sub p}{sup 2} in the Schwarzschild and Painleve coordinates.
Quantized Hall conductance as a topological invariant
International Nuclear Information System (INIS)
Whenever the Fermi level lies in a gap (or mobility gap) the bulk Hall conductance can be expressed in a topologically invariant form showing the quantization explicitly. The new formulation generalizes the earlier result by TKNN to the situation where many body interaction and substrate disorder are also present. When applying to the fractional quantized Hall effect we draw the conclusion that there must be a symmetry breaking in the many body ground state. The possibility of writing the fractionally quantized Hall conductance as a topological invariant is also carefully discussed. 19 references
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.
Hidden invariance of the free classical particle
International Nuclear Information System (INIS)
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
Frustration, scaling, and local gauge invariance
Energy Technology Data Exchange (ETDEWEB)
Cieplak, M. (Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802 (United States) Institute of Physics, Polish Academy of Sciences, 02-668 Warsaw (Poland)); Banavar, J.R. (Department of Physics and Materials Research Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802 (United States)); Li, M.S. (Institute of Physics, Polish Academy of Sciences, 02-668 Warsaw (Poland)); Khurana, A. (Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 85, 1018XE Amsterdam (Netherlands))
1992-01-01
A variety of two- and three-dimensional random frustrated systems with continuous and discrete symmetries are studied within the Migdal-Kadanoff renormalization-group scheme. The continuous-symmetry {ital XY} models are approximated by discretized clock models with a large number of clock states. In agreement with earlier studies of the random gauge {ital XY} model using a {ital T}=0 scaling approach, a nonzero transition temperature is observed in three-dimensional {ital XY} models with O(2) local gauge invariance. Our analysis points to the possible importance of local gauge invariance in determining the lower critical dimensionality of frustrated systems.
Frustration, scaling, and local gauge invariance
International Nuclear Information System (INIS)
A variety of two- and three-dimensional random frustrated systems with continuous and discrete symmetries are studied within the Migdal-Kadanoff renormalization-group scheme. The continuous-symmetry XY models are approximated by discretized clock models with a large number of clock states. In agreement with earlier studies of the random gauge XY model using a T=0 scaling approach, a nonzero transition temperature is observed in three-dimensional XY models with O(2) local gauge invariance. Our analysis points to the possible importance of local gauge invariance in determining the lower critical dimensionality of frustrated systems
Some cosmological consequences of Weyl invariance
International Nuclear Information System (INIS)
We examine some Weyl invariant cosmological models in the framework of generalized dilaton gravity, in which the action is made of a set of N conformally coupled scalar fields. 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 scalar fields 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
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.
A geometric construction for invariant jet differentials
Berczi, Gergely
2010-01-01
Motivated by Demailly's strategy towards the Kobayashi hyperbolicity conjecture, we study the action on the k-jets of germs of holomorphic discs in a complex manifold X of the reparametrization group of k-jets of germs of biholomorphisms of the source. This reparametrization group is a subgroup of the general linear group GL(k) which is not reductive, but nonetheless we show that its invariants for any linear action which extends to GL(k) form a finitely generated algebra, and give a new geometric description of the Demailly-Semple algebra of invariant jet differentials.
Illumination Invariants Based on Markov Random Fields
Czech Academy of Sciences Publication Activity Database
Vácha, Pavel; Haindl, Michal
Vukovar, Croatia : In-Teh, 2010 - (Herout, A.), s. 253-272 ISBN 978-953-7619-90-9 R&D Projects: GA MŠk 1M0572; GA ČR GA102/08/0593 Grant ostatní: GA MŠk(CZ) 2C06019 Institutional research plan: CEZ:AV0Z10750506 Keywords : illumination invariants * textural features * Markov random fields Subject RIV: BD - Theory of Information http://library.utia.cas.cz/separaty/2010/RO/vacha-illumination invariants based on markov random fields.pdf
Invariant distances and metrics in complex analysis
Jarnicki, Marek
2013-01-01
As in the field of ""Invariant Distances and Metrics in Complex Analysis"" there was and is a continuous progress this is the second extended edition of the corresponding monograph. This comprehensive book is about the study of invariant pseudodistances (non-negative functions on pairs of points) and pseudometrics (non-negative functions on the tangent bundle) in several complex variables. It is an overview over a highly active research area at the borderline between complex analysis, functional analysis and differential geometry. New chapters are covering the Wu, Bergman and several other met
PROC LCA: A SAS Procedure for Latent Class Analysis
Lanza, Stephanie T.; Collins, Linda M.; David R. Lemmon; Schafer, Joseph L.
2007-01-01
Latent class analysis (LCA) is a statistical method used to identify a set of discrete, mutually exclusive latent classes of individuals based on their responses to a set of observed categorical variables. In multiple-group LCA, both the measurement part and structural part of the model can vary across groups, and measurement invariance across groups can be empirically tested. LCA with covariates extends the model to include predictors of class membership. In this article, we introduce PROC L...
Symmetries and invariant solutions of the two-dimensional variable coefficient Burgers equation
International Nuclear Information System (INIS)
We discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient. We classify one-dimensional and two-dimensional subalgebras of the Burgers symmetry algebra which is infinite-dimensional into conjugacy classes under the adjoint action of the symmetry group. Invariance under one-dimensional subalgebras provides reductions to lower-dimensional partial differential equations. Further reductions of these equations to second order ordinary differential equations are obtained through invariance under two-dimensional subalgebras. The reduced ODEs are then analysed and shown that they belong to the polynomial class of second-order equations which can be linearized only for particular values of parameters figuring in the coefficient. (author)
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.
Momentum routing invariance in extended QED: Assuring gauge invariance beyond tree level
Vieira, A. R.; Cherchiglia, A. L.; Sampaio, Marcos
2016-01-01
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 γ5 matrices.
Lorentz-invariant non-commutative QED
International Nuclear Information System (INIS)
Lorentz-invariant non-commutative QED (NCQED) is constructed so as to be a part of the Lorentz-invariant non-commutative Standard Model (NCSM), a subject to be treated in later publications. Our NCSM is based on Connes' observation that the total fermion field in the Standard Model can be regarded as a bi-module over a flavor-color algebra. In this paper, it is shown that there exist two massless gauge fields in NCQED that are interchanged by the C' transformation. Since C' is reduced to the conventional charge conjugation C in the commutative limit, in the same limit, the two gauge fields become identical to the photon field which couples to only four spinors, with charges ±2, ±1. Following Carlson, Carone and Zobin, our NCQED respects Lorentz invariance, employing the Doplicher-Fredenhagen-Roberts algebra instead of the usual algebra with constant θμν. In the new version, θμν becomes an integration variable. We show, using a simple NC scalar model, that the θ integration yields an invariant damping factor instead of the oscillating one in the nonplanar self-energy diagram in the one-loop approximation. The Seiberg-Witten map shows that the θ expansion of NCQED generates exotic but well-motivated derivative interactions beyond QED, with allowed charges being only 0, ±1, ±2. (author)
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.
Superconformal invariance and superstring in background fields
International Nuclear Information System (INIS)
We consider the propagation of the superstring on a general classical background containing the effects of the metric, the antisymmetric tensor and the dilaton fields. Using the operator product expansion method for two dimensional superconformal field theories we derive the equations for these fields as a consequence of the superconformal invariance of the theory. (author)
Notes on the knot concordance invariant Upsilon
Livingston, Charles
2014-01-01
The knot concordance invariant Upsilon, recently defined by Ozsvath, Stipsicz, and Szabo, takes values in the group of piecewise linear functions on the closed interval [0,2]. This paper presents a description of one approach to defining Upsilon and of proving its basic properties related to the knot 3-genus, 4-genus, and concordance genus.
Physics Fun with Discrete Scale Invariance
Georgi, Howard
2016-01-01
I construct a quantum field theory model with discrete scale invariance at tree level. The model has some unusual mathematical properties (such as the appearance of $q$-hypergeometric series) and may possibly have some interesting physical properties as well. In this note, I explore some possible physics that could be regarded as a violation of standard effective field theory ideas.
Weak invariance principles for regression rank statistics
Czech Academy of Sciences Publication Activity Database
Hušková, Marie
2004-01-01
Roč. 23, č. 1 (2004), s. 121-140. ISSN 0747-4946 R&D Projects: GA ČR GA201/03/0945 Institutional research plan: CEZ:AV0Z1075907 Keywords : simple linear rank statistics * weak invariance principle * change point analysis Subject RIV: BB - Applied Statistics, Operational Research
New Conformal Invariants in Absolute Parallelism Geometry
Youssef, Nabil L.; Soleiman, A.; Taha, Ebtsam H.
2016-01-01
The aim of the present paper is to investigate conformal changes in absolute parallelism geometry. We find out some new conformal invariants in terms of the Weitzenb\\"ock connection and the Levi-Civita connection of an absolute parallelism space.
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.
Testing local Lorentz invariance with gravitational waves
Kostelecký, V. Alan; Mewes, Matthew
2016-06-01
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.
Testing local Lorentz invariance with gravitational waves
Kostelecky, Alan; Mewes, Matthew
2016-01-01
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.
Curvature Invariants in Algebraically Special Spacetimes
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Bičák, J.
Řím: Scientific World, 2002, s. 864-865. [Marcel Grossmann Meeting/9./. Řím (IT), 02.07.2000-08.07.2000] Institutional research plan: CEZ:AV0Z1019905 Keywords : curvature invariants Subject RIV: BA - General Mathematics
Integral invariants of the Buttin bracket
International Nuclear Information System (INIS)
We study the densities (most general objects which may be integrated over supersurfaces in superspace), invariant with respect to supercanonical transformations which do not change the Buttin bracket. The only such nontrivial object is, in a definite sense, the odd semidensity explicitly constructed here. (orig.)
Neutrinos as Probes of Lorentz Invariance
International Nuclear Information System (INIS)
Neutrinos can be used to search for deviations from exact Lorentz invariance. The worldwide experimental program in neutrino physics makes these particles a remarkable tool to search for a variety of signals that could reveal minute relativity violations. This paper reviews the generic experimental signatures of the breakdown of Lorentz symmetry in the neutrino sector
Conformally Invariant Off-shell Strings
Myers, R C
1993-01-01
Recent advances in non-critical string theory allow a unique continuation of critical Polyakov string amplitudes to off-shell momenta, while preserving conformal invariance. These continuations possess unusual, apparently stringy, characteristics, as we illustrate with our results for three-point functions. (Talk by R.C.M. at Strings '93)
Translation invariance and doubly special relativity
Mignemi, S.
2010-01-01
We propose a new interpretation of doubly special relativity based on the distinction between the momenta and the translation generators in its phase space realization. We also argue that the implementation of the theory does not necessarily require a deformation of the Lorentz symmetry, but only of the translation invariance.
Flop invariance of the topological vertex
Konishi, Yukiko; Minabe, Satoshi
2006-01-01
We prove transformation formulae for generating functions of Gromov-Witten invariants on general toric Calabi-Yau threefolds under flops. Our proof is based on a combinatorial identity on the topological vertex and analysis of fans of toric Calabi-Yau threefolds.
An invariant for open virtual strings
Silver, Daniel S.; Williams, Susan G.
2004-01-01
Extended Alexander groups are used to define an invariant for open virtual strings. Examples of non-commuting open strings and a ribbon-concordance obstruction are given. An example is given of a slice virtual open string that is not ribbon. Definitions are extended to open n-strings.
Lorentz-invariant ensembles of vector backgrounds
International Nuclear Information System (INIS)
We consider gauge field theories in the presence of ensembles of vector backgrounds. While Lorentz invariance is explicitly broken in the presence of any single background, here, the Lorentz invariance of the theory is restored by averaging over a Lorentz-invariant ensemble of backgrounds, i.e., a set of background vectors that is mapped onto itself under Lorentz transformations. This framework is used to study the effects of a non-trivial but Lorentz-invariant vacuum structure or mass dimension two vector condensates by identifying the background with a shift of the gauge field. Up to now, the ensembles used in the literature comprise configurations corresponding to non-zero field tensors together with such with vanishing field strength. We find that even when constraining the ensembles to pure gauge configurations, the usual high-energy degrees of freedom are removed from the spectrum of asymptotic states in the presence of said backgrounds in Euclidean and in Minkowski space. We establish this result not only for the propagators to all orders in the background and otherwise at tree level but for the full propagator
Cubic terms from Casimir invariants in IBM
International Nuclear Information System (INIS)
The Xe and Ba nuclei have been shown to be good examples of O(6) dynamical symmetry of IBM. In particular, one might hope to construct cubic terms out of the Casimir invariants of the groups and subgroups of O(6), U(5) SU(3) which may give rise to triaxiality
OCTONIONS: INVARIANT REPRESENTATION OF THE LEECH LATTICE
Dixon, Geoffrey
1995-01-01
The Leech lattice, $\\Lambda_{24}$, is represented on the space of octonionic 3-vectors. It is built from two octonionic representations of $E_{8}$, and is reached via $\\Lambda_{16}$. It is invariant under the octonion index cycling and doubling maps.
BRST invariance in Coulomb gauge QCD
Andrasi, A
2015-01-01
In the Coulomb gauge, the Hamiltonian of QCD contains terms of order h^2, identified by Christ and Lee, which are non-local but instantaneous. The question is addressed how these terms fit in with BRST invariance. Our discussion is confined to the simplest, O(g^4), example.
BRST invariance in Coulomb gauge QCD
Andraši, A.; Taylor, J. C.
2015-12-01
In the Coulomb gauge, the Hamiltonian of QCD contains terms of order ħ2, identified by Christ and Lee, which are non-local but instantaneous. The question is addressed how do these terms fit in with BRST invariance. Our discussion is confined to the simplest, O(g4) , example.
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…
Gauge invariant formulations of lineal gravity
Cangemi, D; Cangemi, Daniel; Jackiw, Roman
1992-01-01
It is shown that the currently studied ``string-inspired'' model for gravity on a line can be formulated as a gauge invariant theory based on the Poincar\\'e group with central extension -- a formulation that complements and simplifies H.~Verlinde's construction based on the unextended Poincar\\'e group.
Spin squeezing criterion with local unitary invariance
Devi, A R U; Sanders, B C
2003-01-01
We propose a new spin squeezing criterion for arbitrary multi-qubit states that is invariant under local unitary operations. We find that, for arbitrary pure two-qubit states, spin squeezing is equivalent to entanglement, and multi-qubit states are entangled if this new spin squeezing parameter is less than 1.
Broken Scale Invariance and Anomalous Dimensions
Wilson, K. G.
1970-05-01
Mack and Kastrup have proposed that broken scale invariance is a symmetry of strong interactions. There is evidence from the Thirring model and perturbation theory that the dimensions of fields defined by scale transformations will be changed by the interaction from their canonical values. We review these ideas and their consequences for strong interactions.
Quantum aether and an invariant Planck scale
Das, Saurya; Vagenas, Elias C.
2011-01-01
We argue that a quantum aether is consistent with the principle of relativity and can provide an economical way of having an invariant quantum gravity or Planck scale. We also show that it may change the effective scale at which quantum gravity effects may be observable.
Scale Invariance, Conformality, and Generalized Free Fields
Dymarsky, Anatoly; Komargodski, Zohar; Luty, Markus A; Prilepina, Valentina
2014-01-01
This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum field theories with scale invariance but not conformal invariance. An important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen is that trace of the energy-momentum tensor $T$ could be a generalized free field. In this paper we rule out this possibility. The key ingredient is the observation that a unitary theory with scale but not conformal invariance necessarily has a non-vanishing anomaly for global scale transformations. We show that this anomaly cannot be reproduced if $T$ is a generalized free field unless the theory also contains a dimension-2 scalar operator. In the special case where such an operator is present it can be used to redefine ("improve") the energy-momentum tensor, and we show that there is at least one energy-momentum tensor that is not a generalized free field. In addition, we emphasize that, in general, large momentum limits of correlation functio...
Rephasing invariant parametrization for neutrino mixing
Energy Technology Data Exchange (ETDEWEB)
Chiu, S.H., E-mail: schiu@mail.cgu.edu.tw [Physics Group, CGE, Chang Gung University, Kwei-Shan 333, Taiwan (China); Kuo, T.K., E-mail: tkkuo@purdue.edu [Department of Physics, Purdue University, West Lafayette, IN 47907 (United States)
2012-08-15
The neutrino mixing in matter is studied under the three-flavor framework with a rephrasing invariant parametrization. The evolution equations for the parameters as functions of the induced neutrino mass are derived. They are found to preserve approximately some characteristic features of the mixing matrix, resulting in solutions which exhibit striking patterns as the induced mass varies.
Rephasing invariant parametrization for neutrino mixing
International Nuclear Information System (INIS)
The neutrino mixing in matter is studied under the three-flavor framework with a rephrasing invariant parametrization. The evolution equations for the parameters as functions of the induced neutrino mass are derived. They are found to preserve approximately some characteristic features of the mixing matrix, resulting in solutions which exhibit striking patterns as the induced mass varies.
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].
Approximate scale invariance in particle systems: a large-dimensional justification
Maimbourg, Thibaud; Kurchan, Jorge
2016-01-01
Systems of particles interacting via inverse-power law potentials have an invariance with respect to changes in length and temperature, implying a correspondence in the dynamics and thermodynamics between different `isomorphic' sets of temperatures and densities. In a recent series of works, it has been argued that such correspondences hold to a surprisingly good approximation in a much more general class of potentials, an observation that summarizes many properties that have been observed in...
Longitudinal foliation rigidity and Lipschitz-continuous invariant forms for hyperbolic flows
Foulon, Patrick; Hasselblatt, Boris
2010-01-01
In several contexts the defining invariant structures of a hyperbolic dynamical system are smooth only in systems of algebraic origin (smooth rigidity), and we prove new results of this type for a class of flows. For a compact Riemannian manifold and a uniformly quasiconformal transversely symplectic Anosov flow we define the longitudinal KAM-cocycle and use it to prove a rigidity result: The joint stable/unstable subbundle is Zygmund-regular, and higher regularity implies vanishing of the lo...
Free energies as invariants of Teichmüller like structures
Directory of Open Access Journals (Sweden)
F. Vericat
2013-01-01
Full Text Available A Teichmüller like structure on the space of d-degree holomorphic maps on the circle S1, marked by conjugations to the map z $mapsto$ zd, can be defined. Here we introduce a definition of free energy associated to this kind of dynamics as an invariant of equivalence classes in the Teichmüller space. This quantity encodes a length spectrum of rotation cycles in S1.
Geometry of expanding absolutely continuous invariant measures and the liftability problem
International Nuclear Information System (INIS)
We consider a quite broad class of maps on compact manifolds of arbitrary dimension possibly admitting critical points, discontinuities and singularities. Under some mild nondegeneracy assumptions we show that f admits an induced Gibbs-Markov map with integrable inducing times if and only if it has an ergodic invariant probability measure which is absolutely continuous with respect to the Riemannian volume and has all Lyapunov exponents positive. (author)
First-and second-class constraints in super-BRST
International Nuclear Information System (INIS)
Using the recently obtained supersymmetric Becchi-Rouet-Stora-Tyutin transformations, the authors derive BRST- and supersymmetry-invariant equations which consist of the usual first- or second-class constraints plus ghost contributions. The ghost additions to the second-class constraints make them first-class
On the Topological Orbit Equivalence in a Class of Substitution Minimal Systems
Yuasa, Hisatoshi
2002-01-01
We give numerical, complete invariants for topological orbit equivalence and Kakutani orbit equivalence in a class of substitution systems arising from primitive substitutions whose composition matrices have rational Perron-Frobenius eigenvalues.
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.
Partial regularities and $a^*$-invariants of Borel type ideals
Lu, Dancheng; CHU, Lizhong
2014-01-01
We express the Partial regularities and $a^*$-invariants of a Borel type ideal in terms of its irredundant irreducible decomposition. In addition we consider the behaviours of those invariants under intersections and sums.
ABOUT INVARIANCE IN PROBLEM HEAT OF EXCHANGE WITH BORDER MANAGEMENT
MUSTAPOKULOV KHAMDAM YANGIBOEVICH; MINAROVA NIGORA XUDAYBERGANOVNA
2015-01-01
In given work is considered the question about strong and weak invariance of constant ambiguous image for equations heat of exchange with border management. Sufficient conditions are received for strong or weak invariance given ambiguous image.
The second Chern class in Spinning System
Duan, Yishi; Fu, Libin; Liu, Xin
1999-01-01
Topological property in a spinning system should be directly associated with its wavefunction. A complete decomposition formula of SU(2) gauge potential in terms of spinning wavefunction is established rigorously. Based on the $\\phi $-mapping theory and this formula, one proves that the second Chern class is inherent in the spinning system. It is showed that this topological invariant is only determined by the Hopf index and Brouwer degree of the spinning wavefunction.
Equivalence Partitioning as a Basis for Dynamic Conditional Invariant Detection
Isaratham, Worakarn
2015-01-01
Program invariants are statements asserting properties of programs at certain points. They can assist developers and testers in understanding the program, and can be used for automated formal verification of the program. However, despite their usefulness they are often omitted from code. Dynamic invariant detection is a technique that discovers program invariants by observing execution of the program. One type of invariants that presents challenge to this technique is condit...
Invariant feedback control for the kinematic car on the sphere
Collon, Carsten
2012-01-01
The design of an invariant tracking control law for the kinematic car driving on a sphere is discussed. Using a Lie group framework a left-invariant description on SO(3) is derived. Basic geometric considerations allow a direct comparison of the model with the usual planar case. Exploiting the Lie group structure an invariant tracking error is defined and a feedback is designed. Finally, one possible design of an invariant asymptotic observer is sketched.
A Note On Galilean Invariants In Semi-Relativistic Electromagnetism
Song, Yintao
2013-01-01
The incompatibility between the Lorentz invariance of classical electromagnetism and the Galilean invariance of continuum mechanics is one of the major barriers to prevent two theories from merging. In this note, a systematic approach of obtaining Galilean invariant ?eld variables and equations of electromagnetism within the semi-relativistic limit is reviewed and extended. In particular, the Galilean invariant forms of Poynting's theorem and the momentum identity, two most important electrom...
Learning with Group Invariant Features: A Kernel Perspective
Mroueh, Youssef; Voinea, Stephen; Poggio, Tomaso
2015-01-01
We analyze in this paper a random feature map based on a theory of invariance I-theory introduced recently. More specifically, a group invariant signal signature is obtained through cumulative distributions of group transformed random projections. Our analysis bridges invariant feature learning with kernel methods, as we show that this feature map defines an expected Haar integration kernel that is invariant to the specified group action. We show how this non-linear random feature map approxi...
Multigroup Confirmatory Factor Analysis: Locating the Invariant Referent Sets
French, Brian F.; Finch, W. Holmes
2008-01-01
Multigroup confirmatory factor analysis (MCFA) is a popular method for the examination of measurement invariance and specifically, factor invariance. Recent research has begun to focus on using MCFA to detect invariance for test items. MCFA requires certain parameters (e.g., factor loadings) to be constrained for model identification, which are…
Permutation-invariant codes encoding more than one qubit
Ouyang, Yingkai; Fitzsimons, Joseph
2015-01-01
A permutation-invariant code on m qubits is a subspace of the symmetric subspace of the m qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading order spontaneous decay errors. To prove the result, we use elementary number theory with prior theory on permutation invariant codes and quantum error correction.
Permutation-invariant codes encoding more than one qubit
Ouyang, Yingkai; Fitzsimons, Joseph
2016-04-01
A permutation-invariant code on m qubits is a subspace of the symmetric subspace of the m qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading-order spontaneous decay errors. To prove the result, we use elementary number theory with prior theory on permutation-invariant codes and quantum error correction.
ON THE INVARIANT SUBMANIFOLDS OF RIEMANNIAN PRODUCT MANIFOLD
Institute of Scientific and Technical Information of China (English)
M.Atceken; S.Keles
2004-01-01
In this paper, the vertical and horizontal distributions of an invariant submanifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant submanifold of a Riemannian product manifold to be a locally symmetric and real space form.
Basis Invariants in Non--Abelian Gauge Theories
Müller, Uwe
1997-01-01
A basis of Lorentz and gauge-invariant monomials in non--Abelian gauge theories with matter is described, applicable for the inverse mass expansion of effective actions. An algorithm to convert an arbitrarily given invariant expression into a linear combination of the basis elements is presented. The linear independence of the basis invariants is proven.
Dunkl Operators and Canonical Invariants of Reflection Groups
Arkady Berenstein; Yurii Burman
2008-01-01
Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials. We also compute the canonical invariants for all dihedral groups as certain hypergeometric functions.
Perturbation to Mei symmetry and adiabatic invariants for Hamilton systems
Institute of Scientific and Technical Information of China (English)
Ding Ning; Fang Jian-Hui
2008-01-01
Based on the concept of adiabatic invariant,this paper studies the perturbation to Mei symmetry and adiabatic invariants for Hamilton systems.The exact invaxiants of Mei symmetry for the system without perturbation are given.The perturbation to Mei symmetry is discussed and the adiabatic invariants induced from the perturbation to Mei symmetry of the system are obtained.
Possible universal quantum algorithms for generalized Turaev-Viro invariants
Vélez, Mario; Ospina, Juan
2011-05-01
An emergent trend in quantum computation is the topological quantum computation (TQC). Briefly, TQC results from the application of quantum computation with the aim to solve the problems of quantum topology such as topological invariants for knots and links (Jones polynomials, HOMFLY polynomials, Khovanov polynomials); topological invariants for graphs (Tutte polynomial and Bollobás-Riordan polynomial); topological invariants for 3-manifolds (Reshetiskin-Turaev, Turaev-Viro and Turaer-Viro-Ocneanu invariants) and topological invariants for 4-manifolds( Crane-Yetter invariants). In a few words, TQC is concerned with the formulation of quantum algorithms for the computation of these topological invariants in quantum topology. Given that one of the fundamental achievements of quantum topology was the discovery of strong connections between monoidal categories and 3-dimensional manifolds, in TQC is possible and necessary to exploit such connections with the purpose to formulate universal quantum algorithms for topological invariants of 3-manifolds. In the present work we make an exploration of such possibilities. Specifically we search for universal quantum algorithms for generalized Turaev-Viro invariants of 3-manifolds such as the Turaev-Viro-Ocneanu invariants, the Kashaev-Baseilhac-Benedetti invariants of 3-manifolds with links and the Geer-Kashaev-Turaev invariants of 3-manifolds with a link and a principal bundle. We also look for physical systems (three dimensional topological insulators and three-dimensional gravity) over which implement the resulting universal topological quantum algorithms.
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.
Gauge-invariant approach to quark dynamics
Sazdjian, H.
2016-02-01
The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of quantum chromodynamics (QCD) are first reviewed. The role of the parallel transport operation in constructing gauge-invariant Green's functions is then 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 presented. An integro-differential equation, obtained for the quark Green's function defined with a phase factor along a single, straight line segment, 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.
Natural and Projectively Invariant Quantizations on Supermanifolds
Directory of Open Access Journals (Sweden)
Thomas Leuther
2011-03-01
Full Text Available The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001, no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using the framework of Thomas-Whitehead connections. We extend the problem to the context of supermanifolds and adapt M. Bordemann's method in order to solve it. The obtained quantization appears as the natural globalization of the pgl(n+1|m-equivariant quantization on R^{n|m} constructed by P. Mathonet and F. Radoux in [arXiv:1003.3320]. Our quantization is also a prolongation to arbitrary degree symbols of the projectively invariant quantization constructed by J. George in [arXiv:0909.5419] for symbols of degree two.
The Galilean invariance in field theory
International Nuclear Information System (INIS)
In the lecture notes the methods of construction of classical and quantum field theories with the principle of invariance with respect to the Galilei group are presented. The importance of this problem consists in the necessity of rigorous determination of relativistic effects in field theory. The method of construction of the representations of the Galilei group and the necessity of using the projective representations of this group are discussed, the theory of nonrelativistic wave equations for particles of arbitrary spin is constructed and it is shown that there exists a nonrelativistic electrodynamics which predicts the correct values of the magnetic moments of elementary particles. The lecture notes end with the discussion of the Galilean invariant quantum field theories which essentially differ from the relativistic theories
Actions and invariants of algebraic groups
Ferrer Santos, Walter
2005-01-01
Actions and Invariants of Algebraic Groups presents a self-contained introduction to geometric invariant theory that links the basic theory of affine algebraic groups to Mumford''s more sophisticated theory. The authors systematically exploit the viewpoint of Hopf algebra theory and the theory of comodules to simplify and compactify many of the relevant formulas and proofs.The first two chapters introduce the subject and review the prerequisites in commutative algebra, algebraic geometry, and the theory of semisimple Lie algebras over fields of characteristic zero. The authors'' early presentation of the concepts of actions and quotients helps to clarify the subsequent material, particularly in the study of homogeneous spaces. This study includes a detailed treatment of the quasi-affine and affine cases and the corresponding concepts of observable and exact subgroups.Among the many other topics discussed are Hilbert''s 14th problem, complete with examples and counterexamples, and Mumford''s results on quotien...
Adiabatic Invariance of Oscillons/I-balls
Kawasaki, Masahiro; Takeda, Naoyuki
2015-01-01
Real scalar fields are known to fragment into spatially localized and long-lived solitons called oscillons or $I$-balls. We prove the adiabatic invariance of the oscillons/$I$-balls for a potential that allows periodic motion even in the presence of non-negligible spatial gradient energy. We show that such potential is uniquely determined to be the quadratic one with a logarithmic correction, for which the oscillons/$I$-balls are absolutely stable. For slightly different forms of the scalar potential dominated by the quadratic one, the oscillons/$I$-balls are only quasi-stable, because the adiabatic charge is only approximately conserved. We check the conservation of the adiabatic charge of the $I$-balls in numerical simulation by slowly varying the coefficient of logarithmic corrections. This unambiguously shows that the longevity of oscillons/$I$-balls is due to the adiabatic invariance.
Hiding Lorentz Invariance Violation with MOND
Sanders, R H
2011-01-01
Ho\\v{r}ava gravity is a attempt to construct a renormalizable theory of gravity by breaking the Lorentz Invariance of the gravitational action at high energies. The underlying principle is that Lorentz Invariance is an approximate symmetry and its violation by gravitational phenomena is somehow hidden to present limits of observational precision. Here I point out that a simple modification of the low energy limit of Ho\\v{r}ava gravity in its non-projectable form can effectively camouflage the presence of a preferred frame in regions where the Newtonian gravitational field gradient is higher than $cH_0$; this modification results in the phenomenology of MOND at lower accelerations.
Positronium Decay Gauge Invariance and Analyticity
Pestieau, J; Trine, S
2002-01-01
The construction of positronium decay amplitudes is handled through the use of dispersion relations. In this way, emphasis is put on basic QED principles: gauge invariance and soft-photon limits (analyticity). A firm grounding is given to the factorization approaches, and some ambiguities in the spin and energy structures of the positronium wavefunction are removed. Non-factorizable amplitudes are naturally introduced. Their dynamics is described, especially regarding the enforcement of gauge invariance and analyticity through delicate interferences. The important question of the completeness of the present theoretical predictions for the decay rates is then addressed. Indeed, some of those non-factorizable contributions are unaccounted for by NRQED analyses. However, it is shown that such new contributions are highly suppressed, being of order alpha^3. Finally, a particular effective form factor formalism is constructed for parapositronium, allowing a thorough analysis of binding energy effects and analytici...
Symmetric form-invariant dual Pearcey beams.
Ren, Zhijun; Fan, Changjiang; Shi, Yile; Chen, Bo
2016-08-01
We introduce another type of Pearcey beam, namely, dual Pearcey (DP) beams, based on the Pearcey function of catastrophe theory. DP beams are experimentally generated by applying Fresnel diffraction of bright elliptic rings. Form-invariant Bessel distribution beams can be regarded as a special case of DP beams. Subsequently, the basic propagation characteristics of DP beams are identified. DP beams are the result of the interference of two half DP beams instead of two classical Pearcey beams. Moreover, we also verified that half DP beams (including special-case parabolic-like beams) generated by half elliptical rings (circular rings) are a new member of the family of form-invariant beams. PMID:27505650
BMS invariance and the membrane paradigm
Penna, Robert F
2015-01-01
We reinterpret the BMS invariance of gravitational scattering using the membrane paradigm. BMS symmetries imply an infinite number of conserved quantities. Energy conservation at every angle is equivalent to the fluid energy equation on the membrane (a conservation law at each point in the fluid). Momentum conservation at every angle is equivalent to the Damour-Navier-Stokes equation on the membrane. Soft gravitons are encoded in the membrane's mass-energy density, $\\Sigma(z,\\bar{z})$. Fluid dynamics is governed by infinite dimensional reparametrization invariance, which corresponds to the group of volume preserving diffeomorphisms. This coincides with the generalized BMS group, so there is a connection between the fluid and gravity pictures at the level of symmetries. The existence of membrane fluid conservation laws at event horizons implies BMS symmetries also act on event horizons. This may be relevant for the information problem because it implies infalling information can be stored in $\\Sigma(z,\\bar{z})...
Hiding Lorentz invariance violation with MOND
International Nuclear Information System (INIS)
Horava-Lifshitz gravity is an attempt to construct a renormalizable theory of gravity by breaking the Lorentz invariance of the gravitational action at high energies. The underlying principle is that Lorentz invariance is an approximate symmetry and its violation by gravitational phenomena is somehow hidden to present limits of observational precision. Here I point out that a simple modification of the low-energy limit of Horava-Lifshitz gravity in its nonprojectable form can effectively camouflage the presence of a preferred frame in regions where the Newtonian gravitational field gradient is higher than cH0; this modification results in the phenomenology of modified Newtonian dynamics (MOND) at lower accelerations. As a relativistic theory of MOND, this modified Horava-Lifshitz theory presents several advantages over its predecessors.
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.
Topological Invariance under Line Graph Transformations
Directory of Open Access Journals (Sweden)
Allen D. Parks
2012-06-01
Full Text Available It is shown that the line graph transformation G ↦ L(G of a graph G preserves an isomorphic copy of G as the nerve of a finite simplicial complex K which is naturally associated with the Krausz decomposition of L(G. As a consequence, the homology of K is isomorphic to that of G. This homology invariance algebraically confirms several well known graph theoretic properties of line graphs and formally establishes the Euler characteristic of G as a line graph transformation invariant.
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.
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.
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.
Homotopy Invariant Commutative Algebra over fields
Greenlees, J. P. C.
2016-01-01
These notes illustrates the power of formulating ideas of commutative algebra in a homotopy invariant form. They can then be applied to derived categories of rings or ring spectra. These ideas are powerful in classical algebra, in representation theory of groups, in classical algebraic topology and elsewhere. The notes grew out of a series of lectures given during the `Interactions between Representation Theory, Algebraic Topology and Commutative Algebra' (IRTATCA) at the CRM (Barcelona) in S...
Scale invariance, unimodular gravity and dark energy
Shaposhnikov, Mikhail; Zenhausern, Daniel
2008-01-01
We demonstrate that the combination of the ideas of unimodular gravity, scale invariance, and the existence of an exactly massless dilaton leads to the evolution of the universe supported by present observations: inflation in the past, followed by the radiation and matter dominated stages and accelerated expansion at present. All mass scales in this type of theories come from one and the same source. © 2008 Elsevier B.V. All rights reserved.
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.
Affine Moment Invariants Generated by Graph Method
Czech Academy of Sciences Publication Activity Database
Suk, Tomáš; Flusser, Jan
2011-01-01
Roč. 44, č. 9 (2011), 2047 – 2056. ISSN 0031-3203 R&D Projects: GA ČR(CZ) GA102/08/1593 Institutional research plan: CEZ:AV0Z10750506 Keywords : Image moments * Object recognition * Affine transformation * Affine moment invariants * Pseudoinvariants * Graph representation * Irreducibility * Independence Subject RIV: IN - Informatics, Computer Science Impact factor: 2.292, year: 2011 http://library.utia.cas.cz/separaty/2011/ZOI/suk-0359752.pdf
Some Invariant Subspaces in L2H
Ohno, Yoshiki
1996-01-01
Let H be a separable Hilbert space and let A be the algebra of continuous functions on the torus T 2 which are uniform limits of polynomials in e imxe iny where (m,n)∈{(m,0)∈Z 2|m ≥ 0}∪{(m,n)∈Z 2|n ≥ 1}. For this uniform algebra A, we characterize invariant subspaces of LH2.
The Scale-Invariant Scotogenic Model
Ahriche, Amine; Kristian L. McDonald; Nasri, Salah
2016-01-01
We investigate a minimal scale-invariant implementation of the scotogenic model and show that viable electroweak symmetry breaking can occur while simultaneously generating one-loop neutrino masses and the dark matter relic abundance. The model predicts the existence of a singlet scalar (dilaton) that plays the dual roles of triggering electroweak symmetry breaking and sourcing lepton number violation. Important constraints are studied, including those from lepton flavor violating effects and...
Toward an invariant definition of repulsive gravity
Luongo, Orlando; Quevedo, Hernando
2010-01-01
A remarkable property of naked singularities in general relativity is their repulsive nature. The effects generated by repulsive gravity are usually investigated by analyzing the trajectories of test particles which move in the effective potential of a naked singularity. This method is, however, coordinate and observer dependent. We propose to use the properties of the Riemann tensor in order to establish in an invariant manner the regions where repulsive gravity plays a dominant role. In par...
Gauge-Invariant Decomposition of Nucleon Spin
International Nuclear Information System (INIS)
I introduce a gauge-invariant decomposition of the nucleon spin into quark helicity, quark orbital, and gluon contributions. The total quark (and hence the quark orbital) contribution is shown to be measurable through virtual Compton scattering in a special kinematic region where single quark scattering dominates. This deeply virtual Compton scattering has much potential to unravel the quark and gluon structure of the nucleon. copyright 1997 The American Physical Society
Rotationally invariant distortion resistant finite-elements.
Cowan, T.; Coombs, W.M.
2014-01-01
The predictive capability of conventional iso-parametric finite-elements deteriorates with mesh distortion. In the case of geometrically non-linear analysis, changes in geometry causing severe distortion can result in negative Jacobian mapping between the local and global systems resulting in numerical breakdown. This paper presents a finite-element formulation that is resistant to irregular mesh geometries and large element distortions whilst remaining invariant to rigid body motion. The pre...
Quantum group invariants and link polynomials
International Nuclear Information System (INIS)
A general method is developed for constructing quantum group invariants and determining their eigenvalues. Applied to the universal R-matrix this method leads to the construction of a closed formula for link polynomials. To illustrate the application of this formula, the quantum groups Uq(E8), Uq(so(2m+1)) and Uq(gl(m)) are considered as examples, and corresponding link polynomials are obtained. (orig.)
Galilea relativity and its invariant bilinear forms
Ratsimbarison, Herintsitohaina
2006-01-01
We construct the family of bilinear forms gG on R3+1 for which Galilea boosts and spatial rotations are isometries. The key feature of these bilinear forms is that they are parametrized by a Galilea invariant vector whose physical interpretation is rather unclear. At the end of the paper, we construct the Poisson bracket associated to the (nondegenerate) antisymmetric part of gG.
Explicit Traveling Waves and Invariant Algebraic Curves
Gasull, Armengol; Giacomini, Hector
2013-01-01
In this paper we introduce a precise definition of algebraic traveling wave solution for general n-th order partial differential equations. All examples of explicit traveling waves known by the authors fall in this category. Our main result proves that algebraic traveling waves exist if and only if an associated n- dimensional first order ordinary differential system has some invariant algebraic curve. As a paradigmatic application we prove that, for the celebrated Fisher- Kolmogorov equation...
Deep video gesture recognition using illumination invariants
Gupta, Otkrist; Raviv, Dan; Raskar, Ramesh
2016-01-01
In this paper we present architectures based on deep neural nets for gesture recognition in videos, which are invariant to local scaling. We amalgamate autoencoder and predictor architectures using an adaptive weighting scheme coping with a reduced size labeled dataset, while enriching our models from enormous unlabeled sets. We further improve robustness to lighting conditions by introducing a new adaptive filer based on temporal local scale normalization. We provide superior results over kn...
Invariant dependence structures and Archimedean copulas
Czech Academy of Sciences Publication Activity Database
Durante, F.; Jaworski, P.; Mesiar, Radko
2011-01-01
Roč. 81, č. 12 (2011), s. 1995-2003. ISSN 0167-7152 R&D Projects: GA ČR GAP402/11/0378 Institutional research plan: CEZ:AV0Z10750506 Keywords : Archimedean copula * Tail dependence * Clayton model Subject RIV: BA - General Mathematics Impact factor: 0.498, year: 2011 http://library.utia.cas.cz/separaty/2011/E/mesiar-invariant dependence structures and archimedean copulas.pdf
Hodge-type structures as link invariants
Borodzik, Maciej; Nemethi, Andras
2010-01-01
Based on some analogies with the Hodge theory of isolated hypersurface singularities, we define Hodge-type numerical invariants (called H-numbers) of any, not necessarily algebraic, link in $S^3$. They contain the same information as the (normalized) real Seifert matrix. We study their basic properties, we express the Tristram-Levine signatures and the higher order Alexander polynomial in terms of them. Motivated by singularity theory, we also introduce the spectrum of the link (determined fr...
Trojan Horse particle invariance in fusion reactions
Pizzone R.G.; Spitaleril C.; Bertulani C.; Mukhamedzhanov A.; Blokhintsev L.; La Cognata M.; Lamia L.; Spartá R.; Tumino A.
2015-01-01
Trojan Horse method plays an important part for the measurement of several charged particle induced reactions cross sections of astrophysical interest. In order to better understand its cornerstones and the related applications to different astrophysical scenarios several tests were performed to verify all its properties and the possible future perspectives. The Trojan Horse nucleus invariance for the binary reactions d(d,p)t, 6,7Li(p,α)3,4He was therefore tested using the appropriate quasi f...
The multiplicativity of fixed point invariants
Ponto, Kate; Shulman, Michael
2012-01-01
We prove two general factorization theorems for fixed-point invariants of fibrations: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar multiplicativity results for the Lefschetz and Nielsen numbers of a fibration. Moreover, the proofs of these theorems are essentially formal, taking place in the abstract context of bicategorical traces. This makes generalizations to other contexts straightforward.
Evaluating Invariances in Document Layout Functions
MacDonald, Alexander J; Brailsford, David F.; Lumley, John
2006-01-01
With the development of variable-data-driven digital presses - where each document printed is potentially unique - there is a need for pre-press optimization to identify material that is invariant from document to document. In this way rasterisation can be confined solely to those areas which change between successive documents thereby alleviating a potential performance bottleneck. Given a template document specified in terms of layout functions, where actual data is bound at the last pos...
Invariant object recognition based on extended fragments
Bart, Evgeniy; Hegdé, Jay
2012-01-01
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 syst...
Neutrino velocity and local Lorentz invariance
Cardone, Fabio; Mignani, Roberto; Petrucci, Andrea
2015-09-01
We discuss the possible violation of local Lorentz invariance (LLI) arising from a faster-than-light neutrino speed. A toy calculation of the LLI violation parameter δ, based on the (disclaimed) OPERA data, suggests that the values of δ are determined by the interaction involved, and not by the energy range. This hypothesis is further corroborated by the analysis of the more recent results of the BOREXINO, LVD and ICARUS experiments.
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. H...
An invariant distribution in static granular media
T. Aste; Di Matteo, T.; Saadatfar, M.; Senden, T. J.; Schroter, M.; Swinney, Harry L.
2006-01-01
We have discovered an invariant distribution for local packing configurations in static granular media. This distribution holds in experiments for packing fractions covering most of the range from random loose packed to random close packed, for beads packed both in air and in water. Assuming only that there exist elementary cells in which the system volume is subdivided, we derive from statistical mechanics a distribution that is in accord with the observations. This universal distribution fu...
Entanglement entropy, conformal invariance and extrinsic geometry
Solodukhin, Sergey N.
2008-01-01
We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface $\\Sigma$ that separates two subsystems of quantum strongly coupled ${\\mathcal{N}}=4$ SU(N) superconformal gauge theory. We extend this result and calculate entanglement entropy of a generic 4d conformal field theory. As a byproduct, we obtain a closed-form expression for the entanglement entropy in flat space-time when $\\Sigma$ ...
Permutation-invariant distance between atomic configurations
International Nuclear Information System (INIS)
We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables us to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e., fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the root mean square distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e., their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity
Permutation-invariant distance between atomic configurations
Energy Technology Data Exchange (ETDEWEB)
Ferré, Grégoire; Maillet, Jean-Bernard [CEA, DAM, DIF, F-91297 Arpajon (France); Stoltz, Gabriel [Université Paris-Est, CERMICS (ENPC), INRIA, F-77455 Marne-la-Vallée (France)
2015-09-14
We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables us to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e., fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the root mean square distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e., their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity.
Global invariants in ideal magnetohydrodynamic turbulence
International Nuclear Information System (INIS)
Magnetohydrodynamic (MHD) turbulence is an important though incompletely understood factor affecting the dynamics of many astrophysical, geophysical, and technological plasmas. As an approximation, viscosity and resistivity may be ignored, and ideal MHD turbulence may be investigated by statistical methods. Incompressibility is also assumed and finite Fourier series are used to represent the turbulent velocity and magnetic field. The resulting model dynamical system consists of a set of independent Fourier coefficients that form a canonical ensemble described by a Gaussian probability density function (PDF). This PDF is similar in form to that of Boltzmann, except that its argument may contain not just the energy multiplied by an inverse temperature, but also two other invariant integrals, the cross helicity and magnetic helicity, each multiplied by its own inverse temperature. However, the cross and magnetic helicities, as usually defined, are not invariant in the presence of overall rotation or a mean magnetic field, respectively. Although the generalized form of the magnetic helicity is known, a generalized cross helicity may also be found, by adding terms that are linear in the mean magnetic field and angular rotation vectors, respectively. These general forms are invariant even in the presence of overall rotation and a mean magnetic field. We derive these general forms, explore their properties, examine how they extend the statistical theory of ideal MHD turbulence, and discuss how our results may be affected by dissipation and forcing
Sheaves on Graphs and Their Homological Invariants
Friedman, Joel
2011-01-01
We introduce a notion of a sheaf of vector spaces on a graph, and develop the foundations of homology theories for such sheaves. One sheaf invariant, its "maximum excess," has a number of remarkable properties. It has a simple definition, with no reference to homology theory, that resembles graph expansion. Yet it is a "limit" of Betti numbers, and hence has a short/long exact sequence theory and resembles the $L^2$ Betti numbers of Atiyah. Also, the maximum excess is defined via a supermodular function, which gives the maximum excess much stronger properties than one has of a typical Betti number. The maximum excess gives a simple interpretation of an important graph invariant, which will be used to study the Hanna Neumann Conjecture in a future paper. Our sheaf theory can be viewed as a vast generalization of algebraic graph theory: each sheaf has invariants associated to it---such as Betti numbers and Laplacian matrices---that generalize those in classical graph theory.
Nakayama, Yu
2016-01-01
We show that eleven dimensional supergravity in Euclidean signature admits an exact classical solution with isometry corresponding to a three dimensional scale invariant field theory without conformal invariance. We also construct the holographic renormalization group flow that connects the known UV conformal fixed point and the new scale invariant but not conformal fixed point. In view of holography, the existence of such classical solutions suggests that the topologically twisted M2-brane gauge theory possesses a scale invariant but not conformal phase.
Generation of scale invariant magnetic fields in bouncing universes
Sriramkumar, L.; Atmjeet, Kumar; Jain, Rajeev Kumar
2015-09-01
We consider the generation of primordial magnetic fields in a class of bouncing models when the electromagnetic action is coupled non-minimally to a scalar field that, say, drives the background evolution. For scale factors that have the power law form at very early times and non-minimal couplings which are simple powers of the scale factor, one can easily show that scale invariant spectra for the magnetic field can arise before the bounce for certain values of the indices involved. It will be interesting to examine if these power spectra retain their shape after the bounce. However, analytical solutions for the Fourier modes of the electromagnetic vector potential across the bounce are difficult to obtain. In this work, with the help of a new time variable that we introduce, which we refer to as the e-Script N-fold, we investigate these scenarios numerically. Imposing the initial conditions on the modes in the contracting phase, we numerically evolve the modes across the bounce and evaluate the spectra of the electric and magnetic fields at a suitable time after the bounce. As one could have intuitively expected, though the complete spectra depend on the details of the bounce, we find that, under the original conditions, scale invariant spectra of the magnetic fields do arise for wavenumbers much smaller than the scale associated with the bounce. We also show that magnetic fields which correspond to observed strengths today can be generated for specific values of the parameters. But, we find that, at the bounce, the backreaction due to the electromagnetic modes that have been generated can be significantly large calling into question the viability of the model. We briefly discuss the implications of our results.
A Gamma Class Formula for Open Gromov-Witten Calculations
Mahowald, Matthew
2016-01-01
For toric Calabi-Yau threefolds, open Gromov-Witten invariants associated to Riemann surfaces with one boundary component can be written as the product of a disk factor and a closed invariant. When the Lagrangian boundary cycle is preserved by the torus action and can be locally described as the fixed locus of an anti-holomorphic involution, we prove a formula that expresses the disk factor in terms of a gamma class and combinatorial data about the image of the Lagrangian cycle in the moment polytope. As a corollary, we construct a generating function for these invariants using Givental's $J$ function. We then verify that this formula encodes the expected invariants obtained from localization by comparing with several examples. Finally, motivated by large $N$ duality, we show that this formula also unexpectedly applies to Lagrangian cycles on $\\mathcal{O}_{\\mathbb{P}^1}(-1,-1)$ constructed from torus knots.
Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho
2015-05-01
This paper focuses on a class of reinforcement learning (RL) algorithms, named integral RL (I-RL), that solve continuous-time (CT) nonlinear optimal control problems with input-affine system dynamics. First, we extend the concepts of exploration, integral temporal difference, and invariant admissibility to the target CT nonlinear system that is governed by a control policy plus a probing signal called an exploration. Then, we show input-to-state stability (ISS) and invariant admissibility of the closed-loop systems with the policies generated by integral policy iteration (I-PI) or invariantly admissible PI (IA-PI) method. Based on these, three online I-RL algorithms named explorized I-PI and integral Q -learning I, II are proposed, all of which generate the same convergent sequences as I-PI and IA-PI under the required excitation condition on the exploration. All the proposed methods are partially or completely model free, and can simultaneously explore the state space in a stable manner during the online learning processes. ISS, invariant admissibility, and convergence properties of the proposed methods are also investigated, and related with these, we show the design principles of the exploration for safe learning. Neural-network-based implementation methods for the proposed schemes are also presented in this paper. Finally, several numerical simulations are carried out to verify the effectiveness of the proposed methods. PMID:25163070
Using sorted invariant mass variables to evade combinatorial ambiguities in cascade decays
Kim, Doojin; Park, Myeonghun
2015-01-01
The classic method for mass determination in a SUSY-like cascade decay chain relies on measurements of the kinematic endpoints in the invariant mass distributions of suitable collections of visible decay products. However, the procedure is complicated by combinatorial ambiguities: e.g., the visible final state particles may be indistinguishable (as in the case of QCD jets), or one may not know the exact order in which they are emitted along the decay chain. In order to avoid such combinatorial ambiguities, we propose to treat the final state particles fully democratically and consider the sorted set of the invariant masses of all possible partitions of the visible particles in the decay chain. In particular, for a decay to N visible particles, one considers the sorted sets of all possible n-body invariant mass combinations (2 <= n <= N) and determines the kinematic endpoint m_(n,r)^max of the distribution of the r-th largest n-body invariant mass m_(n,r) for each possible value of n and r. For the class...
Conformal Invariance for Non-Relativistic Field Theory
Mehen, T; Wise, M B; Mehen, Thomas; Stewart, Iain W.; Wise, Mark B.
2000-01-01
Momentum space Ward identities are derived for the amputated n-point Green's functions in 3+1 dimensional non-relativistic conformal field theory. For n=4 and 6 the implications for scattering amplitudes (i.e. on-shell amputated Green's functions) are considered. Any scale invariant 2-to-2 scattering amplitude is also conformally invariant. However, conformal invariance imposes constraints on off-shell Green's functions and the three particle scattering amplitude which are not automatically satisfied if they are scale invariant. As an explicit example of a conformally invariant theory we consider non-relativistic particles in the infinite scattering length limit.
White, M. Catherine
Typical 101 courses discourage many students from pursuing higher level science and math courses. Introductory classes in science and math serve largely as a filter, screening out all but the most promising students, and leaving the majority of college graduates—including most prospective teachers—with little understanding of how science works, according to a study conducted for the National Science Foundation. Because few teachers, particularly at the elementary level, experience any collegiate science teaching that stresses skills of inquiry and investigation, they simply never learn to use those methods in their teaching, the report states.
International Nuclear Information System (INIS)
99Tc is formed mostly during nuclear reactions and is released into the environment during weapons testing and inadvertent waste disposal. The long half-life, high environmental mobility (as Tc(VII)O4-) and its possible uptake into the food chain cause 99Tc to be a significant environmental contaminant. In this study, we evaluated the role of Fe(II) in biologically reduced clay mineral, nontronite (NAu-2), in reducing Tc(VII)O4- to poorly soluble Tc(IV) species as a function of pH and Fe(II) concentration. The rate of Tc(VII) reduction by Fe(II) in NAu-2 was higher at neutral pH (pH 7.0) than at acidic and basic pHs when Fe(II) concentration was low (< 1 mmol/g). The effect of pH, however, was insignificant at higher Fe(II) concentrations. The reduction of Tc(VII) by Fe(II) associated with NAu-2 was also studied in the presence of common subsurface oxidants including iron and manganese oxides, nitrate, and oxygen, to evaluate the effect of the oxidants on the enhancement and inhibition of Tc(VII) reduction, and reoxidation of Tc(IV). Addition of iron oxides (goethite and hematite) to the Tc(VII)-NAu-2 system, where Tc(VII) reduction was ongoing, enhanced reduction of Tc(VII), apparently as a result of re-distribution of reactive Fe(II) from NAu-2 to more reactive goethite/hematite surfaces. Addition of manganese oxides stopped further Tc(VII) reduction, and in case of K+-birnessite, it reoxidized previously reduced Tc(IV). Nitrate neither enhanced reduction of Tc(VII) nor promoted reoxidation of Tc(IV). Approximately 11% of Tc(IV) was oxidized by oxygen. The rate and extent of Tc(IV) reoxidation was found to strongly depend on the nature of the oxidants and concentration of Fe(II). When the same oxidants were added to aged Tc reduction products (mainly NAu-2 and TcO2nH2O), the extent of Tc(IV) reoxidation decreased significantly relative to fresh Tc(IV) products. Increasing NAu-2 concentration also resulted in the decreased extent of Tc(IV) reoxidation. The results
Bréhier, Charles-Edouard
2012-01-01
In this article, we consider a stochastic PDE of parabolic type, driven by a space-time white-noise, and its numerical discretization in time with a semi-implicit Euler scheme. When the nonlinearity is assumed to be bounded, then a dissipativity assumption is satisfied, which ensures that the SDPE admits a unique invariant probability measure, which is ergodic and strongly mixing - with exponential convergence to equilibrium. Considering test functions of class $\\mathcal{C}^2$, bounded and with bounded derivatives, we prove that we can approximate this invariant measure using the numerical scheme, with order 1/2 with respect to the time step.
Dedecker, J; Pène, F
2012-01-01
In this paper, we give rates of convergence in the strong invariance principle for non-adapted sequences satisfying projective criteria. The results apply to the iterates of ergodic automorphisms T of the d-dimensional torus, even in the non hyperbolic case. In this context, we give a large class of unbounded functions f from the d-dimensional torus to R, for which the partial sum foT+ foT^2 + ... + foT^n satisfies a strong invariance principle with an explicit rate of convergence.
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.
DPA1*02012: A DPA1*0201-related Mhc class II allele in West Africa
Energy Technology Data Exchange (ETDEWEB)
Meyer, C.G.; May, J.; Spauke, D.; Schnittger, L. [Bernhard Nocht Institute for Tropical Medicine, Hamburg (Germany)
1994-12-31
DNA techniques such as sequence-specific oligonucleotide probe (SSOP) hybridizations, restriction-fragment length polymorphism (RFLP) analyses, and DNA sequencing have greatly supported the characterization of Mhc class II allelic polymorphism. Here the authors describe a DPA 1 allele which has been identified in two male individuals from Liberia and Benin, West Africa, during a survey study on Mhc class II associations with the different manifestations after infection with Onchocerca volvulus. 4 refs., 1 fig.
Learning How to Extract Rotation-Invariant and Scale-Invariant Features from Texture Images
Directory of Open Access Journals (Sweden)
Alexandre X. Falcão
2008-05-01
Full Text Available Learning how to extract texture features from noncontrolled environments characterized by distorted images is a still-open task. By using a new rotation-invariant and scale-invariant image descriptor based on steerable pyramid decomposition, and a novel multiclass recognition method based on optimum-path forest, a new texture recognition system is proposed. By combining the discriminating power of our image descriptor and classifier, our system uses small-size feature vectors to characterize texture images without compromising overall classification rates. State-of-the-art recognition results are further presented on the Brodatz data set. High classification rates demonstrate the superiority of the proposed system.
Bound entangled states invariant under Ux
Institute of Scientific and Technical Information of China (English)
Wang Zhen; Wang Zhi-Xi
2008-01-01
This paper obtains an entangled condition for isotropic-like states by using an atomic map. It constructs a class of bound entangled states from the entangled condition and shows that the partial transposition of the state from the constructed bound entangled class is an edge bound entangled state by using range criterion.
The measurement invariance of schizotypy in Europe.
Fonseca-Pedrero, E; Ortuño-Sierra, J; Sierro, G; Daniel, C; Cella, M; Preti, A; Mohr, C; Mason, O J
2015-10-01
The short version of the Oxford-Liverpool Inventory of Feelings and Experiences (sO-LIFE) is a widely used measure assessing schizotypy. There is limited information, however, on how sO-LIFE scores compare across different countries. The main goal of the present study is to test the measurement invariance of the sO-LIFE scores in a large sample of non-clinical adolescents and young adults from four European countries (UK, Switzerland, Italy, and Spain). The scores were obtained from validated versions of the sO-LIFE in their respective languages. The sample comprised 4190 participants (M=20.87 years; SD=3.71 years). The study of the internal structure, using confirmatory factor analysis, revealed that both three (i.e., positive schizotypy, cognitive disorganisation, and introvertive anhedonia) and four-factor (i.e., positive schizotypy, cognitive disorganisation, introvertive anhedonia, and impulsive nonconformity) models fitted the data moderately well. Multi-group confirmatory factor analysis showed that the three-factor model had partial strong measurement invariance across countries. Eight items were non-invariant across samples. Significant statistical differences in the mean scores of the s-OLIFE were found by country. Reliability scores, estimated with Ordinal alpha ranged from 0.75 to 0.87. Using the Item Response Theory framework, the sO-LIFE provides more accuracy information at the medium and high end of the latent trait. The current results show further evidence in support of the psychometric proprieties of the sO-LIFE, provide new information about the cross-cultural equivalence of schizotypy and support the use of this measure to screen for psychotic-like features and liability to psychosis in general population samples from different European countries. PMID:26443051
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.