WorldWideScience

Sample records for class ii-associated invariant

  1. Characterization of monoclonal antibodies against MHC class II-associated p41 invariant chain fragment

    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)

  2. Class II-associated invariant chain peptide down-modulation enhances the immunogenicity of myeloid leukemic blasts resulting in increased CD4(+) T-cell responses

    NARCIS (Netherlands)

    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

  3. Conformal classes realizing the Yamabe invariant

    OpenAIRE

    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.

  4. Invariants for a Class of Nongeneric Three-qubit States

    CERN Document Server

    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.

  5. Universality Classes of Scale Invariant Inflation

    NARCIS (Netherlands)

    Ozkan, Mehmet; Roest, Diederik

    2015-01-01

    We investigate the inflationary implications of extensions of Poincare symmetry. The simplest constructions with local scale invariance lead to universal predictions: the spectral index is $n_s = 1-2/N$, in excellent agreement with Planck data, while the tensor-to-scalar ratio is determined by a fre

  6. HLA Class-II Associated HIV Polymorphisms Predict Escape from CD4+ T Cell Responses.

    Directory of Open Access Journals (Sweden)

    Nathan Erdmann

    2015-08-01

    Full Text Available Antiretroviral therapy, antibody and CD8+ T cell-mediated responses targeting human immunodeficiency virus-1 (HIV-1 exert selection pressure on the virus necessitating escape; however, the ability of CD4+ T cells to exert selective pressure remains unclear. Using a computational approach on HIV gag/pol/nef sequences and HLA-II allelic data, we identified 29 HLA-II associated HIV sequence polymorphisms or adaptations (HLA-AP in an African cohort of chronically HIV-infected individuals. Epitopes encompassing the predicted adaptation (AE or its non-adapted (NAE version were evaluated for immunogenicity. Using a CD8-depleted IFN-γ ELISpot assay, we determined that the magnitude of CD4+ T cell responses to the predicted epitopes in controllers was higher compared to non-controllers (p<0.0001. However, regardless of the group, the magnitude of responses to AE was lower as compared to NAE (p<0.0001. CD4+ T cell responses in patients with acute HIV infection (AHI demonstrated poor immunogenicity towards AE as compared to NAE encoded by their transmitted founder virus. Longitudinal data in AHI off antiretroviral therapy demonstrated sequence changes that were biologically confirmed to represent CD4+ escape mutations. These data demonstrate an innovative application of HLA-associated polymorphisms to identify biologically relevant CD4+ epitopes and suggests CD4+ T cells are active participants in driving HIV evolution.

  7. The HLA Class II Associations with Rheumatic Heart Disease in South Indian Patients: A Preliminary Study

    OpenAIRE

    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.

  8. Anti-cofactor autoantibodies in systemic lupus erythematosus: prevalence, clinical and HLA class II associations.

    Science.gov (United States)

    Sebastiani, Gian Domenico; Morozzi, Gabriella; Bellisai, Francesca; Fineschi, Irene; Bacarelli, Maria Romana; Simpatico, Antonella; Font, Josep; Cervera, Ricard; Houssiau, Frederic; Fernandez-Nebro, Antonio; De Ramon Garrido, Enrique; De Pità, Ornella; Smolen, Josef; Galeazzi, Mauro

    2008-01-01

    The aim of our study was to evaluate the clinical and HLA-class II allele associations of some anti-cofactor antibodies in a homogeneous group of European patients with SLE. One hundred thirty-six patients with SLE, fulfilling four or more of the ACR 1997 revised criteria for the classification of the disease, coming from 7 European countries, were enrolled consecutively. Anti-prothrombin (anti-PT), anti-annexin V (anti-AnnV), anti-protein C (anti-Cprot) and anti-protein S (anti-Sprot) were determined by using commercial ELISA kits. Molecular typing of HLA-DRB1, DRB3, DRB4, DRB5, DQA1, DQB1 and DPB1 loci was performed by using PCR-SSOP method, carried out using digoxygenin (DIG) labeled probes. The prevalence of anti-AnnV, anti-PT, anti-Cprot and anti-Sprot was 19%, 10.4%, 4.4% and 8.1%, respectively. Twenty-seven % of anti-AnnV positive patients reported migraine vs 5.5% of anti-AnnV negatives (p = 0.003, but p not significant, odds ratio (OR) = 6.4, 95% confidence interval (CI) = 2-21). Anti-PT, anti-AnnV and anti-Sprot were positively associated with some HLA alleles, but pc was not significant. In this study we have shown that some HLA alleles carry the risk to produce antibodies against phospholipid-binding proteins, but these association need confirmation in other studies, because they have never been reported and appear to be weak associations.

  9. Basic polynomial invariants, fundamental representations and the Chern class map

    CERN Document Server

    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.

  10. Conformal invariance and conserved quantities of Birkhoff systems under second-class Mei symmetry

    Institute of Scientific and Technical Information of China (English)

    Luo Yi-Ping; Fu Jin-Li

    2011-01-01

    This paper proposes a new concept of the conformal invariance and the conserved quantities for Birkhoff systems under second-class Mei symmetry. The definition about conformal invariance of Birkhoff systems under second-class Mei symmetry is given. The conformal factor in the determining equations is found. The relationship between Birkhoff system's conformal invariance and second-class Mei symmetry are discussed. The necessary and sufficient conditions of conformal invariance, which are simultaneously of second-class symmetry, are given. And Birkhoff system's conformal invariance may lead to corresponding Mei conserved quantities, which is deduced directly from the second-class Mei symmetry when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.

  11. MHC class II-associated invariant chain linkage of antigen dramatically improves cell-mediated immunity induced by adenovirus vaccines

    DEFF Research Database (Denmark)

    Holst, Peter Johannes; Mandrup Jensen, Camilla Maria; Orskov, Cathrine;

    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...

  12. MHC class II-associated proteins in B-cell exosomes and potential functional implications for exosome biogenesis.

    NARCIS (Netherlands)

    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

  13. Invariant chain as a vehicle to load antigenic peptides on human MHC class I for cytotoxic T-cell activation.

    Science.gov (United States)

    Wälchli, Sébastien; Kumari, Shraddha; Fallang, Lars-Egil; Sand, Kine M K; Yang, Weiwen; Landsverk, Ole J B; Bakke, Oddmund; Olweus, Johanna; Gregers, Tone F

    2014-03-01

    Protective T-cell responses depend on efficient presentation of antigen (Ag) in the context of major histocompatibility complex class I (MHCI) and class II (MHCII) molecules. Invariant chain (Ii) serves as a chaperone for MHCII molecules and mediates trafficking to the endosomal pathway. The genetic exchange of the class II-associated Ii peptide (CLIP) with antigenic peptides has proven efficient for loading of MHCII and activation of specific CD4(+) T cells. Here, we investigated if Ii could similarly activate human CD8(+) T cells when used as a vehicle for cytotoxic T-cell (CTL) epitopes. The results show that wild type Ii, and Ii in which CLIP was replaced by known CTL epitopes from the cancer targets MART-1 or CD20, coprecipitated with HLA-A*02:01 and mediated colocalization in the endosomal pathway. Furthermore, HLA-A*02:01-positive cells expressing CLIP-replaced Ii efficiently activated Ag-specific CD8(+) T cells in a TAP- and proteasome-independent manner. Finally, dendritic cells transfected with mRNA encoding IiMART-1 or IiCD20 primed naïve CD8(+) T cells. The results show that Ii carrying antigenic peptides in the CLIP region can promote efficient presentation of the epitopes to CTLs independently of the classical MHCI peptide loading machinery, facilitating novel vaccination strategies against cancer.

  14. A four step model for the IL-6 amplifier, a regulator of chromic inflammations in tissue specific MHC class II-associated autoimmune diseases

    Directory of Open Access Journals (Sweden)

    Masaaki eMurakami

    2011-06-01

    Full Text Available It is thought autoimmune diseases are caused by the breakdown of self-tolerance, which suggests the recognition of specific antigens by autoreactive CD4+ T cells contribute to the specificity of autoimmune diseases. In several cases, however, even for diseases associated with class II MHC alleles, the causative tissue-specific antigens recognized by memory/activated CD4+ T cells have not been established. Rheumatoid arthritis (RA and arthritis in F759 knock-in mouse line (F759 mice are such examples, even though evidences support a pathogenic role for CD4+ T cells in both diseases. We have recently shown local events such as microbleeding together with an accumulation of activated CD4+ T cells in a manner independent of tissue antigen-recognitions induces arthritis in the joints of F759 mice. For example, local microbleeding-mediated CCL20 expression induced such an accumulation, causing arthritis development via chronic activation of an IL-17A-dependent IL-6 signaling amplification loop in type 1 collagen+ cells that is triggered by CD4+ T cell-derived cytokine(s such as IL-17A, which leads to the synergistic activation of STAT3 and NFκB in non hematopoietic cells in the joint. We named this loop the IL-6-mediated inflammation amplifier, or IL-6 amplifier. Thus, certain class II MHC–associated, tissue-specific autoimmune diseases may be induced by local events that cause an antigen-independent accumulation of effector CD4+ T cells followed by the induction of the IL-6 amplifier in the affected tissue. To explain this hypothesis, we have proposed a Four Step Model for MHC class II associated autoimmune diseases. The interaction of four local events results in chronic activation of the IL-6 amplifier, leading to the manifestation of autoimmune diseases. Thus, we have concluded the IL-6 amplifier is a critical regulator of chromic inflammations in tissue specific MHC class II-associated autoimmune diseases.

  15. A four-step model for the IL-6 amplifier, a regulator of chronic inflammations in tissue-specific MHC class II-associated autoimmune diseases.

    Science.gov (United States)

    Murakami, Masaaki; Hirano, Toshio

    2011-01-01

    short (Ogura et al., 2008; Hirano, 2010; Murakami et al., 2011). Thus, certain class II MHC-associated, tissue-specific autoimmune diseases, including some RA subtypes, may be induced by local events that cause an antigen-independent accumulation of effector CD4+ T cells followed by the induction of the IL-6 amplifier in the affected tissue. In other words, in certain cases, the target tissue itself may determine the specificity of the autoimmune disease via activation of the IL-6 amplifier. To explain this hypothesis, we have proposed a four-step model for MHC class II-associated autoimmune diseases (Murakami et al., 2011): (1) T cell activation regardless of antigen specificity; (2) local events inducing a tissue-specific accumulation of activated T cells; (3) transient activation of the IL-6 amplifier; and (4) enhanced sensitivity to cytokines in the target tissue. The interaction of these events results in chronic activation of the IL-6 amplifier and subsequent manifestation of autoimmune diseases. Thus, the IL-6 amplifier, which is chronically activated by these four events, is a critical regulator of chronic inflammations in tissue-specific MHC class II-associated autoimmune diseases.

  16. Oligoclonal band phenotypes in MS differ in their HLA class II association, while specific KIR ligands at HLA class I show association to MS in general

    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 associ......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...

  17. Localization of the gene encoding the putative human HLA class II associated protein (PHAPI) to chromosome 15q22.3-q23 by fluorescence in situ hybridization

    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.

  18. An Analysis of the Invariance and Conservation Laws of Some Classes of Nonlinear Ostrovsky Equations and Related Systems

    Institute of Scientific and Technical Information of China (English)

    K. Fakhar; A. H. Kara

    2011-01-01

    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.

  19. Intracellular transport of MHC class II and associated invariant chain in antigen presenting cells from AP-3-deficient mocha mice.

    Science.gov (United States)

    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

  20. 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.

  1. MHC class I-related molecule, MR1, and mucosal-associated invariant T cells.

    Science.gov (United States)

    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

  2. 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.

  3. 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.

  4. One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains

    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.

  5. Parasite Manipulation of the Invariant Chain and the Peptide Editor H2-DM Affects Major Histocompatibility Complex Class II Antigen Presentation during Toxoplasma gondii Infection.

    Science.gov (United States)

    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

  6. Solutions by radicals at singular values k_N from new class invariants for N \\equiv 3 mod 8

    CERN Document Server

    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 $\\...

  7. Characterization of system theoretic properties for a class of spatially invariant systems

    NARCIS (Netherlands)

    Fatmawati,; Zwart, Hans; El Jai, A.; Afifi, L.; Zerrik, E.

    2009-01-01

    This paper considers the analysis of the system properties stability and stabilizability for a class of spatially distributed systems on a two-dimensional spatial domain. Using the Fourier transform on the spatial variables, we obtain a mathematically simpler infinite dimensional system. The analysi

  8. College Students' Achievement Goal Orientation and Motivational Regulations in Physical Activity Classes: A Test of Gender Invariance

    Science.gov (United States)

    Su, Xiaoxia; McBride, Ron E.; Xiang, Ping

    2015-01-01

    The current study examined the measurement invariance across 361 male and female college students' 2 × 2 achievement goal orientation and motivational regulations. Participants completed questionnaires assessing their achievement goals and motivational regulations. Multigroup CFA analyses showed that male and female students' scores were fully…

  9. The p41 isoform of invariant chain is a chaperone for cathepsin L

    OpenAIRE

    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...

  10. j 不变量生成 Hilbert 类域的简单证明%A simple proof of j-invariant generates the Hilbert class field

    Institute of Scientific and Technical Information of China (English)

    李加宁; 张起帆

    2015-01-01

    Silverman proved the following theorem:Let E be an elliptic curve over C with complex multi-plication OK,where OKis the ring of integers of an imaginary quadratic field K ,then the Hilbert class field of K is generated by the j-invariant of E over K .In this paper we give a simple proof of this funda-mental theorem.%Silverman证明了如下定理:设K是一个虚二次域,E是定义在复数域上的一条带复乘的椭圆曲线,其自同态环为 OK ,则K的Hilbert类域等于K(j),其中j是椭圆曲线E的j不变量。本文给出了该定理的一个简单证明。

  11. Vitamin D3 Suppresses Class II Invariant Chain Peptide Expression on Activated B-Lymphocytes: A Plausible Mechanism for Downregulation of Acute Inflammatory Conditions

    Directory of Open Access Journals (Sweden)

    Omar K. Danner

    2016-01-01

    Full Text Available Class II invariant chain peptide (CLIP expression has been demonstrated to play a pivotal role in the regulation of B cell function after nonspecific polyclonal expansion. Several studies have shown vitamin D3 helps regulate the immune response. We hypothesized that activated vitamin D3 suppresses CLIP expression on activated B-cells after nonspecific activation or priming of C57BL/6 mice with CpG. This study showed activated vitamin D3 actively reduced CLIP expression and decreased the number of CLIP+ B-lymphocytes in a dose and formulation dependent fashion. Flow cytometry was used to analyze changes in mean fluorescent intensity (MFI based on changes in concentration of CLIP on activated B-lymphocytes after treatment with the various formulations of vitamin D3. The human formulation of activated vitamin D (calcitriol had the most dramatic reduction in CLIP density at an MFI of 257.3 [baseline of 701.1 (P value = 0.01]. Cholecalciferol and alfacalcidiol had no significant reduction in MFI at 667.7 and 743.0, respectively. Calcitriol seemed to best reduce CLIP overexpression in this ex vivo model. Bioactive vitamin D3 may be an effective compliment to other B cell suppression therapeutics to augment downregulation of nonspecific inflammation associated with many autoimmune disorders. Further study is necessary to confirm these findings.

  12. Invariants of 3-Manifolds derived from finite dimensional hopf algebras

    CERN Document Server

    Kauffman, L H; Louis H Kauffman; David E Radford

    1994-01-01

    Abstract: This paper studies invariants of 3-manifolds derived from certain fin ite dimensional Hopf algebras. The invariants are based on right integrals for these algebras. It is shown that the resulting class of invariants is distinct from the class of Witten-Reshetikhin-Turaev invariants.

  13. Invariant death

    Science.gov (United States)

    Frank, Steven A.

    2016-01-01

    In nematodes, environmental or physiological perturbations alter death’s scaling of time. In human cancer, genetic perturbations alter death’s curvature of time. Those changes in scale and curvature follow the constraining contours of death’s invariant geometry. I show that the constraints arise from a fundamental extension to the theories of randomness, invariance and scale. A generalized Gompertz law follows. The constraints imposed by the invariant Gompertz geometry explain the tendency of perturbations to stretch or bend death’s scaling of time. Variability in death rate arises from a combination of constraining universal laws and particular biological processes.

  14. 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...... against challenge with a high dose of the invasive clone 13 strain of LCMV. In contrast, vaccination with adenovirus encoding unlinked LCMV glycoprotein induced weak virus control in the absence of CD4(+) T cells, and mice may die of increased immunopathology associated with incomplete protection. Acute...

  15. 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.

  16. Second order invariants and holography

    CERN Document Server

    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.

  17. Enhanced vaccine-induced CD8+ T cell responses to malaria antigen ME-TRAP by fusion to MHC class ii invariant chain.

    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.

  18. Invariant Solutions for Soil Water Equations

    OpenAIRE

    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.

  19. Parasite Manipulation of the Invariant Chain and the Peptide Editor H2-DM Affects Major Histocompatibility Complex Class II Antigen Presentation during Toxoplasma gondii Infection

    OpenAIRE

    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...

  20. Constructing Invariant Fairness Measures for Surfaces

    DEFF Research Database (Denmark)

    Gravesen, Jens; Ungstrup, Michael

    1998-01-01

    This paper presents a general method which from an invariant curve fairness measure constructs an invariant surface fairness measure. Besides the curve fairness measure one only needs a class of curves on the surface for which one wants to apply the curve measure. The surface measure at a point...... variation.The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family of curves. Such a family is generated by the flow of a vector field, orthogonal to the curves. The first, respectively the second order derivative along the curve...... of the size of this vector field is used as the fairness measure on the family.Six basic 3rd order invariants satisfying two quadratic equations are defined. They form a complete set in the sense that any invariant 3rd order function can be written as a function of the six basic invariants together...

  1. Rotational invariance and the Pauli exclusion principle

    OpenAIRE

    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...

  2. Generalized Donaldson-Thomas invariants

    CERN Document Server

    Joyce, Dominic

    2009-01-01

    This is a summary of the much longer paper arXiv:0810.5645 with Yinan Song. Let X be a Calabi-Yau 3-fold over C. The Donaldson-Thomas invariants of X are integers DT^a(t) which count stable sheaves with Chern character a on X, with respect to a Gieseker stability condition t. They are defined only for Chern characters a for which there are no strictly semistable sheaves on X. They have the good property that they are unchanged under deformations of X. Their behaviour under change of stability condition t was not understood until now. We discuss "generalized Donaldson-Thomas invariants" \\bar{DT}^a(t). These are rational numbers, defined for all Chern characters a, and are equal to DT^a(t) if there are no strictly semistable sheaves in class a. They are deformation-invariant, and have a known transformation law under change of stability condition. We conjecture they can be written in terms of integral "BPS invariants" \\hat{DT}^a(t) when the stability condition t is "generic". We extend the theory to abelian cat...

  3. Enhanced and sustained CD8+ T cell responses with an adenoviral vector-based hepatitis C virus vaccine encoding NS3 linked to the MHC class II chaperone protein invariant chain

    DEFF Research Database (Denmark)

    Mikkelsen, Marianne; Holst, Peter Johannes; Bukh, Jens;

    2011-01-01

    Potent and broad cellular immune responses against the nonstructural (NS) proteins of hepatitis C virus (HCV) are associated with spontaneous viral clearance. In this study, we have improved the immunogenicity of an adenovirus (Ad)-based HCV vaccine by fusing NS3 from HCV (Strain J4; Genotype 1b...... memory. Functionally, the AdIiNS3-vaccinated mice had a significantly increased cytotoxic capacity compared with the AdNS3 group. The AdIiNS3-induced CD8(+) T cells protected mice from infection with recombinant vaccinia virus expressing HCV NS3 of heterologous 1b strains, and studies in knockout mice......) to the MHC class II chaperone protein invariant chain (Ii). We found that, after a single vaccination of C57BL/6 or BALB/c mice with Ad-IiNS3, the HCV NS3-specific CD8(+) T cell responses were significantly enhanced, accelerated, and prolonged compared with the vaccine encoding NS3 alone. The AdIiNS3...

  4. Computational invariant theory

    CERN Document Server

    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 ...

  5. Geometry-Invariant Resonant Cavities

    CERN Document Server

    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.

  6. Local and gauge invariant observables in gravity

    CERN Document Server

    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...

  7. Second-Order Invariants and Holography

    Science.gov (United States)

    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.

  8. Scale-Invariant Random Spatial Networks

    CERN Document Server

    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.

  9. Measurement invariance versus selection invariance : Is fair selection possible?

    NARCIS (Netherlands)

    Borsboom, Denny; Romeijn, Jan-Willem; Wicherts, Jelte M.

    2008-01-01

    This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement instrume

  10. 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

  11. An almost-integral universal Vassiliev invariant of knots

    OpenAIRE

    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.

  12. Invariant sets for Windows

    CERN Document Server

    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

  13. Invariant see-saw models and sequential dominance

    CERN Document Server

    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...

  14. Structure of group invariants of a quasiperiodic flow

    Directory of Open Access Journals (Sweden)

    Lennard F. Bakker

    2004-03-01

    Full Text Available It is shown that the multiplier representation of the generalized symmetry group of a quasiperiodic flow induces a semidirect product structure on certain group invariants (including the generalized symmetry group of the flow's smooth conjugacy class.

  15. Leptogenesis, Yukawa Textures and Weak Basis Invariants

    CERN Document Server

    Branco, Gustavo Castello; Silva-Marcos, J I; Branco, Gustavo C.

    2006-01-01

    We show that a large class of sets of leptonic texture zeros considered in the literature imply the vanishing of certain CP-odd weak-basis invariants. These invariant conditions enable one to recognize a flavour model corresponding to a set of texture zeros, when written in an arbitrary weak-basis where the zeros are not manifest. We also analyse the r\\^ ole of texture zeros in allowing for a connection between leptogenesis and low-energy leptonic masses, mixing and CP violation. For some of the textures the variables relevant for leptogenesis can be fully determined in terms of low energy parameters and heavy neutrino masses.

  16. Center Determination Problem for a Class of Cubic System with a Pair of Invariant Conjugate Imaginary Straight Lines%具有一对共轭复不变直线的三次系统的中心判定问题

    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.

  17. 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.)

  18. Gauge-invariant massive BF models

    Science.gov (United States)

    Bizdadea, Constantin; Saliu, Solange-Odile

    2016-02-01

    Consistent interactions that can be added to a free, Abelian gauge theory comprising a BF model and a finite set of massless real scalar fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of analyticity in the coupling constant, Lorentz covariance, spacetime locality, and Poincaré invariance, supplemented with the requirement of the preservation of the number of derivatives on each field with respect to the free theory, we see that the deformation procedure leads to two classes of gauge-invariant interacting theories with a mass term for the BF vector field A_{μ } with U(1) gauge invariance. In order to derive this result we have not used the Higgs mechanism based on spontaneous symmetry breaking.

  19. Gauge-invariant massive BF models

    CERN Document Server

    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.

  20. 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....

  1. Permutationally invariant state reconstruction

    DEFF Research Database (Denmark)

    Moroder, Tobias; Hyllus, Philipp; Tóth, Géza;

    2012-01-01

    -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...

  2. Anisotropic Weyl invariance

    CERN Document Server

    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.

  3. 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.

  4. Dynamical invariance for random matrices

    CERN Document Server

    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.

  5. Gauge invariant flow equation

    CERN Document Server

    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.

  6. Modular invariant inflation

    CERN Document Server

    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...

  7. Invariant differential operators

    CERN Document Server

    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.

  8. Modular invariant inflation

    Science.gov (United States)

    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.

  9. An adaptive method for computing invariant manifolds in non-autonomous, three-dimensional dynamical systems

    OpenAIRE

    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...

  10. Continuous Integrated Invariant Inference Project

    Data.gov (United States)

    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...

  11. From dynamical scaling to local scale-invariance: a tutorial

    CERN Document Server

    Henkel, Malte

    2016-01-01

    Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced. Schr\\"odinger-invariance, the most simple example of local scale-invariance, will be introduced as a dynamical symmetry in the Edwards-Wilkinson universality class of interface growth. The Lie algebra construction, its representations and the Bargman superselection rules will be combined with non-equilibrium Janssen-de Dominicis field-theory to produce explicit predictions for responses and correlators, which can be compared to the results of explicit model studies. At the next level, the study of non-stationary states requires to go over, from Schr\\"odinger-invariance, to ageing-invariance. The ageing algebra admits new representations, which acts as dynamical symmetries on more general equations, and imply that each non-equilibrium scaling operator is characterised by two distinct, ind...

  12. Permutationally invariant state reconstruction

    CERN Document Server

    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...

  13. Equivariant K3 Invariants

    CERN Document Server

    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...

  14. Galilean-Invariant XEFT

    CERN Document Server

    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.

  15. Rotational invariance and the spin-statistics theorem

    OpenAIRE

    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...

  16. 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.

  17. On Vassiliev invariants of braid groups of the sphere

    CERN Document Server

    Kaabi, N

    2012-01-01

    We construct a universal Vassiliev invariant for braid groups of the sphere and the mapping class groups of the sphere with $n$ punctures. The case of a sphere is different from the classical braid groups or braids of oriented surfaces of genus strictly greater than zero, since Vassiliev invariants in a group without 2-torsion do not distinguish elements of braid group of a sphere.

  18. 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

  19. 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.

  20. 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.

  1. 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.)

  2. 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

  3. Thinning Invariant Partition Structures

    CERN Document Server

    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 $p \\in (0,1)$.

  4. 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

  5. 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

  6. Scale-invariant geometric random graphs

    CERN Document Server

    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.

  7. Invariant visual object recognition: biologically plausible approaches.

    Science.gov (United States)

    Robinson, Leigh; Rolls, Edmund T

    2015-10-01

    Key properties of inferior temporal cortex neurons are described, and then, the biological plausibility of two leading approaches to invariant visual object recognition in the ventral visual system is assessed to investigate whether they account for these properties. Experiment 1 shows that VisNet performs object classification with random exemplars comparably to HMAX, except that the final layer C neurons of HMAX have a very non-sparse representation (unlike that in the brain) that provides little information in the single-neuron responses about the object class. Experiment 2 shows that VisNet forms invariant representations when trained with different views of each object, whereas HMAX performs poorly when assessed with a biologically plausible pattern association network, as HMAX has no mechanism to learn view invariance. Experiment 3 shows that VisNet neurons do not respond to scrambled images of faces, and thus encode shape information. HMAX neurons responded with similarly high rates to the unscrambled and scrambled faces, indicating that low-level features including texture may be relevant to HMAX performance. Experiment 4 shows that VisNet can learn to recognize objects even when the view provided by the object changes catastrophically as it transforms, whereas HMAX has no learning mechanism in its S-C hierarchy that provides for view-invariant learning. This highlights some requirements for the neurobiological mechanisms of high-level vision, and how some different approaches perform, in order to help understand the fundamental underlying principles of invariant visual object recognition in the ventral visual stream.

  8. Invariant Set Theory

    CERN Document Server

    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 $I_U$...

  9. Polynomial invariants of quantum codes

    CERN Document Server

    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]).

  10. Tractors, Mass and Weyl Invariance

    CERN Document Server

    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...

  11. Factorization invariants in numerical monoids

    OpenAIRE

    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 ...

  12. Invariants and Likelihood Ratio Statistics

    OpenAIRE

    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...

  13. Tractors, mass, and Weyl invariance

    Science.gov (United States)

    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.

  14. Invariant and Absolute Invariant Means of Double Sequences

    Directory of Open Access Journals (Sweden)

    Abdullah Alotaibi

    2012-01-01

    Full Text Available We examine some properties of the invariant mean, define the concepts of strong σ-convergence and absolute σ-convergence for double sequences, and determine the associated sublinear functionals. We also define the absolute invariant mean through which the space of absolutely σ-convergent double sequences is characterized.

  15. Lorentz invariant intrinsic decoherence

    CERN Document Server

    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...

  16. Invariants of Lagrangian surfaces

    OpenAIRE

    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...

  17. Permutation Centralizer Algebras and Multi-Matrix Invariants

    CERN Document Server

    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...

  18. The Axion Mass in Modular Invariant Supergravity

    CERN Document Server

    Butter, D; Butter, Daniel; Gaillard, Mary K.

    2005-01-01

    When supersymmetry is broken by condensates with a single condensing gauge group, there is a nonanomalous R-symmetry that prevents the universal axion from acquiring a mass. It has been argued that, in the context of supergravity, higher dimension operators will break this symmetry and may generate an axion mass too large to allow the identification of the universal axion with the QCD axion. We show that such contributions to the axion mass are highly suppressed in a class of models where the effective Lagrangian for gaugino and matter condensation respects modular invariance (T-duality).

  19. 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...

  20. 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.

  1. Invariant Measures for Cherry Flows

    Science.gov (United States)

    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.

  2. 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...

  3. Three +1 Faces of Invariance

    CERN Document Server

    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.

  4. Gluing formulae for Donaldson invariants for connected sums along surfaces

    CERN Document Server

    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).

  5. Physical Invariants of Intelligence

    Science.gov (United States)

    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

  6. 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

  7. Assessment of Rotationally-Invariant Clustering Using Streamlet Tractography

    DEFF Research Database (Denmark)

    Liptrot, Matthew George; Lauze, Francois Bernard

    We present a novel visualisation-based strategy for the assessment of a recently proposed clustering technique for raw DWI volumes which derives rotationally-invariant metrics to classify voxels. The validity of the division of all brain tissue voxels into such classes was assessed using...

  8. Gauge-invariant coherent states in loop quantum gravity

    Energy Technology Data Exchange (ETDEWEB)

    Bahr, B. [Albert-Einstein Inst., Golm/Potsdam (Germany)

    2007-07-01

    I will demostrate results about the projection of the complexified coherent states in Loop Quantum Gravity to the gauge-invariant sector. In particular, I will demonstrate peakedness and semiclassical properties of a selected class of states and different gauge groups. These states can then be used as a starting point for dynamical semiclassical analysis of Loop Quantum Gravity. (orig.)

  9. Relations between 1D shape invariant potentials and the commutation relations of the Lie algebra sl(2,c)

    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)

  10. Relations between 1D shape invariant potentials and the commutation relations of the Lie algebra /sl(2,c)

    Science.gov (United States)

    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).

  11. Notes on Group Invariants and Positivity of Density Matrices and Superoperators

    CERN Document Server

    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.

  12. Invariant manifolds and global bifurcations.

    Science.gov (United States)

    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.

  13. Invariants of Toric Seiberg Duality

    CERN Document Server

    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.

  14. On density of the Vassiliev invariants

    DEFF Research Database (Denmark)

    Røgen, Peter

    1999-01-01

    The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots......The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots...

  15. 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.

  16. On Invariant Notions of Segre Varieties in Binary Projective Spaces

    CERN Document Server

    Havlicek, Hans; Saniga, Metod

    2010-01-01

    Invariant notions of a class of Segre varieties $\\Segrem(2)$ of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains $\\Segrem(2)$ and is invariant under its projective stabiliser group $\\Stab{m}{2}$. By embedding PG(2^m - 1, 2) into \\PG(2^m - 1, 4), a basis of the latter space is constructed that is invariant under $\\Stab{m}{2}$ as well. Such a basis can be split into two subsets of an odd and even parity whose spans are either real or complex-conjugate subspaces according as $m$ is even or odd. In the latter case, these spans can, in addition, be viewed as indicator sets of a $\\Stab{m}{2}$-invariant geometric spread of lines of PG(2^m - 1, 2). This spread is also related with a $\\Stab{m}{2}$-invariant non-singular Hermitian variety. The case $m=3$ is examined in detail to illustrate the theory. Here, the lines of the invariant spread are found to fall into four ...

  17. 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.

  18. On Invariant Measures for the Vlasov Equation with a Regular Potential

    CERN Document Server

    Zhidkov, P E

    2003-01-01

    We consider a Vlasov equation with a smooth bounded potential of interaction between particles in a class of measure-valued solutions and construct a measure which is invariant for this problem in a sense.

  19. New higher-derivative invariants in N=2 supergravity and the Gauss-Bonnet term

    CERN Document Server

    Butter, Daniel; Kuzenko, Sergei M; Lodato, Ivano

    2013-01-01

    A new class of N=2 locally supersymmetric higher-derivative invariants is constructed based on logarithms of conformal primary chiral superfields. They characteristically involve a coupling to R_{\\mu\

  20. Invariant measures for Cherry flows

    CERN Document Server

    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.

  1. 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.

  2. Local Scale Invariance and Inflation

    CERN Document Server

    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.

  3. Invariant foliations for parabolic equations

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    It is proved for parabolic equations that under certain conditions the weak (un-)stable manifolds possess invariant foliations, called strongly (un-)stable foliations. The relevant results on center manifolds are generalized to weak hyperbolic manifolds.

  4. Invariant foliations for parabolic equations

    Institute of Scientific and Technical Information of China (English)

    张伟年

    2000-01-01

    It is proved for parabolle eguations that under certain conditions the weak (un-) stable manifolds possess invariant foliations, called strongly (un-)stable foliations. The relevant results on center manifolds are generalized to weak hyperbolic manifolds.

  5. Classification of simple current invariants

    CERN Document Server

    Gato-Rivera, Beatriz

    1992-01-01

    We summarize recent work on the classification of modular invariant partition functions that can be obtained with simple currents in theories with a center (Z_p)^k with p prime. New empirical results for other centers are also presented. Our observation that the total number of invariants is monodromy-independent for (Z_p)^k appears to be true in general as well. (Talk presented in the parallel session on string theory of the Lepton-Photon/EPS Conference, Geneva, 1991.)

  6. Classification of Simple Current Invariants

    CERN Document Server

    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.)

  7. Invariant Manifolds and Collective Coordinates

    CERN Document Server

    Papenbrock, T

    2001-01-01

    We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction.

  8. Operator equations and invariant subspaces

    Directory of Open Access Journals (Sweden)

    Valentin Matache

    1994-05-01

    Full Text Available Banach space operators acting on some fixed space X are considered. If two such operators A and B verify the condition A2=B2 and if A has nontrivial hyperinvariant subspaces, then B has nontrivial invariant subspaces. If A and B commute and satisfy a special type of functional equation, and if A is not a scalar multiple of the identity, the author proves that if A has nontrivial invariant subspaces, then so does B.

  9. Hidden scale invariance of metals

    Science.gov (United States)

    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.

  10. Invariant sets for discontinuous parabolic area-preserving torus maps

    CERN Document Server

    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.

  11. On Quasiperiodic Space Tilings, Inflation and Dehn Invariants

    OpenAIRE

    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...

  12. Invariant sets and solutions to the generalized thin film equation

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The invariant sets and the solutions of the 1+2-dimensional generalized thin film equation are discussed. It is shown that there exists a class of solutions to the equations, which are invariant with respect to the set E0 = {u : ux = vxF(u), uy = vyF(u)}, where v is a smooth function of variables x, y and F is a smooth function of u. This extends the results of Galaktionov (2001) and for the l+l-dimensional nonlinear evolution equations.

  13. Gauge Invariants and Correlators in Flavoured Quiver Gauge Theories

    CERN Document Server

    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.

  14. 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).

  15. Renormalization group invariants in supersymmetric theories: one- and two-loop results

    CERN Document Server

    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.

  16. Rotation invariant moments and transforms for geometrically invariant image watermarking

    Science.gov (United States)

    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.

  17. Topological invariants of edge states for periodic two-dimensional models

    CERN Document Server

    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.

  18. 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.

  19. Generalized Donaldson-Thomas Invariants of 2-Dimensional sheaves on local P^2

    CERN Document Server

    Gholampour, Amin

    2013-01-01

    Let X be the total space of the canonical bundle of P^2. We study the generalized Donaldson-Thomas invariants, defined in the work of Joyce-Song, of the moduli spaces of the 2-dimensional Gieseker semistable sheaves on X with first Chern class equal to k times the class of the zero section of X. When k=1, 2 or 3, and semistability implies stability, we express the invariants in terms of known modular forms. We prove a combinatorial formula for the invariants when k=2 in the presence of the strictly semistable sheaves, and verify the BPS integrality conjecture of Joyce-Song in some cases.

  20. On the motivic Donaldson-Thomas invariants of quivers with potentials

    CERN Document Server

    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.

  1. Generalized Donaldson-Thomas Invariants of 2-Dimensional sheaves on local P^2

    DEFF Research Database (Denmark)

    Gholampour, Amin; Sheshmani, Artan

    2013-01-01

    Let X be the total space of the canonical bundle of P^2. We study the generalized Donaldson-Thomas invariants, defined in the work of Joyce-Song, of the moduli spaces of the 2-dimensional Gieseker semistable sheaves on X with first Chern class equal to k times the class of the zero section of X....... When k=1, 2 or 3, and semistability implies stability, we express the invariants in terms of known modular forms. We prove a combinatorial formula for the invariants when k=2 in the presence of the strictly semistable sheaves, and verify the BPS integrality conjecture of Joyce-Song in some cases....

  2. Weyl invariance with a nontrivial mass scale

    CERN Document Server

    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.

  3. Weyl invariance with a nontrivial mass scale

    Science.gov (United States)

    Álvarez, Enrique; González-Martín, Sergio

    2016-09-01

    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.

  4. On higher rank Donaldson-Thomas invariants

    CERN Document Server

    Nagao, Kentaro

    2010-01-01

    We study higher rank Donaldson-Thomas invariants of a Calabi-Yau 3-fold using Joyce-Song's wall-crossing formula. We construct quivers whose counting invariants coincide with the Donaldson-Thomas invariants. As a corollary, we prove the integrality and a certain symmetry for the higher rank invariants.

  5. Evolving Planck Mass in Classically Scale-Invariant Theories

    CERN Document Server

    Kannike, K; Spethmann, C; Veermäe, H

    2016-01-01

    We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg po- tential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories....

  6. Lectures on Gromov invariants for symplectic 4-manifolds

    CERN Document Server

    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.

  7. Early Universe Cosmology, Effective Supergravity, and Invariants of Algebraic Forms

    CERN Document Server

    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...

  8. Topological invariants in Fermi systems with time-reversal invariance

    Science.gov (United States)

    Avron, J. E.; Sadun, L.; Segert, J.; Simon, B.

    1988-09-01

    We discuss topological invariants for Fermi systems that have time-reversal invariance. The TKN2 integers (first Chern numbers) are replaced by second Chern numbers, and Berry's phase becomes a unit quaternion, or equivalently an element of SU(2). The canonical example playing much the same role as spin (1/2 in a magnetic field is spin (3/2 in a quadrupole electric field. In particular, the associated bundles are nontrivial and have +/-1 second Chern number. The connection that governs the adiabatic evolution coincides with the symmetric SU(2) Yang-Mills instanton.

  9. Natural Inflation with Hidden Scale Invariance

    CERN Document Server

    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.

  10. 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.

  11. Invariant probabilities of transition functions

    CERN Document Server

    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...

  12. 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.

  13. Invariant manifolds and collective coordinates

    Energy Technology Data Exchange (ETDEWEB)

    Papenbrock, T. [Centro Internacional de Ciencias, Cuernavaca, Morelos (Mexico); Institute for Nuclear Theory, University of Washington, Seattle, WA (United States); Seligman, T.H. [Centro Internacional de Ciencias, Cuernavaca, Morelos (Mexico); Centro de Ciencias Fisicas, University of Mexico (UNAM), Cuernavaca (Mexico)

    2001-09-14

    We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction. (author)

  14. Leptogenesis and a Jarlskog Invariant

    CERN Document Server

    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.

  15. Weights on cohomology and invariants of singularities

    CERN Document Server

    Arapura, Donu; Włodarczyk, Jarosław

    2011-01-01

    In this paper, we extract natural invariants of a singularity by using the Deligne weight filtration on the cohomology of an exceptional fibre of a resolution, and also on the intersection cohomology of the link. Our primary goal is to study and give natural bounds on the weights in terms of direct images of differential forms. These bounds can be made explicit for various standard classes such as rational, isolated normal Cohen-Macaulay and toroidal singularities, and lead to strong restrictions on the topology of these singularities. A secondary goal of this paper is to make the weight filtration, and related constructions, more widely accessible. So we have tried to make the presentation somewhat self contained. This is supersedes our earlier preprint arXiv:0902.4234.

  16. Kahler stabilized, modular invariant heterotic string models

    Energy Technology Data Exchange (ETDEWEB)

    Gaillard, Mary K.; Gaillard, Mary K.; Nelson, Brent D.

    2007-03-19

    We review the theory and phenomenology of effective supergravity theories based on orbifold compactifications of the weakly-coupled heterotic string. In particular, we consider theories in which the four-dimensional theory displays target space modular invariance and where the dilatonic mode undergoes Kahler stabilization. A self-contained exposition of effective Lagrangian approaches to gaugino condensation and heterotic string theory is presented, leading to the development of the models of Binétruy, Gaillard and Wu. Various aspects of the phenomenology of this class of models are considered. These include issues of supersymmetry breaking and superpartner spectra, the role of anomalous U(1) factors, issues of flavor and R-parity conservation, collider signatures, axion physics, and early universe cosmology. For the vast majority of phenomenological considerations the theories reviewed here compare quite favorably to other string-derived models in the literature. Theoretical objections to the framework and directions for further research are identified and discussed.

  17. 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)

  18. 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.)

  19. Exact invariants in the form of momentum resonances for particle motion in one-dimensional, time-dependent potentials

    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

  20. Permutations and the combinatorics of gauge invariants for general N

    CERN Document Server

    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.

  1. Duality and scale invariant magnetic fields from bouncing universes

    CERN Document Server

    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.

  2. 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.

  3. Group Invariance in Mathematical Morphology

    NARCIS (Netherlands)

    Roerdink, J.B.T.M.

    1995-01-01

    In this paper we discuss how invariance of operators arising in binary mathematical morphology can be achieved for the collection of groups commonly denoted as `the computer vision groups'. We present an overview, starting with set mappings such as dilations, erosions, openings and closings, which a

  4. Some Tests on CPT Invariance

    OpenAIRE

    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.

  5. Hidden scale invariance of metals

    DEFF Research Database (Denmark)

    Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.;

    2015-01-01

    Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general “hidden” scale invariance of m...

  6. 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

  7. Conjectured enumeration of Vassiliev invariants

    CERN Document Server

    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.

  8. Donaldson invariants for connected sums along surfaces of genus 2

    CERN Document Server

    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.

  9. LIMIT CYCLES AND INVARIANT PARABOLA IN A KUKLES SYSTEM OF DEGREE THREE

    Institute of Scientific and Technical Information of China (English)

    Liu Zhenhai; E. Sáez L Szántó

    2008-01-01

    In this article, the authors consider a class of Kukles planar polynomial differ-ential system of degree three having an invariant parabola. For this class of second-order differential systems, it is shown that for certain values of the parameters the invariant parabola coexists with a center. For other values it can coexist with one, two or three small amplitude limit cycles which are constructed by Hopf bifurcation. This result gives an answer for the question given in [4], about the existence of limit cycles for such class of system.

  10. 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)

  11. 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.)

  12. Complete classification of simple current modular invariants for RCFT's with a center (Z p ) k

    Science.gov (United States)

    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.

  13. Gauge-invariant coherent states for loop quantum gravity: II. Non-Abelian gauge groups

    Energy Technology Data Exchange (ETDEWEB)

    Bahr, Benjamin; Thiemann, Thomas, E-mail: bbahr@aei.mpg.d, E-mail: thomas.thiemann@aei.mpg.d [MPI fuer Gravitationsphysik, Albert-Einstein Institut, Am Muehlenberg 1, 14467 Golm (Germany)

    2009-02-21

    This is the second paper concerning gauge-invariant coherent states for loop quantum gravity. Here, we deal with the gauge group SU(2), this being a significant complication compared to the Abelian U(1) case encountered in the previous article (Class. Quantum Grav. 26 045011). We study gauge-invariant coherent states on certain special graphs by analytical and numerical methods. We find that their overlap is Gauss peaked in gauge-invariant quantities, as long as states are not labeled by degenerate gauge orbits, i.e. points where the gauge-invariant configuration space has singularities. In these cases the overlaps are still concentrated around these points, but the peak profile exhibits a plateau structure. This shows how the semiclassical properties of the states are influenced by the geometry of the gauge-invariant phase space.

  14. Energy balance invariance for interacting particle systems

    OpenAIRE

    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...

  15. Gauge-invariant extensions of the Proca model in a noncommutative space-time

    CERN Document Server

    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.

  16. Invariant manifolds for flows in Banach Spaces

    Energy Technology Data Exchange (ETDEWEB)

    Lu Kening.

    1989-01-01

    The author considers the existence, smoothness and exponential attractivity of global invariant manifolds for flow in Banach Spaces. He shows that every global invariant manifold can be expressed as a graph of a C{sup k} map, provided that the invariant manifolds are exponentially attractive. Applications go to the Reaction-Diffusion equation, the Kuramoto-Sivashinsky equation, and singular perturbed wave equation.

  17. Finite type invariants and fatgraphs

    DEFF Research Database (Denmark)

    Andersen, Jørgen Ellegaard; Bene, Alex; Meilhan, Jean-Baptiste Odet Thierry;

    2010-01-01

    –Murakami–Ohtsuki of the link invariant of Andersen–Mattes–Reshetikhin computed relative to choices determined by the fatgraph G; this provides a basic connection between 2d geometry and 3d quantum topology. For each fixed G, this invariant is shown to be universal for homology cylinders, i.e., G establishes an isomorphism...... from an appropriate vector space of homology cylinders to a certain algebra of Jacobi diagrams. Via composition for any pair of fatgraph spines G,G′ of Σ, we derive a representation of the Ptolemy groupoid, i.e., the combinatorial model for the fundamental path groupoid of Teichmüller space, as a group...... of automorphisms of this algebra. The space comes equipped with a geometrically natural product induced by stacking cylinders on top of one another and furthermore supports related operations which arise by gluing a homology handlebody to one end of a cylinder or to another homology handlebody. We compute how G...

  18. 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.

  19. Invariance for Single Curved Manifold

    KAUST Repository

    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.

  20. Neutrinos and electromagnetic gauge invariance

    Energy Technology Data Exchange (ETDEWEB)

    Pisano, F.; Silva-Sobrinho, J.A. [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Tonasse, M.D. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica

    1996-02-01

    It is discussed a recently proposed connection among electromagnetic gauge invariance U(1){sub em} and the nature of the neutrino mass terms in the framework of SU(3){sub C} x G{sub W} x U(1){sub N}, G{sub W} SU(3){sub L}, extensions of the Standard Model. The impossibility of that connection, also in the case G{sub W} = SU(4){sub L}, is demonstrated. (author). 7 refs.

  1. A reparametrization invariant surface ordering

    OpenAIRE

    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.

  2. Gauge Invariance in Classical Electrodynamics

    CERN Document Server

    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.

  3. Elementary examples of adiabatic invariance

    Energy Technology Data Exchange (ETDEWEB)

    Crawford, F.S. (Physics Department, University of California, Berkeley, CA (USA) Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720 (USA))

    1990-04-01

    Simple classical one-dimensional systems subject to adiabatic (gradual) perturbations are examined. The first examples are well known: the adiabatic invariance of the product {ital E}{tau} of energy {ital E} and period {tau} for the simple pendulum and for the simple harmonic oscillator. Next, the adiabatic invariants of the vertical bouncer are found---a ball bouncing elastically from the floor of a rising elevator having slowly varying velocity and acceleration. These examples lead to consideration of adiabatic invariance for one-dimensional systems with potentials of the form {ital V}={ital ax}{sup {ital n}}, with {ital a}={ital a}({ital t}) slowly varying in time. Then, the horizontal bouncer is considered---a mass sliding on a smooth floor, bouncing back and forth between two impenetrable walls, one of which is slowly moving. This example is generalized to a particle in a bound state of a general potential with one slowly moving turning point.'' Finally, circular motion of a charged particle in a magnetic field slowly varying in time under three different configurations is considered: (a) a free particle in a uniform field; (b) a free particle in a nonuniform betatron'' field; and (c) a particle constrained to a circular orbit in a uniform field.

  4. A Note on Unification of Translational Shape Invariant Potential and Scaling Shape Invariant Potential

    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.

  5. On the Iwasawa invariants of a link in the 3-sphere

    CERN Document Server

    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.

  6. Time Invariant Surface Roughness Evolution during Atmospheric Pressure Thin Film Depositions

    OpenAIRE

    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...

  7. Mutually Quadratically Invariant Information Structures in Two-Team Stochastic Dynamic Games

    OpenAIRE

    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...

  8. Tests of Non-Equivalence among Absolutely Nonsingular Tensors through Geometric Invariants

    OpenAIRE

    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 ...

  9. Screen Conformal Invariant Light-like Hypersurfaces of Indefinite Sasakian Space Forms

    OpenAIRE

    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...

  10. Volume conjecture for $SU(n)$-invariants

    CERN Document Server

    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.

  11. An Invariant of Topologically Ordered States Under Local Unitary Transformations

    Science.gov (United States)

    Haah, Jeongwan

    2016-03-01

    For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can compute the S-matrix from a single ground state wave function. Here, we define a class of Hamiltonians consisting of local commuting projectors and an associated matrix that is invariant under local unitary transformations. We argue that the invariant is equivalent to the topological S-matrix. The definition does not require degeneracy of the ground state. We prove that the invariant depends on the state only, in the sense that it can be computed by any Hamiltonian in the class of which the state is a ground state. As a corollary, we prove that any local quantum circuit that connects two ground states of quantum double models (discrete gauge theories) with non-isomorphic abelian groups must have depth that is at least linear in the system's diameter. As a tool for the proof, a manifestly Hamiltonian-independent notion of locally invisible operators is introduced. This gives a sufficient condition for a many-body state not to be generated from a product state by any small depth quantum circuit; this is a many-body entanglement witness.

  12. Quantum Weyl invariance and cosmology

    Directory of Open Access Journals (Sweden)

    Atish Dabholkar

    2016-09-01

    Full Text Available Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly decaying vacuum energy. A natural generalization to four dimensions implies a quantum modification of Einstein field equations at long distances. It offers a new perspective on time-dependence of couplings and naturalness with potentially far-reaching consequences for the cosmological constant problem, inflation, and dark energy.

  13. Quantum Weyl invariance and cosmology

    Science.gov (United States)

    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.

  14. 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

  15. 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....... Input silhouettes are matched to the database using the Hungarian method. A classifier is defined based on the dissimilarity between the input silhouettes and the gait actions of the database. The overall recognition rate is 88.2% on a large and diverse test set. The recognition rate is better than...

  16. Invariant patterns in crystal lattices: Implications for protein folding algorithms

    Energy Technology Data Exchange (ETDEWEB)

    HART,WILLIAM E.; ISTRAIL,SORIN

    2000-06-01

    Crystal lattices are infinite periodic graphs that occur naturally in a variety of geometries and which are of fundamental importance in polymer science. Discrete models of protein folding use crystal lattices to define the space of protein conformations. Because various crystal lattices provide discretizations of the same physical phenomenon, it is reasonable to expect that there will exist invariants across lattices related to fundamental properties of the protein folding process. This paper considers whether performance-guaranteed approximability is such an invariant for HP lattice models. The authors define a master approximation algorithm that has provable performance guarantees provided that a specific sublattice exists within a given lattice. They describe a broad class of crystal lattices that are approximable, which further suggests that approximability is a general property of HP lattice models.

  17. 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.

  18. Yang-Baxter invariance of the Nappi-Witten model

    CERN Document Server

    Kyono, Hideki

    2015-01-01

    We study Yang-Baxter deformations of the Nappi-Witten model by adopting a prescription invented by Delduc-Magro-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 adopting the most general classical $r$-matrix. Then the Yang-Baxter invariance of the background follows from the requirement that the one-loop $\\beta$-function should vanish. As a result, it is shown that the Nappi-Witten model is the unique conformal theory in the present class of Yang-Baxter deformations.

  19. Gauge coupling unification in a classically scale invariant model

    Science.gov (United States)

    Haba, Naoyuki; Ishida, Hiroyuki; Takahashi, Ryo; Yamaguchi, Yuya

    2016-02-01

    There are a lot of works within a class of classically scale invariant model, which is motivated by solving the gauge hierarchy problem. In this context, the Higgs mass vanishes at the UV scale due to the classically scale invariance, and is generated via the Coleman-Weinberg mechanism. Since the mass generation should occur not so far from the electroweak scale, we extend the standard model only around the TeV scale. We construct a model which can achieve the gauge coupling unification at the UV scale. In the same way, the model can realize the vacuum stability, smallness of active neutrino masses, baryon asymmetry of the universe, and dark matter relic abundance. The model predicts the existence vector-like fermions charged under SU(3) C with masses lower than 1 TeV, and the SM singlet Majorana dark matter with mass lower than 2.6 TeV.

  20. Invariant currents in lossy acoustic waveguides with complete local symmetry

    CERN Document Server

    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.

  1. Scale-invariance as the origin of dark radiation?

    Directory of Open Access Journals (Sweden)

    Dmitry Gorbunov

    2014-12-01

    Full Text Available Recent cosmological data favor R2-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.

  2. Projectively related metrics, Weyl nullity, and metric projectively invariant equations

    CERN Document Server

    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 ...

  3. 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.

  4. Gauge coupling unification in a classically scale invariant model

    CERN Document Server

    Haba, Naoyuki; Takahashi, Ryo; Yamaguchi, Yuya

    2015-01-01

    There are a lot of works within a class of classically scale invariant model, which is motivated by solving the gauge hierarchy problem. In this context, the Higgs mass vanishes at the UV scale due to the classically scale invariance, and is generated via the Coleman-Weinberg mechanism. Since the mass generation should occur not so far from the electroweak scale, we extend the standard model only around the TeV scale. We construct a model which can achieve the gauge coupling unification at the UV scale. In the same way, the model can realize the vacuum stability, smallness of active neutrino masses, baryon asymmetry of the universe, and dark matter relic abundance. The model predicts the existence vector-like fermions charged under $SU(3)_C$ with masses lower than $1\\,{\\rm TeV}$, and the SM singlet Majorana dark matter with mass lower than $2.6\\,{\\rm TeV}$.

  5. The relativistic invariant Lie algebra for the kinematical observables in quantum space-time

    CERN Document Server

    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.

  6. Exceptional Lie Algebra $E_{7(-25)}$ (Multiplets and Invariant Differential Operators)

    CERN Document Server

    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.

  7. Fundamental Solution via Invariant Approach for a Brain Tumor Model and its Extensions

    Science.gov (United States)

    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.

  8. Dualities and geometrical invariants for static and spherically symmetric spacetimes

    Science.gov (United States)

    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.

  9. 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.

  10. Wall-Crossing Invariants from Spectral Networks

    CERN Document Server

    Longhi, Pietro

    2016-01-01

    A new construction of BPS monodromies for 4d ${\\mathcal N}=2$ theories of class S is introduced. A novel feature of this construction is its manifest invariance under Kontsevich-Soibelman wall crossing, in the sense that no information on the 4d BPS spectrum is employed. The BPS monodromy is encoded by topological data of a finite graph, embedded into the UV curve $C$ of the theory. The graph arises from a degenerate limit of spectral networks, constructed at maximal intersections of walls of marginal stability in the Coulomb branch of the gauge theory. The topology of the graph, together with a notion of framing, encode equations that determine the monodromy. We develop an algorithmic technique for solving the equations, and compute the monodromy in several examples. The graph manifestly encodes the symmetries of the monodromy, providing some support for conjectural relations to specializations of the superconformal index. For $A_1$-type theories, the graphs encoding the monodromy are "dessins d'enfants" on ...

  11. Equivalent topological invariants of topological insulators

    OpenAIRE

    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...

  12. Knot invariants and higher representation theory

    OpenAIRE

    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...

  13. Light Speed Invariance is a Remarkable Illusion

    OpenAIRE

    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...

  14. On factorization invariants and Hilbert functions

    OpenAIRE

    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...

  15. Wilson loop invariants from WN conformal blocks

    Science.gov (United States)

    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.

  16. 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.

  17. 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.

  18. 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.

  19. Invariants of pure 2-dimensional sheaves inside threefolds and modular forms

    CERN Document Server

    Gholampour, Amin

    2013-01-01

    Motivated by S-duality modularity conjectures in string theory, we study the Donaldson-Thomas type invariants of pure 2-dimensional sheaves inside a nonsingular threefold X in three different situations: (1). X is a K3 fibration over a curve. We study the Donaldson-Thomas invariants of the 2 dimensional Gieseker stable sheaves in X supported on the fibers. Analogous to the Gromov-Witten theory formula established in the work of M.P., we express these invariants in terms of the Euler characteristic of the Hilbert scheme of points on the K3 surface and the Noether-Lefschetz numbers of the fibration, and prove that the invariants have modular properties. (2). X is the total space of the canonical bundle of P^2. We study the generalized Donaldson-Thomas invariants defined by J.S. of the moduli spaces of the 2-dimensional Gieseker semistable sheaves on X with first Chern class equal to k times the class of the zero section of X. When k=1,2 or 3, and semistability implies stability, we express the invariants in ter...

  20. Refined BPS invariants, Chern-Simons theory, and the quantum dilogarithm

    Science.gov (United States)

    Dimofte, Tudor Dan

    In this thesis, we consider two main subjects: the refined BPS invariants of Calabi-Yau threefolds, and three-dimensional Chern-Simons theory with complex gauge group. We study the wall-crossing behavior of refined BPS invariants using a variety of techniques, including a four-dimensional supergravity analysis, statistical-mechanical melting crystal models, and relations to new mathematical invariants. We conjecture an equivalence between refined invariants and the motivic Donaldson-Thomas invariants of Kontsevich and Soibelman. We then consider perturbative Chern-Simons theory with complex gauge group, combining traditional and novel approaches to the theory (including a new state integral model) to obtain exact results for perturbative partition functions. We thus obtain a new class of topological invariants, which are not of finite type, defined in the background of genuinely nonabelian flat connections. The two main topics, BPS invariants and Chern-Simons theory, are connected at both a formal and (we believe) deeper conceptual level by the striking central role that the quantum dilogarithm function plays in each.

  1. Emergent diffeomorphism invariance in a discrete loop quantum gravity model

    Energy Technology Data Exchange (ETDEWEB)

    Gambini, Rodolfo [Instituto de Fisica, Facultad de Ciencias, Igua 4225, esq. Mataojo, Montevideo (Uruguay); Pullin, Jorge [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001 (United States)

    2009-02-07

    Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first-class algebra of constraints of the continuum theory becomes second class upon discretization. If one treats the second-class constraints properly, the resulting theories have very different dynamics and number of degrees of freedom than those of the continuum theory. It is therefore questionable how these theories could be considered a starting point for the quantization and the definition of a continuum theory through a continuum limit. We show explicitly in a model that the uniform discretizations approach to the quantization of constrained systems overcomes these difficulties. We consider here a simple diffeomorphism invariant one-dimensional model and complete the quantization using uniform discretizations. The model can be viewed as a spherically symmetric reduction of the well-known Husain-Kuchar model of diffeomorphism invariant theory. We show that the correct quantum continuum limit can be satisfactorily constructed for this model. This opens the possibility of treating (1 + 1)-dimensional dynamical situations of great interest in quantum gravity taking into account the full dynamics of the theory and preserving the spacetime covariance at a quantum level.

  2. Inflation and classical scale invariance

    CERN Document Server

    Racioppi, Antonio

    2014-01-01

    BICEP2 measurement of primordial tensor modes in CMB suggests that cosmological inflation is due to a slowly rolling inflaton taking trans-Planckian values and provides further experimental evidence for the absence of large $M_{\\rm P}$ induced operators. We show that classical scale invariance solves the problem and allows for a remarkably simple scale-free inflaton model without any gauge group. Due to trans-Planckian inflaton values and VEVs, a dynamically induced Coleman-Weinberg-type inflaton potential of the model can predict tensor-to-scalar ratio $r$ in a large range. Precise determination of $r$ in future experiments will allow to test the proposed field-theoretic framework.

  3. Gromov-Witten invariants of $\\bp^1$ and Eynard-Orantin invariants

    CERN Document Server

    Norbury, Paul

    2011-01-01

    We prove that stationary Gromov-Witten invariants of $\\bp^1$ arise as the Eynard-Orantin invariants of the spectral curve $x=z+1/z$, $y=\\ln{z}$. As an application we show that tautological intersection numbers on the moduli space of curves arise in the asymptotics of large degree Gromov-Witten invariants of $\\bp^1$.

  4. FAST PARALLELIZABLE METHODS FOR COMPUTING INVARIANT SUBSPACES OF HERMITIAN MATRICES

    Institute of Scientific and Technical Information of China (English)

    Zhenyue Zhang; Hongyuan Zha; Wenlong Ying

    2007-01-01

    We propose a quadratically convergent algorithm for computing the invariant subspaces of an Hermitian matrix.Each iteration of the algorithm consists of one matrix-matrix multiplication and one QR decomposition.We present an accurate convergence analysis of the algorithm without using the big O notation.We also propose a general framework based on implicit rational transformations which allows us to make connections with several existing algorithms and to derive classes of extensions to our basic algorithm with faster convergence rates.Several numerical examples are given which compare some aspects of the existing algorithms and the new Mgorithms.

  5. Polynomial Invariant Theory of the Classical Groups

    CERN Document Server

    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 ...

  6. INVARIANT RANDOM APPROXIMATION IN NONCONVEX DOMAIN

    Directory of Open Access Journals (Sweden)

    R. Shrivastava

    2012-05-01

    Full Text Available Random fixed point results in the setup of compact and weakly compact domain of Banach spaces which is not necessary starshaped have been obtained in the present work. Invariant random approximation results have also been determined asits application. In this way, random version of invariant approximation results due toMukherjee and Som [13] and Singh [17] have been given.

  7. 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.

  8. Synthesizing Chaotic Maps with Prescribed Invariant Densities

    OpenAIRE

    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.

  9. Invariants and submanifolds in almost complex geometry

    OpenAIRE

    Kruglikov, Boris

    2007-01-01

    In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of higher-dimensional pseudoholomorphic submanifolds.

  10. Uniqueness in ergodic decomposition of invariant probabilities

    OpenAIRE

    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.

  11. 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.

  12. Borromean surgery formula for the Casson invariant

    DEFF Research Database (Denmark)

    Meilhan, Jean-Baptiste Odet Thierry

    2008-01-01

    It is known that every oriented integral homology 3-sphere can be obtained from S3 by a finite sequence of Borromean surgeries. We give an explicit formula for the variation of the Casson invariant under such a surgery move. The formula involves simple classical invariants, namely the framing, li...

  13. 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.

  14. Weyl-Conformally Invariant p-Brane Theories

    CERN Document Server

    Guendelman, E; Nissimov, E; Pacheva, S; Guendelman, Eduardo; Kaganovich, Alexander; Nissimov, Emil; Pacheva, Svetlana

    2005-01-01

    We discuss in some detail the properties of a novel class of Weyl-conformally invariant p-brane theories which describe intrinsically light-like branes for any odd world-volume dimension and whose dynamics significantly differs from that of the ordinary (conformally non-invariant) Nambu-Goto p-branes. We present explicit solutions of the WILL-brane (Weyl-Invariant Light-Like brane) equations of motion in various gravitational backgrounds of physical relevance exhibiting the following new phenomena: (i) In spherically symmetric static backgrounds the WILL-brane automatically positions itself on (materializes) the event horizon of the corresponding black hole solutions, thus providing an explicit dynamical realization of the membrane paradigm in black hole physics; (ii) In product spaces (of interest in Kaluza-Klein context) the WILL-brane wrappes non-trivially around the compact (internal) dimensions and moves as a whole with the speed of light in the non-compact (space-time) dimensions.

  15. On the geometry of four-qubit invariants

    Energy Technology Data Exchange (ETDEWEB)

    Levay, Peter [Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1521 Budapest (Hungary)

    2006-07-28

    The geometry of four-qubit entanglement is investigated. We replace some of the polynomial invariants for four qubits introduced recently by new ones of direct geometrical meaning. It is shown that these invariants describe four points, six lines and four planes in complex projective space CP{sup 3}. For the generic entanglement class of stochastic local operations and classical communication they take a very simple form related to the elementary symmetric polynomials in four complex variables. Moreover, suitable powers of their magnitudes are entanglement monotones that fit nicely into the geometric set of n-qubit ones related to Grassmannians of l-planes found recently. We also show that in terms of these invariants the hyperdeterminant of order 24 in the four-qubit amplitudes takes a more instructive form than the previously published expressions available in the literature. Finally, in order to understand two-, three- and four-qubit entanglement in geometric terms we propose a unified setting based on CP{sup 3} furnished with a fixed quadric.

  16. On a Class Almost Contact Manifolds with Norden Metric

    CERN Document Server

    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.

  17. Identity for the Exponential-Type Molecule Potentials and the Supersymmetry Shape Invariance

    Institute of Scientific and Technical Information of China (English)

    JIA Chun-Sheng; ZHANG Ying; ZENG Xiang-Lin; SUN Liang-Tian

    2001-01-01

    The identity and the supersymmetry shape invariance for a class of exponential-type molecule potentials are studied by introducing a deformed five-parameter exponential-type potential (DFPEP) and via the multi-parameter deformations. It has been shown that the DFPEP is a shape-invariant potential with a translation of parameters. By making use of the shape invariance approach, the exact energy levels are determined for the bound states with zero angular momentum. A class of molecule potentials and their exact energy spectra for the zero angular momentum states are reduced from the DFPEP and a general energy spectrum formula, respectively. The interrelations for some molecule potentials are also discussed.

  18. Geometric invariance of compressible turbulent boundary layers

    Science.gov (United States)

    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.

  19. Factorial invariance in multilevel confirmatory factor analysis.

    Science.gov (United States)

    Ryu, Ehri

    2014-02-01

    This paper presents a procedure to test factorial invariance in multilevel confirmatory factor analysis. When the group membership is at level 2, multilevel factorial invariance can be tested by a simple extension of the standard procedure. However level-1 group membership raises problems which cannot be appropriately handled by the standard procedure, because the dependency between members of different level-1 groups is not appropriately taken into account. The procedure presented in this article provides a solution to this problem. This paper also shows Muthén's maximum likelihood (MUML) estimation for testing multilevel factorial invariance across level-1 groups as a viable alternative to maximum likelihood estimation. Testing multilevel factorial invariance across level-2 groups and testing multilevel factorial invariance across level-1 groups are illustrated using empirical examples. SAS macro and Mplus syntax are provided.

  20. Rational solutions for the Riccati-Schr\\"odinger equations associated to translationally shape invariant potentials

    CERN Document Server

    Grandati, Yves

    2009-01-01

    We develop a new approach to build the eigenfunctions of a translationally shape-invariant potential. For this we show that their logarithmic derivatives can be expressed as terminating continued fractions in an appropriate variable. We give explicit formulas for all the eigenstates, their specific form depending on the Barclay-Maxwell class to which the considered potential belongs.

  1. Optimal demand for contingent claims when agents have law invariant utilities

    OpenAIRE

    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.

  2. 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....

  3. Feedback-Driven Dynamic Invariant Discovery

    Science.gov (United States)

    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.

  4. 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.

  5. A Note on the Invariance Properties and Conservation Laws of the Kadomstev-Petviashvili Equation with Power Law Nonlinearity

    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.

  6. 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

  7. On Metrizability of Invariant Affine Connections

    CERN Document Server

    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.

  8. Gromov-Witten invariants and localization

    CERN Document Server

    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.

  9. Comment on ``Pairing interaction and Galilei invariance''

    Science.gov (United States)

    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.

  10. On link invariants and topological string amplitudes

    Energy Technology Data Exchange (ETDEWEB)

    Ramadevi, P. E-mail: rama@phy.iitb.ernet.in; Sarkar, Tapobrata E-mail: tapo@theory.tifr.res.in

    2001-04-30

    We explicitly show that the new polynomial invariants for knots, upto nine crossings, agree with the Ooguri-Vafa conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold.

  11. On Link Invariants and Topological String Amplitudes

    OpenAIRE

    Ramadevi, P.; Sarkar, Tapobrata

    2000-01-01

    We explicitly show that the new polynomial invariants for knots, upto nine crossings, agree with the Ooguri-Vafa conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold.

  12. Testing gauge-invariant perturbation theory

    CERN Document Server

    Törek, Pascal

    2016-01-01

    Gauge-invariant perturbation theory for theories with a Brout-Englert-Higgs effect, as developed by Fr\\"ohlich, Morchio and Strocchi, starts out from physical, exactly gauge-invariant quantities as initial and final states. These are composite operators, and can thus be considered as bound states. In case of the standard model, this reduces almost entirely to conventional perturbation theory. This explains the success of conventional perturbation theory for the standard model. However, this is due to the special structure of the standard model, and it is not guaranteed to be the case for other theories. Here, we review gauge-invariant perturbation theory. Especially, we show how it can be applied and that it is little more complicated than conventional perturbation theory, and that it is often possible to utilize existing results of conventional perturbation theory. Finally, we present tests of the predictions of gauge-invariant perturbation theory, using lattice gauge theory, in three different settings. In ...

  13. Invariant Spectral Hashing of Image Saliency Graph

    CERN Document Server

    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...

  14. Ermakov–Lewis invariants and Reid systems

    Energy Technology Data Exchange (ETDEWEB)

    Mancas, Stefan C., E-mail: stefan.mancas@erau.edu [Department of Mathematics, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la presa San José 2055, Col. Lomas 4a Sección, 78216 San Luis Potosí, S.L.P. (Mexico)

    2014-06-13

    Reid's mth-order generalized Ermakov systems of nonlinear coupling constant α are equivalent to an integrable Emden–Fowler equation. The standard Ermakov–Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m≥3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden–Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy. - Highlights: • Reid systems of order m are connected to Emden–Fowler equations. • General expressions for the Ermakov–Lewis invariants both for m=2 and m≥3 are obtained. • Parametric solutions of the Emden–Fowler equations related to Reid systems are obtained.

  15. 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.

  16. 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....

  17. Conformal Invariance of Black Hole Temperature

    OpenAIRE

    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 ...

  18. On Lorentz invariants in relativistic magnetic reconnection

    Science.gov (United States)

    Yang, Shu-Di; Wang, Xiao-Gang

    2016-08-01

    Lorentz invariants whose nonrelativistic correspondences play important roles in magnetic reconnection are discussed in this paper. Particularly, the relativistic invariant of the magnetic reconnection rate is defined and investigated in a covariant two-fluid model. Certain Lorentz covariant representations for energy conversion and magnetic structures in reconnection processes are also investigated. Furthermore, relativistic measures for topological features of reconnection sites, particularly magnetic nulls and separatrices, are analyzed.

  19. 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.)

  20. Computer calculation of Witten's 3-manifold invariant

    Science.gov (United States)

    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.

  1. Gauge Invariant Monopoles in SU(2) Gluodynamics

    CERN Document Server

    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.

  2. A Homeomorphism Invariant for Substitution Tiling Spaces

    OpenAIRE

    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 ...

  3. Invariants of Fokker-Planck equations

    CERN Document Server

    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.

  4. Weyl Invariance and the Origins of Mass

    CERN Document Server

    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.

  5. Invariant Spectral Hashing of Image Saliency Graph

    OpenAIRE

    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....

  6. Conformal Invariance in Classical Field Theory

    OpenAIRE

    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.

  7. On adiabatic invariant in generalized Galileon theories

    OpenAIRE

    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...

  8. Nonvanishing Local Scalar Invariants even in VSI Spacetimes with all Polynomial Curvature Scalar Invariants Vanishing

    OpenAIRE

    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...

  9. Shift-invariant target in allocation problems.

    Science.gov (United States)

    Mandal, Saumen; Biswas, Atanu

    2014-07-10

    We provide a template for finding target allocation proportions in optimal allocation designs where the target will be invariant for both shifts in location and scale of the response distributions. One possible application of such target allocation proportions is to carry out a response-adaptive allocation. While most of the existing designs are invariant for any change in scale of the underlying distributions, they are not location invariant in most of the cases. First, we indicate this serious flaw in the existing literature and illustrate how this lack of location invariance makes the performance of the designs very poor in terms of allocation for any drastic change in location, such as the changes from degrees centigrade to degrees Fahrenheit. We illustrate that unless a target allocation is location invariant, it might lead to a completely irrelevant and useless target for allocation. Then we discuss how such location invariance can be achieved for general continuous responses. We illustrate the proposed method using some real clinical trial data. We also indicate the possible extension of the procedure for more than two treatments at hand and in the presence of covariates.

  10. U(N) invariant dynamics for a simplified Loop Quantum Gravity model

    CERN Document Server

    Borja, Enrique F; Garay, Iñaki; Livine, Etera R

    2010-01-01

    The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We use the recently introduced U(N) framework in order to construct SU(2) invariant operators and define a global U(N) symmetry that will select the homogeneous/isotropic states. Finally, we propose a Hamiltonian operator invariant under area-preserving deformations of the boundary surface and we identify possible connections of this model with Loop Quantum Cosmology.

  11. U(N) invariant dynamics for a simplified loop quantum gravity model

    Energy Technology Data Exchange (ETDEWEB)

    Borja, Enrique F; Diaz-Polo, Jacobo; Garay, Inaki; Livine, Etera R, E-mail: efborja@theorie3.physik.uni-erlangen.de, E-mail: jacobo@gravity.psu.edu, E-mail: igael@theorie3.physik.uni-erlangen.de, E-mail: etera.livine@ens-lyon.fr

    2011-09-22

    The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We use the recently introduced U(N) framework in order to construct SU(2) invariant operators and define a global U(N) symmetry that will select the homogeneous/isotropic states. Finally, we propose a Hamiltonian operator invariant under area-preserving deformations of the boundary surface and we identify possible connections of this model with Loop Quantum Cosmology.

  12. U(N) invariant dynamics for a simplified loop quantum gravity model

    Science.gov (United States)

    Borja, Enrique F.; Díaz-Polo, Jacobo; Garay, Iñaki; Livine, Etera R.

    2011-09-01

    The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We use the recently introduced U(N) framework in order to construct SU(2) invariant operators and define a global U(N) symmetry that will select the homogeneous/isotropic states. Finally, we propose a Hamiltonian operator invariant under area-preserving deformations of the boundary surface and we identify possible connections of this model with Loop Quantum Cosmology.

  13. Asymptotics of the quantum invariants for surgeries on the figure 8 knot

    DEFF Research Database (Denmark)

    Andersen, Jørgen Ellegaard; Hansen, Søren Kold

    2006-01-01

    a formula for the leading asymptotics of the invariants in the limit of large quantum level. We analyze this expression using the saddle point method. We construct a certain surjection from the set of stationary points for the relevant phase functions onto the space of conjugacy classes of nonabelian SL(2......, ℂ)-representations of the fundamental group of M and prove that the values of these phase functions at the relevant stationary points equals the classical Chern–Simons invariants of the corresponding flat SU(2)-connections. Our findings are in agreement with the asymptotic expansion conjecture...

  14. 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)

  15. The invariance assumption in process-dissociation models: an evaluation across three domains.

    Science.gov (United States)

    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

  16. Cognitive Invariants of Geographic Event Conceptualization: What Matters and What Refines?

    Science.gov (United States)

    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.

  17. On gauge-invariant and phase-invariant spinor analysis. II

    Science.gov (United States)

    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.

  18. Liquidity Constraints of the Middle Class

    NARCIS (Netherlands)

    Campbell, J.R.; Hercowitz, Zvi

    2015-01-01

    Among U.S. middle-class households, the marginal propensity to consume is either invariant to household wealth or a U-shaped function thereof. In contrast, precautionary savings models predict that wealth reduces the marginal propensity to consume. We bridge this gap between theory and data with ter

  19. Quantum principal bundles and their characteristic classes

    CERN Document Server

    Durdevic, M

    1996-01-01

    A brief exposition of the general theory of characteristic classes of quantum principal bundles is given. The theory of quantum characteristic classes incorporates ideas of classical Weil theory into the conceptual framework of non-commutative differential geometry. A purely cohomological interpretation of the Weil homomorphism is given, together with a standard geometrical interpretation via quantum invariant polynomials. A natural spectral sequence is described. Some quantum phenomena appearing in the formalism are discussed.

  20. Invariant object recognition based on extended fragments.

    Science.gov (United States)

    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

  1. 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.

  2. Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis

    CERN Document Server

    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...

  3. U(N) framed links, three-manifold invariants, and topological strings

    Energy Technology Data Exchange (ETDEWEB)

    Borhade, Pravina E-mail: pravina@phy.iitb.ac.in; Ramadevi, P. E-mail: ramadevi@phy.iitb.ac.in; Sarkar, Tapobrata E-mail: tapo@ictp.trieste.it

    2004-02-09

    Three-manifolds can be obtained through surgery of framed links in S{sup 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{sup 3}. 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.

  4. Local energy-momentum conservation in scalar-tensor-like gravity with generic curvature invariants

    Science.gov (United States)

    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".

  5. Bulk and boundary invariants for complex topological insulators from K-theory to physics

    CERN Document Server

    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...

  6. 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.

  7. Buchstaber numbers and classical invariants of simplicial complexes

    OpenAIRE

    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...

  8. World-line quantization of a reciprocally invariant system

    Energy Technology Data Exchange (ETDEWEB)

    Govaerts, Jan [Institute of Theoretical Physics, Department of Physics, University of Stellenbosch, Stellenbosch 7600 (South Africa); Jarvis, Peter D [School of Mathematics and Physics, University of Tasmania, GPO Box 252C, 7001 Hobart, Tasmania (Australia); Morgan, Stuart O [School of Mathematics and Physics, University of Tasmania, GPO Box 252C, 7001 Hobart, Tasmania (Australia); Low, Stephen G [Austin, TX (United States)

    2007-10-05

    We present the world-line quantization of a system invariant under the symmetries of reciprocal relativity (pseudo-unitary transformations on 'phase-space coordinates' (x{sup {mu}}({tau}), p{sup {mu}}({tau})) which preserve the Minkowski metric and the symplectic form, and global shifts in these coordinates, together with coordinate-dependent transformations of an additional compact phase coordinate, {theta}({tau})). The action is that of free motion over the corresponding Weyl-Heisenberg group. Imposition of the first class constraint, the generator of local time reparametrizations, on physical states enforces identification of the world-line cosmological constant with a fixed value of the quadratic Casimir of the quaplectic symmetry group Q(D-1,1){approx_equal}U(D-1,1)xH(D), the semi-direct product of the pseudo-unitary group with the Weyl-Heisenberg group (the central extension of the global translation group, with central extension associated with the phase variable {theta}({tau})). The spacetime spectrum of physical states is identified. Even though for an appropriate range of values the restriction enforced by the cosmological constant projects out negative norm states from the physical gauge invariant spectrum, leaving over spin zero states only, in this purely bosonic setting the mass-squared spectrum is continuous over the entire real line and thus includes a tachyonic branch as well.

  9. World-line quantization of a reciprocally invariant system

    Science.gov (United States)

    Govaerts, Jan; Jarvis, Peter D.; Morgan, Stuart O.; Low, Stephen G.

    2007-10-01

    We present the world-line quantization of a system invariant under the symmetries of reciprocal relativity (pseudo-unitary transformations on 'phase-space coordinates' (xμ(τ), pμ(τ)) which preserve the Minkowski metric and the symplectic form, and global shifts in these coordinates, together with coordinate-dependent transformations of an additional compact phase coordinate, θ(τ)). The action is that of free motion over the corresponding Weyl-Heisenberg group. Imposition of the first class constraint, the generator of local time reparametrizations, on physical states enforces identification of the world-line cosmological constant with a fixed value of the quadratic Casimir of the quaplectic symmetry group Q(D-1,1){\\;\\raise 0.4ex\\\\sim\\kern -0.78em \\lower 0.26ex \\=\\;} U(D-1,1)\\ltimes H(D) , the semi-direct product of the pseudo-unitary group with the Weyl-Heisenberg group (the central extension of the global translation group, with central extension associated with the phase variable θ(τ)). The spacetime spectrum of physical states is identified. Even though for an appropriate range of values the restriction enforced by the cosmological constant projects out negative norm states from the physical gauge invariant spectrum, leaving over spin zero states only, in this purely bosonic setting the mass-squared spectrum is continuous over the entire real line and thus includes a tachyonic branch as well.

  10. Conformal Laplace superintegrable systems in 2D: polynomial invariant subspaces

    Science.gov (United States)

    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.

  11. 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.

  12. Rainbow gravity and scale-invariant fluctuations

    CERN Document Server

    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.

  13. Lorentz invariance in chiral kinetic theory.

    Science.gov (United States)

    Chen, Jing-Yuan; Son, Dam T; Stephanov, Mikhail A; Yee, Ho-Ung; Yin, Yi

    2014-10-31

    We show that Lorentz invariance is realized nontrivially in the classical action of a massless spin-1/2 particle with definite helicity. We find that the ordinary Lorentz transformation is modified by a shift orthogonal to the boost vector and the particle momentum. The shift ensures angular momentum conservation in particle collisions and implies a nonlocality of the collision term in the Lorentz-invariant kinetic theory due to side jumps. We show that 2/3 of the chiral-vortical effect for a uniformly rotating particle distribution can be attributed to the magnetic moment coupling required by the Lorentz invariance. We also show how the classical action can be obtained by taking the classical limit of the path integral for a Weyl particle. PMID:25396362

  14. Some Cosmological Consequences of Weyl Invariance

    CERN Document Server

    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.

  15. INVARIANTS UNDER STABLE EQUIVALENCES OF MORITA TYPE

    Institute of Scientific and Technical Information of China (English)

    Li Fang; Sun Longgang

    2012-01-01

    The aim of this article is to study some invariants of associative algebras under stable equivalences of Morita type.First of all,we show that,if two finite-dimensional selfinjective k-algebras are stably equivalent of Morita type,then their orbit algebras are isomorphic.Secondly,it is verified that the quasitilted property of an algebra is invariant under stable equivalences of Morita type.As an application of this result,it is obtained that if an algebra is of finite representation type,then its tilted property is invariant under stable equivalences of Morita type; the other application to partial tilting modules is given in Section 4. Finally,we prove that when two finite-dimensional k-algebras are stably equivalent of Morita type,their repetitive algebras are also stably equivalent of Morita type under certain conditions.

  16. Gravity as the breakdown of conformal invariance

    CERN Document Server

    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.

  17. Gauge-Invariant Formulation of Circular Dichroism.

    Science.gov (United States)

    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

  18. Topological invariants for interacting topological insulators. I. Efficient numerical evaluation scheme and implementations

    Science.gov (United States)

    He, Yuan-Yao; Wu, Han-Qing; Meng, Zi Yang; Lu, Zhong-Yi

    2016-05-01

    The aim of this series of two papers is to discuss topological invariants for interacting topological insulators (TIs). In the first paper (I), we provide a paradigm of efficient numerical evaluation scheme for topological invariants, in which we demystify the procedures and techniques employed in calculating Z2 invariant and spin Chern number via zero-frequency single-particle Green's function in quantum Monte Carlo (QMC) simulations. Here we introduce an interpolation process to overcome the ubiquitous finite-size effect, so that the calculated spin Chern number shows ideally quantized values. We also show that making use of symmetry properties of the underlying systems can greatly reduce the computational effort. To demonstrate the effectiveness of our numerical evaluation scheme, especially the interpolation process, for calculating topological invariants, we apply it on two independent two-dimensional models of interacting topological insulators. In the subsequent paper (II), we apply the scheme developed here to wider classes of models of interacting topological insulators, for which certain limitation of constructing topological invariant via single-particle Green's functions will be presented.

  19. Local and nonlocal advected invariants and helicities in magnetohydrodynamics and gas dynamics I: Lie dragging approach

    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)

  20. 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.)

  1. 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.

  2. Some cosmological consequences of Weyl invariance

    Energy Technology Data Exchange (ETDEWEB)

    Alvarez, Enrique; González-Martín, Sergio; Herrero-Valea, Mario [Departamento de Física Teórica and Instituto de Física Teórica, IFT-UAM/CSIC, Universidad Autónoma, 20849 Madrid (Spain)

    2015-03-19

    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.

  3. Invariant distances and metrics in complex analysis

    CERN Document Server

    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

  4. Invariants of contact structures from open books

    OpenAIRE

    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).

  5. Galilean invariant resummation schemes of cosmological perturbations

    CERN Document Server

    Peloso, Marco

    2016-01-01

    Many of the methods proposed so far to go beyond Standard Perturbation Theory break invariance under time-dependent boosts (denoted here as extended Galilean Invariance, or GI). This gives rise to spurious large scale effects which spoil the small scale predictions of these approximation schemes. By using consistency relations we derive fully non-perturbative constraints that GI imposes on correlation functions. We then introduce a method to quantify the amount of GI breaking of a given scheme, and to correct it by properly tailored counterterms. Finally, we formulate resummation schemes which are manifestly GI, discuss their general features, and implement them in the so called Time-Flow, or TRG, equations.

  6. Affine Invariant Character Recognition by Progressive Removing

    Science.gov (United States)

    Iwamura, Masakazu; Horimatsu, Akira; Niwa, Ryo; Kise, Koichi; Uchida, Seiichi; Omachi, Shinichiro

    Recognizing characters in scene images suffering from perspective distortion is a challenge. Although there are some methods to overcome this difficulty, they are time-consuming. In this paper, we propose a set of affine invariant features and a new recognition scheme called “progressive removing” that can help reduce the processing time. Progressive removing gradually removes less feasible categories and skew angles by using multiple classifiers. We observed that progressive removing and the use of the affine invariant features reduced the processing time by about 60% in comparison to a trivial one without decreasing the recognition rate.

  7. 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.)

  8. The decomposition of global conformal invariants

    CERN Document Server

    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

  9. Burning invariant manifolds in reactive front propagation

    CERN Document Server

    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.

  10. Scaling theory of {{{Z}}_{2}} topological invariants

    Science.gov (United States)

    Chen, Wei; Sigrist, Manfred; Schnyder, Andreas P.

    2016-09-01

    For inversion-symmetric topological insulators and superconductors characterized by {{{Z}}2} topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling schemes renormalize either the phase gradient or the second derivative of the Pfaffian of the time-reversal operator, through which the renormalization group flow of the driving energy parameter can be obtained. The Pfaffian near the time-reversal invariant momentum is revealed to display a universal critical behavior for a great variety of models examined.

  11. Hidden invariance of the free classical particle

    CERN Document Server

    García, S

    1993-01-01

    A formalism describing the dynamics of classical and quantum systems from a group theoretical point of view is presented. We apply it to the simple example of the classical free particle. The Galileo group $G$ is the symmetry group of the free equations of motion. Consideration of the free particle Lagrangian semi-invariance under $G$ leads to a larger symmetry group, which is a central extension of the Galileo group by the real numbers. We study the dynamics associated with this group, and characterize quantities like Noether invariants and evolution equations in terms of group geometric objects. An extension of the Galileo group by $U(1)$ leads to quantum mechanics.

  12. 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

  13. A Family of Invariant Stress Surfaces

    DEFF Research Database (Denmark)

    Krenk, S.

    A family of invariant stress surfaces with a cubic dependence on the deviatoric stress components is expressed as a linear combination of the second and third deviatori stress invariants. A simple geometric derivation demonstrates the convexity of the contours in the deviatoric plane. An explicit...... contour is given in explicit form. Several special cases are considered: a generalized Drucker-Prager criterion with straight generators and a smooth triangular deviatoric contour, surfaces with parabolic compression and tension generators, and the Lade failure surface for cohesionless soils. The use...

  14. Time invariance violating nuclear electric octupole moments

    CERN Document Server

    Flambaum, V V; Orton, S R

    1997-01-01

    The existence of a nuclear electric octupole moment (EOM) requires both parity and time invariance violation. The EOMs of odd $Z$ nuclei that are induced by a particular T- and P-odd interaction are calculated. We compare such octupole moments with the collective EOMs that can occur in nuclei having a static octupole deformation. A nuclear EOM can induce a parity and time invariance violating atomic electric dipole moment, and the magnitude of this effect is calculated. The contribution of a nuclear EOM to such a dipole moment is found, in most cases, to be smaller than that of other mechanisms of atomic electric dipole moment production.

  15. Disambiguating Seesaw Models using Invariant Mass Variables at Hadron Colliders

    CERN Document Server

    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...

  16. Rotationally invariant clustering of diffusion MRI data using spherical harmonics

    DEFF Research Database (Denmark)

    Liptrot, Matthew George; Lauze, Francois Bernard

    2016-01-01

    classification of DWI data can be performed without the need for a model reconstruction step. This avoids the potential confounds and uncertainty that such models may impose, and has the benefit of being computable directly from the DWI volumes. As such, the method could prove useful in subsequent pre-processing...... simple features that are invariant to the rotation of the highly orientational diffusion data. This provides a way to directly classify voxels whose diffusion characteristics are similar yet whose primary diffusion orientations differ. Subsequent application of machine-learning to the spherical harmonic...... data as a collection of spherical basis functions. We use the derived coefficients as voxelwise feature vectors for classification. Using a simple Gaussian mixture model, we examined the classification performance for a range of sub-classes (3-20). The results were compared against existing...

  17. Rotationally invariant clustering of diffusion MRI data using spherical harmonics

    DEFF Research Database (Denmark)

    Liptrot, Matthew George; Lauze, Francois Bernard

    classification of DWI data can be performed without the need for a model reconstruction step. This avoids the potential confounds and uncertainty that such models may impose, and has the benefit of being computable directly from the DWI volumes. As such, the method could prove useful in subsequent pre-processing...... simple features that are invariant to the rotation of the highly orientational diffusion data. This provides a way to directly classify voxels whose diffusion characteristics are similar yet whose primary diffusion orientations differ. Subsequent application of machine-learning to the spherical harmonic...... data as a collection of spherical basis functions. We use the derived coefficients as voxelwise feature vectors for classification. Using a simple Gaussian mixture model, we examined the classification performance for a range of sub-classes (3-20). The results were compared against existing...

  18. Contrast/offset-invariant generic low-order MGRF models of uniform textures

    Science.gov (United States)

    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.

  19. Universality class in conformal inflation

    Energy Technology Data Exchange (ETDEWEB)

    Kallosh, Renata; Linde, Andrei, E-mail: kallosh@stanford.edu, E-mail: alinde@stanford.edu [Department of Physics and SITP, Stanford University, Stanford, California 94305 (United States)

    2013-07-01

    We develop a new class of chaotic inflation models with spontaneously broken conformal invariance. Observational consequences of a broad class of such models are stable with respect to strong deformations of the scalar potential. This universality is a critical phenomenon near the point of enhanced symmetry, SO(1,1), in case of conformal inflation. It appears because of the exponential stretching of the moduli space and the resulting exponential flattening of scalar potentials upon switching from the Jordan frame to the Einstein frame in this class of models. This result resembles stretching and flattening of inhomogeneities during inflationary expansion. It has a simple interpretation in terms of velocity versus rapidity near the Kähler cone in the moduli space, similar to the light cone of special theory of relativity. This effect makes inflation possible even in the models with very steep potentials. We describe conformal and superconformal versions of this cosmological attractor mechanism.

  20. Multiple HLA class I and II associations in classical Hodgkin lymphoma and EBV status defined subgroups (Retracted article. See vol. 118, pg. 5211, 2011)

    NARCIS (Netherlands)

    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

  1. Heritable major histocompatibility complex class II-associated differences in production of tumor necrosis factor. alpha. : Relevance to genetic predisposition to systemic lupus erythematosus

    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.

  2. Momentum Routing Invariance in Extended QED: Assuring Gauge Invariance Beyond Tree Level

    CERN Document Server

    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.

  3. Testing Lorentz and CPT invariance with neutrinos

    CERN Document Server

    Diaz, Jorge S

    2016-01-01

    Neutrino experiments can be considered sensitive tools to test Lorentz and CPT invariance. Taking advantage of the great variety of neutrino experiments, including neutrino oscillations, weak decays, and astrophysical neutrinos, the generic experimental signatures of the breakdown of these fundamental symmetries in the neutrino sector are presented.

  4. 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)

  5. Invariance Properties for General Diagnostic Classification Models

    Science.gov (United States)

    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…

  6. Physics Fun with Discrete Scale Invariance

    CERN Document Server

    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.

  7. Conformally Invariant Off-shell Strings

    CERN Document Server

    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)

  8. Translation invariance and doubly special relativity

    OpenAIRE

    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.

  9. 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].

  10. Scale invariance, conformality, and generalized free fields

    Science.gov (United States)

    Dymarsky, Anatoly; Farnsworth, Kara; Komargodski, Zohar; Luty, Markus A.; Prilepina, Valentina

    2016-02-01

    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 functions cannot be understood from the leading terms of the coordinate space OPE. This invalidates a recent argument by Farnsworth-Luty-Prilepina (FLP). Despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context.

  11. Scale invariant density perturbations from cyclic cosmology

    Science.gov (United States)

    Frampton, Paul Howard

    2016-04-01

    It is shown how quantum fluctuations of the radiation during the contraction era of a comes back empty (CBE) cyclic cosmology can provide density fluctuations which re-enter the horizon during the subsequent expansion era and at lowest order are scale invariant, in a Harrison-Zel’dovich-Peebles sense. It is necessary to be consistent with observations of large scale structure.

  12. BRST invariance in Coulomb gauge QCD

    CERN Document Server

    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.

  13. BRST invariance in Coulomb gauge QCD

    Science.gov (United States)

    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.

  14. Automatic invariant detection in dynamic web applications

    NARCIS (Netherlands)

    Groeneveld, F.; Mesbah, A.; Van Deursen, A.

    2010-01-01

    The complexity of modern web applications increases as client-side JavaScript and dynamic DOM programming are used to offer a more interactive web experience. In this paper, we focus on improving the dependability of such applications by automatically inferring invariants from the client-side and us

  15. Holography for chiral scale-invariant models

    NARCIS (Netherlands)

    R.N. Caldeira Costa; M. Taylor

    2010-01-01

    Deformation of any d-dimensional conformal field theory by a constant null source for a vector operator of dimension (d + z -1) is exactly marginal with respect to anisotropic scale invariance, of dynamical exponent z. The holographic duals to such deformations are AdS plane waves, with z=2 being th

  16. Broken Scale Invariance and Anomalous Dimensions

    Science.gov (United States)

    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.

  17. Scale Invariance, Conformality, and Generalized Free Fields

    CERN Document Server

    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...

  18. η-Invariant and Flat Vector Bundles

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    We present an alternate definition of the mod Z component of the AtiyahPatodi-Singer η invariant associated to (not necessary unitary) fiat vector bundles, which identifies explicitly its real and imaginary parts. This is done by combining a deformation of flat connections introduced in a previous paper with the analytic continuation procedure appearing in the original article of Atiyah, Parodi and Singer.

  19. Invariant algebraic surfaces for a virus dynamics

    Science.gov (United States)

    Valls, Claudia

    2015-08-01

    In this paper, we provide a complete classification of the invariant algebraic surfaces and of the rational first integrals for a well-known virus system. In the proofs, we use the weight-homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations.

  20. 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.

  1. Shape invariant potentials in SUSY quantum mechanics

    Directory of Open Access Journals (Sweden)

    A. Dadkhah

    2007-12-01

    Full Text Available   We give a brief review on the known shape invariant potentials. We derive the all of them by introducing a general superpotential with two constant and four variable parameters. Finally we examine those potentials which lead to the equally-spaced energy spectrum for the Klein-Gordon equation.

  2. Invariant properties between stroke features in handwriting

    NARCIS (Netherlands)

    Teulings, H L; Schomaker, L R

    1993-01-01

    A handwriting pattern is considered as a sequence of ballistic strokes. Replications of a pattern may be generated from a single, higher-level memory representation, acting as a motor program. Therefore, those stroke features which show the most invariant pattern are probably related to the paramete

  3. A functional LMO invariant for Lagrangian cobordisms

    DEFF Research Database (Denmark)

    Cheptea, Dorin; Habiro, Kazuo; Massuyeau, Gwénaël

    2008-01-01

    Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le–Murakami–Ohtsuki invariant of homology three-spheres to a functor from the category of Lagrangian cobordisms to a certain category...

  4. Invariant Hilbert spaces of holomorphic functions

    NARCIS (Netherlands)

    Faraut, J; Thomas, EGF

    1999-01-01

    A Hilbert space of holomorphic functions on a complex manifold Z, which is invariant under a group G of holomorphic automorphisms of Z, can be decomposed into irreducible subspaces by using Choquet theory. We give a geometric condition on Z and G which implies that this decomposition is multiplicity

  5. 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.

  6. 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

  7. Average sampling theorems for shift invariant subspaces

    Institute of Scientific and Technical Information of China (English)

    孙文昌; 周性伟

    2000-01-01

    The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.

  8. OCTONIONS: INVARIANT REPRESENTATION OF THE LEECH LATTICE

    OpenAIRE

    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.

  9. Adaptivity and group invariance in mathematical morphology

    NARCIS (Netherlands)

    Roerdink, Jos B.T.M.

    2009-01-01

    The standard morphological operators are (i) defined on Euclidean space, (ii) based on structuring elements, and (iii) invariant with respect to translation. There are several ways to generalise this. One way is to make the operators adaptive by letting the size or shape of structuring elements depe

  10. Global invariant methods for object recognition

    Science.gov (United States)

    Stiller, Peter F.

    2001-11-01

    The general problem of single-view recognition is central to man image understanding and computer vision tasks; so central, that it has been characterized as the holy grail of computer vision. In previous work, we have shown how to approach the general problem of recognizing three dimensional geometric configurations (such as arrangements of lines, points, and conics) from a single two dimensional view, in a manner that is view independent. Our methods make use of advanced mathematical techniques from algebraic geometry, notably the theory of correspondences, and a novel equivariant geometric invariant theory. The machinery gives us a way to understand the relationship that exists between the 3D geometry and its residual in a 2D image. This relationship is shown to be a correspondence in the technical sense of algebraic geometry. Exploiting this, one can compute a set of fundamental equations in 3D and 2D invariants which generate the ideal of the correspondence, and which completely describe the mutual 3D/2D constraints. We have chosen to call these equations object/image equations. They can be exploited in a number of ways. For example, from a given 2D configuration, we can determine a set of non-linear constraints on the geometric invariants of a 3D configurations capable of imaging to the given 2D configuration (features on an object), we can derive a set of equations that constrain the images of that object; helping us to determine if that particular object appears in various images. One previous difficulty has been that the usual numerical geometric invariants get expressed as rational functions of the geometric parameters. As such they are not always defined. This leads to degeneracies in algorithms based on these invariants. We show how to replace these invariants by certain toric subvarieties of Grassmannians where the object/image equations become resultant like expressions for the existence of a non- trivial intersection of these subvarieties with

  11. Invariant Inhomogeneous Bianchi Type-I Cosmological Models with Electromagnetic Fields Using Lie Group Analysis in Lyra Geometry

    Directory of Open Access Journals (Sweden)

    Ahmad T. Ali

    2014-01-01

    Full Text Available We find a new class of invariant inhomogeneous Bianchi type-I cosmological models in electromagnetic field with variable magnetic permeability. For this, Lie group analysis method is used to identify the generators that leave the given system of nonlinear partial differential equations (NLPDEs (Einstein field equations invariant. With the help of canonical variables associated with these generators, the assigned system of PDEs is reduced to ordinary differential equations (ODEs whose simple solutions provide nontrivial solutions of the original system. A new class of exact (invariant-similarity solutions have been obtained by considering the potentials of metric and displacement field as functions of coordinates x and t. We have assumed that F12 is only nonvanishing component of electromagnetic field tensor Fij. The Maxwell equations show that F12 is the function of x alone whereas the magnetic permeability μ¯ is the function of x and t both. The physical behavior of the obtained model is discussed.

  12. Approximate scale invariance in particle systems: a large-dimensional justification

    OpenAIRE

    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...

  13. Longitudinal foliation rigidity and Lipschitz-continuous invariant forms for hyperbolic flows

    OpenAIRE

    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...

  14. Ultra-High Energy Astrophysical Neutrino Detection, and the Search for Lorentz Invariance Violations

    CERN Document Server

    Hanson, J C

    2016-01-01

    A growing class of ultra-high energy neutrino (UHE-nu) observatories based on the Askaryan effect and Antarctic ice is able to search for Lorentz invariance violation (LIV). The ARA, ARIANNA, ANITA and EVA collaborations have the power to constrain the Standard Model Extension (SME) by measuring the flux and energy distribution of neutrinos created through the GZK process. The future expansion of ARA, at the South Pole, pushes the discovery potential further.

  15. Chern-Simons Theory, Vassiliev Invariants, Loop Quantum Gravity and Functional Integration Without Integration

    Science.gov (United States)

    Kauffman, Louis H.

    This paper is an exposition of the relationship between Witten's Chern-Simons functional integral and the theory of Vassiliev invariants of knots and links in three-dimensional space. We conceptualize the functional integral in terms of equivalence classes of functionals of gauge fields and we do not use measure theory. This approach makes it possible to discuss the mathematics intrinsic to the functional integral rigorously and without functional integration. Applications to loop quantum gravity are discussed.

  16. Dualities between Scale Invariant and Magnitude Invariant Perturbation Spectra in Inflationary/Bouncing Cosmos

    CERN Document Server

    Li, Chonghong

    2012-01-01

    We study cosmological perturbation spectra using the dynamical equations of gauge invariant perturbations with a generalized blue/red-shift term. Combined with the power-law index of cosmological background, {\

  17. Markov invariants, plethysms, and phylogenetics (the long version)

    CERN Document Server

    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.

  18. Cardinal invariants associated with Fubini product of ideals

    Institute of Scientific and Technical Information of China (English)

    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.

  19. Invariants and discriminant ideals of orthogonal complements in a quadratic space

    CERN Document Server

    Murata, Manabu

    2011-01-01

    This paper studies two topics concerning on the orthogonal complement of one dimensional subspace with respect to a given quadratic form on a vector space over a number field. One is to determine the invariants for the isomorphism class of such a complement in the sense of Shimura. The other is to investigate an ideal of the base field, which may be viewed as a difference between the genus of maximal lattices and an integral lattice in the complement. We shall discuss about the class number of the genus of maximal lattices as an application.

  20. Equivalence Partitioning as a Basis for Dynamic Conditional Invariant Detection

    OpenAIRE

    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...

  1. A Note On Galilean Invariants In Semi-Relativistic Electromagnetism

    OpenAIRE

    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...

  2. Conformal invariance and Hojman conserved quantities of canonical Hamilton systems

    Institute of Scientific and Technical Information of China (English)

    Liu Chang; Liu Shi-Xing; Mei Feng-Xiang; Guo Yong-Xin

    2009-01-01

    This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invariance being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.

  3. Invariant feedback control for the kinematic car on the sphere

    CERN Document Server

    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.

  4. A scale invariant covariance structure on jet space

    DEFF Research Database (Denmark)

    Pedersen, Kim Steenstrup; Loog, Marco; Markussen, Bo

    2005-01-01

    This paper considers scale invariance of statistical image models. We study statistical scale invariance of the covariance structure of jet space under scale space blurring and derive the necessary structure and conditions of the jet covariance matrix in order for it to be scale invariant. As part...... results where we estimate the scale invariant jet covariance of natural images and show that it resembles that of Brownian images....

  5. 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.

  6. 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.

  7. Conformal projective invariants in the problem of image recognition.

    Directory of Open Access Journals (Sweden)

    Надежда Григорьевна Коновенко

    2014-11-01

    Full Text Available In this paper we reduce local classification of differential 1-forms on the plane with respect to group SL_2(C of Mobius transformations. We find the field of rational conformal differential invariants and show that the field is generated by two differential invariant derivations and by differential invariants of the first and second orders.

  8. Lie-form invariance of the Lagrange system

    Institute of Scientific and Technical Information of China (English)

    Wu Hui-Bin

    2005-01-01

    In this paper, the Lie-form invariance of the Lagrange system is studied. The definition and the criterion of the Lie-form invariance of the Lagrange system are given. The Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. Finally, two examples are presented to illustrate the application of the results.

  9. FORM INVARIANCE AND LIE SYMMETRY OF THE GENERALIZED HAMILTONIAN SYSTEM

    Institute of Scientific and Technical Information of China (English)

    WuHuibin; MeiFengxiang

    2004-01-01

    The form invariance and the Lie symmetry of the generalized Hamiltonian system are studied. Firstly, definitions and criteria of the form invariance and the Lie symmetry of the system are given. Next, the relation between the form invariance and the Lie symmetry is studied.Finally, two examples are given to illustrate the application of the results.

  10. Basis Invariants in Non--Abelian Gauge Theories

    OpenAIRE

    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.

  11. Hiding Lorentz Invariance Violation with MOND

    CERN Document Server

    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.

  12. Mutation, Witten Index, and Quiver Invariant

    CERN Document Server

    Kim, Heeyeon; Yi, Piljin

    2015-01-01

    We explore Seiberg-like dualities, or mutations, for ${\\cal N}=4$ quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed Fayet-Iliopoulos constants, at most two nodes can be mutated, one left and the other right, mapping a chamber of a quiver into a chamber of a mutated quiver. We delineate this complex pattern for triangle quivers and show how the Witten indices are preserved under such finely chosen mutations. On the other hand, the quiver invariants, or wall-crossing-safe part of supersymmetric spectra, mutate more straightforwardly, whereby a quiver is mapped to a quiver. The mutation rule that preserves the quiver invariant is different from the usual one, however, which we explore and confirm numerically.

  13. Gauge-invariant approach to quark dynamics

    Science.gov (United States)

    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.

  14. Non-boost-invariant dissipative hydrodynamics

    CERN Document Server

    Florkowski, Wojciech; Strickland, Michael; Tinti, Leonardo

    2016-01-01

    The one-dimensional non-boost-invariant evolution of the quark-gluon plasma, presumably produced during the early stages of heavy-ion collisions, is analyzed within the frameworks of viscous and anisotropic hydrodynamics. We neglect transverse dynamics and assume homogeneous conditions in the transverse plane but, differently from Bjorken expansion, we relax longitudinal boost invariance in order to study the rapidity dependence of various hydrodynamical observables. We compare the results obtained using several formulations of second-order viscous hydrodynamics with a recent approach to anisotropic hydrodynamics, which treats the large initial pressure anisotropy in a non-perturbative fashion. The results obtained with second-order viscous hydrodynamics depend on the particular choice of the second-order terms included, which suggests that the latter should be included in the most complete way. The results of anisotropic hydrodynamics and viscous hydrodynamics agree for the central hot part of the system, ho...

  15. Symmetric form-invariant dual Pearcey beams.

    Science.gov (United States)

    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

  16. Extended Weyl Invariance in a Bimetric Model

    CERN Document Server

    Hassan, S F; von Strauss, Mikael

    2015-01-01

    We revisit a particular ghost-free bimetric model which is related to both partial masslessness as well conformal gravity. Its equations of motion can be recast in the form of a perturbative series in derivatives which exhibits a remarkable amount of structure. In a perturbative (but fully nonlinear) analysis, we demonstrate that the equations are invariant under scalar gauge transformations up to six orders in derivatives, the lowest-order term being a local Weyl scaling of the metrics. More specifically, we develop a procedure for constructing terms in the gauge transformations order by order in the perturbative framework. This allows us to derive sufficient conditions for the existence of a gauge symmetry at the nonlinear level. It is explicitly demonstrated that these conditions are satisfied at the first relevant order and, consequently, the equations are gauge invariant up to six orders in derivatives. We furthermore show that the model propagates six instead of seven degrees of freedom not only around ...

  17. Field redefinition invariance in quantum field theory

    CERN Document Server

    Apfeldorf, K M; Apfeldorf, Karyn M; Ordonez, Carlos

    1994-01-01

    We investigate the consequences of field redefinition invariance in quantum field theory by carefully performing nonlinear transformations in the path integral. We first present a ``paradox'' whereby a 1+1 freemassless scalar theory on a Minkowskian cylinder is reduced to an effectively quantum mechanical theory. We perform field redefinitions both before and after reduction to suggest that one should not ignore operator ordering issues in quantum field theory. We next employ a discretized version of the path integral for a free massless scalar quantum field in d dimensions to show that beyond the usual jacobian term, an infinite series of divergent ``extra'' terms arises in the action whenever a nonlinear field redefinition is made. The explicit forms for the first couple of these terms are derived. We evaluate Feynman diagrams to illustrate the importance of retaining the extra terms, and conjecture that these extra terms are the exact counterterms necessary to render physical quantities invariant under fie...

  18. Scale invariant features extraction for stereo vision

    Institute of Scientific and Technical Information of China (English)

    Liu Li; Peng Fuyuan; Tian Yan; Wan Yaping

    2009-01-01

    Stable local feature detection is a fundamental component of many stereo vision problems such as 3-D reconstruction, object localization, and object tracking. A robust method for extracting scale-invariant feature points is presented. First, the Harris corners in three-level pyramid are extracted. Then, the points detected at the highest level of the pyramid are correctly propagated to the lower level by pyramid based scale invariant (PBSI) method. The corners detected repeatedly in different levels are chosen as final feature points. Finally, the characteristic scale is obtained based on maximum entropy method. The experimental results show that the algorithm has low computation cost, strong antinoise capability, and excellent performance in the presence of significant scale changes.

  19. 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.

  20. 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.

  1. The relativistic virial theorem and scale invariance

    CERN Document Server

    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.

  2. Adiabatic Invariance of Oscillons/I-balls

    CERN Document Server

    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.

  3. Unimodular Gravity with Pseudo-scale Invariance

    CERN Document Server

    Jain, Pankaj; Singh, Naveen K

    2011-01-01

    We consider a model of gravity and matter fields which is invariant only under unimodular general coordinate transformations (GCT). The determinant of the metric is treated as a separate field which transforms as a scalar under unimodular GCT. Furthermore we also demand that the theory obeys pseudo-scale invariance. We study the implications of the resulting theory. We solve the resulting field equations for a sperically symmetric system in vacuum. We find that the resulting solution contains an additional term in comparison to the standard Schwarzchild solution. We also study the cosmological implications of the model. We find that both in case of radiation and matter dominated universe it predicts an accelerated expansion. Furthermore the model does not admit a cosmological constant, thereby solving its fine tuning problem.

  4. BMS invariance and the membrane paradigm

    CERN Document Server

    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})...

  5. 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.

  6. Scale-invariant nonlinear optics in gases

    CERN Document Server

    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.

  7. 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.

  8. Gauge-invariant approach to quark dynamics

    CERN Document Server

    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.

  9. Invariant holomorphic extension in several complex variables

    Institute of Scientific and Technical Information of China (English)

    ZHOU Xiangyu

    2006-01-01

    Two fundamental problems on the invariant holomorphic extensions have been posed, which are naturally arose from our solution of the extended future tube conjecture and closely and deeply related to the general theory of Stein manifolds due to Cartan-Serre. In this paper, the relationship is presented between the two problems, the motivation of considering the problems, and the methods to approach the problems. We have also posed some questions and conjectures related to this two problems.

  10. Scale invariance, unimodular gravity and dark energy

    OpenAIRE

    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.

  11. Some Invariant Subspaces in L2H

    OpenAIRE

    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.

  12. Toward an invariant definition of repulsive gravity

    OpenAIRE

    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...

  13. Evaluating Invariances in Document Layout Functions

    OpenAIRE

    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...

  14. Invariant object recognition based on extended fragments

    OpenAIRE

    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...

  15. Liaison, Schottky Problem and Invariant Theory

    CERN Document Server

    Alonso, Maria Emilia; Mallavibarrena, Raquel; Sols, Ignacio

    2010-01-01

    This volume is a homage to the memory of the Spanish mathematician Federico Gaeta (1923-2007). Apart from a historical presentation of his life and interaction with the classical Italian school of algebraic geometry, the volume presents surveys and original research papers on the mathematics he studied. Specifically, it is divided into three parts: linkage theory, Schottky problem and invariant theory. On this last topic a hitherto unpublished article by Federico Gaeta is also included.

  16. Explicit Traveling Waves and Invariant Algebraic Curves

    OpenAIRE

    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...

  17. Entanglement entropy, conformal invariance and extrinsic geometry

    OpenAIRE

    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 $\\Sigma$ ...

  18. 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.

  19. The multiplicativity of fixed point invariants

    OpenAIRE

    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.

  20. An invariant distribution in static granular media

    OpenAIRE

    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...

  1. Deep video gesture recognition using illumination invariants

    OpenAIRE

    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...

  2. 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.)

  3. Test of CP invariance in decay

    Energy Technology Data Exchange (ETDEWEB)

    Chauvat, P.; Erhan, S.; Hayes, K.; Smith, A.M.; Meritet, L.; Reyrolle, M.; Vazeille, F.; Bonino, R.; Cousins, R.; Kroll, I.J.; Medinnis, M.; Schlein, P.E.; Sherwood, P.; Zweizig, J.G.; Alitti, J.; Bloch-Devaux, B.; Cheze, J.B.; Montag, A.; Pichard, B.; Zsembery, J.; R608 Collaboration.

    1985-11-21

    In an experiment at the CERN intersecting storage rings with s = 31 GeV, we have measured P, the product of asymmetry parameter and polarization, for anti 's and 's produced in anti pp interactions, respectively. The ratio, ( P)anti /( P)sub( ) = -1.04+-0.29, is consistent with the value -1, and constitutes the first test of CP invariance in decay. (orig.).

  4. Conformally Invariant Spinorial Equations in Six Dimensions

    CERN Document Server

    Batista, Carlos

    2016-01-01

    This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for some of these equations are established. Moreover, in the course of the article, some useful identities involving the curvature of the spinorial connection are attained and a digression about harmonic forms and more general massless fields is made.

  5. CLASSIFICATION OF MPSK SIGNALS USING CUMULANT INVARIANTS

    Institute of Scientific and Technical Information of China (English)

    Yang Shaoquan; Chen Weidong

    2002-01-01

    A new feature based on higher order statistics is proposed for classification of MPSKsignals, which is invariant with respect to translation (shift), scale and rotation transforms of MPSK signal constellations, and can suppress additive color or white Gaussian noise. Application of the new feature to classification of MPSK signals, at medium signal-to-noise ratio with specified sample size, results in high probability of correct identification. Finally, computer simulations and comparisons with existing algorithms are given.

  6. The relativistic virial theorem and scale invariance

    OpenAIRE

    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...

  7. Hodge-type structures as link invariants

    OpenAIRE

    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...

  8. Trojan Horse particle invariance in fusion reactions

    OpenAIRE

    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...

  9. Nonequilibrium invariant measure under heat flow.

    Science.gov (United States)

    Delfini, Luca; Lepri, Stefano; Livi, Roberto; Politi, Antonio

    2008-09-19

    We provide an explicit representation of the nonequilibrium invariant measure for a chain of harmonic oscillators with conservative noise in the presence of stationary heat flow. By first determining the covariance matrix, we are able to express the measure as the product of Gaussian distributions aligned along some collective modes that are spatially localized with power-law tails. Numerical studies show that such a representation applies also to a purely deterministic model, the quartic Fermi-Pasta-Ulam chain.

  10. On the Topological Orbit Equivalence in a Class of Substitution Minimal Systems

    OpenAIRE

    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.

  11. 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.

  12. Sheaves on Graphs and Their Homological Invariants

    CERN Document Server

    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.

  13. Invariance algorithms for processing NDE signals

    Science.gov (United States)

    Mandayam, Shreekanth; Udpa, Lalita; Udpa, Satish S.; Lord, William

    1996-11-01

    Signals that are obtained in a variety of nondestructive evaluation (NDE) processes capture information not only about the characteristics of the flaw, but also reflect variations in the specimen's material properties. Such signal changes may be viewed as anomalies that could obscure defect related information. An example of this situation occurs during in-line inspection of gas transmission pipelines. The magnetic flux leakage (MFL) method is used to conduct noninvasive measurements of the integrity of the pipe-wall. The MFL signals contain information both about the permeability of the pipe-wall and the dimensions of the flaw. Similar operational effects can be found in other NDE processes. This paper presents algorithms to render NDE signals invariant to selected test parameters, while retaining defect related information. Wavelet transform based neural network techniques are employed to develop the invariance algorithms. The invariance transformation is shown to be a necessary pre-processing step for subsequent defect characterization and visualization schemes. Results demonstrating the successful application of the method are presented.

  14. Euclidean M-theory background dual to three-dimensional scale invariant field theory without conformal invariance

    CERN Document Server

    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.

  15. Generation of scale invariant magnetic fields in bouncing universes

    Science.gov (United States)

    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.

  16. Levels of complexity in scale-invariant neural signals

    Science.gov (United States)

    Ivanov, Plamen Ch.; Ma, Qianli D. Y.; Bartsch, Ronny P.; Hausdorff, Jeffrey M.; Nunes Amaral, Luís A.; Schulte-Frohlinde, Verena; Stanley, H. Eugene; Yoneyama, Mitsuru

    2009-04-01

    Many physical and physiological signals exhibit complex scale-invariant features characterized by 1/f scaling and long-range power-law correlations, indicating a possibly common control mechanism. Specifically, it has been suggested that dynamical processes, influenced by inputs and feedback on multiple time scales, may be sufficient to give rise to 1/f scaling and scale invariance. Two examples of physiologic signals that are the output of hierarchical multiscale physiologic systems under neural control are the human heartbeat and human gait. Here we show that while both cardiac interbeat interval and gait interstride interval time series under healthy conditions have comparable 1/f scaling, they still may belong to different complexity classes. Our analysis of the multifractal scaling exponents of the fluctuations in these two signals demonstrates that in contrast to the multifractal behavior found in healthy heartbeat dynamics, gait time series exhibit less complex, close to monofractal behavior. Further, we find strong anticorrelations in the sign and close to random behavior for the magnitude of gait fluctuations at short and intermediate time scales, in contrast to weak anticorrelations in the sign and strong positive correlation for the magnitude of heartbeat interval fluctuations—suggesting that the neural mechanisms of cardiac and gait control exhibit different linear and nonlinear features. These findings are of interest because they underscore the limitations of traditional two-point correlation methods in fully characterizing physiological and physical dynamics. In addition, these results suggest that different mechanisms of control may be responsible for varying levels of complexity observed in physiological systems under neural regulation and in physical systems that possess similar 1/f scaling.

  17. The potential of the HAWC Observatory to observe violations of Lorentz Invariance

    CERN Document Server

    Nellen, Lukas

    2015-01-01

    The framework of relativistic quantum-field theories requires Lorentz Invariance. Many theories of quantum gravity, on the other hand, include violations of Lorentz Invariance at small scales and high energies. This generates a lot of interest in establishing limits on such effects, and, if possible, observing them directly. Gamma-ray observatories provide a tool to probe parts of the parameter space of models of Lorentz Invariance Violation that is not accessible in terrestrial laboratories and man-made accelerators. Transients, especially gamma-ray bursts, are a particularly promising class of events to search for such phenomena. By combining cosmological distances with high energy emission and short duration, emitting photons up to 30 GeV in less than a second, one can measure the energy dependence of the speed of photons to one part in $10^{16}$. We will discuss the potential of HAWC to detect effects of the violation of Lorentz Invariance and place its sensitivity in the context of existing limits.

  18. Rates of convergence in the strong invariance principle for non adapted sequences. Application to ergodic automorphisms of the torus

    CERN Document Server

    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.

  19. My Class

    Institute of Scientific and Technical Information of China (English)

    赵传怡

    2006-01-01

    My name is Zhao Chuanyi.I am in Class Ten Grade seven.There are 61 students in our class.And 26 are girls and 35 are boys.One is from America.Boys like football and basketball.Girls like singing and dancing.We are all

  20. Word classes

    DEFF Research Database (Denmark)

    Rijkhoff, Jan

    2007-01-01

    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 – Adjective...

  1. 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...... outcomes. This study uses new microdata from East Africa, incorporating test score data for over 250,000 children, to compare the likely efficacy of these two types of interventions. Endogeneity bias is addressed via fixed effects and instrumental variables techniques. Although these may not fully mitigate...

  2. Social class, power, and selfishness: when and why upper and lower class individuals behave unethically.

    Science.gov (United States)

    Dubois, David; Rucker, Derek D; Galinsky, Adam D

    2015-03-01

    Are the rich more unethical than the poor? To answer this question, the current research introduces a key conceptual distinction between selfish and unethical behavior. Based on this distinction, the current article offers 2 novel findings that illuminate the relationship between social class and unethical behavior. First, the effects of social class on unethical behavior are not invariant; rather, the effects of social class are moderated by whether unethical behavior benefits the self or others. Replicating past work, social class positively predicted unethical behavior; however, this relationship was only observed when that behavior was self-beneficial. When unethical behavior was performed to benefit others, social class negatively predicted unethical behavior; lower class individuals were more likely than upper class individuals to engage in unethical behavior. Overall, social class predicts people's tendency to behave selfishly, rather than predicting unethical behavior per se. Second, individuals' sense of power drove the effects of social class on unethical behavior. Evidence for this relationship was provided in three forms. First, income, but not education level, predicted unethical behavior. Second, feelings of power mediated the effect of social class on unethical behavior, but feelings of status did not. Third, two distinct manipulations of power produced the same moderation by self-versus-other beneficiary as was found with social class. The current theoretical framework and data both synthesize and help to explain a range of findings in the social class and power literatures. PMID:25621858

  3. The measurement invariance of schizotypy in Europe.

    Science.gov (United States)

    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

  4. A Gamma Class Formula for Open Gromov-Witten Calculations

    CERN Document Server

    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.

  5. Donaldson invariants for nonsimply connected manifolds

    CERN Document Server

    Marino, M; Marino, Marcos; Moore, Gregory

    1999-01-01

    We study Coulomb branch (``u-plane'') integrals for $\\CN=2$ supersymmetric $SU(2),SO(3)$ Yang-Mills theory on 4-manifolds $X$ of $b_1(X)>0, b_2^+(X)=1$. Using wall-crossing arguments we derive expressions for the Donaldson invariants for manifolds with $b_1(X)>0, b_2^+(X)>0$. Explicit expressions for $X=\\IC P^1 \\times F_g$, where $F_g$ is a Riemann surface of genus $g$ are obtained using Kronecker's double series identity. The result might be useful in future studies of quantum cohomology.

  6. Invariant Regularization of Supersymmetric Chiral Gauge Theory

    CERN Document Server

    Suzuki, H

    1999-01-01

    We present a regularization scheme which respects the supersymmetry and the maximal background gauge covariance in supersymmetric chiral gauge theories. When the anomaly cancellation condition is satisfied, the effective action in the superfield background field method automatically restores the gauge invariance without counterterms. The scheme also provides a background gauge covariant definition of composite operators that is especially useful in analyzing anomalies. We present several applications: The minimal consistent gauge anomaly; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.

  7. Gauge invariant actions for string models

    Energy Technology Data Exchange (ETDEWEB)

    Banks, T.

    1986-06-01

    String models of unified interactions are elegant sets of Feynman rules for the scattering of gravitons, gauge bosons, and a host of massive excitations. The purpose of these lectures is to describe the progress towards a nonperturbative formulation of the theory. Such a formulation should make the geometrical meaning of string theory manifest and explain the many ''miracles'' exhibited by the string Feynman rules. There are some new results on gauge invariant observables, on the cosmological constant, and on the symmetries of interacting string field theory. 49 refs.

  8. Broken Lifshitz invariance, spin waves and hydrodynamics

    CERN Document Server

    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.

  9. Origin of gauge invariance in string theory

    Science.gov (United States)

    Horowitz, G. T.; Strominger, A.

    1986-01-01

    A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.

  10. Higgs boson mass from gauge invariant operators

    CERN Document Server

    Jora, Renata

    2016-01-01

    We make the assumption that the vacuum correlators of the gauge invariant kinetic term of the Higgs doublet are the same before and after the spontaneous symmetry breaking of the theory. Based on this we determine the mass of the standard model Higgs boson at $m_h \\approx 125.07$ GeV by considering one loop and the most relevant two loop corrections. This result might suggest that there is a single Higgs boson doublet that contributes to the electroweak symmetry breaking.

  11. Sheaves on Graphs and Their Homological Invariants

    OpenAIRE

    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 supermodul...

  12. Translational invariant shell model for Λ hypernuclei

    Directory of Open Access Journals (Sweden)

    Jolos R.V.

    2016-01-01

    Full Text Available We extend shell model for Λ hypernuclei suggested by Gal and Millener by including 2ћω excitations in the translation invariant version to estimate yields of different hyperfragments from primary p-shell hypernuclei. We are inspired by the first successful experiment done at MAMI which opens way to study baryon decay of hypernuclei. We use quantum numbers of group SU(4, [f], and SU(3, (λμ, to classify basis wave functions and calculate coefficients of fractional parentage.

  13. Gauge invariant actions for string models

    International Nuclear Information System (INIS)

    String models of unified interactions are elegant sets of Feynman rules for the scattering of gravitons, gauge bosons, and a host of massive excitations. The purpose of these lectures is to describe the progress towards a nonperturbative formulation of the theory. Such a formulation should make the geometrical meaning of string theory manifest and explain the many ''miracles'' exhibited by the string Feynman rules. There are some new results on gauge invariant observables, on the cosmological constant, and on the symmetries of interacting string field theory. 49 refs

  14. Neutrinos superluminality and Local Lorentz Invariance

    CERN Document Server

    Cardone, F; Petrucci, A

    2011-01-01

    The recent measurement of the neutrino velocity with the OPERA detector in the CNGS beam, on whose basis it was found that (v-c)/c = (2.48 \\pm 0.28 (stat.) \\pm 0.30 (sys.)) 10e-5, does not contain any significant violation of Local Lorentz Invariance (LLI), since the corresponding value of the parameter delta=(u/c)^2-1, that represents the upper limit of the breakdown of LLI, is at least three orders of magnitude higher than the known lower limit reported in literature and is compatible with the values estimated by other experiments carried out so far.

  15. Gauge Invariance of Thermal Transport Coefficients

    Science.gov (United States)

    Ercole, Loris; Marcolongo, Aris; Umari, Paolo; Baroni, Stefano

    2016-10-01

    Thermal transport coefficients are independent of the specific microscopic expression for the energy density and current from which they can be derived through the Green-Kubo formula. We discuss this independence in terms of a kind of gauge invariance resulting from energy conservation and extensivity, and demonstrate it numerically for a Lennard-Jones fluid, where different forms of the microscopic energy density lead to different time correlation functions for the heat flux, all of them, however, resulting in the same value for the thermal conductivity.

  16. Invariant quantities of a nondepolarizing Mueller matrix

    CERN Document Server

    Gil, Jose J

    2016-01-01

    Orthogonal Mueller matrices can be considered either as corresponding to retarders or to generalized transformations of the polarization basis for the representation of Stokes vectors, so that they constitute the only type of Mueller matrices that preserve the degree of polarization and the intensity of any partially-polarized input Stokes vector. The physical quantities which remain invariant when a nondepolarizing Mueller matrix is transformed through its product by different types of orthogonal Mueller matrices are identified and interpreted, providing a better knowledge of the information contained in a nondepolarizing Mueller matrix.

  17. Invariant quantities of a nondepolarizing Mueller matrix.

    Science.gov (United States)

    Gil, José J; José, Ignacio San

    2016-07-01

    Orthogonal Mueller matrices can be considered as corresponding either to retarders or to generalized transformations of the polarization basis for the representation of Stokes vectors, so that they constitute the only type of Mueller matrices that preserve the degree of polarization and the intensity of any partially polarized input Stokes vector. The physical quantities that remain invariant when a nondepolarizing Mueller matrix is transformed through its product by different types of orthogonal Mueller matrices are identified and interpreted, providing a better knowledge of the information contained in a nondepolarizing Mueller matrix. PMID:27409687

  18. Lower bounds for the strict invariance entropy

    International Nuclear Information System (INIS)

    In this paper, we present a new method for obtaining lower bounds of the strict invariance entropy by combining an approach from the theory of escape rates and geometric methods used in the dimension theory of dynamical systems. For uniformly expanding systems and for inhomogeneous bilinear systems we can describe the lower bounds in terms of uniform volume growth rates on subbundles of the tangent bundle. In particular, we obtain criteria for positive entropy. We also apply the estimates to bilinear systems on projective space

  19. Modular invariance and covariant loop calculus

    International Nuclear Information System (INIS)

    The covariant loop calculus provides and efficient technique for computing explicit expressions for the density on moduli space corresponding to arbitrary (bosonic string) loop diagrams. Since modular invariance is not manifest, however, we carry out a detailed comparison with known explicit 2- and 3- loop results derived using analytic geometry (1 loop is known to be ok). We establish identity to 'high' order in some moduli and exactly in others. Agreement is found as a result of various non-trivial cancellations, in part related to number theory. We feel our results provide very strong support for the correctness of the covariant loop calculus approach. (orig.)

  20. 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.

  1. Geometric local invariants and pure three-qubit states

    International Nuclear Information System (INIS)

    We explore a geometric approach to generating local SU(2) and SL(2,C) invariants for a collection of qubits inspired by lattice gauge theory. Each local invariant or ''gauge'' invariant is associated with a distinct closed path (or plaquette) joining some or all of the qubits. In lattice gauge theory, the lattice points are the discrete space-time points, the transformations between the points of the lattice are defined by parallel transporters, and the gauge invariant observable associated with a particular closed path is given by the Wilson loop. In our approach the points of the lattice are qubits, the link transformations between the qubits are defined by the correlations between them, and the gauge invariant observable, the local invariants associated with a particular closed path, are also given by a Wilson looplike construction. The link transformations share many of the properties of parallel transporters, although they are not undone when one retraces one's steps through the lattice. This feature is used to generate many of the invariants. We consider a pure three-qubit state as a test case and find we can generate a complete set of algebraically independent local invariants in this way; however, the framework given here is applicable to generating local unitary invariants for mixed states composed of any number of d-level quantum systems. We give an operational interpretation of these invariants in terms of observables.

  2. Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation

    DEFF Research Database (Denmark)

    Fyhn, Karsten; Duarte, Marco F.; Jensen, Søren Holdt

    2015-01-01

    -invariant signals, exemplified with the time delay estimation problem. The evaluation is based on three performance metrics: estimator precision, sampling rate and computational complexity. We use compressive sensing with all the algorithms to lower the necessary sampling rate and show that it is still possible......-resolution algorithm. The algorithms studied here provide various tradeoffs between computational complexity, estimation precision, and necessary sampling rate. The work shows that compressive sensing for the class of sparse translation-invariant signals allows for a decrease in sampling rate and that the use of polar......We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in two aspects: (i) we extend the formulation from real non...

  3. A Covariant Master Theory for Novel Galilean Invariant Models and Massive Gravity

    CERN Document Server

    Gabadadze, Gregory; Khoury, Justin; Pirtskhalava, David; Trodden, Mark

    2012-01-01

    Coupling the galileons to a curved background has been a tradeoff between maintaining second order equations of motion, maintaining the galilean shift symmetries, and allowing the background metric to be dynamical. We propose a construction which can achieve all three for a novel class of galilean invariant models, by coupling a scalar with the galilean symmetry to a massive graviton. This generalizes the brane construction for galileons, by adding to the brane a dynamical metric, (non-universally) interacting with the galileon field. Alternatively, it can be thought of as an extension of the ghost-free massive gravity, or as a massive graviton-galileon scalar-tensor theory. In the decoupling limit of these theories, new kinds of galileon invariant interactions arise between the scalar and the longitudinal mode of the graviton. These have higher order equations of motion and infinite powers of the field, yet are ghost-free.

  4. A TQFT associated to the LMO invariant of three-dimensional manifolds

    DEFF Research Database (Denmark)

    Cheptea, Dorin; Le, Thang

    2007-01-01

    We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. This is ......We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category....... This is built together with its truncations with respect to a natural grading, and we prove that these TQFTs are non-degenerate and anomaly-free. The TQFT(s) induce(s) a (series of) representation(s) of a subgroup ${\\cal L}_g$ of the Mapping Class Group that contains the Torelli group. The $N=1$ truncation...

  5. Longitudinal foliation rigidity and Lipschitz-continuous invariant forms for hyperbolic flows

    CERN Document Server

    Foulon, Patrick

    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 longitudinal KAM-cocycle, which in turn implies that the subbundle is Lipschitz-continuous and indeed that the flow is smoothly conjugate to an algebraic one. To establish the latter, we prove results for algebraic Anosov systems that imply smoothness and a special structure for any Lipschitz-continuous invariant 1-form. Several features of the reasoning are interesting: The use of exterior calculus for Lipschitz-continuous forms, that the arguments for geodesic flows and infranilmanifoldautomorphisms are quite different, a...

  6. Time Invariant Surface Roughness Evolution during Atmospheric Pressure Thin Film Depositions.

    Science.gov (United States)

    Merkh, Thomas; Spivey, Robert; Lu, Toh Ming

    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-shadowing growth mechanism responsible for this regime occurs when particles undergo binary collisions beneath the surface apexes. Hence, this mechanism is applicable when the mean free path of the depositing species is comparable to the amplitude of the surface features. Computationally this has been modeled by allowing particles to change direction at a specified height above the local film surface. This modification of the incoming flux trajectory consequently has a dramatic smoothening effect, and the resulting surfaces appear in agreement with recent experimental observations. PMID:26814165

  7. Invariant differential operators for non-compact Lie groups: The main su(n, n) cases

    Energy Technology Data Exchange (ETDEWEB)

    Dobrev, V. K., E-mail: vkdobrev@yahoo.com [Bulgarian Academy of Sciences, Institute of Nuclear Research and Nuclear Energy (Bulgaria)

    2013-08-15

    In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras su(n, n). Our choice of these algebras is motivated by the fact that for n = 2 this is the conformal algebra of 4-dimensional Minkowski space-time. Furthermore for general n these algebras belong to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of n{sup 2}-dimensional Minkowski space-time. We give the main multiplets of indecomposable elementary representations for n = 2, 3, 4, including the necessary data for all relevant invariant differential operators.

  8. Invariant Measures with Bounded Variation Densities for Piecewise Area Preserving Maps

    CERN Document Server

    Zhang, Yiwei

    2011-01-01

    We investigate the properties of absolutely continuous invariant probability measures (ACIPs) for piecewise area preserving maps (PAPs) on $\\mathbb{R}^d$. This class of maps unifies piecewise isometries (PWIs) and piecewise hyperbolic maps where Lebesgue measure is locally preserved. In particular for PWIs, we use a functional approach to explore the relationship between topological transitivity and uniqueness of ACIPs, especially those measures with bounded variation densities. Our results "partially" answer one of the fundamental questions posed in \\cite{Goetz03} - determine all invariant non-atomic probability Borel measures in piecewise rotations. When reducing to interval exchange transformations (IETs), we demonstrate that for non-uniquely ergodic IETs with two or more ACIPs, these ACIPs have very irregular densities (namely of unbounded variation and discontinuous everywhere) and intermingle with each other.

  9. Emergent Cosmology, Inflation and Dark Energy from Spontaneous Breaking of Scale Invariance

    CERN Document Server

    Guendelman, Eduardo; Nissimov, Emil; Pacheva, Svetlana

    2014-01-01

    A new class of gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold are studied in some detail. These models involve an additional R^2 (square of the scalar curvature) term as well as scalar matter field potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry. Scale invariance is spontaneously broken upon integration of the equations of motion. After performing transition to the physical Einstein frame we obtain: (i) An effective potential for the scalar field with two flat regions which allows for a unified description of both early universe inflation as well as of present dark energy epoch; (ii) For a definite parameter range the model possesses a non-singular "emergent universe" solution which describes an initial phase of evolution that precedes the inflationary phase.

  10. Gauge-invariant theories of linear response for strongly correlated superconductors

    Science.gov (United States)

    Boyack, Rufus; Anderson, Brandon M.; Wu, Chien-Te; Levin, K.

    2016-09-01

    We present a diagrammatic theory for determining consistent electromagnetic response functions in strongly correlated fermionic superfluids. While a gauge-invariant electromagnetic response is well understood at the BCS level, a treatment of correlations beyond BCS theory requires extending this theoretical formalism. The challenge in such systems is to maintain gauge invariance, while simultaneously incorporating additional self-energy terms arising from strong correlation effects. Central to our approach is the application of the Ward-Takahashi identity, which introduces collective mode contributions in the response functions and guarantees that the f -sum rule is satisfied. We outline a powerful method, which determines these collective modes in the presence of correlation effects and in a manner compatible with gauge invariance. Since this method is based on fundamental aspects of quantum field theory, the underlying principles are broadly applicable to strongly correlated superfluids. As an illustration of the technique, we apply it to a simple class of theoretical models that contain a frequency-independent order parameter. These models include BCS-BEC crossover theories of the ultracold Fermi gases, along with models specifically associated with the high-Tc cuprates. Finally, as an alternative approach, we contrast with the path integral formalism. Here, the calculation of gauge-invariant response appears more straightforward. However, the collective modes introduced are those of strict BCS theory, without any modification from additional correlations. As the path integral simultaneously addresses electrodynamics and thermodynamics, we emphasize that it should be subjected to a consistency test beyond gauge invariance, namely that of the compressibility sum rule. We show how this sum rule fails in the conventional path integral approach.

  11. INVARIANT FORM AND INTEGRAL INVARIANTS ON K(A)HLER MANIFOLD

    Institute of Scientific and Technical Information of China (English)

    ZHANG Rong-ye

    2006-01-01

    The important notions and results of the integral invariants of Poincaré and lished first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on K(a)hler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider and deeper results.

  12. Hidden Supersymmetry May Imply Duality Invariance

    CERN Document Server

    Carrasco, John Joseph M

    2013-01-01

    We provide evidence that a particular hidden supersymmetry, when combined with half-maximal deformed global supersymmetry, implies that the theory is invariant under duality rotations of the vector and spinor fields. Based on a complete 8+8 supersymmetric model constructed recently, we argue that this hidden supersymmetry happens if and only if there is a Born-Infeld dependence on the Maxwell field strength and a Volkov-Akulov dependence on the Goldstino, up to local non-linear field redefinitions. We have tested our proposal for the N=2 superfield action with manifest N=2 supersymmetry and hidden N=2 supersymmetry at the level W^{10}, the highest level of deformation known for this model. We have established that it is N=2 self-dual, although the self-duality was not required in the original construction of this model. Highlighting the utility of considering duality-conserving sources of deformation, we can verify this invariance directly in an alternate construction of this very same action.

  13. Noise-assisted estimation of attractor invariants

    Science.gov (United States)

    Restrepo, Juan F.; Schlotthauer, Gastón

    2016-07-01

    In this article, the noise-assisted correlation integral (NCI) is proposed. The purpose of the NCI is to estimate the invariants of a dynamical system, namely the correlation dimension (D ), the correlation entropy (K2), and the noise level (σ ). This correlation integral is induced by using random noise in a modified version of the correlation algorithm, i.e., the noise-assisted correlation algorithm. We demonstrate how the correlation integral by Grassberger et al. and the Gaussian kernel correlation integral (GCI) by Diks can be thought of as special cases of the NCI. A third particular case is the U -correlation integral proposed herein, from which we derived coarse-grained estimators of the correlation dimension (DmU), the correlation entropy (KmU), and the noise level (σmU). Using time series from the Henon map and the Mackey-Glass system, we analyze the behavior of these estimators under different noise conditions and data lengths. The results show that the estimators DmU and σmU behave in a similar manner to those based on the GCI. However, for the calculation of K2, the estimator KmU outperforms its GCI-based counterpart. On the basis of the behavior of these estimators, we have proposed an automatic algorithm to find D ,K2, and σ from a given time series. The results show that by using this approach, we are able to achieve statistically reliable estimations of those invariants.

  14. Test of Lorentz Invarience from Compton Scattering

    CERN Document Server

    Mohanmurthy, Prajwal; Narayan, Amrendra

    2015-01-01

    In the recent times, test of Lorentz Invariance has been used as a means to probe theories of physics beyond the standard model, especially those such as extensions to String Theory and Quantum Gravity. Tests of Lorentz invariance could go a long way in setting the stage for possible quantum gravity theories which are beyond the standard model. We describe a simple way of utilizing the polarimeters, which are a critical beam instrument at precision and intensity frontier nuclear physics labs such as Stanford Linear Accelerator Center (SLAC) and Jefferson Lab (JLab), to limit the dependence of speed of light with the energy of the photons. Furthermore, we also describe a way of limiting directional dependence of speed of light at previously unprecedented levels of precision by studying the sidereal variations. We obtain a limit of MSME parameters: $\\sqrt{\\kappa_X^2 + \\kappa_Y^2} < 2.4 \\times 10^{-17}$ and $\\sqrt{\\left( 2c_{TX} - (\\tilde{\\kappa}_{0^+}^{YZ} \\right)^2 + \\left( 2c_{TY} - (\\tilde{\\kappa}_{0^+}^{...

  15. Quasi-Invariants of Complex Reflection Groups

    CERN Document Server

    Berest, Yuri

    2009-01-01

    We introduce quasi-invariant polynomials for an arbitrary finite complex reflection group W. Unlike in the Coxeter case, the space Q_k of quasi-invariants of a given multiplicity is not, in general, an algebra but a module over the coordinate ring of some (singular) affine variety X_k. We extend the main results of Etingof, Ginzburg and the first author (see [BEG]) to this setting: in particular, we show that the variety X_k and the module Q_k are Cohen-Macaulay, and the rings of differential operators on X_k and Q_k are simple rings, Morita equivalent to the Weyl algebra A_n(C), where n = dim X_k . Our approach relies on representation theory of complex Cherednik algebras and is parallel to that of [BEG]. As a by-product, we prove the existence of shift operators for an arbitrary complex reflection group, confirming a conjecture of Dunkl and Opdam. Another result is a proof of a conjecture of Opdam, concerning certain operations (KZ twists) on the set of irreducible representations of W.

  16. The Manifestly Gauge Invariant Exact Renormalisation Group

    CERN Document Server

    Rosten, O J

    2005-01-01

    We construct a manifestly gauge invariant Exact Renormalisation Group (ERG) whose form is suitable for computation in SU(N) Yang-Mills theory, beyond one-loop. An effective cutoff is implemented by embedding the physical SU(N) theory in a spontaneously broken SU(N|N) Yang-Mills theory. To facilitate computations within this scheme, which proceed at every step without fixing the gauge, we develop a set of diagrammatic techniques. As an initial test of the formalism, the one-loop SU(N) Yang-Mills beta-function, beta_1, is computed, and the standard, universal answer is reproduced. It is recognised that the computational technique can be greatly simplified. Using these simplifications, a partial proof is given that, to all orders in perturbation theory, the explicit dependence of perturbative $\\beta$-function coefficients, beta_n, on certain non-universal elements of the manifestly gauge invariant ERG cancels out. This partial proof yields an extremely compact, diagrammatic form for the surviving contributions t...

  17. An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation

    CERN Document Server

    Wu, Panyu

    2011-01-01

    The classical law of the iterated logarithm (LIL for short)as fundamental limit theorems in probability theory play an important role in the development of probability theory and its applications. Strassen (1964) extended LIL to large classes of functional random variables, it is well known as the invariance principle for LIL which provide an extremely powerful tool in probability and statistical inference. But recently many phenomena show that the linearity of probability is a limit for applications, for example in finance, statistics. As while a nonlinear expectation--- G-expectation has attracted extensive attentions of mathematicians and economists, more and more people began to study the nature of the G-expectation space. A natural question is: Can the classical invariance principle for LIL be generalized under G-expectation space? This paper gives a positive answer. We present the invariance principle of G-Brownian motion for the law of the iterated logarithm under G-expectation.

  18. Conformal invariance in the long-range Ising model

    Directory of Open Access Journals (Sweden)

    Miguel F. Paulos

    2016-01-01

    Full Text Available We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.

  19. Conformal Invariance in the Long-Range Ising Model

    CERN Document Server

    Paulos, Miguel F; van Rees, Balt C; Zan, Bernardo

    2016-01-01

    We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.

  20. Disambiguating seesaw models using invariant mass variables at hadron colliders

    Science.gov (United States)

    Dev, P. S. Bhupal; Kim, Doojin; Mohapatra, Rabindra N.

    2016-01-01

    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 discuss the future prospects of testing these scenarios at the √{s}=14 and 100 TeV hadron colliders.

  1. S-duality invariant perturbation theory improved by holography

    CERN Document Server

    Chowdhury, Abhishek; Thakur, Somyadip

    2016-01-01

    We study anomalous dimensions of unprotected low twist operators in the four-dimensional $SU(N)$ $\\mathcal{N}=4$ supersymmetric Yang-Mills theory. We construct a class of interpolating functions to approximate the dimensions of the leading twist operators for arbitrary gauge coupling $\\tau$. The interpolating functions are consistent with previous results on the perturbation theory, holographic computation and full S-duality. We use our interpolating functions to test the recent conjecture by the $\\mathcal{N}=4$ superconformal bootstrap that upper bounds on the dimensions are saturated at one of the duality-invariant points $\\tau =i$ and $\\tau =e^{i\\pi /3}$. It turns out that our interpolating functions have maximum at $\\tau =e^{i\\pi /3}$, which are close to the conjectural values by the conformal bootstrap. In terms of the interpolating functions, we draw image of conformal manifold in the space of the dimensions. We find that the image is almost a line despite the conformal manifold is two-dimensional. We a...

  2. Generation of scale invariant magnetic fields in bouncing universes

    CERN Document Server

    Sriramkumar, L; Jain, Rajeev Kumar

    2015-01-01

    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 fields can arise {\\it before the bounce} for certain values of the indices involved. It will be interesting to examine if these power spectra retain their shape {\\it 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 ${\\rm e}$-${\\cal N}$-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 eva...

  3. Topological invariants for interacting topological insulators with inversion symmetry

    OpenAIRE

    Wang, Zhong; Qi, Xiao-Liang; Zhang, Shou-Cheng

    2012-01-01

    For interacting Z_2 topological insulators with inversion symmetry, we propose a simple topological invariant expressed in terms of the parity eigenvalues of the interacting Green's function at time-reversal invariant momenta. We derive this result from our previous formula involving the integral over the frequency-momenta space. This formula greatly simplifies the explicit calculation of Z_2 topological invariants in inversion symmetric insulators with strong interactions.

  4. Quantum Hyperbolic Invariants for Diffeomorphisms of Small Surfaces

    Institute of Scientific and Technical Information of China (English)

    Xiaobo LIU

    2012-01-01

    An earlier article [Bonahon,F.,Liu,X.B.:Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms.Geom. Topol.,11,889-937 (2007)] introduced new invariants for pseudo-Anosov diffeomorphisms of surface,based on the representation theory of the quantum Teichmüller space.We explicitly compute these quantum hyperbolic invariants in the case of the 1-puncture torus and the 4-puncture sphere.

  5. Complex dynamical invariants for two-dimensional complex potentials

    Indian Academy of Sciences (India)

    J S Virdi; F Chand; C N Kumar; S C Mishra

    2012-08-01

    Complex dynamical invariants are searched out for two-dimensional complex potentials using rationalization method within the framework of an extended complex phase space characterized by $x = x_{1} + ip_{3}. y = x_{2} + ip_{4}, p_{x} = p_{1} + ix_{3}, p_{y} = p_{2} + ix_{4}$. It is found that the cubic oscillator and shifted harmonic oscillator admit quadratic complex invariants. THe obtained invariants may be useful for studying non-Hermitian Hamiltonian systems.

  6. Form Invariance and Noether Symmetries of Rotational Relativistic Birkhoff Systems

    Institute of Scientific and Technical Information of China (English)

    LUOShao-Kai

    2002-01-01

    Under the infinitesimal transformations of groups,a form invariance of rotational relativistic Birkhoff systems is studied and the definition and criteria are given,In view of the invariance of rotational relativistic Pfaff-Birkhoff-D' Alembert principle under the infinitesimal transformations of groups,the theory of Noether symmetries of rotational relativistic Birkhoff systems are constructed.The relation between the form invariance and the Noether symmetries is studied ,and the conserved quantities of rotational relativistic Birkhoff systems are obtained.

  7. Form Invariance and Noether Symmetries of Rotational Relativistic Birkhoff Systems

    Institute of Scientific and Technical Information of China (English)

    LUO Shao-Kai

    2002-01-01

    Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoffsystems is studied and the definition and criteria are given. In view of the invariance of rotational relativistic PfaffBirkhoff D'Alcmbert principle under the infinitesimal transformations of groups, the theory of Noether symmetries ofrotational relativistic Birkhoff systems are constructed. The relation between the form invariance and the Noethersymmetries is studied, and the conserved quantities of rotational relativistic Birkhoff systems are obtained.

  8. BIFURCATIONS OF INVARIANT CURVES OF A DIFFERENCE EQUATION

    Institute of Scientific and Technical Information of China (English)

    贺天兰

    2001-01-01

    Bifurcation of the invariant curves of a difference equation is studied. The system defined by the difference equation is integrable , so the study of the invariant curves of the difference system can become the study of topological classification of the planar phase portraits defined by a planar Hamiltonian system. By strict qualitative analysis, the classification of the invariant curves in parameter space can be obtained.

  9. Graph Invariants of Finite Groups via a Theorem of Lagarias

    OpenAIRE

    Akman, Fusun

    2006-01-01

    We introduce a new graph invariant of finite groups that provides a complete characterization of the splitting types of unramified prime ideals in normal number field extensions entirely in terms of the Galois group. In particular, each connected component corresponds to a division (Abteilung) of the group. We compute the divisions of the alternating group, and compile a list of characteristics of groups that the invariant reveals. We conjecture that the invariant distinguishes finite groups....

  10. Scale-invariant correlations and the distribution of prime numbers

    International Nuclear Information System (INIS)

    Negative correlations in the distribution of prime numbers are found to display a scale invariance. This occurs in conjunction with a nonstationary behavior. We compare the prime number series to a type of fractional Brownian motion which incorporates both the scale invariance and the nonstationary behavior. Interesting discrepancies remain. The scale invariance also appears to imply the Riemann hypothesis and we study the use of the former as a test of the latter.

  11. Three-order form invariance and conserved quantity

    Institute of Scientific and Technical Information of China (English)

    Yang Xue-Hui; Ma Shan-Jun

    2006-01-01

    In this paper,the definition of three-order form invariance is given.Then the relation between the three-order form invariance and the three-order Lie symmetry is discussed and the sufficient and necessary condition of Lie symmetry, which comes from the three-order form invariance,is obtained.Finally a three-order Hojman conserved quantity isstudied and an example is given to illustrate the application of the obtained results.

  12. Chern-Simons Invariants of Torus Knots and Links

    CERN Document Server

    Stevan, Sébastien

    2010-01-01

    We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus links and we obtain an analogous formula for Kauffman invariants. We also derive a formula for cable knots. We use our results to test a recently proposed conjecture that relates HOMFLY and Kauffman invariants.

  13. Symplectic invariants, entropic measures and correlations of Gaussian states

    OpenAIRE

    Serafini, Alessio; Illuminati, Fabrizio; De Siena, Silvio

    2003-01-01

    We present a derivation of the Von Neumann entropy and mutual information of arbitrary two--mode Gaussian states, based on the explicit determination of the symplectic eigenvalues of a generic covariance matrix. The key role of the symplectic invariants in such a determination is pointed out. We show that the Von Neumann entropy depends on two symplectic invariants, while the purity (or the linear entropy) is determined by only one invariant, so that the two quantities provide two different h...

  14. Vassiliev invariants a new framework for quantum gravity

    CERN Document Server

    Gambini, R; Pullin, J; Gambini, Rodolfo; Griego, Jorge; Pullin, Jorge

    1998-01-01

    We show that Vassiliev invariants of knots, appropriately generalized to the spin network context, are loop differentiable in spite of being diffeomorphism invariant. This opens the possibility of defining rigorously the constraints of quantum gravity as geometrical operators acting on the space of Vassiliev invariants of spin nets. We show how to explicitly realize the diffeomorphism constraint on this space and present proposals for the construction of Hamiltonian constraints.

  15. Two Dimensional Hamiltonian with Generalized Shape Invariance Symmetry

    OpenAIRE

    Panahi-Talemi, H.; Jafarizadeh, M. A.

    2002-01-01

    The two dimensional Hamiltonian with generalized shape invariance symmetry over $S^2$, has been obtained via Fourier transformation over the three coordinates of the $SU(3)$ Casimir operator defined on $SU(3)/SU(2)$ symmetric space. It is shown that the generalized shape invariance is equivalent to $SU(3)$ symmetry and that there is one to one correspondence between the representations of the generalized shape invariance and $SU(3)$ Verma modules. Also the two dimensional Hamiltonian in $\\mat...

  16. Class distinction

    Science.gov (United States)

    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.

  17. Baer-invariants with Respect to Two Varieties of Groups

    Institute of Scientific and Technical Information of China (English)

    Mohammad Reza R. Moghaddam; Ali Reza Salemkar; Mostafa Taheri

    2001-01-01

    This paper is devoted to present some properties of the Baer-invariants of groups with respect to two varieties V and W of groups. We give some inequalities for such Baer-invariants of finite groups. A generalized version of the Stalling type theorem is presented. Also, if N is a normal subgroup of a group G in the variety W, then we give a necessary and sufficient condition for which the Baer-invariant of G can be embedded into the Baer-invariant of the factor group G/N.

  18. Binary optical filters for scale invariant pattern recognition

    Science.gov (United States)

    Reid, Max B.; Downie, John D.; Hine, Butler P.

    1992-01-01

    Binary synthetic discriminant function (BSDF) optical filters which are invariant to scale changes in the target object of more than 50 percent are demonstrated in simulation and experiment. Efficient databases of scale invariant BSDF filters can be designed which discriminate between two very similar objects at any view scaled over a factor of 2 or more. The BSDF technique has considerable advantages over other methods for achieving scale invariant object recognition, as it also allows determination of the object's scale. In addition to scale, the technique can be used to design recognition systems invariant to other geometric distortions.

  19. Reconstruction algorithm in lattice-invariant signal spaces

    Institute of Scientific and Technical Information of China (English)

    XIAN Jun

    2005-01-01

    In this paper, we mainly pay attention to the weighted sampling and reconstruction algorithm in lattice-invariant signal spaces. We give the reconstruction formula in lattice-invariant signal spaces, which is a generalization of former results in shift-invariant signal spaces. That is, we generalize and improve Aldroubi, Grochenig and Chen's results, respectively. So we obtain a general reconstruction algorithm in lattice-invariant signal spaces, which the signal spaces is sufficiently large to accommodate a large number of possible models. They are maybe useful for signal processing and communication theory.

  20. Treatment of non-Gaussian noise in invariant mass calculations

    OpenAIRE

    2012-01-01

    The Gaussian Sum Filter is a track reconstruction algorithm for treating energy loss by bremsstrahlung, and produces non-Gaussian estimates for the track parameters. This thesis explores a method of propagating these non-Gaussian errors into a non-Gaussian estimate of the invariant mass. It is tested if the method can be used to improve the invariant mass resolution in ATLAS, and if it gives a good description of the errors on the invariant mass. The result showed that the invariant mas...

  1. Invariants of some compactified Picard modular surfaces and applications

    OpenAIRE

    Džambić, Amir

    2014-01-01

    The paper investigates invariants of compactified Picard modular surfaces by principal congruence subgroups of Picard modular groups. The applications to the surface classification and modular forms are discussed.

  2. Massive neutrinos, massless neutrinos, and so(4,2)invariance

    OpenAIRE

    Bracken, A. J.

    2005-01-01

    Dirac's equation for a massless particle is conformal invariant, and accordingly has an so(4,2)invariance algebra. It is known that although Dirac's equation for a massive spin 1/2 particle is not conformal invariant, it too has an so(4,2) invariance algebra. It is shown here that the algebra of operators associated with a 4-component massless particle, or two flavors of 2-component massless particles, can be deformed into the algebra of operators associated with a spin 1/2 particle with posi...

  3. Massive neutrinos, massless neutrinos, and so(4,2)invariance

    CERN Document Server

    Bracken, A J

    2005-01-01

    Dirac's equation for a massless particle is conformal invariant, and accordingly has an so(4,2)invariance algebra. It is known that although Dirac's equation for a massive spin 1/2 particle is not conformal invariant, it too has an so(4,2) invariance algebra. It is shown here that the algebra of operators associated with a 4-component massless particle, or two flavors of 2-component massless particles, can be deformed into the algebra of operators associated with a spin 1/2 particle with positive rest mass. It is speculated that this may be exploited to describe massless neutrino mixing.

  4. Metric Ranking of Invariant Networks with Belief Propagation

    Energy Technology Data Exchange (ETDEWEB)

    Tao, Changxia [Xi' an Jiaotong University, China; Ge, Yong [University of North Carolina, Charlotte; Song, Qinbao [Xi' an Jiaotong University, China; Ge, Yuan [Anhui Polytechnic University, China; Omitaomu, Olufemi A [ORNL

    2014-01-01

    The management of large-scale distributed information systems relies on the effective use and modeling of monitoring data collected at various points in the distributed information systems. A promising approach is to discover invariant relationships among the monitoring data and generate invariant networks, where a node is a monitoring data source (metric) and a link indicates an invariant relationship between two monitoring data. Such an invariant network representation can help system experts to localize and diagnose the system faults by examining those broken invariant relationships and their related metrics, because system faults usually propagate among the monitoring data and eventually lead to some broken invariant relationships. However, at one time, there are usually a lot of broken links (invariant relationships) within an invariant network. Without proper guidance, it is difficult for system experts to manually inspect this large number of broken links. Thus, a critical challenge is how to effectively and efficiently rank metrics (nodes) of invariant networks according to the anomaly levels of metrics. The ranked list of metrics will provide system experts with useful guidance for them to localize and diagnose the system faults. To this end, we propose to model the nodes and the broken links as a Markov Random Field (MRF), and develop an iteration algorithm to infer the anomaly of each node based on belief propagation (BP). Finally, we validate the proposed algorithm on both realworld and synthetic data sets to illustrate its effectiveness.

  5. On the Invariance of Residues of Feynman Graphs

    CERN Document Server

    Bierenbaum, I; Kreimer, D; Bierenbaum, Isabella; Kreckel, Richard; Kreimer, Dirk

    2002-01-01

    We use simple iterated one-loop graphs in massless Yukawa theory and QED to pose the following question: what are the symmetries of the residues of a graph under a permutation of places to insert subdivergences. The investigation confirms partial invariance of the residue under such permutations: the highest weight transcendental is invariant under such a permutation. For QED this result is gauge invariant, ie the permutation invariance holds for any gauge. Computations are done making use of the Hopf algebra structure of graphs and employing GiNaC to automate the calculations.

  6. Mutation classes of skew-symmetrizable 3x3 matrices

    CERN Document Server

    Seven, Ahmet

    2010-01-01

    In this paper, we determine representatives for the mutation classes of skew-symmetrizable 3x3 matrices and associated graphs using a natural minimality condition, generalizing and strengthening results of Beineke-Brustle-Hille and Felikson-Shapiro-Tumarkin. Furthermore, we obtain a new numerical invariant for the mutation operation on skew-symmetrizable matrices of arbitrary size.

  7. Kelvin principle for a class of singular equations

    Directory of Open Access Journals (Sweden)

    Abdullah Altin

    1989-01-01

    Full Text Available The classical Kelvin principle concerns invariance of solutions of the Laplace equation with respect to inversion in a sphere. By employing a hyperbolic-polar coordinate system, the principle is extended to cover a class of singular equations, which include the ultrahyperbolic equation.

  8. 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.

  9. Tightness of invariant distributions of a large-scale flexible service system under a priority discipline

    Directory of Open Access Journals (Sweden)

    Alexander L. Stolyar

    2012-01-01

    Full Text Available We consider large-scale service systems with multiple customer classes and multiple server pools; interarrival and service times are exponentially distributed, and mean service times depend both on the customer class and server pool. It is assumed that the allowed activities (routing choices form a tree (in the graph with vertices being both customer classes and server pools. We study the behavior of the system under a Leaf Activity Priority (LAP policy, which assigns static priorities to the activities in the order of sequential ''elimination'' of the tree leaves.We consider the scaling limit of the system as the arrival rate of customers and number of servers in each pool tend to infinity in proportion to a scaling parameter r, while the overall system load remains strictly subcritical. Indexing the systems by parameter r, we show that (a the system under LAP discipline is stochastically stable for all sufficiently large r and (b the family of the invariant distributions is tight on scales r1/2 + ε for all ε > 0. (More precisely, the sequence of invariant distributions, centered at the equilibrium point and scaled down by r− (1/2 + ε, is tight.

  10. Quasi invariant modi?ed Sobolev norms for semi linear reversible PDEs

    CERN Document Server

    Faou, Erwan

    2009-01-01

    We consider a general class of infinite dimensional reversible differential systems. Assuming a non resonance condition on the linear frequencies, we construct for such systems almost invariant pseudo norms that are closed to Sobolev-like norms. This allows us to prove that if the Sobolev norm of index $s$ of the initial data $z_0$ is sufficiently small (of order $\\epsilon$) then the Sobolev norm of the solution is bounded by $2\\epsilon$ during very long time (of order $\\epsilon^{-r}$ with $r$ arbitrary). It turns out that this theorem applies to a large class of reversible semi linear PDEs including the non linear Schr\\"odinger equation on the d-dimensional torus. We also apply our method to a system of coupled NLS equations which is reversible but not Hamiltonian. We also notice that for the same class of reversible systems we can prove a Birkhoff normal form theorem that in turn implies the same bounds on the Sobolev norms. Nevertheless the technics that we use to prove the existence of quasi invariant pse...

  11. A signal invariant wavelet function selection algorithm.

    Science.gov (United States)

    Garg, Girisha

    2016-04-01

    This paper addresses the problem of mother wavelet selection for wavelet signal processing in feature extraction and pattern recognition. The problem is formulated as an optimization criterion, where a wavelet library is defined using a set of parameters to find the best mother wavelet function. For estimating the fitness function, adopted to evaluate the performance of the wavelet function, analysis of variance is used. Genetic algorithm is exploited to optimize the determination of the best mother wavelet function. For experimental evaluation, solutions for best mother wavelet selection are evaluated on various biomedical signal classification problems, where the solutions of the proposed algorithm are assessed and compared with manual hit-and-trial methods. The results show that the solutions of automated mother wavelet selection algorithm are consistent with the manual selection of wavelet functions. The algorithm is found to be invariant to the type of signals used for classification. PMID:26253283

  12. Scale vs Conformal invariance from Entanglement Entropy

    CERN Document Server

    Naseh, Ali

    2016-01-01

    For a generic conformal field theory (CFT) in four dimensions, the scale anomaly dictates that the universal part of entanglement entropy across a sphere ($\\mathcal{C}_{\\text{univ}}(S^{2})$) is positive. Based on this fact, we explore the consequences of assuming positive sign for $\\mathcal{C}_{\\text{univ}}(S^{2})$ in a four dimensional scale invariant theory (SFT). In absence of a dimension two scalar operator $\\mathcal{O}_{2}$ in the spectrum of a SFT, we show that this assumption suggests that SFT is a CFT. In presence of $\\mathcal{O}_{2}$, we show that this assumption can fix the coefficient of the nonlinear coupling term $\\int\\hspace{-.5mm} d^{4}x\\sqrt{g} R\\mathcal{O}_{2}$ to a conformal value.

  13. Local electromagnetic duality and gauge invariance

    CERN Document Server

    Saa, Alberto

    2011-01-01

    Bunster and Henneaux and, separately, Deser have very recently considered the possibility of gauging the usual electromagnetic duality of Maxwell equations. By using off-shell manipulations in the context of the Principle of least action, they conclude that this is not possible, at least with the conventional compensating gauge fields scheme. Such a conclusion contradicts, however, an old result of Malik and Pradhan, who showed that it is indeed possible to introduce an extra abelian gauge field directly in the vacuum Maxwell equations in order to render them covariant under local duality transformations. Since it is well known that the equations of motion can, in general, admit more symmetries than the associate Lagrangian, this would not be a paradoxal result, in principle. Here, we revisit these works and identify the source of the different conclusions. We show that the Malik-Pradhan procedure does not preserve the original Maxwell gauge invariance, while Bunster, Henneaux, and Deser sought for generaliza...

  14. Lorentz Invariance Violation and Generalized Uncertainty Principle

    CERN Document Server

    Tawfik, A; Ali, A Farag

    2016-01-01

    Recent approaches for quantum gravity are conjectured to give predictions for a minimum measurable length, a maximum observable momentum and an essential generalization for the Heisenberg uncertainty principle (GUP). The latter is based on a momentum-dependent modification in the standard dispersion relation and leads to Lorentz invariance violation (LIV). The main features of the controversial OPERA measurements on the faster-than-light muon neutrino anomaly are used to calculate the time of flight delays $\\Delta t$ and the relative change $\\Delta v$ in the speed of neutrino in dependence on the redshift $z$. The results are compared with the OPERA measurements. We find that the measurements are too large to be interpreted as LIV. Depending on the rest mass, the propagation of high-energy muon neutrino can be superluminal. The comparison with the ultra high energy cosmic rays seems to reveals an essential ingredient of the approach combining string theory, loop quantum gravity, black hole physics and doubly ...

  15. Constructing invariant fairness measures for surfaces

    DEFF Research Database (Denmark)

    Gravesen, Jens; Ungstrup, Michael

    2002-01-01

    The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given...... curves should be fair with respect to an appropriate curve fairness measure. The method is applied to the field of ship hull design where the curves are plane intersections. The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family...... of curves. Six basic third order invariants by which the fairing measures can be expressed are defined. Furthermore, the geometry of a plane intersection curve is studied, and the variation of the total, the normal, and the geodesic curvature and the geodesic torsion is determined....

  16. Rotationally invariant ensembles of integrable matrices

    Science.gov (United States)

    Yuzbashyan, Emil A.; Shastry, B. Sriram; Scaramazza, Jasen A.

    2016-05-01

    We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT)—a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M family of integrable matrices consists of exactly N -M independent commuting N ×N matrices linear in a real parameter. We first develop a rotationally invariant parametrization of such matrices, previously only constructed in a preferred basis. For example, an arbitrary choice of a vector and two commuting Hermitian matrices defines a type-1 family and vice versa. Higher types similarly involve a random vector and two matrices. The basis-independent formulation allows us to derive the joint probability density for integrable matrices, similar to the construction of Gaussian ensembles in the RMT.

  17. Extended tachyon field using form invariance symmetry

    CERN Document Server

    G, Iván E Sánchez

    2014-01-01

    In this work we illustrate how form-invariance transformations (FIT) can be used to construct phantom and complementary tachyon cosmologies from standard tachyon field universes. We show how these transformations act on the Hubble expansion rate, the energy density, and pressure of the tachyon field. The FIT generate new cosmologies from a known "seed" one, in particular from the ordinary tachyon field we obtain two types of tachyon species, denominated phantom and complementary tachyon. We see that the FIT allow us to pass from a non-stable cosmology to a stable one and vice-versa, as appeared in the literature. Finally, as an example, we apply the transformations to a cosmological fluid with an inverse square potential, $V \\propto \\phi^{-2}$, and generate the extended tachyon field.

  18. Gauge invariance and Weyl-polymer quantization

    CERN Document Server

    Strocchi, Franco

    2016-01-01

    The book gives an introduction to Weyl non-regular quantization suitable for the description of physically interesting quantum systems, where the traditional Dirac-Heisenberg quantization is not applicable.  The latter implicitly assumes that the canonical variables describe observables, entailing necessarily the regularity of their exponentials (Weyl operators). However, in physically interesting cases -- typically in the presence of a gauge symmetry -- non-observable canonical variables are introduced for the description of the states, namely of the relevant representations of the observable algebra. In general, a gauge invariant ground state defines a non-regular representation of the gauge dependent Weyl operators, providing a mathematically consistent treatment of familiar quantum systems -- such as the electron in a periodic potential (Bloch electron), the Quantum Hall electron, or the quantum particle on a circle -- where the gauge transformations are, respectively, the lattice translations, the magne...

  19. Conformal transformations and conformal invariance in gravitation

    CERN Document Server

    Dabrowski, Mariusz P; Blaschke, David B

    2008-01-01

    Conformal transformations are frequently used tools in order to study relations between various theories of gravity and Einstein relativity. Because of that, in this paper we discuss the rules of conformal transformations for geometric quantities in general relativity. In particular, we discuss the conformal transformations of the matter energy-momentum tensor. We thoroughly discuss the latter and show the subtlety of the conservation law (i.e., the geometrical Bianchi identity) imposed in one of the conformal frames in reference to the other. The subtlety refers to the fact that conformal transformation ``creates'' an extra matter term composed of the conformal factor which enters the conservation law. In an extreme case of the flat original spacetime the matter is ``created'' due to work done by the conformal transformation to bend the spacetime which was originally flat. We also discuss how to construct the conformally invariant gravity which, in the simplest version, is a special case of the Brans-Dicke t...

  20. Onboard Image Registration from Invariant Features

    Science.gov (United States)

    Wang, Yi; Ng, Justin; Garay, Michael J.; Burl, Michael C

    2008-01-01

    This paper describes a feature-based image registration technique that is potentially well-suited for onboard deployment. The overall goal is to provide a fast, robust method for dynamically combining observations from multiple platforms into sensors webs that respond quickly to short-lived events and provide rich observations of objects that evolve in space and time. The approach, which has enjoyed considerable success in mainstream computer vision applications, uses invariant SIFT descriptors extracted at image interest points together with the RANSAC algorithm to robustly estimate transformation parameters that relate one image to another. Experimental results for two satellite image registration tasks are presented: (1) automatic registration of images from the MODIS instrument on Terra to the MODIS instrument on Aqua and (2) automatic stabilization of a multi-day sequence of GOES-West images collected during the October 2007 Southern California wildfires.