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Sample records for local graph invariants

  1. Convex Graph Invariants

    DTIC Science & Technology

    2010-12-02

    evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in

  2. In search for graph invariants of chemical interes

    NASA Astrophysics Data System (ADS)

    Randić, Milan; Trinajstić, Nenad

    1993-12-01

    This article encourages readers to search for novel graph invariants that may be of potential interest in chemical applications of graph theory. It is also hoped that theoreticians, with their different backgrounds and different viewpoints, may identify or design novel graph invariants that have not yet been tested in chemistry and in this way enrich the pool of descriptors for use in studies of structure—property relationships. An outline of desirable attributes for graph invariants that have found use in chemistry is followed by a brief review of a selection of known ad hoc invariants. This continues with a description of families of structurally related invariants. We discuss some promising routes to construction of novel descriptors such as those based on consideration of graph fragments. A warning against useless and misleading descriptors is given. We end with a call for design of or verification of basis graphs.

  3. Image Registration Through The Exploitation Of Perspective Invariant Graphs

    NASA Astrophysics Data System (ADS)

    Gilmore, John F.

    1983-10-01

    This paper describes two new techniques of image registration as applied to scenes consisting of natural terrain. The first technique is a syntactic pattern recognition approach which combines the spatial relationships of a point pattern with point classifications to accurately perform image registration. In this approach, a preprocessor analyzes each image in order to identify points of interest and to classify these points based on statistical features. A classified graph possessing perspective invariant properties is created and is converted into a classification-based grammar string. A local match analysis is performed and the best global match is con-structed. A probability-of-match metric is computed in order to evaluate match confidence. The second technique described is an isomorphic graph matching approach called Mean Neighbors (MN). A MN graph is constructed from a given point pattern taking into account the elliptical projections of real world scenes onto a two dimensional surface. This approach exploits the spatial relationships of the given points of interest but neglects the point classifications used in syntactic processing. A projective, perspective invariant graph is constructed for both the reference and sensed images and a mapping of the coincidence edges occurs. A probability of match metric is used to evaluate the confidence of the best mapping.

  4. Percolation critical polynomial as a graph invariant.

    PubMed

    Scullard, Christian R

    2012-10-01

    Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0,1] providing the threshold. Recent work has demonstrated that this polynomial may be generalized through a definition that can be applied on any periodic lattice. The polynomial depends on the lattice and on its decomposition into identical finite subgraphs, but once these are specified, the polynomial is essentially unique. On lattices for which the exact percolation threshold is unknown, the polynomials provide approximations for the critical probability with the estimates appearing to converge to the exact answer with increasing subgraph size. In this paper, I show how this generalized critical polynomial can be viewed as a graph invariant, similar to the Tutte polynomial. In particular, the critical polynomial is computed on a finite graph and may be found using the recursive deletion-contraction algorithm. This allows calculation on a computer, and I present such results for the kagome lattice using subgraphs of up to 36 bonds. For one of these, I find the prediction p(c)=0.52440572..., which differs from the numerical value, p(c)=0.52440503(5), by only 6.9×10(-7).

  5. Percolation critical polynomial as a graph invariant

    NASA Astrophysics Data System (ADS)

    Scullard, Christian R.

    2012-10-01

    Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0,1] providing the threshold. Recent work has demonstrated that this polynomial may be generalized through a definition that can be applied on any periodic lattice. The polynomial depends on the lattice and on its decomposition into identical finite subgraphs, but once these are specified, the polynomial is essentially unique. On lattices for which the exact percolation threshold is unknown, the polynomials provide approximations for the critical probability with the estimates appearing to converge to the exact answer with increasing subgraph size. In this paper, I show how this generalized critical polynomial can be viewed as a graph invariant, similar to the Tutte polynomial. In particular, the critical polynomial is computed on a finite graph and may be found using the recursive deletion-contraction algorithm. This allows calculation on a computer, and I present such results for the kagome lattice using subgraphs of up to 36 bonds. For one of these, I find the prediction pc=0.52440572⋯, which differs from the numerical value, pc=0.52440503(5), by only 6.9×10-7.

  6. On c_2 invariants of some 4-regular Feynman graphs

    NASA Astrophysics Data System (ADS)

    Doryn, Dmitry

    2017-03-01

    The obstruction for application of techniques like denominator reduction for the computation of the c_2 invariant of Feynman graphs in general is the absence of a 3-valent vertex. In this paper such a formula for a 4-valent vertex is derived. The formula allows us to compute the c_2 invariant of new graphs, for instance, some 4-regular graphs with small loop number.

  7. On c_2 invariants of some 4-regular Feynman graphs

    NASA Astrophysics Data System (ADS)

    Doryn, Dmitry

    2017-08-01

    The obstruction for application of techniques like denominator reduction for the computation of the c_2 invariant of Feynman graphs in general is the absence of a 3-valent vertex. In this paper such a formula for a 4-valent vertex is derived. The formula allows us to compute the c_2 invariant of new graphs, for instance, some 4-regular graphs with small loop number.

  8. Learning molecular energies using localized graph kernels.

    PubMed

    Ferré, Grégoire; Haut, Terry; Barros, Kipton

    2017-03-21

    Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. We benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.

  9. Learning molecular energies using localized graph kernels

    NASA Astrophysics Data System (ADS)

    Ferré, Grégoire; Haut, Terry; Barros, Kipton

    2017-03-01

    Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. We benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.

  10. Learning molecular energies using localized graph kernels

    DOE PAGES

    Ferré, Grégoire; Haut, Terry Scot; Barros, Kipton Marcos

    2017-03-21

    We report that recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturallymore » incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. Finally, we benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.« less

  11. All degree 6 local unitary invariants of k qudits

    NASA Astrophysics Data System (ADS)

    Szalay, Szilárd

    2012-02-01

    We give explicit index-free formulae for all the degree 6 (and also degree 4 and 2) algebraically independent local unitary invariant polynomials for finite-dimensional k-partite pure and mixed quantum states. We carry this out using graph-technical methods, which provide illustrations for this abstract topic.

  12. Polynomial Invariants for Arbitrary Rank D Weakly-Colored Stranded Graphs

    NASA Astrophysics Data System (ADS)

    Avohou, Remi Cocou

    2016-03-01

    Polynomials on stranded graphs are higher dimensional generalization of Tutte and Bollobás-Riordan polynomials [Math. Ann. 323 (2002), 81-96]. Here, we deepen the analysis of the polynomial invariant defined on rank 3 weakly-colored stranded graphs introduced in arXiv:1301.1987. We successfully find in dimension D≥3 a modified Euler characteristic with D-2 parameters. Using this modified invariant, we extend the rank 3 weakly-colored graph polynomial, and its main properties, on rank 4 and then on arbitrary rank D weakly-colored stranded graphs.

  13. Local and gauge invariant observables in gravity

    NASA Astrophysics Data System (ADS)

    Khavkine, Igor

    2015-09-01

    It is well known that general relativity (GR) does not possess any non-trivial local (in a precise standard sense) and diffeomorphism invariant observable. 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 defining generalized local gauge invariant observables in arbitrary gauge theories, which happens to agree with well-known results for Maxwell and Yang-Mills theories.

  14. Graph states and local unitary transformations beyond local Clifford operations

    NASA Astrophysics Data System (ADS)

    Tsimakuridze, Nikoloz; Gühne, Otfried

    2017-05-01

    Graph states are quantum states that can be described by a stabilizer formalism and play an important role in quantum information processing. We consider the action of local unitary operations on graph states and hypergraph states. We focus on non-Clifford operations and find for certain transformations a graphical description in terms of weighted hypergraphs. This leads to the indentification of hypergraph states that are locally equivalent to graph states. Moreover, we present a systematic way to construct pairs of graph states which are equivalent under local unitary operations, but not equivalent under local Clifford operations. This generates counterexamples to a conjecture known as LU-LC conjecture. So far, the only counterexamples to this conjecture were found by random search. Our method reproduces the smallest known counterexample as a special case and provides a physical interpretation.

  15. Learning Rotation-Invariant Local Binary Descriptor.

    PubMed

    Duan, Yueqi; Lu, Jiwen; Feng, Jianjiang; Zhou, Jie

    2017-08-01

    In this paper, we propose a rotation-invariant local binary descriptor (RI-LBD) learning method for visual recognition. Compared with hand-crafted local binary descriptors, such as local binary pattern and its variants, which require strong prior knowledge, local binary feature learning methods are more efficient and data-adaptive. Unlike existing learning-based local binary descriptors, such as compact binary face descriptor and simultaneous local binary feature learning and encoding, which are susceptible to rotations, our RI-LBD first categorizes each local patch into a rotational binary pattern (RBP), and then jointly learns the orientation for each pattern and the projection matrix to obtain RI-LBDs. As all the rotation variants of a patch belong to the same RBP, they are rotated into the same orientation and projected into the same binary descriptor. Then, we construct a codebook by a clustering method on the learned binary codes, and obtain a histogram feature for each image as the final representation. In order to exploit higher order statistical information, we extend our RI-LBD to the triple rotation-invariant co-occurrence local binary descriptor (TRICo-LBD) learning method, which learns a triple co-occurrence binary code for each local patch. Extensive experimental results on four different visual recognition tasks, including image patch matching, texture classification, face recognition, and scene classification, show that our RI-LBD and TRICo-LBD outperform most existing local descriptors.

  16. New invariants of weighted graphs for calculating the critical properties of freons

    NASA Astrophysics Data System (ADS)

    Kruglyak, Yu. A.; Peredunova, I. V.

    2015-12-01

    A new approach to structure-property problems using new invariants of fully weighted graphs to provide a quantitative description of the critical properties of freons is proposed. A general principle for constructing topological invariants of fully weighted graphs for structure-property correlations is formulated. Two new invariants are proposed and used to calculate critical properties of freons of the methane, ethane, and propane series. It is shown that unlike all other known incremental methods, the proposed approach does not require the use of experimental data or calibrations to calculate critical properties. It ensures a statistically reliable linear dependence of all critical properties of freons on the value of the matching index for our corresponding molecular graph. Over 2.5 thousand previously unknown values of the critical properties of lower freons are calculated.

  17. Testing local Lorentz invariance with gravitational waves

    DOE PAGES

    Kostelecký, V. Alan; Mewes, Matthew

    2016-04-20

    The effects of local Lorentz violation on dispersion and birefringence of gravitational waves are investigated. The covariant dispersion relation for gravitational waves involving gauge-invariant Lorentz violating operators of arbitrary mass dimension is constructed. The chirp signal from the gravitational wave event GW150914 is used to place numerous first constraints on gravitational Lorentz violation. (C) 2016 The Authors. Published by Elsevier B.V.

  18. Neutrino velocity and local Lorentz invariance

    NASA Astrophysics Data System (ADS)

    Cardone, Fabio; Mignani, Roberto; Petrucci, Andrea

    2015-09-01

    We discuss the possible violation of local Lorentz invariance (LLI) arising from a faster-than-light neutrino speed. A toy calculation of the LLI violation parameter δ, based on the (disclaimed) OPERA data, suggests that the values of δ are determined by the interaction involved, and not by the energy range. This hypothesis is further corroborated by the analysis of the more recent results of the BOREXINO, LVD and ICARUS experiments.

  19. The Role of Graph-Theoretical Invariants in Chemistry.

    DTIC Science & Technology

    1987-03-06

    graphs) form members of the Fibonacci series while corresponding values for monocycles form members of the Lucas series. Broadly speaking, polynomial...date in terms of its number of applications is the molecular connectivity index of Randi6. The index was put forward in 1975 and was originally intended...INSTRUCTIONSI1 REPOIRT DOCUMENTATION PAGE BEOECMLEIGFR 1. REPORT 4UME ~2. GGVT ACCESSION6 NO. 3. RECIPIENT’S CATALOG NUMBER Technical Report No. 43

  20. On local invariants of singular symplectic forms

    NASA Astrophysics Data System (ADS)

    Domitrz, Wojciech

    2017-04-01

    We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a 2 n-dimensional manifold. In the C-analytic category this set consists of the Martinet hypersurface Σ2, the restriction of the singular symplectic form ω to TΣ2 and the kernel of ω n - 1 at the point p ∈Σ2. In the R-analytic and smooth categories this set contains one more invariant: the canonical orientation of Σ2. We find the conditions to determine the kernel of ω n - 1 at p by the other invariants. In dimension 4 we find sufficient conditions to determine the equivalence class of a singular symplectic form-germ with the structurally smooth Martinet hypersurface by the Martinet hypersurface and the restriction of the singular symplectic form to it. We also study the singular symplectic forms with singular Martinet hypersurfaces. We prove that the equivalence class of such singular symplectic form-germ is determined by the Martinet hypersurface, the canonical orientation of its regular part and the restriction of the singular symplectic form to its regular part if the Martinet hypersurface is a quasi-homogeneous hypersurface with an isolated singularity.

  1. Address block localization based on graph theory

    NASA Astrophysics Data System (ADS)

    Gaceb, Djamel; Eglin, Véronique; Lebourgeois, Frank; Emptoz, Hubert

    2008-01-01

    An efficient mail sorting system is mainly based on an accurate optical recognition of the addresses on the envelopes. However, the localizing of the address block (ABL) should be done before the OCR recognition process. The location step is very crucial as it has a great impact on the global performance of the system. Currently, a good localizing step leads to a better recognition rate. The limit of current methods is mainly caused by modular linear architectures used for ABL: their performances greatly depend on each independent module performance. We are presenting in this paper a new approach for ABL based on a pyramidal data organization and on a hierarchical graph coloring for classification process. This new approach presents the advantage to guarantee a good coherence between different modules and reduces both the computation time and the rejection rate. The proposed method gives a very satisfying rate of 98% of good locations on a set of 750 envelope images.

  2. Graph cuts with invariant object-interaction priors: application to intervertebral disc segmentation.

    PubMed

    Ben Ayed, Ismail; Punithakumar, Kumaradevan; Garvin, Gregory; Romano, Walter; Li, Shuo

    2011-01-01

    This study investigates novel object-interaction priors for graph cut image segmentation with application to intervertebral disc delineation in magnetic resonance (MR) lumbar spine images. The algorithm optimizes an original cost function which constrains the solution with learned prior knowledge about the geometric interactions between different objects in the image. Based on a global measure of similarity between distributions, the proposed priors are intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive an original fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed priors relax the need of costly pose estimation (or registration) procedures and large training sets (we used a single subject for training), and can tolerate shape deformations, unlike template-based priors. Our formulation leads to an NP-hard problem which does not afford a form directly amenable to graph cut optimization. We proceeded to a relaxation of the problem via an auxiliary function, thereby obtaining a nearly real-time solution with few graph cuts. Quantitative evaluations over 60 intervertebral discs acquired from 10 subjects demonstrated that the proposed algorithm yields a high correlation with independent manual segmentations by an expert. We further demonstrate experimentally the invariance of the proposed geometric attributes. This supports the fact that a single subject is sufficient for training our algorithm, and confirms the relevance of the proposed priors to disc segmentation.

  3. Geometric local invariants and pure three-qubit states

    SciTech Connect

    Williamson, Mark S.; Ericsson, Marie; Johansson, Markus; Sjoeqvist, Erik; Sudbery, Anthony; Vedral, Vlatko; Wootters, William K.

    2011-06-15

    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.

  4. Geometric local invariants and pure three-qubit states

    NASA Astrophysics Data System (ADS)

    Williamson, Mark S.; Ericsson, Marie; Johansson, Markus; Sjöqvist, Erik; Sudbery, Anthony; Vedral, Vlatko; Wootters, William K.

    2011-06-01

    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.

  5. Localization via Automorphisms of the CARs: Local Gauge Invariance

    NASA Astrophysics Data System (ADS)

    Grundling, Hendrik; Neeb, Karl-Hermann

    2010-08-01

    The classical matter fields are sections of a vector bundle E with base manifold M, and the space L 2( E) of square integrable matter fields w.r.t. a locally Lebesgue measure on M, has an important module action of {C_b^infty(M)} on it. This module action defines restriction maps and encodes the local structure of the classical fields. For the quantum context, we show that this module action defines an automorphism group on the algebra of the canonical anticommutation relations, CAR( L 2( E)), with which we can perform the analogous localization. That is, the net structure of the CAR( L 2( E)) w.r.t. appropriate subsets of M can be obtained simply from the invariance algebras of appropriate subgroups. We also identify the quantum analogues of restriction maps, and as a corollary, we prove a well-known “folk theorem,” that the CAR( L 2( E)) contains only trivial gauge invariant observables w.r.t. a local gauge group acting on E.

  6. Nonuniversality in the spectral properties of time-reversal-invariant microwave networks and quantum graphs

    NASA Astrophysics Data System (ADS)

    Dietz, Barbara; Yunko, Vitalii; Białous, Małgorzata; Bauch, Szymon; Ławniczak, Michał; Sirko, Leszek

    2017-05-01

    We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide an ideal basis for the experimental study of problems originating from the field of quantum chaos and random matrix theory. Our objective is to demonstrate that this is true only for short-range fluctuation properties in the spectra, whereas the observation of deviations in the long-range fluctuations is typical for quantum graphs. This may be attributed to the unavoidable occurrence of short periodic orbits, which explore only the individual bonds forming a graph and thus do not sense the chaoticity of its dynamics. In order to corroborate our supposition, we performed numerous experimental and corresponding numerical studies of long-range fluctuations in terms of the number variance and the power spectrum. Furthermore, we evaluated length spectra and compared them to semiclassical ones obtained from the exact trace formula for quantum graphs.

  7. Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

    NASA Astrophysics Data System (ADS)

    Białous, Małgorzata; Yunko, Vitalii; Bauch, Szymon; Ławniczak, Michał; Dietz, Barbara; Sirko, Leszek

    2016-09-01

    We present experimental studies of the power spectrum and other fluctuation properties in the spectra of microwave networks simulating chaotic quantum graphs with violated time reversal invariance. On the basis of our data sets, we demonstrate that the power spectrum in combination with other long-range and also short-range spectral fluctuations provides a powerful tool for the identification of the symmetries and the determination of the fraction of missing levels. Such a procedure is indispensable for the evaluation of the fluctuation properties in the spectra of real physical systems like, e.g., nuclei or molecules, where one has to deal with the problem of missing levels.

  8. Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance.

    PubMed

    Białous, Małgorzata; Yunko, Vitalii; Bauch, Szymon; Ławniczak, Michał; Dietz, Barbara; Sirko, Leszek

    2016-09-30

    We present experimental studies of the power spectrum and other fluctuation properties in the spectra of microwave networks simulating chaotic quantum graphs with violated time reversal invariance. On the basis of our data sets, we demonstrate that the power spectrum in combination with other long-range and also short-range spectral fluctuations provides a powerful tool for the identification of the symmetries and the determination of the fraction of missing levels. Such a procedure is indispensable for the evaluation of the fluctuation properties in the spectra of real physical systems like, e.g., nuclei or molecules, where one has to deal with the problem of missing levels.

  9. On local invariants of pure three-qubit states

    NASA Astrophysics Data System (ADS)

    Sudbery, Anthony

    2001-01-01

    We study invariants of three-qubit states under local unitary transformations, i.e. functions on the space of entanglement types, which is known to have dimension six. We show that there is no set of six algebraically independent polynomial invariants of degree ≤ 6, and find such a set with maximum degree eight. We describe an intrinsic definition of a canonical state on each orbit, and discuss the (non-polynomial) invariants associated with it.

  10. Invariant currents and scattering off locally symmetric potential landscapes

    SciTech Connect

    Kalozoumis, P.A.; Morfonios, C.V.; Diakonos, F.K.; Schmelcher, P.

    2015-11-15

    We study the effect of discrete symmetry breaking in inhomogeneous scattering media within the framework of generic wave propagation. Our focus is on one-dimensional scattering potentials exhibiting local symmetries. We find a class of spatially invariant nonlocal currents, emerging when the corresponding generalized potential exhibits symmetries in arbitrary spatial domains. These invariants characterize the wave propagation and provide a spatial mapping of the wave function between any symmetry related domains. This generalizes the Bloch and parity theorems for broken reflection and translational symmetries, respectively. Their nonvanishing values indicate the symmetry breaking, whereas a zero value denotes the restoration of the global symmetry where the well-known forms of the two theorems are recovered. These invariants allow for a systematic treatment of systems with any local symmetry combination, providing a tool for the investigation of the scattering properties of aperiodic but locally symmetric systems. To this aim we express the transfer matrix of a locally symmetric potential unit via the corresponding invariants and derive quantities characterizing the complete scattering device which serve as key elements for the investigation of transmission spectra and particularly of perfect transmission resonances. -- Highlights: •We show that local discrete symmetries yield invariant currents. •Bloch and parity theorems are generalized when the associated symmetries are broken. •Formulation of scattering via the symmetry-induced invariant currents. •We provide sum rules for the invariant currents characterizing perfect transmission.

  11. Translationally invariant conservation laws of local Lindblad equations

    SciTech Connect

    Žnidarič, Marko; Benenti, Giuliano; Casati, Giulio

    2014-02-15

    We study the conditions under which one can conserve local translationally invariant operators by local translationally invariant Lindblad equations in one-dimensional rings of spin-1/2 particles. We prove that for any 1-local operator (e.g., particle density) there exist Lindblad dissipators that conserve that operator, while on the other hand we prove that among 2-local operators (e.g., energy density) only trivial ones of the Ising type can be conserved, while all the other cannot be conserved, neither locally nor globally, by any 2- or 3-local translationally invariant Lindblad equation. Our statements hold for rings of any finite length larger than some minimal length determined by the locality of Lindblad equation. These results show in particular that conservation of energy density in interacting systems is fundamentally more difficult than conservation of 1-local quantities.

  12. Jamming graphs: A local approach to global mechanical rigidity

    NASA Astrophysics Data System (ADS)

    Lopez, Jorge H.; Cao, L.; Schwarz, J. M.

    2013-12-01

    We revisit the concept of minimal rigidity as applied to frictionless, repulsive soft sphere packings in two dimensions with the introduction of the jamming graph. Minimal rigidity is a purely combinatorial property encoded via Laman's theorem in two dimensions. It constrains the global, average coordination number of the graph, for example. However, minimal rigidity does not address the geometry of local mechanical stability. The jamming graph contains both properties of global mechanical stability at the onset of jamming and local mechanical stability. We demonstrate how jamming graphs can be constructed using local moves via the Henneberg construction such that these graphs fall under the jurisdiction of correlated percolation. We then probe how jamming graphs destabilize, or become unjammed, by deleting a bond and computing the resulting rigid cluster distribution. We also study how the system restabilizes with the addition of new contacts and how a jamming graph with extra (redundant) contacts destabilizes. The latter endeavor allows us to probe a disk packing in the rigid phase and uncover a potentially new diverging length scale associated with the random deletion of contacts as compared to the study of cut-out (or frozen-in) subsystems.

  13. Localization in random bipartite graphs: Numerical and empirical study

    NASA Astrophysics Data System (ADS)

    Slanina, František

    2017-05-01

    We investigate adjacency matrices of bipartite graphs with a power-law degree distribution. Motivation for this study is twofold: first, vibrational states in granular matter and jammed sphere packings; second, graphs encoding social interaction, especially electronic commerce. We establish the position of the mobility edge and show that it strongly depends on the power in the degree distribution and on the ratio of the sizes of the two parts of the bipartite graph. At the jamming threshold, where the two parts have the same size, localization vanishes. We found that the multifractal spectrum is nontrivial in the delocalized phase, but still near the mobility edge. We also study an empirical bipartite graph, namely, the Amazon reviewer-item network. We found that in this specific graph the mobility edge disappears, and we draw a conclusion from this fact regarding earlier empirical studies of the Amazon network.

  14. A local search for a graph clustering problem

    NASA Astrophysics Data System (ADS)

    Navrotskaya, Anna; Il'ev, Victor

    2016-10-01

    In the clustering problems one has to partition a given set of objects (a data set) into some subsets (called clusters) taking into consideration only similarity of the objects. One of most visual formalizations of clustering is graph clustering, that is grouping the vertices of a graph into clusters taking into consideration the edge structure of the graph whose vertices are objects and edges represent similarities between the objects. In the graph k-clustering problem the number of clusters does not exceed k and the goal is to minimize the number of edges between clusters and the number of missing edges within clusters. This problem is NP-hard for any k ≥ 2. We propose a polynomial time (2k-1)-approximation algorithm for graph k-clustering. Then we apply a local search procedure to the feasible solution found by this algorithm and hold experimental research of obtained heuristics.

  15. K-theory of locally finite graph C∗-algebras

    NASA Astrophysics Data System (ADS)

    Iyudu, Natalia

    2013-09-01

    We calculate the K-theory of the Cuntz-Krieger algebra OE associated with an infinite, locally finite graph, via the Bass-Hashimoto operator. The formulae we get express the Grothendieck group and the Whitehead group in purely graph theoretic terms. We consider the category of finite (black-and-white, bi-directed) subgraphs with certain graph homomorphisms and construct a continuous functor to abelian groups. In this category K0 is an inductive limit of K-groups of finite graphs, which were calculated in Cornelissen et al. (2008) [3]. In the case of an infinite graph with the finite Betti number we obtain the formula for the Grothendieck group K0(OE)=Z, where β(E) is the first Betti number and γ(E) is the valency number of the graph E. We note that in the infinite case the torsion part of K0, which is present in the case of a finite graph, vanishes. The Whitehead group depends only on the first Betti number: K1(OE)=Z. These allow us to provide a counterexample to the fact, which holds for finite graphs, that K1(OE) is the torsion free part of K0(OE).

  16. A global/local affinity graph for image segmentation.

    PubMed

    Xiaofang Wang; Yuxing Tang; Masnou, Simon; Liming Chen

    2015-04-01

    Construction of a reliable graph capturing perceptual grouping cues of an image is fundamental for graph-cut based image segmentation methods. In this paper, we propose a novel sparse global/local affinity graph over superpixels of an input image to capture both short- and long-range grouping cues, and thereby enabling perceptual grouping laws, including proximity, similarity, continuity, and to enter in action through a suitable graph-cut algorithm. Moreover, we also evaluate three major visual features, namely, color, texture, and shape, for their effectiveness in perceptual segmentation and propose a simple graph fusion scheme to implement some recent findings from psychophysics, which suggest combining these visual features with different emphases for perceptual grouping. In particular, an input image is first oversegmented into superpixels at different scales. We postulate a gravitation law based on empirical observations and divide superpixels adaptively into small-, medium-, and large-sized sets. Global grouping is achieved using medium-sized superpixels through a sparse representation of superpixels' features by solving a ℓ0-minimization problem, and thereby enabling continuity or propagation of local smoothness over long-range connections. Small- and large-sized superpixels are then used to achieve local smoothness through an adjacent graph in a given feature space, and thus implementing perceptual laws, for example, similarity and proximity. Finally, a bipartite graph is also introduced to enable propagation of grouping cues between superpixels of different scales. Extensive experiments are carried out on the Berkeley segmentation database in comparison with several state-of-the-art graph constructions. The results show the effectiveness of the proposed approach, which outperforms state-of-the-art graphs using four different objective criteria, namely, the probabilistic rand index, the variation of information, the global consistency error, and the

  17. Local scale invariance for wetting and confined interfaces

    NASA Astrophysics Data System (ADS)

    Parry, A. O.; Rascón, C.

    2010-03-01

    When a fluid or Ising-like magnet is confined between two parallel walls that are each completely wet by different bulk phases, the interface separating the phases is subject to large-scale fluctuations determined by the slit width. It was noted some time ago that, in two dimensions, the scaling expression for the probability distribution function describing the interfacial height across the slit shows remarkable similarities with predictions of conformal invariance. However, this local scale invariance appears to contradict the strongly anisotropic nature of (1 + 1)-dimensional interfacial fluctuations along and perpendicular to the interface, characterized by the wandering exponent. In this paper, we show that similarity with conformal invariance is not coincidental and can be understood explicitly as the projection of a local scale invariance for a wandering line in 2 + 1 dimensions.

  18. Interaction graph mining for protein complexes using local clique merging.

    PubMed

    Li, Xiao-Li; Tan, Soon-Heng; Foo, Chuan-Sheng; Ng, See-Kiong

    2005-01-01

    While recent technological advances have made available large datasets of experimentally-detected pairwise protein-protein interactions, there is still a lack of experimentally-determined protein complex data. To make up for this lack of protein complex data, we explore the mining of existing protein interaction graphs for protein complexes. This paper proposes a novel graph mining algorithm to detect the dense neighborhoods (highly connected regions) in an interaction graph which may correspond to protein complexes. Our algorithm first locates local cliques for each graph vertex (protein) and then merge the detected local cliques according to their affinity to form maximal dense regions. We present experimental results with yeast protein interaction data to demonstrate the effectiveness of our proposed method. Compared with other existing techniques, our predicted complexes can match or overlap significantly better with the known protein complexes in the MIPS benchmark database. Novel protein complexes were also predicted to help biologists in their search for new protein complexes.

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

    NASA Astrophysics Data System (ADS)

    Henkel, Malte

    2017-03-01

    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. Schrödinger-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 Schrödinger-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, independent scaling dimensions. Tests of ageing-invariance are described, in the Glauber-Ising and spherical models of a phase-ordering ferromagnet and the Arcetri model of interface growth.

  20. Analysis of Graph Invariants in Functional Neocortical Circuitry Reveals Generalized Features Common to Three Areas of Sensory Cortex

    PubMed Central

    Gururangan, Suchin S.; Sadovsky, Alexander J.; MacLean, Jason N.

    2014-01-01

    Correlations in local neocortical spiking activity can provide insight into the underlying organization of cortical microcircuitry. However, identifying structure in patterned multi-neuronal spiking remains a daunting task due to the high dimensionality of the activity. Using two-photon imaging, we monitored spontaneous circuit dynamics in large, densely sampled neuronal populations within slices of mouse primary auditory, somatosensory, and visual cortex. Using the lagged correlation of spiking activity between neurons, we generated functional wiring diagrams to gain insight into the underlying neocortical circuitry. By establishing the presence of graph invariants, which are label-independent characteristics common to all circuit topologies, our study revealed organizational features that generalized across functionally distinct cortical regions. Regardless of sensory area, random and -nearest neighbors null graphs failed to capture the structure of experimentally derived functional circuitry. These null models indicated that despite a bias in the data towards spatially proximal functional connections, functional circuit structure is best described by non-random and occasionally distal connections. Eigenvector centrality, which quantifies the importance of a neuron in the temporal flow of circuit activity, was highly related to feedforwardness in all functional circuits. The number of nodes participating in a functional circuit did not scale with the number of neurons imaged regardless of sensory area, indicating that circuit size is not tied to the sampling of neocortex. Local circuit flow comprehensively covered angular space regardless of the spatial scale that we tested, demonstrating that circuitry itself does not bias activity flow toward pia. Finally, analysis revealed that a minimal numerical sample size of neurons was necessary to capture at least 90 percent of functional circuit topology. These data and analyses indicated that functional circuitry

  1. Efficient and Accurate Indoor Localization Using Landmark Graphs

    NASA Astrophysics Data System (ADS)

    Gu, F.; Kealy, A.; Khoshelham, K.; Shang, J.

    2016-06-01

    Indoor localization is important for a variety of applications such as location-based services, mobile social networks, and emergency response. Fusing spatial information is an effective way to achieve accurate indoor localization with little or with no need for extra hardware. However, existing indoor localization methods that make use of spatial information are either too computationally expensive or too sensitive to the completeness of landmark detection. In this paper, we solve this problem by using the proposed landmark graph. The landmark graph is a directed graph where nodes are landmarks (e.g., doors, staircases, and turns) and edges are accessible paths with heading information. We compared the proposed method with two common Dead Reckoning (DR)-based methods (namely, Compass + Accelerometer + Landmarks and Gyroscope + Accelerometer + Landmarks) by a series of experiments. Experimental results show that the proposed method can achieve 73% accuracy with a positioning error less than 2.5 meters, which outperforms the other two DR-based methods.

  2. A novel eye localization method with rotation invariance.

    PubMed

    Ren, Yan; Wang, Shuang; Hou, Biao; Ma, Jingjing

    2014-01-01

    This paper presents a novel learning method for precise eye localization, a challenge to be solved in order to improve the performance of face processing algorithms. Few existing approaches can directly detect and localize eyes with arbitrary angels in predicted eye regions, face images, and original portraits at the same time. To preserve rotation invariant property throughout the entire eye localization framework, a codebook of invariant local features is proposed for the representation of eye patterns. A heat map is then generated by integrating a 2-class sparse representation classifier with a pyramid-like detecting and locating strategy to fulfill the task of discriminative classification and precise localization. Furthermore, a series of prior information is adopted to improve the localization precision and accuracy. Experimental results on three different databases show that our method is capable of effectively locating eyes in arbitrary rotation situations (360° in plane).

  3. Testing local Lorentz invariance with short-range gravity

    NASA Astrophysics Data System (ADS)

    Kostelecký, V. Alan; Mewes, Matthew

    2017-03-01

    The Newton limit of gravity is studied in the presence of Lorentz-violating gravitational operators of arbitrary mass dimension. The linearized modified Einstein equations are obtained and the perturbative solutions are constructed and characterized. We develop a formalism for data analysis in laboratory experiments testing gravity at short range and demonstrate that these tests provide unique sensitivity to deviations from local Lorentz invariance.

  4. Testing local Lorentz invariance with short-range gravity

    DOE PAGES

    Kostelecký, V. Alan; Mewes, Matthew

    2017-01-10

    The Newton limit of gravity is studied in the presence of Lorentz-violating gravitational operators of arbitrary mass dimension. The linearized modified Einstein equations are obtained and the perturbative solutions are constructed and characterized. We develop a formalism for data analysis in laboratory experiments testing gravity at short range and demonstrate that these tests provide unique sensitivity to deviations from local Lorentz invariance.

  5. Invariant currents and scattering off locally symmetric potential landscapes

    NASA Astrophysics Data System (ADS)

    Kalozoumis, P. A.; Morfonios, C. V.; Diakonos, F. K.; Schmelcher, P.

    2015-11-01

    We study the effect of discrete symmetry breaking in inhomogeneous scattering media within the framework of generic wave propagation. Our focus is on one-dimensional scattering potentials exhibiting local symmetries. We find a class of spatially invariant nonlocal currents, emerging when the corresponding generalized potential exhibits symmetries in arbitrary spatial domains. These invariants characterize the wave propagation and provide a spatial mapping of the wave function between any symmetry related domains. This generalizes the Bloch and parity theorems for broken reflection and translational symmetries, respectively. Their nonvanishing values indicate the symmetry breaking, whereas a zero value denotes the restoration of the global symmetry where the well-known forms of the two theorems are recovered. These invariants allow for a systematic treatment of systems with any local symmetry combination, providing a tool for the investigation of the scattering properties of aperiodic but locally symmetric systems. To this aim we express the transfer matrix of a locally symmetric potential unit via the corresponding invariants and derive quantities characterizing the complete scattering device which serve as key elements for the investigation of transmission spectra and particularly of perfect transmission resonances.

  6. Local feature descriptor invariant to monotonic illumination changes

    NASA Astrophysics Data System (ADS)

    Yan, Pu; Liang, Dong; Tang, Jun; Zhu, Ming

    2016-01-01

    This paper presents a monotonic invariant intensity descriptor (MIID) via spectral embedding and nonsubsampled contourlet transform (NSCT). To make the proposed descriptor discriminative, NSCT is used for the construction of multiple support regions. Specifically, the directed graph and the spectral feature vectors of the signless Laplacian matrix are exploited to construct the MIID. We theoretically demonstrate that the proposed descriptor is able to tackle monotonic illumination changes and many other geometric and photometric transformations. We conduct extensive experiments on the standard Oxford dataset and the complex illumination dataset to demonstrate the superiority of proposed descriptor over the existing state-of-the-art descriptors in dealing with image blur, viewpoint changes, illumination changes, and JPEG compression.

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

    NASA Astrophysics Data System (ADS)

    Kalozoumis, P. A.; Richoux, O.; Diakonos, F. K.; Theocharis, G.; Schmelcher, P.

    2015-07-01

    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 that 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 they clearly indicate that completely locally symmetric devices constitute a promising class of setups with regard to the manipulation of wave propagation.

  8. Derivatives in discrete mathematics: a novel graph-theoretical invariant for generating new 2/3D molecular descriptors. I. Theory and QSPR application.

    PubMed

    Marrero-Ponce, Yovani; Santiago, Oscar Martínez; López, Yoan Martínez; Barigye, Stephen J; Torrens, Francisco

    2012-11-01

    In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ([Formula: see text]) of a molecular graph (MG) with respect to a given event (E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph's theory's traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub-graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns (n) and rows (m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Δ(i), can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j's atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ(i) for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating

  9. Reflection symmetry detection using locally affine invariant edge correspondence.

    PubMed

    Wang, Zhaozhong; Tang, Zesheng; Zhang, Xiao

    2015-04-01

    Reflection symmetry detection receives increasing attentions in recent years. The state-of-the-art algorithms mainly use the matching of intensity-based features (such as the SIFT) within a single image to find symmetry axes. This paper proposes a novel approach by establishing the correspondence of locally affine invariant edge-based features, which are superior to the intensity based in the aspects that it is insensitive to illumination variations, and applicable to textureless objects. The locally affine invariance is achieved by simple linear algebra for efficient and robust computations, making the algorithm suitable for detections under object distortions like perspective projection. Commonly used edge detectors and a voting process are, respectively, used before and after the edge description and matching steps to form a complete reflection detection pipeline. Experiments are performed using synthetic and real-world images with both multiple and single reflection symmetry axis. The test results are compared with existing algorithms to validate the proposed method.

  10. Tests of Local Position Invariance Using Continuously Running Atomic Clocks

    DTIC Science & Technology

    2013-01-22

    principle) and that nongravitational measurements should be independent of the velocity of the freely falling reference frame (local Lorentz invariance...be independent of the clock composition, for example. Violation of LPI may manifest itself in an anomalous gravitational redshift of an atomic clock... violating parameters β1 and β2, the relative frequencies should vary with the gravitational potential as (ν/ν)1,2 = (β1 − β2)U/c2. (2) *steven.peil

  11. Protein localization prediction using random walks on graphs

    PubMed Central

    2013-01-01

    Background Understanding the localization of proteins in cells is vital to characterizing their functions and possible interactions. As a result, identifying the (sub)cellular compartment within which a protein is located becomes an important problem in protein classification. This classification issue thus involves predicting labels in a dataset with a limited number of labeled data points available. By utilizing a graph representation of protein data, random walk techniques have performed well in sequence classification and functional prediction; however, this method has not yet been applied to protein localization. Accordingly, we propose a novel classifier in the site prediction of proteins based on random walks on a graph. Results We propose a graph theory model for predicting protein localization using data generated in yeast and gram-negative (Gneg) bacteria. We tested the performance of our classifier on the two datasets, optimizing the model training parameters by varying the laziness values and the number of steps taken during the random walk. Using 10-fold cross-validation, we achieved an accuracy of above 61% for yeast data and about 93% for gram-negative bacteria. Conclusions This study presents a new classifier derived from the random walk technique and applies this classifier to investigate the cellular localization of proteins. The prediction accuracy and additional validation demonstrate an improvement over previous methods, such as support vector machine (SVM)-based classifiers. PMID:23815126

  12. Visual odometry based on structural matching of local invariant features using stereo camera sensor.

    PubMed

    Núñez, Pedro; Vázquez-Martín, Ricardo; Bandera, Antonio

    2011-01-01

    This paper describes a novel sensor system to estimate the motion of a stereo camera. Local invariant image features are matched between pairs of frames and linked into image trajectories at video rate, providing the so-called visual odometry, i.e., motion estimates from visual input alone. Our proposal conducts two matching sessions: the first one between sets of features associated to the images of the stereo pairs and the second one between sets of features associated to consecutive frames. With respect to previously proposed approaches, the main novelty of this proposal is that both matching algorithms are conducted by means of a fast matching algorithm which combines absolute and relative feature constraints. Finding the largest-valued set of mutually consistent matches is equivalent to finding the maximum-weighted clique on a graph. The stereo matching allows to represent the scene view as a graph which emerge from the features of the accepted clique. On the other hand, the frame-to-frame matching defines a graph whose vertices are features in 3D space. The efficiency of the approach is increased by minimizing the geometric and algebraic errors to estimate the final displacement of the stereo camera between consecutive acquired frames. The proposed approach has been tested for mobile robotics navigation purposes in real environments and using different features. Experimental results demonstrate the performance of the proposal, which could be applied in both industrial and service robot fields.

  13. Visual Odometry Based on Structural Matching of Local Invariant Features Using Stereo Camera Sensor

    PubMed Central

    Núñez, Pedro; Vázquez-Martín, Ricardo; Bandera, Antonio

    2011-01-01

    This paper describes a novel sensor system to estimate the motion of a stereo camera. Local invariant image features are matched between pairs of frames and linked into image trajectories at video rate, providing the so-called visual odometry, i.e., motion estimates from visual input alone. Our proposal conducts two matching sessions: the first one between sets of features associated to the images of the stereo pairs and the second one between sets of features associated to consecutive frames. With respect to previously proposed approaches, the main novelty of this proposal is that both matching algorithms are conducted by means of a fast matching algorithm which combines absolute and relative feature constraints. Finding the largest-valued set of mutually consistent matches is equivalent to finding the maximum-weighted clique on a graph. The stereo matching allows to represent the scene view as a graph which emerge from the features of the accepted clique. On the other hand, the frame-to-frame matching defines a graph whose vertices are features in 3D space. The efficiency of the approach is increased by minimizing the geometric and algebraic errors to estimate the final displacement of the stereo camera between consecutive acquired frames. The proposed approach has been tested for mobile robotics navigation purposes in real environments and using different features. Experimental results demonstrate the performance of the proposal, which could be applied in both industrial and service robot fields. PMID:22164016

  14. MEG source localization using invariance of noise space.

    PubMed

    Zhang, Junpeng; Raij, Tommi; Hämäläinen, Matti; Yao, Dezhong

    2013-01-01

    We propose INvariance of Noise (INN) space as a novel method for source localization of magnetoencephalography (MEG) data. The method is based on the fact that modulations of source strengths across time change the energy in signal subspace but leave the noise subspace invariant. We compare INN with classical MUSIC, RAP-MUSIC, and beamformer approaches using simulated data while varying signal-to-noise ratios as well as distance and temporal correlation between two sources. We also demonstrate the utility of INN with actual auditory evoked MEG responses in eight subjects. In all cases, INN performed well, especially when the sources were closely spaced, highly correlated, or one source was considerably stronger than the other.

  15. MEG Source Localization Using Invariance of Noise Space

    PubMed Central

    Zhang, Junpeng; Raij, Tommi; Hämäläinen, Matti; Yao, Dezhong

    2013-01-01

    We propose INvariance of Noise (INN) space as a novel method for source localization of magnetoencephalography (MEG) data. The method is based on the fact that modulations of source strengths across time change the energy in signal subspace but leave the noise subspace invariant. We compare INN with classical MUSIC, RAP-MUSIC, and beamformer approaches using simulated data while varying signal-to-noise ratios as well as distance and temporal correlation between two sources. We also demonstrate the utility of INN with actual auditory evoked MEG responses in eight subjects. In all cases, INN performed well, especially when the sources were closely spaced, highly correlated, or one source was considerably stronger than the other. PMID:23505502

  16. Local unitary invariants for N-qubit pure states

    SciTech Connect

    Sharma, S. Shelly; Sharma, N. K.

    2010-11-15

    The concept of negativity font, a basic unit of multipartite entanglement, is introduced. Transformation properties of determinants of negativity fonts under local unitary (LU) transformations are exploited to obtain relevant N-qubit polynomial invariants and construct entanglement monotones from first principles. It is shown that entanglement monotones that detect the entanglement of specific parts of the composite system may be constructed to distinguish between states with distinct types of entanglement. The structural difference between entanglement monotones for an odd and even number of qubits is brought out.

  17. Graph-Based Cooperative Localization Using Symmetric Measurement Equations

    PubMed Central

    Gulati, Dhiraj; Zhang, Feihu; Clarke, Daniel; Knoll, Alois

    2017-01-01

    Precise localization is a key requirement for the success of highly assisted or autonomous vehicles. The diminishing cost of hardware has resulted in a proliferation of the number of sensors in the environment. Cooperative localization (CL) presents itself as a feasible and effective solution for localizing the ego-vehicle and its neighboring vehicles. However, one of the major challenges to fully realize the effective use of infrastructure sensors for jointly estimating the state of a vehicle in cooperative vehicle-infrastructure localization is an effective data association. In this paper, we propose a method which implements symmetric measurement equations within factor graphs in order to overcome the data association challenge with a reduced bandwidth overhead. Simulated results demonstrate the benefits of the proposed approach in comparison with our previously proposed approach of topology factors. PMID:28629141

  18. Graph-Based Cooperative Localization Using Symmetric Measurement Equations.

    PubMed

    Gulati, Dhiraj; Zhang, Feihu; Clarke, Daniel; Knoll, Alois

    2017-06-17

    Precise localization is a key requirement for the success of highly assisted or autonomous vehicles. The diminishing cost of hardware has resulted in a proliferation of the number of sensors in the environment. Cooperative localization (CL) presents itself as a feasible and effective solution for localizing the ego-vehicle and its neighboring vehicles. However, one of the major challenges to fully realize the effective use of infrastructure sensors for jointly estimating the state of a vehicle in cooperative vehicle-infrastructure localization is an effective data association. In this paper, we propose a method which implements symmetric measurement equations within factor graphs in order to overcome the data association challenge with a reduced bandwidth overhead. Simulated results demonstrate the benefits of the proposed approach in comparison with our previously proposed approach of topology factors.

  19. Discrete Derivatives for Atom-Pairs as a Novel Graph-Theoretical Invariant for Generating New Molecular Descriptors: Orthogonality, Interpretation and QSARs/QSPRs on Benchmark Databases.

    PubMed

    Martínez-Santiago, Oscar; Millán-Cabrera, Reisel; Marrero-Ponce, Yovani; Barigye, Stephen J; Martínez-López, Yoan; Torrens, Francisco; Pérez-Giménez, Facundo

    2014-05-01

    This report presents a new mathematical method based on the concept of the derivative of a molecular graph (G) with respect to a given event (S) to codify chemical structure information. The derivate over each pair of atoms in the molecule is defined as ∂G/∂S(vi  , vj )=(fi -2fij +fj )/fij , where fi (or fj ) and fij are the individual frequency of atom i (or j) and the reciprocal frequency of the atoms i and j, respectively. These frequencies characterize the participation intensity of atom pairs in S. Here, the event space is composed of molecular sub-graphs which participate in the formation of the G skeleton that could be complete (representing all possible connected sub-graphs) or comprised of sub-graphs of certain orders or types or combinations of these. The atom level graph derivative index, Δi , is expressed as a linear combination of all atom pair derivatives that include the atomic nuclei i. Global [total or local (group or atom-type)] indices are obtained by applying the so called invariants over a vector of Δi values. The novel MDs are validated using a data set of 28 alkyl-alcohols and other benchmark data sets proposed by the International Academy of Mathematical Chemistry. Also, the boiling point for the alcohols, the adrenergic blocking activity of N,N-dimethyl-2-halo-phenethylamines and physicochemical properties of polychlorinated biphenyls and octanes are modeled. These models exhibit satisfactory predictive power compared with other 0-3D indices implemented successfully by other researchers. In addition, tendencies of the proposed indices are investigated using examples of various types of molecular structures, including chain-lengthening, branching, heteroatoms-content, and multiple bonds. On the other hand, the relation of atom-based derivative indices with (17) O NMR of a series of ethers and carbonyls reflects that the new MDs encode electronic, topological and steric information. Linear independence between the graph derivative

  20. Localization of compact invariant sets of the Lorenz' 1984 model

    NASA Astrophysics Data System (ADS)

    Starkov, K. E.

    In 1984 E. Lorenz published a paper [1] in which he proposed "the simplest possible general circulation model": dot{x} = -y^2 - z^2 - ax + aF, dot{y} = xy -bxz - y+G, dot{z} = bxy + xz -z which is referred to as the Lorenz'1984 model. The existence of chaos was shown in [1, 2] for different values of parameters. Dynamical studies of this system were realized in papers [1, 2]; [3], [4]. This paper is devoted to study of a localization problem of compact invariant sets of the Lorenz'1984 model with help of one approach elaborated in papers of Krishchenko and Starkov, see e.g. [5]. This problem is an important topic in studies of dynamics of a chaotic system because of the interest to a long-time behavior of a system. In this work we establish that all compact invariant sets of the Lorenz' 1984 model are contained in the set \\{ x le F;x^2 + y^2 + z^2 le η ^2 = {2left( {a + 2} right)F^2 + 3G^2 + 2Gsqrt {aF^2 + G^2 } }/4\\} . Further, we improve this localization with help of refining bound η using additional localizations sets. By applying cylindrical coordinates to the Lorenz' 1984 model we derive yet another localization set of the form \\{ y^2 + z^2 le G^2 (1 + b^{ - 2} )exp (4π b^{ - 1} )\\}. Finally, we discuss how to improve the final localization set and consider one example.

  1. Localization of compact invariant sets of the Lorenz' 1984 model

    NASA Astrophysics Data System (ADS)

    Starkov, K. E.

    In 1984 E. Lorenz published a paper [1] in which he proposed "the simplest possible general circulation model": dot{x} = -y^2 - z^2 - ax + aF, dot{y} = xy -bxz - y+G, dot{z} = bxy + xz -z which is referred to as the Lorenz'1984 model. The existence of chaos was shown in [1, 2] for different values of parameters. Dynamical studies of this system were realized in papers [1, 2]; [3], [4]. This paper is devoted to study of a localization problem of compact invariant sets of the Lorenz'1984 model with help of one approach elaborated in papers of Krishchenko and Starkov, see e.g. [5]. This problem is an important topic in studies of dynamics of a chaotic system because of the interest to a long-time behavior of a system. In this work we establish that all compact invariant sets of the Lorenz' 1984 model are contained in the set { x le F;x^2 + y^2 + z^2 le η ^2 = {2left( {a + 2} right)F^2 + 3G^2 + 2Gsqrt {aF^2 + G^2 } }/4} . Further, we improve this localization with help of refining bound η using additional localizations sets. By applying cylindrical coordinates to the Lorenz' 1984 model we derive yet another localization set of the form { y^2 + z^2 le G^2 (1 + b^{ - 2} )exp (4π b^{ - 1} )}. Finally, we discuss how to improve the final localization set and consider one example.

  2. Exposing region duplication through local geometrical color invariant features

    NASA Astrophysics Data System (ADS)

    Gong, Jiachang; Guo, Jichang

    2015-05-01

    Many advanced image-processing softwares are available for tampering images. How to determine the authenticity of an image has become an urgent problem. Copy-move is one of the most common image forgery operations. Many methods have been proposed for copy-move forgery detection (CMFD). However, most of these methods are designed for grayscale images without any color information used. They are usually not suitable when the duplicated regions have little structure or have undergone various transforms. We propose a CMFD method using local geometrical color invariant features to detect duplicated regions. The method starts by calculating the color gradient of the inspected image. Then, we directly take the color gradient as the input for scale invariant features transform (SIFT) to extract color-SIFT descriptors. Finally, keypoints are matched and clustered before their geometrical relationship is estimated to expose the duplicated regions. We evaluate the detection performance and computational complexity of the proposed method together with several popular CMFD methods on a public database. Experimental results demonstrate the efficacy of the proposed method in detecting duplicated regions with various transforms and poor structure.

  3. Geodesic invariant feature: a local descriptor in depth.

    PubMed

    Liu, Yazhou; Lasang, Pongsak; Siegel, Mel; Sun, Quansen

    2015-01-01

    Different from the photometric images, depth images resolve the distance ambiguity of the scene, while the properties, such as weak texture, high noise, and low resolution, may limit the representation ability of the well-developed descriptors, which are elaborately designed for the photometric images. In this paper, a novel depth descriptor, geodesic invariant feature (GIF), is presented for representing the parts of the articulate objects in depth images. GIF is a multilevel feature representation framework, which is proposed based on the nature of depth images. Low-level, geodesic gradient is introduced to obtain the invariance to the articulate motion, such as scale and rotation variation. Midlevel, superpixel clustering is applied to reduce depth image redundancy, resulting in faster processing speed and better robustness to noise. High-level, deep network is used to exploit the nonlinearity of the data, which further improves the classification accuracy. The proposed descriptor is capable of encoding the local structures in the depth data effectively and efficiently. Comparisons with the state-of-the-art methods reveal the superiority of the proposed method.

  4. Local graph regularized coding for salient object detection

    NASA Astrophysics Data System (ADS)

    Huo, Lina; Yang, Shuyuan; Jiao, Licheng; Wang, Shuang; Shi, Jiao

    2016-07-01

    Subspace segmentation based salient object detection has received increasing interests in recent years. To preserve the locality and similarity of regions, a grouping effect of representation is introduced to segment the salient object and background in subspace. Then a new saliency map is calculated by incorporating this local graph regularizer into coding, which explicitly explores the data self-representation model and thus locate more accurate salient regions. Moreover, a heuristic object-based dictionary from background superpixels is obtained in border set removing the image regions within the potential object regions. Experimental results on four large benchmark databases demonstrate that the proposed method performs favorably against eight recent state-of-the-art methods in terms of three evaluation criterions, with a reduction of MAE by 19.8% than GR and 29.3% than CB in the two SED datasets, respectively. Meanwhile, our method also runs faster than the comparative detection approaches.

  5. Template match using local feature with view invariance

    NASA Astrophysics Data System (ADS)

    Lu, Cen; Zhou, Gang

    2013-10-01

    Matching the template image in the target image is the fundamental task in the field of computer vision. Aiming at the deficiency in the traditional image matching methods and inaccurate matching in scene image with rotation, illumination and view changing, a novel matching algorithm using local features are proposed in this paper. The local histograms of the edge pixels (LHoE) are extracted as the invariable feature to resist view and brightness changing. The merits of the LHoE is that the edge points have been little affected with view changing, and the LHoE can resist not only illumination variance but also the polution of noise. For the process of matching are excuded only on the edge points, the computation burden are highly reduced. Additionally, our approach is conceptually simple, easy to implement and do not need the training phase. The view changing can be considered as the combination of rotation, illumination and shear transformation. Experimental results on simulated and real data demonstrated that the proposed approach is superior to NCC(Normalized cross-correlation) and Histogram-based methods with view changing.

  6. On the reanimation of a local BRST invariance in the (Refined) Gribov-Zwanziger formalism

    NASA Astrophysics Data System (ADS)

    Dudal, D.; Vandersickel, N.

    2011-06-01

    We localize a previously established nonlocal BRST invariance of the Gribov-Zwanziger (GZ) action by the introduction of additional fields. We obtain a modified GZ action with a corresponding local, albeit not nilpotent, BRST invariance. We show that correlation functions of the original elementary GZ fields do not change upon evaluation with the modified partition function. We discuss that for vanishing Gribov mass, we are brought back to the original Yang-Mills theory with standard BRST invariance.

  7. Local invariants vanishing on stationary horizons: a diagnostic for locating black holes.

    PubMed

    Page, Don N; Shoom, Andrey A

    2015-04-10

    Inspired by the example of Abdelqader and Lake for the Kerr metric, we construct local scalar polynomial curvature invariants that vanish on the horizon of any stationary black hole: the squared norms of the wedge products of n linearly independent gradients of scalar polynomial curvature invariants, where n is the local cohomogeneity of the spacetime.

  8. Anderson localization and ergodicity on random regular graphs

    NASA Astrophysics Data System (ADS)

    Tikhonov, K. Â. S.; Mirlin, A. Â. D.; Skvortsov, M. Â. A.

    2016-12-01

    A numerical study of Anderson transition on random regular graphs (RRGs) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity. In a certain sense, the RRG ensemble can be seen as an infinite-dimensional (d →∞ ) cousin of the Anderson model in d dimensions. We focus on the delocalized side of the transition and stress the importance of finite-size effects. We show that the data can be interpreted in terms of the finite-size crossover from a small (N ≪Nc ) to a large (N ≫Nc ) system, where Nc is the correlation volume diverging exponentially at the transition. A distinct feature of this crossover is a nonmonotonicity of the spectral and wave-function statistics, which is related to properties of the critical phase in the studied model and renders the finite-size analysis highly nontrivial. Our results support an analytical prediction that states in the delocalized phase (and at N ≫Nc ) are ergodic in the sense that their inverse participation ratio scales as 1 /N .

  9. Graphical rule of transforming continuous-variable graph states by local homodyne detection

    SciTech Connect

    Zhang Jing

    2010-09-15

    Graphical rule, describing that any single-mode homodyne detection turns a given continuous-variable (CV) graph state into a new one, is presented. Employing two simple graphical rules--local complement operation and vertex deletion (single quadrature-amplitude x measurement)--the graphical rule for any single-mode quadrature component measurement can be obtained. The shape of CV weighted graph state may be designed and constructed easily from a given larger graph state by applying this graphical rule.

  10. On local adjacency metric dimension of some wheel related graphs with pendant points

    NASA Astrophysics Data System (ADS)

    Rinurwati, Suprajitno, Herry; Slamin

    2017-08-01

    Let G = (V(G),E(G)) be any connected graph of order n = |V(G)| and measure m = |E(G)|. For an order set of vertices S = { s1, s2, …, sk} and a vertex v in G, the adjacency representation of v with respect to S is the ordered k-tuple rA(v|S) = (dA(v, s1), dA(v, s2), …, dA(v, sk)), where dA(u,v) represents the adjacency distance between the vertices u and v. The set S is called a local adjacency resolving set of G if for every two distinct vertices u and v in G, u adjacent v then rA(u|S)≠rA(v|S). A minimum local adjacency resolving set for G is a local adjacency metric basis of G. Local adjacency metric dimension for G, dimA,l(G), is the cardinality of vertices in a local adjacency metric basis for G. In this paper, we study and determine the local adjacency metric dimension of some wheel related graphs G (namely gear graph, helm, sunflower and friendship graph) with pendant points, that is edge corona product of G and a trivial graph K1, G◊K1. Moreover, we compare among the local adjacency metric dimension of G◊K1 graph,of Wn◊K1 graph and metric dimension of Wn.

  11. Local dependence in random graph models: characterization, properties and statistical inference.

    PubMed

    Schweinberger, Michael; Handcock, Mark S

    2015-06-01

    Dependent phenomena, such as relational, spatial and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-defined sense are dependent. In contrast with spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighbourhood structure in the sense that it is unknown which units are close and thus dependent. Owing to the challenge of characterizing local dependence and constructing random graph models with local dependence, many conventional exponential family random graph models induce strong dependence and are not amenable to statistical inference. We take first steps to characterize local dependence in random graph models, inspired by the notion of finite neighbourhoods in spatial statistics and M-dependence in time series, and we show that local dependence endows random graph models with desirable properties which make them amenable to statistical inference. We show that random graph models with local dependence satisfy a natural domain consistency condition which every model should satisfy, but conventional exponential family random graph models do not satisfy. In addition, we establish a central limit theorem for random graph models with local dependence, which suggests that random graph models with local dependence are amenable to statistical inference. We discuss how random graph models with local dependence can be constructed by exploiting either observed or unobserved neighbourhood structure. In the absence of observed neighbourhood structure, we take a Bayesian view and express the uncertainty about the neighbourhood structure by specifying a prior on a set of suitable neighbourhood structures. We present simulation results and applications to two real world networks with 'ground truth'.

  12. Local dependence in random graph models: characterization, properties and statistical inference

    PubMed Central

    Schweinberger, Michael; Handcock, Mark S.

    2015-01-01

    Summary Dependent phenomena, such as relational, spatial and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-defined sense are dependent. In contrast with spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighbourhood structure in the sense that it is unknown which units are close and thus dependent. Owing to the challenge of characterizing local dependence and constructing random graph models with local dependence, many conventional exponential family random graph models induce strong dependence and are not amenable to statistical inference. We take first steps to characterize local dependence in random graph models, inspired by the notion of finite neighbourhoods in spatial statistics and M-dependence in time series, and we show that local dependence endows random graph models with desirable properties which make them amenable to statistical inference. We show that random graph models with local dependence satisfy a natural domain consistency condition which every model should satisfy, but conventional exponential family random graph models do not satisfy. In addition, we establish a central limit theorem for random graph models with local dependence, which suggests that random graph models with local dependence are amenable to statistical inference. We discuss how random graph models with local dependence can be constructed by exploiting either observed or unobserved neighbourhood structure. In the absence of observed neighbourhood structure, we take a Bayesian view and express the uncertainty about the neighbourhood structure by specifying a prior on a set of suitable neighbourhood structures. We present simulation results and applications to two real world networks with ‘ground truth’. PMID:26560142

  13. Seven Experiments to Test the Local Lorentz Invariance of c

    NASA Technical Reports Server (NTRS)

    Gezari, Daniel Y.

    2005-01-01

    The speed of light has never been measured directly with a moving detector to test the fundamental assertion of special relativity that c is invariant to motion of the observer. Seven simple experiments are proposed, four of which could test the invariance of c to motion of the detector. Three other observations of moving sources could test Einstein s second postulate and the relativity of stellar aberration. There are lingering concerns that the speed of light may depend on the motion of the observer, after all. This issue can now be resolved by experiment.

  14. Exposing local symmetries in distorted driven lattices via time-averaged invariants

    NASA Astrophysics Data System (ADS)

    Wulf, T.; Morfonios, C. V.; Diakonos, F. K.; Schmelcher, P.

    2016-05-01

    Time-averaged two-point currents are derived and shown to be spatially invariant within domains of local translation or inversion symmetry for arbitrary time-periodic quantum systems in one dimension. These currents are shown to provide a valuable tool for detecting deformations of a spatial symmetry in static and driven lattices. In the static case the invariance of the two-point currents is related to the presence of time-reversal invariance and/or probability current conservation. The obtained insights into the wave functions are further exploited for a symmetry-based convergence check which is applicable for globally broken but locally retained potential symmetries.

  15. Rational Conformal Correlation Functions of Gauge-Invariant Local Fields in Four Dimensions

    SciTech Connect

    Nikolov, N.M.; Stanev, Ya.S.; Todorov, I.T.

    2005-11-01

    Global conformal invariance in Minkowski space and the Wightman axioms imply strong locality (Huygens principle) and rationality of correlation functions, thus providing an extension of the concept of a vertex algebra to higher (even) dimensions D. We (p)review current work on a model of a Hermitian scalar field L of scale dimension 4 (D = 4) which can be interpreted as the Lagrangian of a gauge field theory that generates the algebra of gauge-invariant local observables in a conformally invariant renormalization group fixed point.

  16. Comparison of Different Generalizations of Clustering Coefficient and Local Efficiency for Weighted Undirected Graphs.

    PubMed

    Wang, Yu; Ghumare, Eshwar; Vandenberghe, Rik; Dupont, Patrick

    2017-02-01

    Binary undirected graphs are well established, but when these graphs are constructed, often a threshold is applied to a parameter describing the connection between two nodes. Therefore, the use of weighted graphs is more appropriate. In this work, we focus on weighted undirected graphs. This implies that we have to incorporate edge weights in the graph measures, which require generalizations of common graph metrics. After reviewing existing generalizations of the clustering coefficient and the local efficiency, we proposed new generalizations for these graph measures. To be able to compare different generalizations, a number of essential and useful properties were defined that ideally should be satisfied. We applied the generalizations to two real-world networks of different sizes. As a result, we found that not all existing generalizations satisfy all essential properties. Furthermore, we determined the best generalization for the clustering coefficient and local efficiency based on their properties and the performance when applied to two networks. We found that the best generalization of the clustering coefficient is [Formula: see text], defined in Miyajima and Sakuragawa ( 2014 ), while the best generalization of the local efficiency is [Formula: see text], proposed in this letter. Depending on the application and the relative importance of sensitivity and robustness to noise, other generalizations may be selected on the basis of the properties investigated in this letter.

  17. Local quality functions for graph clustering with non-negative matrix factorization

    NASA Astrophysics Data System (ADS)

    van Laarhoven, Twan; Marchiori, Elena

    2014-12-01

    Many graph clustering quality functions suffer from a resolution limit, namely the inability to find small clusters in large graphs. So-called resolution-limit-free quality functions do not have this limit. This property was previously introduced for hard clustering, that is, graph partitioning. We investigate the resolution-limit-free property in the context of non-negative matrix factorization (NMF) for hard and soft graph clustering. To use NMF in the hard clustering setting, a common approach is to assign each node to its highest membership cluster. We show that in this case symmetric NMF is not resolution-limit free, but that it becomes so when hardness constraints are used as part of the optimization. The resulting function is strongly linked to the constant Potts model. In soft clustering, nodes can belong to more than one cluster, with varying degrees of membership. In this setting resolution-limit free turns out to be too strong a property. Therefore we introduce locality, which roughly states that changing one part of the graph does not affect the clustering of other parts of the graph. We argue that this is a desirable property, provide conditions under which NMF quality functions are local, and propose a novel class of local probabilistic NMF quality functions for soft graph clustering.

  18. Texture classification using rotation invariant models on integrated local binary pattern and Zernike moments

    NASA Astrophysics Data System (ADS)

    Wang, Yu; Zhao, Yongsheng; Chen, Yi

    2014-12-01

    More and more attention has been paid to the invariant texture analysis, because the training and testing samples generally have not identical or similar orientations, or are not acquired from the same viewpoint in many practical applications, which often has negative influences on texture analysis. Local binary pattern (LBP) has been widely applied to texture classification due to its simplicity, efficiency, and rotation invariant property. In this paper, an integrated local binary pattern (ILBP) scheme including original rotation invariant LBP, improved contrast rotation invariant LBP, and direction rotation invariant LBP is proposed which can effectively overcome the deficiency of original LBP that is ignoring contrast and direction information. In addition, for surmounting another major drawback of LBP such as locality which can result in the lack of shape and space expression of the holistic texture image, Zernike moment features are fused into the improved LBP texture features in the proposed method because they comprise orthogonal and rotation invariant property and can be easily and rapidly calculated to an arbitrary high order. Experimental results show that the proposed method can be remarkably superior to the other state-of-the-art methods when rotation invariant texture features are extracted and classified.

  19. A test of local Lorentz invariance with Compton scattering asymmetry

    DOE PAGES

    Mohanmurthy, Prajwal; Narayan, Amrendra; Dutta, Dipangkar

    2016-12-14

    Here, we report on a measurement of the constancy and anisotropy of the speed of light relative to the electrons in photon-electron scattering. We also used the Compton scattering asymmetry measured by the new Compton polarimeter in Hall~C at Jefferson Lab to test for deviations from unity of the vacuum refractive index (more » $n$). For photon energies in the range of 9 - 46 MeV, we obtain a new limit of $$1-n < 1.4 \\times 10^{-8}$$. In addition, the absence of sidereal variation over the six month period of the measurement constrains any anisotropies in the speed of light. These constitute the first study of Lorentz invariance using Compton asymmetry. Within the minimal standard model extension framework, our result yield limits on the photon and electron coefficients $$\\tilde{\\kappa}_{0^+}^{YZ}, c_{TX}, \\tilde{\\kappa}_{0^+}^{ZX}$$, and $$c_{TY}$$. Though, these limits are several orders of magnitude larger than the current best limits, they demonstrate the feasibility of using Compton asymmetry for tests of Lorentz invariance. For future parity violating electron scattering experiments at Jefferson Lab we will use higher energy electrons enabling better constraints.« less

  20. A test of local Lorentz invariance with Compton scattering asymmetry

    SciTech Connect

    Mohanmurthy, Prajwal; Narayan, Amrendra; Dutta, Dipangkar

    2016-12-14

    Here, we report on a measurement of the constancy and anisotropy of the speed of light relative to the electrons in photon-electron scattering. We also used the Compton scattering asymmetry measured by the new Compton polarimeter in Hall~C at Jefferson Lab to test for deviations from unity of the vacuum refractive index ($n$). For photon energies in the range of 9 - 46 MeV, we obtain a new limit of $1-n < 1.4 \\times 10^{-8}$. In addition, the absence of sidereal variation over the six month period of the measurement constrains any anisotropies in the speed of light. These constitute the first study of Lorentz invariance using Compton asymmetry. Within the minimal standard model extension framework, our result yield limits on the photon and electron coefficients $\\tilde{\\kappa}_{0^+}^{YZ}, c_{TX}, \\tilde{\\kappa}_{0^+}^{ZX}$, and $c_{TY}$. Though, these limits are several orders of magnitude larger than the current best limits, they demonstrate the feasibility of using Compton asymmetry for tests of Lorentz invariance. For future parity violating electron scattering experiments at Jefferson Lab we will use higher energy electrons enabling better constraints.

  1. Sequential generation of polynomial invariants and N-body non-local correlations

    NASA Astrophysics Data System (ADS)

    Sharma, S. Shelly; Sharma, N. K.

    2016-12-01

    We report an inductive process that allows for sequential construction of local unitary invariant polynomials of state coefficients for multipartite quantum states. The starting point can be a physically meaningful invariant of a smaller part of the system. The process is applied to construct a chain of invariants that quantify non-local N-way correlations in an N-qubit pure state. It also yields the invariants to quantify the sum of N-way and ( N-1)-way correlations. Analytic expressions for four-way and three-way correlation quantifiers for four-qubit states, as well as, five-way and four-way correlation quantifiers for five-qubit pure states are given.

  2. On (local) metric dimension of graphs with m-pendant points

    NASA Astrophysics Data System (ADS)

    Rinurwati; Slamin; Suprajitno, H.

    2017-06-01

    An ordered set of vertices S is called as a (local) resolving set of a connected graph G = (V G , E G ) if for any two adjacent vertices s ≠ t ∈ V G have distinct representation with respect to S, that is r(s | S) ≠ r(t | S). A representation of a vertex in G is a vector of distances to vertices in S. The minimum (local) resolving set for G is called as a (local) basis of G. A (local) metric dimension for G denoted by dim(G), is the cardinality of vertices in a basis for G, and its local variant by dim l (G). Given two graphs, G with vertices s 1, s 2, …, sp and edges e 1, e 2, …, eq , and H. An edge-corona of G and H, G⋄H is defined as a graph obtained by taking a copy of G and q copies of H and for each edge ej = sish of G joining edges between the two end-vertices si, sh of ej and each vertex of j-copy of H. In this paper, we determine and compare between the metric dimension of graphs with m-pendant points, G⋄mK 1, and its local variant for any connected graph G. We give an upper bound of the dimensions.

  3. A test of local Lorentz invariance with Compton scattering asymmetry

    NASA Astrophysics Data System (ADS)

    Mohanmurthy, Prajwal; Narayan, Amrendra; Dutta, Dipangkar

    2016-11-01

    We report on a measurement of the constancy and anisotropy of the speed of light relative to the electrons in photon-electron scattering. We used the Compton scattering asymmetry measured by the new Compton polarimeter in Hall C at Jefferson Lab (JLab) to test for deviations from unity of the vacuum refractive index (n). For photon energies in the range of 9-46 MeV, we obtain a new limit of 1 - n < 1.4 × 10-8. In addition, the absence of sidereal variation over the six-month period of the measurement constrains any anisotropies in the speed of light. These constitute the first study of Lorentz invariance (LI) using Compton asymmetry. Within the minimal Standard Model extension (MSME) framework, our result yield limits on the photon and electron coefficients κ˜0+Y Z, cTX, κ˜0+ZX and cTY. Although these limits are several orders of magnitude larger than the current best limits, they demonstrate the feasibility of using Compton asymmetry for tests of LI. Future parity-violating electron-scattering experiments at JLab will use higher energy electrons enabling better constraints.

  4. Test of local position invariance using a double-cavity laser system

    SciTech Connect

    Agachev, A. R.; Belov, I. Yu.; Bochkarev, V. V.; Daishev, R. A.; Mavrin, S. V.; Murzakhanov, Z. G.; Skochilov, A. F. Chugunov, Yu. P.; Shindyaev, O. P.

    2010-01-15

    The results of testing local position invariance, which is a constituent of the Einstein equivalence principle, in a 'null' gravitational redshift experiment are reported. The processing of the experimental data collected during the five-month operation of a double-c avity laser system, where one cavity operates in the free generation mode and the frequency of the second cavity is stabilized with the nonlinear ultranarrow absorption resonance of the methane molecule, has confirmed the universality of the gravitational redshift law at a level of 0.9%. This result almost doubly improves the best existing accuracy (1.7%) of testing local position invariance for clocks of different physical natures.

  5. Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays

    NASA Astrophysics Data System (ADS)

    Morfonios, C. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.

    2017-10-01

    We develop a formalism relating nonlocal current continuity to spatial symmetries of subparts in discrete Schrödinger systems. Breaking of such local symmetries hereby generates sources or sinks for the associated nonlocal currents. The framework is applied to locally inversion-(time-) and translation-(time-) symmetric one-dimensional photonic waveguide arrays with Hermitian or non-Hermitian effective tight-binding Hamiltonians. For stationary states the nonlocal currents become translationally invariant within symmetric domains, exposing different types of local symmetry. They are further employed to derive a mapping between wave amplitudes of symmetry-related sites, generalizing also the global Bloch and parity mapping to local symmetry in discrete systems. In scattering setups, perfectly transmitting states are characterized by aligned invariant currents in attached symmetry domains, whose vanishing signifies a correspondingly symmetric density. For periodically driven arrays, the invariance of the nonlocal currents is retained on period average for quasi-energy eigenstates. The proposed theory of symmetry-induced continuity and local invariants may contribute to the understanding of wave structure and response in systems with localized spatial order.

  6. Optimal neighbor graph-based orthogonal tensor locality preserving projection for image recognition

    NASA Astrophysics Data System (ADS)

    Yuan, Sen; Mao, Xia

    2016-11-01

    As a typical multilinear dimensionality reduction (DR) method, tensor locality preserving projection (TLPP) has been successfully applied in many practical problems. However, TLPP depends mainly on preserving its local neighbor graph which often suffers from the following issues: (1) the neighbor graph is constructed with the Euclidean distance which fails to consider the relationships among different coordinates for tensor data; (2) the affinity matrix only focuses on the local structure information of samples while ignoring the existing label information; (3) the projection matrices are nonorthogonal, thus it is difficult to preserve the local manifold structure. To address these problems, a multilinear DR algorithm called optimal neighbor graph-based orthogonal tensor locality preserving projection (OG-OTLPP) is proposed. In OG-OTLPP, an optimal neighbor graph is first built according to tensor distance. Then the affinity matrix of data is defined by utilizing both the label information and the intrinsic local geometric properties of the data. Finally, in order to improve the manifold preserving ability, an efficient and stable scheme is designed to iteratively learn the orthogonal projections. We evaluate the proposed algorithm by applying it to image recognition. The experimental results on five public image databases demonstrate the effectiveness of our algorithm.

  7. Hydrodynamic and magnetohydrodynamic turbulence: Invariants, cascades, and locality

    NASA Astrophysics Data System (ADS)

    Aluie, Hussein

    This dissertation employs the coarse-graining approach, commonly used as a modeling tool in the LES community, to analyze scale interactions in turbulent flows, following [1]. The main scientific contributions of this dissertation to the fields of hydrodynamic and magnetohydrodynamic (MHD) turbulence are: (1) Establishing necessary conditions for turbulent MHD flows to sustain cascades of energy and cross-helicity to arbitrarily small scales, and proving that it is impossible for magnetic-helicity to undergo a forward cascade. These results provide rigorous constraints on any phenomenological theory of MHD turbulence. (2) Presenting both rigorous results and physical theory on the breakdown of magnetic flux conservation for plasmas by nonlinear effects, independent of any microscopic non-ideality. It shows that instantaneous violation of flux-conservation can occur if singular current sheets and vortex sheets both exist and intersect in sets of non-zero length. This result gives analytical support to and rigorous constraints on theories of fast turbulent reconnection. (3) Establishing scale-locality of the energy cascade in a turbulent flow using Fourier analysis and showing that the primary participants in the process are triplets of "eddies" comprised of adjacent logarithmic bands of Fourier modes. The analysis disproves an alternate picture of "local transfer by nonlocal triads" by showing that such triads make a vanishingly small contribution to the energy flux in the inertial range and that it is only the aggregate effect of a geometrically increasing number of local wavenumber triads which can sustain the cascade to small scales. It also shows that the SGS definition of the flux is the proper measure of the cascading energy and demonstrates the danger in the widespread notion that the elementary interactions in turbulence are those involving triads of single Fourier modes. Numerical support is presented from simulations of Navier-Stokes turbulence. (4

  8. Limitations in the spectral method for graph partitioning: Detectability threshold and localization of eigenvectors.

    PubMed

    Kawamoto, Tatsuro; Kabashima, Yoshiyuki

    2015-06-01

    Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both un-normalized and normalized Laplacians in sparse graphs. The detectability threshold is the critical point at which the result of the spectral method is completely uncorrelated to the planted partition. We also analyze whether the localization of eigenvectors affects the partitioning performance in the detectable region. We use the replica method, which is often used in the field of spin-glass theory, and focus on the case of bisection. We show that the gap between the estimated threshold for the spectral method and the threshold obtained from Bayesian inference is considerable in sparse graphs, even without eigenvector localization. This gap closes in a dense limit.

  9. Limitations in the spectral method for graph partitioning: Detectability threshold and localization of eigenvectors

    NASA Astrophysics Data System (ADS)

    Kawamoto, Tatsuro; Kabashima, Yoshiyuki

    2015-06-01

    Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both un-normalized and normalized Laplacians in sparse graphs. The detectability threshold is the critical point at which the result of the spectral method is completely uncorrelated to the planted partition. We also analyze whether the localization of eigenvectors affects the partitioning performance in the detectable region. We use the replica method, which is often used in the field of spin-glass theory, and focus on the case of bisection. We show that the gap between the estimated threshold for the spectral method and the threshold obtained from Bayesian inference is considerable in sparse graphs, even without eigenvector localization. This gap closes in a dense limit.

  10. A three-colour graph as a complete topological invariant for gradient-like diffeomorphisms of surfaces

    SciTech Connect

    Grines, V Z; Pochinka, O V; Kapkaeva, S Kh

    2014-10-31

    In a paper of Oshemkov and Sharko, three-colour graphs were used to make the topological equivalence of Morse-Smale flows on surfaces obtained by Peixoto more precise. In the present paper, in the language of three-colour graphs equipped with automorphisms, we obtain a complete (including realization) topological classification of gradient-like cascades on surfaces. Bibliography: 25 titles.

  11. Topological invariants of band insulators derived from the local-orbital based embedding potential

    NASA Astrophysics Data System (ADS)

    Ishida, H.; Liebsch, A.; Wortmann, D.

    2017-09-01

    We demonstrate that topological invariants of band insulators can be derived efficiently from the eigenvalues of the local-orbital (LO) based embedding potential, called also the contact (lead) self-energy. The LO based embedding potential is a bulk quantity. Given the tight-binding Hamiltonian describing the bulk valence and conduction bands, it is constructed straightforwardly from the bulk wave functions satisfying the generalized Bloch condition. When the one-electron energy ɛ is located within a projected bulk band gap at a given planar wave vector k , the embedding potential becomes Hermitian. Its real eigenvalues exhibit distinctly different behavior depending on the topological properties of the valence bands, thus enabling unambiguous identification of bulk topological invariants. We consider the Bernevig-Hughes-Zhang model as an example of a time-reversal invariant topological insulator and tin telluride (SnTe) crystallized in a rock-salt structure as an example of a topological crystalline insulator.

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

    NASA Astrophysics Data System (ADS)

    Webb, G. M.; Dasgupta, B.; McKenzie, J. F.; Hu, Q.; Zank, G. P.

    2014-03-01

    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.

  13. The invariant measure for Anderson localized negative index metamaterials continuously disordered

    NASA Astrophysics Data System (ADS)

    Kissel, Glen J.; Williams, Aaron

    We consider one-dimensional photonic bandgap structures with negative index of refraction materials modeled in every layer, or in every other layer. When the index of refraction is randomized, and the number of layers becomes large, the light waves undergo Anderson localization, resulting in confinement of the transmitted energy. Such a photonic bandgap structure can be modeled by a long product of random transfer matrices, from which the (upper) Lyapunov exponent can be calculated to characterize the localization effect. Furstenberg's theorem gives a precise formula to calculate the Lyapunov exponent when the random matrices, under general conditions, are independent and identically distributed. Specifically, Furstenberg's integral formula can be used to calculate the Lyapunov exponent via integration with respect to the probability measure of the random matrices, and with respect to the so-called invariant probability measure of the direction of the vector propagated by the long chain of random matrices. It is this latter invariant probability measure, so fundamental to Furstenberg's theorem, which is generally impossible to determine analytically. Here we use a bin counting technique with Monte Carlo chosen random parameters from a continuous distribution to numerically estimate the invariant measure and then calculate Lyapunov exponents from Furstenberg's integral formula. This result, one of the first times an invariant measure has been calculated for a continuously disordered structure made of alternating layers of positive and negative index materials, is compared to results for all negative index or equivalently all positive index structures.

  14. New test of local Lorentz invariance using a 21Ne-Rb-K comagnetometer.

    PubMed

    Smiciklas, M; Brown, J M; Cheuk, L W; Smullin, S J; Romalis, M V

    2011-10-21

    We develop a new comagnetometer using (21)Ne atoms with nuclear spin I=3/2 and Rb atoms polarized by spin exchange with K atoms to search for tensor interactions that violate local Lorentz invariance. We frequently reverse the orientation of the experiment and search for signals at the first and second harmonics of the sidereal frequency. We constrain 4 of the 5 spatial Lorentz-violating coefficients c(jk)(n) that parametrize anisotropy of the maximum attainable velocity of a neutron at a level of 10(-29), improving previous limits by 2 to 4 orders of magnitude and placing the most stringent constraint on deviations from local Lorentz invariance. © 2011 American Physical Society

  15. Scale-invariant hidden local symmetry, topology change, and dense baryonic matter

    NASA Astrophysics Data System (ADS)

    Paeng, Won-Gi; Kuo, Thomas T. S.; Lee, Hyun Kyu; Rho, Mannque

    2016-05-01

    When scale symmetry is implemented into hidden local symmetry in low-energy strong interactions to arrive at a scale-invariant hidden local symmetric (HLS) theory, the scalar f0(500 ) may be interpreted as pseudo-Nambu-Goldstone (pNG) boson, i.e., dilaton, of spontaneously broken scale invariance, joining the pseudoscalar pNG bosons π and the matter fields V =(ρ ,ω ) as relevant degrees of freedom. Implementing the skyrmion-half-skyrmion transition predicted at large Nc in QCD at a density roughly twice the nuclear matter density found in the crystal simulation of dense skyrmion matter, we determine the intrinsically density-dependent "bare parameters" of the scale-invariant HLS Lagrangian matched to QCD at a matching scale ΛM. The resulting effective Lagrangian, with the parameters scaling with the density of the system, is applied to nuclear matter and dense baryonic matter relevant to massive compact stars by means of the double-decimation renormalization-group Vlow k formalism. We satisfactorily postdict the properties of normal nuclear matter and more significantly predict the equation of state of dense compact-star matter that quantitatively accounts for the presently available data coming from both the terrestrial and space laboratories. We interpret the resulting structure of compact-star matter as revealing how the combination of hidden-scale symmetry and hidden local symmetry manifests itself in compressed baryonic matter.

  16. Classification of EEG Single Trial Microstates Using Local Global Graphs and Discrete Hidden Markov Models.

    PubMed

    Michalopoulos, Kostas; Zervakis, Michalis; Deiber, Marie-Pierre; Bourbakis, Nikolaos

    2016-09-01

    We present a novel synergistic methodology for the spatio-temporal analysis of single Electroencephalogram (EEG) trials. This new methodology is based on the novel synergy of Local Global Graph (LG graph) to characterize define the structural features of the EEG topography as a global descriptor for robust comparison of dominant topographies (microstates) and Hidden Markov Models (HMM) to model the topographic sequence in a unique way. In particular, the LG graph descriptor defines similarity and distance measures that can be successfully used for the difficult comparison of the extracted LG graphs in the presence of noise. In addition, hidden states represent periods of stationary distribution of topographies that constitute the equivalent of the microstates in the model. The transitions between the different microstates and the formed syntactic patterns can reveal differences in the processing of the input stimulus between different pathologies. We train the HMM model to learn the transitions between the different microstates and express the syntactic patterns that appear in the single trials in a compact and efficient way. We applied this methodology in single trials consisting of normal subjects and patients with Progressive Mild Cognitive Impairment (PMCI) to discriminate these two groups. The classification results show that this approach is capable to efficiently discriminate between control and Progressive MCI single trials. Results indicate that HMMs provide physiologically meaningful results that can be used in the syntactic analysis of Event Related Potentials.

  17. Differentials on graph complexes II: hairy graphs

    NASA Astrophysics Data System (ADS)

    Khoroshkin, Anton; Willwacher, Thomas; Živković, Marko

    2017-10-01

    We study the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory. We provide spectral sequences converging to zero whose first pages contain the hairy graph cohomology. Our results yield a way to construct many nonzero hairy graph cohomology classes out of (known) non-hairy classes by studying the cancellations in those sequences. This provide a first glimpse at the tentative global structure of the hairy graph cohomology.

  18. How many invariant polynomials are needed to decide local unitary equivalence of qubit states?

    SciTech Connect

    Maciążek, Tomasz; Oszmaniec, Michał

    2013-09-15

    Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if two states can be connected by local unitary operations. Interestingly, this number is not the same for every collection of the spectra. Some spectra require less polynomials to solve LU equivalence problem than others. The result is obtained using geometric methods, i.e., by calculating the dimensions of reduced spaces, stemming from the symplectic reduction procedure.

  19. Identifying subcellular localizations of mammalian protein complexes based on graph theory with a random forest algorithm.

    PubMed

    Li, Zhan-Chao; Lai, Yan-Hua; Chen, Li-Li; Chen, Chao; Xie, Yun; Dai, Zong; Zou, Xiao-Yong

    2013-04-05

    In the post-genome era, one of the most important and challenging tasks is to identify the subcellular localizations of protein complexes, and further elucidate their functions in human health with applications to understand disease mechanisms, diagnosis and therapy. Although various experimental approaches have been developed and employed to identify the subcellular localizations of protein complexes, the laboratory technologies fall far behind the rapid accumulation of protein complexes. Therefore, it is highly desirable to develop a computational method to rapidly and reliably identify the subcellular localizations of protein complexes. In this study, a novel method is proposed for predicting subcellular localizations of mammalian protein complexes based on graph theory with a random forest algorithm. Protein complexes are modeled as weighted graphs containing nodes and edges, where nodes represent proteins, edges represent protein-protein interactions and weights are descriptors of protein primary structures. Some topological structure features are proposed and adopted to characterize protein complexes based on graph theory. Random forest is employed to construct a model and predict subcellular localizations of protein complexes. Accuracies on a training set by a 10-fold cross-validation test for predicting plasma membrane/membrane attached, cytoplasm and nucleus are 84.78%, 71.30%, and 82.00%, respectively. And accuracies for the independent test set are 81.31%, 69.95% and 81.00%, respectively. These high prediction accuracies exhibit the state-of-the-art performance of the current method. It is anticipated that the proposed method may become a useful high-throughput tool and plays a complementary role to the existing experimental techniques in identifying subcellular localizations of mammalian protein complexes. The source code of Matlab and the dataset can be obtained freely on request from the authors.

  20. Existence of positive solutions to some nonlinear equations on locally finite graphs

    NASA Astrophysics Data System (ADS)

    Grigor'yan, Alexander; Lin, Yong; Yang, YunYan

    2017-07-01

    Let $G=(V,E)$ be a locally finite graph, whose measure $\\mu(x)$ have positive lower bound, and $\\Delta$ be the usual graph Laplacian. Applying the mountain-pass theorem due to Ambrosetti-Rabinowitz, we establish existence results for some nonlinear equations, namely $\\Delta u+hu=f(x,u)$, $x\\in V$. In particular, we prove that if $h$ and $f$ satisfy certain assumptions, then the above mentioned equation has strictly positive solutions. Also, we consider existence of positive solutions of the perturbed equation $\\Delta u+hu=f(x,u)+\\epsilon g$. Similar problems have been extensively studied on the Euclidean space as well as on Riemannian manifolds.

  1. Many-body self-localization in a translation-invariant Hamiltonian

    NASA Astrophysics Data System (ADS)

    Mondaini, Rubem; Cai, Zi

    2017-07-01

    We study the statistical and dynamical aspects of a translation-invariant Hamiltonian, without quench disorder, as an example of the manifestation of the phenomenon of many-body localization. This is characterized by the breakdown of thermalization and by information preservation of initial preparations at long times. To realize this, we use quasiperiodic long-range interactions, which are now achievable in high-finesse cavity experiments, to find evidence suggestive of a divergent time-scale in which charge inhomogeneities in the initial state survive asymptotically. This is reminiscent of a glassy behavior, which appears in the ground state of this system, being also present at infinite temperatures.

  2. Pattern vectors from algebraic graph theory.

    PubMed

    Wilson, Richard C; Hancock, Edwin R; Luo, Bin

    2005-07-01

    Graph structures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low-dimensional space using a number of alternative strategies, including principal components analysis (PCA), multidimensional scaling (MDS), and locality preserving projection (LPP). Experimentally, we demonstrate that the embeddings result in well-defined graph clusters. Our experiments with the spectral representation involve both synthetic and real-world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real-world experiments show that the method can be used to locate clusters of graphs.

  3. Retinal vessel segmentation: an efficient graph cut approach with retinex and local phase.

    PubMed

    Zhao, Yitian; Liu, Yonghuai; Wu, Xiangqian; Harding, Simon P; Zheng, Yalin

    2015-01-01

    Our application concerns the automated detection of vessels in retinal images to improve understanding of the disease mechanism, diagnosis and treatment of retinal and a number of systemic diseases. We propose a new framework for segmenting retinal vasculatures with much improved accuracy and efficiency. The proposed framework consists of three technical components: Retinex-based image inhomogeneity correction, local phase-based vessel enhancement and graph cut-based active contour segmentation. These procedures are applied in the following order. Underpinned by the Retinex theory, the inhomogeneity correction step aims to address challenges presented by the image intensity inhomogeneities, and the relatively low contrast of thin vessels compared to the background. The local phase enhancement technique is employed to enhance vessels for its superiority in preserving the vessel edges. The graph cut-based active contour method is used for its efficiency and effectiveness in segmenting the vessels from the enhanced images using the local phase filter. We have demonstrated its performance by applying it to four public retinal image datasets (3 datasets of color fundus photography and 1 of fluorescein angiography). Statistical analysis demonstrates that each component of the framework can provide the level of performance expected. The proposed framework is compared with widely used unsupervised and supervised methods, showing that the overall framework outperforms its competitors. For example, the achieved sensitivity (0:744), specificity (0:978) and accuracy (0:953) for the DRIVE dataset are very close to those of the manual annotations obtained by the second observer.

  4. Rotation-invariant multi-contrast non-local means for MS lesion segmentation.

    PubMed

    Guizard, Nicolas; Coupé, Pierrick; Fonov, Vladimir S; Manjón, Jose V; Arnold, Douglas L; Collins, D Louis

    2015-01-01

    Multiple sclerosis (MS) lesion segmentation is crucial for evaluating disease burden, determining disease progression and measuring the impact of new clinical treatments. MS lesions can vary in size, location and intensity, making automatic segmentation challenging. In this paper, we propose a new supervised method to segment MS lesions from 3D magnetic resonance (MR) images using non-local means (NLM). The method uses a multi-channel and rotation-invariant distance measure to account for the diversity of MS lesions. The proposed segmentation method, rotation-invariant multi-contrast non-local means segmentation (RMNMS), captures the MS lesion spatial distribution and can accurately and robustly identify lesions regardless of their orientation, shape or size. An internal validation on a large clinical magnetic resonance imaging (MRI) dataset of MS patients demonstrated a good similarity measure result (Dice similarity = 60.1% and sensitivity = 75.4%), a strong correlation between expert and automatic lesion load volumes (R(2) = 0.91), and a strong ability to detect lesions of different sizes and in varying spatial locations (lesion detection rate = 79.8%). On the independent MS Grand Challenge (MSGC) dataset validation, our method provided competitive results with state-of-the-art supervised and unsupervised methods. Qualitative visual and quantitative voxel- and lesion-wise evaluations demonstrated the accuracy of RMNMS method.

  5. Object matching using a locally affine invariant and linear programming techniques.

    PubMed

    Li, Hongsheng; Huang, Xiaolei; He, Lei

    2013-02-01

    In this paper, we introduce a new matching method based on a novel locally affine-invariant geometric constraint and linear programming techniques. To model and solve the matching problem in a linear programming formulation, all geometric constraints should be able to be exactly or approximately reformulated into a linear form. This is a major difficulty for this kind of matching algorithm. We propose a novel locally affine-invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming-based methods do. The key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points, whose weights can be solved easily by least squares. Errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points. The resulting overall objective function can be solved efficiently by linear programming techniques. Our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm.

  6. Improving scale invariant feature transform with local color contrastive descriptor for image classification

    NASA Astrophysics Data System (ADS)

    Guo, Sheng; Huang, Weilin; Qiao, Yu

    2017-01-01

    Image representation and classification are two fundamental tasks toward version understanding. Shape and texture provide two key features for visual representation and have been widely exploited in a number of successful local descriptors, e.g., scale invariant feature transform (SIFT), local binary pattern descriptor, and histogram of oriented gradient. Unlike these gradient-based descriptors, this paper presents a simple yet efficient local descriptor, named local color contrastive descriptor (LCCD), which captures the contrastive aspects among local regions or color channels for image representation. LCCD is partly inspired by the neural science facts that color contrast plays important roles in visual perception and there exist strong linkages between color and shape. We leverage f-divergence as a robust measure to estimate the contrastive features between different spatial locations and multiple channels. Our descriptor enriches local image representation with both color and contrast information. Due to that LCCD does not explore any gradient information, individual LCCD does not yield strong performance. But we verified experimentally that LCCD can compensate strongly SIFT. Extensive experimental results on image classification show that our descriptor improves the performance of SIFT substantially by combination on three challenging benchmarks, including MIT Indoor-67 database, SUN397, and PASCAL VOC 2007.

  7. Dynamics of many-body localization in a translation-invariant quantum glass model

    NASA Astrophysics Data System (ADS)

    van Horssen, Merlijn; Levi, Emanuele; Garrahan, Juan P.

    2015-09-01

    We study the real-time dynamics of a translationally invariant quantum spin chain, based on the East kinetically constrained glass model, in search for evidence of many-body localization in the absence of disorder. Numerical simulations indicate a change, controlled by a coupling parameter, from a regime of fast relaxation-corresponding to thermalization-to a regime of very slow relaxation. This slowly relaxing regime is characterized by dynamical features usually associated with nonergodicity and many-body localization (MBL): memory of initial conditions, logarithmic growth of entanglement entropy, and nonexponential decay of time correlators. We show that slow relaxation is a consequence of sensitivity to spatial fluctuations in the initial state. While numerical results and physical considerations indicate that relaxation time scales grow markedly with size, our finite size results are consistent both with an MBL transition, expected to only occur in disordered systems, and with a pronounced quasi-MBL crossover.

  8. New limits on the violation of local position invariance of gravity

    NASA Astrophysics Data System (ADS)

    Shao, Lijing; Wex, Norbert

    2013-08-01

    Within the parameterized post-Newtonian (PPN) formalism, there could be an anisotropy of local gravity induced by an external matter distribution, even for a fully conservative metric theory of gravity. It reflects the breakdown of the local position invariance of gravity and, within the PPN formalism, is characterized by the Whitehead parameter ξ. We present three different kinds of observation, from the Solar system and radio pulsars, to constrain it. The most stringent limit comes from recent results on the extremely stable pulse profiles of solitary millisecond pulsars, that gives |\\hat{\\xi }| < 3.9 \\times 10^{-9} (95% CL), where the hat denotes the strong-field generalization of ξ. This limit is six orders of magnitude more constraining than the current best limit from superconducting gravimeter experiments. It can be converted into an upper limit of ˜4 × 10-16 on the spatial anisotropy of the gravitational constant. Communicated by C M Will

  9. Braided Categories of Endomorphisms as Invariants for Local Quantum Field Theories

    NASA Astrophysics Data System (ADS)

    Giorgetti, Luca; Rehren, Karl-Henning

    2017-08-01

    We want to establish the "braided action" (defined in the paper) of the DHR category on a universal environment algebra as a complete invariant for completely rational chiral conformal quantum field theories. The environment algebra can either be a single local algebra, or the quasilocal algebra, both of which are model-independent up to isomorphism. The DHR category as an abstract structure is captured by finitely many data (superselection sectors, fusion, and braiding), whereas its braided action encodes the full dynamical information that distinguishes models with isomorphic DHR categories. We show some geometric properties of the "duality pairing" between local algebras and the DHR category that are valid in general (completely rational) chiral CFTs. Under some additional assumptions whose status remains to be settled, the braided action of its DHR category completely classifies a (prime) CFT. The approach does not refer to the vacuum representation, or the knowledge of the vacuum state.

  10. Automated Image Retrieval of Chest CT Images Based on Local Grey Scale Invariant Features.

    PubMed

    Arrais Porto, Marcelo; Cordeiro d'Ornellas, Marcos

    2015-01-01

    Textual-based tools are regularly employed to retrieve medical images for reading and interpretation using current retrieval Picture Archiving and Communication Systems (PACS) but pose some drawbacks. All-purpose content-based image retrieval (CBIR) systems are limited when dealing with medical images and do not fit well into PACS workflow and clinical practice. This paper presents an automated image retrieval approach for chest CT images based local grey scale invariant features from a local database. Performance was measured in terms of precision and recall, average retrieval precision (ARP), and average retrieval rate (ARR). Preliminary results have shown the effectiveness of the proposed approach. The prototype is also a useful tool for radiology research and education, providing valuable information to the medical and broader healthcare community.

  11. Tests of local Lorentz invariance violation of gravity in the standard model extension with pulsars.

    PubMed

    Shao, Lijing

    2014-03-21

    The standard model extension is an effective field theory introducing all possible Lorentz-violating (LV) operators to the standard model and general relativity (GR). In the pure-gravity sector of minimal standard model extension, nine coefficients describe dominant observable deviations from GR. We systematically implemented 27 tests from 13 pulsar systems to tightly constrain eight linear combinations of these coefficients with extensive Monte Carlo simulations. It constitutes the first detailed and systematic test of the pure-gravity sector of minimal standard model extension with the state-of-the-art pulsar observations. No deviation from GR was detected. The limits of LV coefficients are expressed in the canonical Sun-centered celestial-equatorial frame for the convenience of further studies. They are all improved by significant factors of tens to hundreds with existing ones. As a consequence, Einstein's equivalence principle is verified substantially further by pulsar experiments in terms of local Lorentz invariance in gravity.

  12. Optimal preparation of graph states

    SciTech Connect

    Cabello, Adan; Lopez-Tarrida, Antonio J.; Danielsen, Lars Eirik; Portillo, Jose R.

    2011-04-15

    We show how to prepare any graph state of up to 12 qubits with (a) the minimum number of controlled-Z gates and (b) the minimum preparation depth. We assume only one-qubit and controlled-Z gates. The method exploits the fact that any graph state belongs to an equivalence class under local Clifford operations. We extend up to 12 qubits the classification of graph states according to their entanglement properties, and identify each class using only a reduced set of invariants. For any state, we provide a circuit with both properties (a) and (b), if it does exist, or, if it does not, one circuit with property (a) and one with property (b), including the explicit one-qubit gates needed.

  13. Local scale-invariance of the 2  +  1 dimensional Kardar–Parisi–Zhang model

    NASA Astrophysics Data System (ADS)

    Kelling, Jeffrey; Ódor, Géza; Gemming, Sibylle

    2017-03-01

    Local scale-invariance theory is tested by extensive dynamical simulations of the driven dimer lattice gas model, describing the surface growth of the 2  +  1 dimensional Kardar–Parisi–Zhang surfaces. Very precise measurements of the universal autoresponse function enabled us to perform nonlinear fitting with the scaling forms, suggested by local scale-invariance (LSI). While the simple LSI ansatz does not seem to work, forms based on logarithmic extension of LSI provide satisfactory description of the full (measured) time evolution of the autoresponse function.

  14. Radiation Induced Chromatin Conformation Changes Analysed by Fluorescent Localization Microscopy, Statistical Physics, and Graph Theory

    PubMed Central

    Müller, Patrick; Hillebrandt, Sabina; Krufczik, Matthias; Bach, Margund; Kaufmann, Rainer; Hausmann, Michael; Heermann, Dieter W.

    2015-01-01

    It has been well established that the architecture of chromatin in cell nuclei is not random but functionally correlated. Chromatin damage caused by ionizing radiation raises complex repair machineries. This is accompanied by local chromatin rearrangements and structural changes which may for instance improve the accessibility of damaged sites for repair protein complexes. Using stably transfected HeLa cells expressing either green fluorescent protein (GFP) labelled histone H2B or yellow fluorescent protein (YFP) labelled histone H2A, we investigated the positioning of individual histone proteins in cell nuclei by means of high resolution localization microscopy (Spectral Position Determination Microscopy = SPDM). The cells were exposed to ionizing radiation of different doses and aliquots were fixed after different repair times for SPDM imaging. In addition to the repair dependent histone protein pattern, the positioning of antibodies specific for heterochromatin and euchromatin was separately recorded by SPDM. The present paper aims to provide a quantitative description of structural changes of chromatin after irradiation and during repair. It introduces a novel approach to analyse SPDM images by means of statistical physics and graph theory. The method is based on the calculation of the radial distribution functions as well as edge length distributions for graphs defined by a triangulation of the marker positions. The obtained results show that through the cell nucleus the different chromatin re-arrangements as detected by the fluorescent nucleosomal pattern average themselves. In contrast heterochromatic regions alone indicate a relaxation after radiation exposure and re-condensation during repair whereas euchromatin seemed to be unaffected or behave contrarily. SPDM in combination with the analysis techniques applied allows the systematic elucidation of chromatin re-arrangements after irradiation and during repair, if selected sub-regions of nuclei are

  15. Radiation induced chromatin conformation changes analysed by fluorescent localization microscopy, statistical physics, and graph theory.

    PubMed

    Zhang, Yang; Máté, Gabriell; Müller, Patrick; Hillebrandt, Sabina; Krufczik, Matthias; Bach, Margund; Kaufmann, Rainer; Hausmann, Michael; Heermann, Dieter W

    2015-01-01

    It has been well established that the architecture of chromatin in cell nuclei is not random but functionally correlated. Chromatin damage caused by ionizing radiation raises complex repair machineries. This is accompanied by local chromatin rearrangements and structural changes which may for instance improve the accessibility of damaged sites for repair protein complexes. Using stably transfected HeLa cells expressing either green fluorescent protein (GFP) labelled histone H2B or yellow fluorescent protein (YFP) labelled histone H2A, we investigated the positioning of individual histone proteins in cell nuclei by means of high resolution localization microscopy (Spectral Position Determination Microscopy = SPDM). The cells were exposed to ionizing radiation of different doses and aliquots were fixed after different repair times for SPDM imaging. In addition to the repair dependent histone protein pattern, the positioning of antibodies specific for heterochromatin and euchromatin was separately recorded by SPDM. The present paper aims to provide a quantitative description of structural changes of chromatin after irradiation and during repair. It introduces a novel approach to analyse SPDM images by means of statistical physics and graph theory. The method is based on the calculation of the radial distribution functions as well as edge length distributions for graphs defined by a triangulation of the marker positions. The obtained results show that through the cell nucleus the different chromatin re-arrangements as detected by the fluorescent nucleosomal pattern average themselves. In contrast heterochromatic regions alone indicate a relaxation after radiation exposure and re-condensation during repair whereas euchromatin seemed to be unaffected or behave contrarily. SPDM in combination with the analysis techniques applied allows the systematic elucidation of chromatin re-arrangements after irradiation and during repair, if selected sub-regions of nuclei are

  16. Local unit invariance, back-reacting tractors and the cosmological constant problem

    NASA Astrophysics Data System (ADS)

    Bonezzi, R.; Corradini, O.; Waldron, A.

    2012-02-01

    When physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of fields necessary to keep local unit invariance manifest). The relationship between these weights and masses is through the scalar curvature. As a consequence mass terms are spacetime dependent for off-shell gravitational backgrounds, but happily constant for physical, Einstein manifolds. Unfortunately this introduces a naturalness problem because the scalar curvature is proportional to the cosmological constant. By writing down tractor stress tensors (multiplets built from the standard stress tensor and its first and second derivatives), we show how back-reaction solves this naturalness problem. We also show that classical back-reaction generates an interesting potential for scalar fields. We speculate that a proper description of how physical systems couple to scale, could improve our understanding of naturalness problems caused by the disparity between the particle physics and observed, cosmological constants. We further give some ideas how an ambient description of tractor calculus could lead to a Ricci-flat/CFT correspondence which generalizes the AdS side of Maldacena's duality to a Ricci-flat space of one higher dimension.

  17. Preliminary bounds of the gravitational local position invariance from Solar system planetary precessions

    NASA Astrophysics Data System (ADS)

    Iorio, L.

    2014-02-01

    In the framework of the parametrized post-Newtonian (PPN) formalism, we calculate the long-term preferred location (PL) effects, proportional to the Whitehead parameter ξ, affecting all the Keplerian orbital elements of a localized two-body system, apart from the semimajor axis a. They violate the gravitational local position invariance, fulfilled by general relativity. We obtain preliminary bounds on ξ by using the latest results in the field of the Solar system planetary ephemerides. The non-detection of any anomalous perihelion precession for Mars allows us to indirectly infer |ξ| ≤ 5.8 × 10-6. Such a bound is close to the constraint, of the order of 10-6, expected from the future BepiColombo mission to Mercury. As a complementary approach, the PL effects should be explicitly included in the dynamical models fitted to planetary data sets to estimate ξ in a least-squares fashion in a dedicated ephemerides orbit solution. The ratio of the anomalous perihelion precessions for Venus and Jupiter, determined with the EPM2011 ephemerides at the <3σ level, if confirmed as genuine physical effects needing explanation by future studies, rules out the hypothesis ξ ≠ 0. A critical discussion of the |ξ| ≲ 10-6-10-7 upper bounds obtained in the literature from the close alignment of the Sun's spin axis and the total angular momentum of the Solar system is presented.

  18. Khovanov homology of graph-links

    SciTech Connect

    Nikonov, Igor M

    2012-08-31

    Graph-links arise as the intersection graphs of turning chord diagrams of links. Speaking informally, graph-links provide a combinatorial description of links up to mutations. Many link invariants can be reformulated in the language of graph-links. Khovanov homology, a well-known and useful knot invariant, is defined for graph-links in this paper (in the case of the ground field of characteristic two). Bibliography: 14 titles.

  19. Contact-free palm-vein recognition based on local invariant features.

    PubMed

    Kang, Wenxiong; Liu, Yang; Wu, Qiuxia; Yue, Xishun

    2014-01-01

    Contact-free palm-vein recognition is one of the most challenging and promising areas in hand biometrics. In view of the existing problems in contact-free palm-vein imaging, including projection transformation, uneven illumination and difficulty in extracting exact ROIs, this paper presents a novel recognition approach for contact-free palm-vein recognition that performs feature extraction and matching on all vein textures distributed over the palm surface, including finger veins and palm veins, to minimize the loss of feature information. First, a hierarchical enhancement algorithm, which combines a DOG filter and histogram equalization, is adopted to alleviate uneven illumination and to highlight vein textures. Second, RootSIFT, a more stable local invariant feature extraction method in comparison to SIFT, is adopted to overcome the projection transformation in contact-free mode. Subsequently, a novel hierarchical mismatching removal algorithm based on neighborhood searching and LBP histograms is adopted to improve the accuracy of feature matching. Finally, we rigorously evaluated the proposed approach using two different databases and obtained 0.996% and 3.112% Equal Error Rates (EERs), respectively, which demonstrate the effectiveness of the proposed approach.

  20. The Existence of Bifurcating Invariant Tori in a Spatially Extended Reaction-Diffusion-Convection System with Spatially Localized Amplification

    NASA Astrophysics Data System (ADS)

    Düll, Wolf-Patrick; Kirchhoff, Andreas; Schneider, Guido

    2014-04-01

    We consider a spatially extended reaction-diffusion-convection system with a marginally stable ground state and a spatially localized amplification. We are interested in solutions bifurcating from the spatially homogeneous ground state in the case when pairs of imaginary eigenvalues simultaneously cross the imaginary axis. For this system we prove the bifurcation of a family of invariant tori which may contain quasiperiodic solutions. There is a serious difficulty in obtaining this result, because the linearization at the ground state possesses an essential spectrum up to the imaginary axis for all values of the bifurcation parameter. To construct the invariant tori, we use their invariance under the flow which manifests in a condition in PDE form. The nonlinear terms of this resulting PDE exhibit a loss of regularity. Since the linear part of this PDE is not smoothing, an adaption of the hard implicit function theorem (or Nash-Moser scheme) and energy estimates will be used to prove our result.

  1. Graph-Based Object Class Discovery

    NASA Astrophysics Data System (ADS)

    Xia, Shengping; Hancock, Edwin R.

    We are interested in the problem of discovering the set of object classes present in a database of images using a weakly supervised graph-based framework. Rather than making use of the ”Bag-of-Features (BoF)” approach widely used in current work on object recognition, we represent each image by a graph using a group of selected local invariant features. Using local feature matching and iterative Procrustes alignment, we perform graph matching and compute a similarity measure. Borrowing the idea of query expansion , we develop a similarity propagation based graph clustering (SPGC) method. Using this method class specific clusters of the graphs can be obtained. Such a cluster can be generally represented by using a higher level graph model whose vertices are the clustered graphs, and the edge weights are determined by the pairwise similarity measure. Experiments are performed on a dataset, in which the number of images increases from 1 to 50K and the number of objects increases from 1 to over 500. Some objects have been discovered with total recall and a precision 1 in a single cluster.

  2. Image Geo-Localization Based on Multiple Nearest Neighbor Feature Matching Using Generalized Graphs.

    PubMed

    Zamir, Amir Roshan; Shah, Mubarak

    2014-08-01

    In this paper, we present a new framework for geo-locating an image utilizing a novel multiple nearest neighbor feature matching method using Generalized Minimum Clique Graphs (GMCP). First, we extract local features (e.g., SIFT) from the query image and retrieve a number of nearest neighbors for each query feature from the reference data set. Next, we apply our GMCP-based feature matching to select a single nearest neighbor for each query feature such that all matches are globally consistent. Our approach to feature matching is based on the proposition that the first nearest neighbors are not necessarily the best choices for finding correspondences in image matching. Therefore, the proposed method considers multiple reference nearest neighbors as potential matches and selects the correct ones by enforcing consistency among their global features (e.g., GIST) using GMCP. In this context, we argue that using a robust distance function for finding the similarity between the global features is essential for the cases where the query matches multiple reference images with dissimilar global features. Towards this end, we propose a robust distance function based on the Gaussian Radial Basis Function (G-RBF). We evaluated the proposed framework on a new data set of 102k street view images; the experiments show it outperforms the state of the art by 10 percent.

  3. A matrix product algorithm for stochastic dynamics on locally tree-like graphs

    NASA Astrophysics Data System (ADS)

    Barthel, Thomas; de Bacco, Caterina; Franz, Silvio

    In this talk, I describe a novel algorithm for the efficient simulation of generic stochastic dynamics of classical degrees of freedom defined on the vertices of locally tree-like graphs. Such models correspond for example to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon the cavity method and ideas from quantum many-body theory, the algorithm is based on a matrix product approximation of the so-called edge messages - conditional probabilities of vertex variable trajectories. The matrix product edge messages (MPEM) are constructed recursively. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the MPEM in truncations. In contrast to Monte Carlo simulations, the approach has a better error scaling and works for both, single instances as well as the thermodynamic limit. Due to the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations with unprecedented accuracy. The method is demonstrated for the prototypical non-equilibrium Glauber dynamics of an Ising spin system. Reference: arXiv:1508.03295.

  4. Aggressiveness as a latent personality trait of domestic dogs: Testing local independence and measurement invariance

    PubMed Central

    2017-01-01

    Studies of animal personality attempt to uncover underlying or “latent” personality traits that explain broad patterns of behaviour, often by applying latent variable statistical models (e.g., factor analysis) to multivariate data sets. Two integral, but infrequently confirmed, assumptions of latent variable models in animal personality are: i) behavioural variables are independent (i.e., uncorrelated) conditional on the latent personality traits they reflect (local independence), and ii) personality traits are associated with behavioural variables in the same way across individuals or groups of individuals (measurement invariance). We tested these assumptions using observations of aggression in four age classes (4–10 months, 10 months–3 years, 3–6 years, over 6 years) of male and female shelter dogs (N = 4,743) in 11 different contexts. A structural equation model supported the hypothesis of two positively correlated personality traits underlying aggression across contexts: aggressiveness towards people and aggressiveness towards dogs (comparative fit index: 0.96; Tucker-Lewis index: 0.95; root mean square error of approximation: 0.03). Aggression across contexts was moderately repeatable (towards people: intraclass correlation coefficient (ICC) = 0.479; towards dogs: ICC = 0.303). However, certain contexts related to aggressiveness towards people (but not dogs) shared significant residual relationships unaccounted for by latent levels of aggressiveness. Furthermore, aggressiveness towards people and dogs in different contexts interacted with sex and age. Thus, sex and age differences in displays of aggression were not simple functions of underlying aggressiveness. Our results illustrate that the robustness of traits in latent variable models must be critically assessed before making conclusions about the effects of, or factors influencing, animal personality. Our findings are of concern because inaccurate “aggressive personality” trait attributions

  5. Aggressiveness as a latent personality trait of domestic dogs: Testing local independence and measurement invariance.

    PubMed

    Goold, Conor; Newberry, Ruth C

    2017-01-01

    Studies of animal personality attempt to uncover underlying or "latent" personality traits that explain broad patterns of behaviour, often by applying latent variable statistical models (e.g., factor analysis) to multivariate data sets. Two integral, but infrequently confirmed, assumptions of latent variable models in animal personality are: i) behavioural variables are independent (i.e., uncorrelated) conditional on the latent personality traits they reflect (local independence), and ii) personality traits are associated with behavioural variables in the same way across individuals or groups of individuals (measurement invariance). We tested these assumptions using observations of aggression in four age classes (4-10 months, 10 months-3 years, 3-6 years, over 6 years) of male and female shelter dogs (N = 4,743) in 11 different contexts. A structural equation model supported the hypothesis of two positively correlated personality traits underlying aggression across contexts: aggressiveness towards people and aggressiveness towards dogs (comparative fit index: 0.96; Tucker-Lewis index: 0.95; root mean square error of approximation: 0.03). Aggression across contexts was moderately repeatable (towards people: intraclass correlation coefficient (ICC) = 0.479; towards dogs: ICC = 0.303). However, certain contexts related to aggressiveness towards people (but not dogs) shared significant residual relationships unaccounted for by latent levels of aggressiveness. Furthermore, aggressiveness towards people and dogs in different contexts interacted with sex and age. Thus, sex and age differences in displays of aggression were not simple functions of underlying aggressiveness. Our results illustrate that the robustness of traits in latent variable models must be critically assessed before making conclusions about the effects of, or factors influencing, animal personality. Our findings are of concern because inaccurate "aggressive personality" trait attributions can be costly

  6. Local metric dimension of circulant graph c i r c (n :1 ,2 ,…,n/+1 2 )

    NASA Astrophysics Data System (ADS)

    Rimadhany, Ruzika; Darmaji

    2017-08-01

    Let G be a connected graph with two vertices u and v. The distance between u and v, denoted by d(u, v), is defined as length of the shortest path from u to v in G. For an ordered set W = {w1, w2, w3, … , wk} of k distinct vertices in a nontrivial connected graph G, the representation of a vertex v of V(G) respect to W is r(v|W) = (d(v, w1), d(v, w2), … , d(v, wk)). The set W is a resolving set of G if r(v|W) for each vertex v ∈ V(G) is distinct. A resolving set of minimum cardinality is a metric dimension and denoted by dim(G). The set W is a local resolving set of G if r(v|W) for every two adjacent vertices of V(G) is distinct. The minimum cardinality of local resolving set of G is a local metric dimension and denoted by ldim(G). In this research, we determine local metric dimension of circulant graph c i r c (n :1 ,2 ,3 ,…,n/+1 2 ) .

  7. Segmentation of cytoplasm and nuclei of abnormal cells in cervical cytology using global and local graph cuts.

    PubMed

    Zhang, Ling; Kong, Hui; Chin, Chien Ting; Liu, Shaoxiong; Chen, Zhi; Wang, Tianfu; Chen, Siping

    2014-07-01

    Automation-assisted reading (AAR) techniques have the potential to reduce errors and increase productivity in cervical cancer screening. The sensitivity of AAR relies heavily on automated segmentation of abnormal cervical cells, which is handled poorly by current segmentation algorithms. In this paper, a global and local scheme based on graph cut approach is proposed to segment cervical cells in images with a mix of healthy and abnormal cells. For cytoplasm segmentation, the multi-way graph cut is performed globally on the a* channel enhanced image, which can be effective when the image histogram presents a non-bimodal distribution. For segmentation of nuclei, especially when they are abnormal, we propose to use graph cut adaptively and locally, which allows the combination of intensity, texture, boundary and region information. Two concave points-based approaches are integrated to split the touching-nuclei. As part of an ongoing clinical trial, preliminary validation results obtained from 21 cervical cell images with non-ideal imaging condition and pathology show that our segmentation method achieved 93% accuracy for cytoplasm, and 88.4% F-measure for abnormal nuclei, outperforming state of the art methods in terms of accuracy. Our method has the potential to improve the sensitivity of AAR in screening for cervical cancer.

  8. Testing Periodic Local Position Invariance Using Long-Term Comparison of the Syrte Atomic Fountains and H-Masers

    NASA Astrophysics Data System (ADS)

    Tobar, M. E.; Stanwix, P. L.; McFerran, J. J.; Guena, J.; Abgrall, M.; Bize, S.; Clairon, A.; Laurent, Ph.; Rosenbusch, P.; Rovera, D.; Santarelli, G.

    2014-01-01

    The frequencies of Cs and Rb fountain clocks have been compared to various H-masers to search for periodic changes correlated with the gravitational potential and boost with respect to the cosmic microwave background. The data span about eight years and the main sources of long-term noise are the offsets and linear drifts associated with the H-masers. To circumvent these effects we apply a numerical derivative to the data, which significantly reduces the standard error. We determine a limit for the Local Position Invariance (LPI) coefficient with respect to gravity to be 4.8×10-6 and 10-5 for a Cs-H and Rb-H comparison, respectively. From the same data the boost LPI coefficients were measured to parts in 1011. From these results and others, independent limits on all coefficients of the boost violation vector with respect to fundamental constant invariance were determined to parts in 1010.

  9. Testing Local Position Invariance with Four Cesium-Fountain Primary Frequency Standards and Four NIST Hydrogen Masers

    SciTech Connect

    Ashby, N.; Heavner, T. P.; Jefferts, S. R.; Parker, T. E.; Radnaev, A. G.; Dudin, Y. O.

    2007-02-16

    We report the most sensitive tests to date of the assumption of local position invariance (LPI) underlying general relativity, based on a 7 yr comparison of cesium and hydrogen atomic clocks (frequency standards). The latest results place an upper limit that is over 20 times smaller than the previous most sensitive tests; this is consistent with the null shift predicted by LPI. The result is based on precise comparisons of frequencies of four hydrogen masers maintained by NIST, with four independent Cs fountain clocks--one at NIST and three in Europe--as the Sun's gravitational potential at Earth's surface varies due to Earth's orbital eccentricity.

  10. Testing local position invariance with four cesium-fountain primary frequency standards and four NIST hydrogen masers.

    PubMed

    Ashby, N; Heavner, T P; Jefferts, S R; Parker, T E; Radnaev, A G; Dudin, Y O

    2007-02-16

    We report the most sensitive tests to date of the assumption of local position invariance (LPI) underlying general relativity, based on a 7 yr comparison of cesium and hydrogen atomic clocks (frequency standards). The latest results place an upper limit that is over 20 times smaller than the previous most sensitive tests; this is consistent with the null shift predicted by LPI. The result is based on precise comparisons of frequencies of four hydrogen masers maintained by NIST, with four independent Cs fountain clocks--one at NIST and three in Europe--as the Sun's gravitational potential at Earth's surface varies due to Earth's orbital eccentricity.

  11. Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles

    SciTech Connect

    Pastur, L. |; Shcherbina, M.

    1997-01-01

    This paper is devoted to the rigorous proof of the universality conjecture of random matrix theory, according to which the limiting eigenvalue statistics of n x n random matrices within spectral intervals of O(n{sup -1}) is determined by the type of matrix (real symmetric, Hermitian, or quaternion real) and by the density of states. We prove this conjecture for a certain class of the Hermitian matrix ensembles that arise in the quantum field theory and have the unitary invariant distribution defined by a certain function (the potential in the quantum field theory) satisfying some regularity conditions.

  12. Classification of 4-qubit Entangled Graph States According to Bipartite Entanglement, Multipartite Entanglement and Non-local Properties

    NASA Astrophysics Data System (ADS)

    Assadi, Leila; Jafarpour, Mojtaba

    2016-11-01

    We use concurrence to study bipartite entanglement, Meyer-Wallach measure and its generalizations to study multi-partite entanglement and MABK and SASA inequalities to study the non-local properties of the 4-qubit entangled graph states, quantitatively. Then, we present 3 classifications, each one in accordance with one of the aforementioned properties. We also observe that the classification according to multipartite entanglement does exactly coincide with that according to nonlocal properties, but does not match with that according to bipartite entanglement. This observation signifies the fact that non-locality and multipartite entanglement enjoy the same basic underlying principles, while bipartite entanglement may not reveal the non-locality issue in its entirety.

  13. Simultaneous localization of multiple broadband non-impulsive acoustic sources in an ocean waveguide using the array invariant.

    PubMed

    Gong, Zheng; Ratilal, Purnima; Makris, Nicholas C

    2015-11-01

    The array invariant method, previously derived for instantaneous range and bearing estimation of a single broadband impulsive source in a horizontally stratified ocean waveguide, can be generalized to simultaneously localize multiple uncorrelated broadband noise sources that are not necessarily impulsive in the time domain by introducing temporal pulse compression and an image processing technique similar to the Radon transform. This can be done by estimating the range and bearing of broadband non-impulsive sources from measured beam-time migration lines of modal arrivals along a horizontal array arising from differences in modal group velocity and modal polar angle for each propagating mode. The generalized array invariant approach is used to estimate the range of a vertical source array and vocalizing humpback whales over wide areas from measurements made by a towed horizontal receiver array during the Gulf of Maine 2006 Experiment. The localization results are shown to have roughly 12% root-mean-squared errors from Global Positioning System measured ground truth positions for controlled source transmissions and less than 10% discrepancy from those obtained independently via moving array triangulation for vocalizing humpbacks, respectively.

  14. Cross-Domain Fault Localization: A Case for a Graph Digest Approach

    DTIC Science & Technology

    2008-10-01

    Gi. • Gj = ( n ] i6=j f(Gi) ) ] Gj , where j is a domain performing cross-domain inference and ] is a model-specific union. Gj is the cross-domain...perform inference over Gj . Before a practical graph digest approach can be imple- mented, interoperability standards must be developed. Do- mains...Snoeren, and J. Yates , “Cross-layer visibility as a service,” Proc.of fourth workshop on Hot Topics in Networks (HotNet-IV), 2005. [10] M. Steinder

  15. Invariant bandwidth of erbium in ZnO-PbO-tellurite glasses: Local probe/model

    SciTech Connect

    Ramamoorthy, Raj Kumar; Bhatnagar, Anil K.

    2014-04-24

    A series of [(70TeO{sub 2}−(30−x)ZnO−xPbO){sub 0.99}−(Er{sub 2}O{sub 3}){sub 0.01}; where x = 5, 10, 15 and 20] tellurite glasses, were prepared using the melt quenching technique. Crucial emission bandwidth of erbium at 1.5 μm has been derived and found to be the same for all the glasses, irrespective of PbO content. This identical bandwidth in all tellurite glasses is attributed to the presence of erbium in tellurium rich disordered environments. This result has been complemented through XANES spectra and the obtained invariant first shell of 6.5 oxygen atoms, confirm the unchanged environment in these glasses for all PbO content.

  16. Graph Regularized Auto-Encoders for Image Representation.

    PubMed

    Yiyi Liao; Yue Wang; Yong Liu

    2017-06-01

    Image representation has been intensively explored in the domain of computer vision for its significant influence on the relative tasks such as image clustering and classification. It is valuable to learn a low-dimensional representation of an image which preserves its inherent information from the original image space. At the perspective of manifold learning, this is implemented with the local invariant idea to capture the intrinsic low-dimensional manifold embedded in the high-dimensional input space. Inspired by the recent successes of deep architectures, we propose a local invariant deep nonlinear mapping algorithm, called graph regularized auto-encoder (GAE). With the graph regularization, the proposed method preserves the local connectivity from the original image space to the representation space, while the stacked auto-encoders provide explicit encoding model for fast inference and powerful expressive capacity for complex modeling. Theoretical analysis shows that the graph regularizer penalizes the weighted Frobenius norm of the Jacobian matrix of the encoder mapping, where the weight matrix captures the local property in the input space. Furthermore, the underlying effects on the hidden representation space are revealed, providing insightful explanation to the advantage of the proposed method. Finally, the experimental results on both clustering and classification tasks demonstrate the effectiveness of our GAE as well as the correctness of the proposed theoretical analysis, and it also suggests that GAE is a superior solution to the current deep representation learning techniques comparing with variant auto-encoders and existing local invariant methods.

  17. Integer sequence discovery from small graphs

    PubMed Central

    Hoppe, Travis; Petrone, Anna

    2015-01-01

    We have exhaustively enumerated all simple, connected graphs of a finite order and have computed a selection of invariants over this set. Integer sequences were constructed from these invariants and checked against the Online Encyclopedia of Integer Sequences (OEIS). 141 new sequences were added and six sequences were extended. From the graph database, we were able to programmatically suggest relationships among the invariants. It will be shown that we can readily visualize any sequence of graphs with a given criteria. The code has been released as an open-source framework for further analysis and the database was constructed to be extensible to invariants not considered in this work. PMID:27034526

  18. Presurgery resting-state local graph-theory measures predict neurocognitive outcomes after brain surgery in temporal lobe epilepsy.

    PubMed

    Doucet, Gaelle E; Rider, Robert; Taylor, Nathan; Skidmore, Christopher; Sharan, Ashwini; Sperling, Michael; Tracy, Joseph I

    2015-04-01

    This study determined the ability of resting-state functional connectivity (rsFC) graph-theory measures to predict neurocognitive status postsurgery in patients with temporal lobe epilepsy (TLE) who underwent anterior temporal lobectomy (ATL). A presurgical resting-state functional magnetic resonance imaging (fMRI) condition was collected in 16 left and 16 right TLE patients who underwent ATL. In addition, patients received neuropsychological testing pre- and postsurgery in verbal and nonverbal episodic memory, language, working memory, and attention domains. Regarding the functional data, we investigated three graph-theory properties (local efficiency, distance, and participation), measuring segregation, integration and centrality, respectively. These measures were only computed in regions of functional relevance to the ictal pathology, or the cognitive domain. Linear regression analyses were computed to predict the change in each neurocognitive domain. Our analyses revealed that cognitive outcome was successfully predicted with at least 68% of the variance explained in each model, for both TLE groups. The only model not significantly predictive involved nonverbal episodic memory outcome in right TLE. Measures involving the healthy hippocampus were the most common among the predictors, suggesting that enhanced integration of this structure with the rest of the brain may improve cognitive outcomes. Regardless of TLE group, left inferior frontal regions were the best predictors of language outcome. Working memory outcome was predicted mostly by right-sided regions, in both groups. Overall, the results indicated our integration measure was the most predictive of neurocognitive outcome. In contrast, our segregation measure was the least predictive. This study provides evidence that presurgery rsFC measures may help determine neurocognitive outcomes following ATL. The results have implications for refining our understanding of compensatory reorganization and predicting

  19. Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance.

    PubMed

    Fortier, T M; Ashby, N; Bergquist, J C; Delaney, M J; Diddams, S A; Heavner, T P; Hollberg, L; Itano, W M; Jefferts, S R; Kim, K; Levi, F; Lorini, L; Oskay, W H; Parker, T E; Shirley, J; Stalnaker, J E

    2007-02-16

    We report tests of local position invariance and the variation of fundamental constants from measurements of the frequency ratio of the 282-nm 199Hg+ optical clock transition to the ground state hyperfine splitting in 133Cs. Analysis of the frequency ratio of the two clocks, extending over 6 yr at NIST, is used to place a limit on its fractional variation of <5.8x10(-6) per change in normalized solar gravitational potential. The same frequency ratio is also used to obtain 20-fold improvement over previous limits on the fractional variation of the fine structure constant of |alpha/alpha|<1.3x10(-16) yr-1, assuming invariance of other fundamental constants. Comparisons of our results with those previously reported for the absolute optical frequency measurements in H and 171Yb+ vs other 133Cs standards yield a coupled constraint of -1.5x10(-15)

  20. A locally supersymmetric SO(10, 2) invariant action for D = 12 supergravity

    NASA Astrophysics Data System (ADS)

    Castellani, Leonardo

    2017-06-01

    We present an action for N = 1 supergravity in 10 + 2 dimensions, containing the gauge fields of the OSp(1|64) superalgebra, i.e. one-forms B ( n) with n=1,2,5,6,9,10 antisymmetric D=12 Lorentz indices and a Majorana gravitino ψ. The vielbein and spin connection correspond to B (1) and B (2) respectively. The action is not gauge invariant under the full OSp(1|64) superalgebra, but only under a subalgebra \\tilde{F} (containing the F algebra OSp(1|32)), whose gauge fields are B (2), B (6), B (10) and the Weyl projected Majorana gravitino 1/2(1+{Γ}_{13})ψ . Supersymmetry transformations are therefore generated by a Majorana-Weyl supercharge and, being part of a gauge superalgebra, close off-shell. The action is simply ∫ STr( R 6 Γ) where R is the OSp(1|64) curvature supermatrix two-form, and Γ is a constant supermatrix involving Γ13 and breaking OSp(1|64) to its \\tilde{F} subalgebra. The usual Einstein-Hilbert term is included in the action.

  1. Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds

    NASA Astrophysics Data System (ADS)

    Liu, Chiu-Chu Melissa; Sheshmani, Artan

    2017-07-01

    An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use virtual localization to express equivariant Gromov-Witten invariants of any algebraic GKM manifold (which is not necessarily compact) in terms of Hodge integrals over moduli stacks of stable curves and the GKM graph of the GKM manifold.

  2. Conformal differential invariants

    NASA Astrophysics Data System (ADS)

    Kruglikov, Boris

    2017-03-01

    We compute the Hilbert polynomial and the Poincaré function counting the number of fixed jet-order differential invariants of conformal metric structures modulo local diffeomorphisms, and we describe the field of rational differential invariants separating generic orbits of the diffeomorphism pseudogroup action. This resolves the local recognition problem for conformal structures.

  3. Graphing Matters.

    ERIC Educational Resources Information Center

    Paine, Carolyn

    1983-01-01

    An explanation is given of the uses of graphs for conveying information pictorially. Picture, bar, line, and area graphs are illustrated. Graphing projects for science, social studies, mathematics, economics, and language arts are listed, and teaching tips are suggested. (FG)

  4. Local directional pattern of phase congruency features for illumination invariant face recognition

    NASA Astrophysics Data System (ADS)

    Essa, Almabrok E.; Asari, Vijayan K.

    2014-04-01

    An illumination-robust face recognition system using Local Directional Pattern (LDP) descriptors in Phase Congruency (PC) space is proposed in this paper. The proposed Directional Pattern of Phase Congruency (DPPC) is an oriented and multi-scale local descriptor that is able to encode various patterns of face images under different lighting conditions. It is constructed by applying LDP on the oriented PC images. A LDP feature is obtained by computing the edge response values in eight directions at each pixel position and encoding them into an eight bit binary code using the relative strength magnitude of these edge responses. Phase congruency and local directional pattern have been independently used in the field of face and facial expression recognition, since they are robust to illumination changes. When the PC extracts the discontinuities in the image such as edges and corners, the LDP computes the edge response values in different directions and uses these to encode the image texture. The local directional pattern descriptor on the phase congruency image is subjected to principal component analysis (PCA) for dimensionality reduction for fast and effective face recognition application. The performance evaluation of the proposed DPPC algorithm is conducted on several publicly available databases and observed promising recognition rates. Better classification accuracy shows the superiority of the LDP descriptor against other appearance-based feature descriptors such as Local Binary Pattern (LBP). In other words, our result shows that by using the LDP descriptor the Euclidean distance between reference image and testing images in the same class is much less than that between reference image and testing images from the other classes.

  5. Adaptive weighted local textural features for illumination, expression, and occlusion invariant face recognition

    NASA Astrophysics Data System (ADS)

    Cui, Chen; Asari, Vijayan K.

    2014-03-01

    Biometric features such as fingerprints, iris patterns, and face features help to identify people and restrict access to secure areas by performing advanced pattern analysis and matching. Face recognition is one of the most promising biometric methodologies for human identification in a non-cooperative security environment. However, the recognition results obtained by face recognition systems are a affected by several variations that may happen to the patterns in an unrestricted environment. As a result, several algorithms have been developed for extracting different facial features for face recognition. Due to the various possible challenges of data captured at different lighting conditions, viewing angles, facial expressions, and partial occlusions in natural environmental conditions, automatic facial recognition still remains as a difficult issue that needs to be resolved. In this paper, we propose a novel approach to tackling some of these issues by analyzing the local textural descriptions for facial feature representation. The textural information is extracted by an enhanced local binary pattern (ELBP) description of all the local regions of the face. The relationship of each pixel with respect to its neighborhood is extracted and employed to calculate the new representation. ELBP reconstructs a much better textural feature extraction vector from an original gray level image in different lighting conditions. The dimensionality of the texture image is reduced by principal component analysis performed on each local face region. Each low dimensional vector representing a local region is now weighted based on the significance of the sub-region. The weight of each sub-region is determined by employing the local variance estimate of the respective region, which represents the significance of the region. The final facial textural feature vector is obtained by concatenating the reduced dimensional weight sets of all the modules (sub-regions) of the face image

  6. Rotational speed invariant fault diagnosis in bearings using vibration signal imaging and local binary patterns.

    PubMed

    Khan, Sheraz Ali; Kim, Jong-Myon

    2016-04-01

    Structural vibrations of bearing housings are used for diagnosing fault conditions in bearings, primarily by searching for characteristic fault frequencies in the envelope power spectrum of the vibration signal. The fault frequencies depend on the non-stationary angular speed of the rotating shaft. This paper explores an imaging-based approach to achieve rotational speed independence. Cycle length segments of the rectified vibration signal are stacked to construct grayscale images which exhibit unique textures for each fault. These textures show insignificant variation with the rotational speed, which is confirmed by the classification results using their local binary pattern histograms.

  7. Robust Eye Center Localization through Face Alignment and Invariant Isocentric Patterns.

    PubMed

    Pang, Zhiyong; Wei, Chuansheng; Teng, Dongdong; Chen, Dihu; Tan, Hongzhou

    2015-01-01

    The localization of eye centers is a very useful cue for numerous applications like face recognition, facial expression recognition, and the early screening of neurological pathologies. Several methods relying on available light for accurate eye-center localization have been exploited. However, despite the considerable improvements that eye-center localization systems have undergone in recent years, only few of these developments deal with the challenges posed by the profile (non-frontal face). In this paper, we first use the explicit shape regression method to obtain the rough location of the eye centers. Because this method extracts global information from the human face, it is robust against any changes in the eye region. We exploit this robustness and utilize it as a constraint. To locate the eye centers accurately, we employ isophote curvature features, the accuracy of which has been demonstrated in a previous study. By applying these features, we obtain a series of eye-center locations which are candidates for the actual position of the eye-center. Among these locations, the estimated locations which minimize the reconstruction error between the two methods mentioned above are taken as the closest approximation for the eye centers locations. Therefore, we combine explicit shape regression and isophote curvature feature analysis to achieve robustness and accuracy, respectively. In practical experiments, we use BioID and FERET datasets to test our approach to obtaining an accurate eye-center location while retaining robustness against changes in scale and pose. In addition, we apply our method to non-frontal faces to test its robustness and accuracy, which are essential in gaze estimation but have seldom been mentioned in previous works. Through extensive experimentation, we show that the proposed method can achieve a significant improvement in accuracy and robustness over state-of-the-art techniques, with our method ranking second in terms of accuracy

  8. Robust Eye Center Localization through Face Alignment and Invariant Isocentric Patterns

    PubMed Central

    Teng, Dongdong; Chen, Dihu; Tan, Hongzhou

    2015-01-01

    The localization of eye centers is a very useful cue for numerous applications like face recognition, facial expression recognition, and the early screening of neurological pathologies. Several methods relying on available light for accurate eye-center localization have been exploited. However, despite the considerable improvements that eye-center localization systems have undergone in recent years, only few of these developments deal with the challenges posed by the profile (non-frontal face). In this paper, we first use the explicit shape regression method to obtain the rough location of the eye centers. Because this method extracts global information from the human face, it is robust against any changes in the eye region. We exploit this robustness and utilize it as a constraint. To locate the eye centers accurately, we employ isophote curvature features, the accuracy of which has been demonstrated in a previous study. By applying these features, we obtain a series of eye-center locations which are candidates for the actual position of the eye-center. Among these locations, the estimated locations which minimize the reconstruction error between the two methods mentioned above are taken as the closest approximation for the eye centers locations. Therefore, we combine explicit shape regression and isophote curvature feature analysis to achieve robustness and accuracy, respectively. In practical experiments, we use BioID and FERET datasets to test our approach to obtaining an accurate eye-center location while retaining robustness against changes in scale and pose. In addition, we apply our method to non-frontal faces to test its robustness and accuracy, which are essential in gaze estimation but have seldom been mentioned in previous works. Through extensive experimentation, we show that the proposed method can achieve a significant improvement in accuracy and robustness over state-of-the-art techniques, with our method ranking second in terms of accuracy

  9. Scale-invariant hidden local symmetry, topology change, and dense baryonic matter. II.

    NASA Astrophysics Data System (ADS)

    Paeng, Won-Gi; Kuo, Thomas T. S.; Lee, Hyun Kyu; Ma, Yong-Liang; Rho, Mannque

    2017-07-01

    Exploiting certain robust topological inputs from the skyrmion description of compressed baryonic matter with a scale-chiral symmetric Lagrangian, we predict the equation of state that is consistent with the properties of nuclear matter at the equilibrium density, supports the maximum mass of massive compact star ˜2 M⊙ and surprisingly gives the sound velocity close to the "conformal velocity" 1 /√{3 } at densities ≳3 n0 . At the core of this result is the observation that parity-doubling occurs in the nucleon structure as density goes above ˜2 n0 with a chiral-singlet mass m0˜(0.6 - 0.9 )mN , hinting at a possible up-to-date unsuspected source of proton mass and an emergence at high density of scale symmetry and flavor local symmetry, both hidden in the QCD vacuum.

  10. Non-local meta-conformal invariance in diffusion-limited erosion

    NASA Astrophysics Data System (ADS)

    Henkel, Malte

    2016-12-01

    The non-stationary relaxation and physical ageing in the diffusion-limited erosion process (dle) is studied through the exact solution of its Langevin equation, in d spatial dimensions. The dynamical exponent z = 1, the growth exponent β =\\max (0,(1-d)/2) and the ageing exponents a=b=d-1 and {λ }C={λ }R=d are found. In d = 1 spatial dimension, a new representation of the meta-conformal Lie algebra, isomorphic to {sl}(2,{{R}})\\oplus {sl}(2,{{R}}), acts as a dynamical symmetry of the noise-averaged dle Langevin equation. Its infinitesimal generators are non-local in space. The exact form of the full time-space dependence of the two-time response function of dle is reproduced for d = 1 from this symmetry. The relationship to the terrace-step-kink model of vicinal surfaces is discussed.

  11. Regular homotopy for immersions of graphs into surfaces

    NASA Astrophysics Data System (ADS)

    Permyakov, D. A.

    2016-06-01

    We study invariants of regular immersions of graphs into surfaces up to regular homotopy. The concept of the winding number is used to introduce a new simple combinatorial invariant of regular homotopy. Bibliography: 20 titles.

  12. Graph Library

    SciTech Connect

    Schulz, Martin; Arnold, Dorian

    2007-06-12

    GraphLib is a support library used by other tools to create, manipulate, store, and export graphs. It provides a simple interface to specifS’ arbitrary directed and undirected graphs by adding nodes and edges. Each node and edge can be associated with a set of attributes describing size, color, and shape. Once created, graphs can be manipulated using a set of graph analysis algorithms, including merge, prune, and path coloring operations. GraphLib also has the ability to export graphs into various open formats such as DOT and GML.

  13. Discontinuous local semiflows for Kurzweil equations leading to LaSalle's invariance principle for differential systems with impulses at variable times

    NASA Astrophysics Data System (ADS)

    Afonso, S. M.; Bonotto, E. M.; Federson, M.; Schwabik, Š.

    2011-04-01

    In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle's invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle's invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times.

  14. Higher-order graph wavelets and sparsity on circulant graphs

    NASA Astrophysics Data System (ADS)

    Kotzagiannidis, Madeleine S.; Dragotti, Pier Luigi

    2015-08-01

    The notion of a graph wavelet gives rise to more advanced processing of data on graphs due to its ability to operate in a localized manner, across newly arising data-dependency structures, with respect to the graph signal and underlying graph structure, thereby taking into consideration the inherent geometry of the data. In this work, we tackle the problem of creating graph wavelet filterbanks on circulant graphs for a sparse representation of certain classes of graph signals. The underlying graph can hereby be data-driven as well as fixed, for applications including image processing and social network theory, whereby clusters can be modelled as circulant graphs, respectively. We present a set of novel graph wavelet filter-bank constructions, which annihilate higher-order polynomial graph signals (up to a border effect) defined on the vertices of undirected, circulant graphs, and are localised in the vertex domain. We give preliminary results on their performance for non-linear graph signal approximation and denoising. Furthermore, we provide extensions to our previously developed segmentation-inspired graph wavelet framework for non-linear image approximation, by incorporating notions of smoothness and vanishing moments, which further improve performance compared to traditional methods.

  15. On designing heteroclinic networks from graphs

    NASA Astrophysics Data System (ADS)

    Ashwin, Peter; Postlethwaite, Claire

    2013-12-01

    Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a complicated structure determined to a large extent by the constraints and dimension of the system. As these networks are of great interest as dynamical models of biological and cognitive processes, it is useful to understand how particular directed graphs can be realised as attracting robust heteroclinic networks between states in phase space. This paper presents two methods of realising arbitrarily complex directed graphs as robust heteroclinic networks for flows generated by ODEs-we say the ODEs realise the graphs as heteroclinic networks between equilibria that represent the vertices. Suppose we have a directed graph on nv vertices with ne edges. The “simplex realisation” embeds the graph as an invariant set of a flow on an (nv-1)-simplex. This method realises the graph as long as it is one- and two-cycle free. The “cylinder realisation” embeds a graph as an invariant set of a flow on a (ne+1)-dimensional space. This method realises the graph as long as it is one-cycle free. In both cases we realise the graph as an invariant set within an attractor, and discuss some illustrative examples, including the influence of noise and parameters on the dynamics. In particular we show that the resulting heteroclinic network may or may not display “memory” of the vertices visited.

  16. Continuous-time quantum walks on star graphs

    SciTech Connect

    Salimi, S.

    2009-06-15

    In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N-fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K{sub 2} graphs (complete graph with two vertices) and the probability of observing walk tends to the uniform distribution.

  17. Quantum causal graph dynamics

    NASA Astrophysics Data System (ADS)

    Arrighi, Pablo; Martiel, Simon

    2017-07-01

    Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded speed, with respect to the distance given by the graph. Suppose, moreover, that the graph itself is subject to the evolution, and may be driven to be in a quantum superposition of graphs—in accordance to the superposition principle. We show that these unitary causal operators must decompose as a finite-depth circuit of local unitary gates. This unifies a result on quantum cellular automata with another on reversible causal graph dynamics. Along the way we formalize a notion of causality which is valid in the context of quantum superpositions of time-varying graphs, and has a number of good properties. We discuss some of the implications for quantum gravity.

  18. Scale invariance vs conformal invariance

    NASA Astrophysics Data System (ADS)

    Nakayama, Yu

    2015-03-01

    In this review article, we discuss the distinction and possible equivalence between scale invariance and conformal invariance in relativistic quantum field theories. Under some technical assumptions, we can prove that scale invariant quantum field theories in d = 2 space-time dimensions necessarily possess the enhanced conformal symmetry. The use of the conformal symmetry is well appreciated in the literature, but the fact that all the scale invariant phenomena in d = 2 space-time dimensions enjoy the conformal property relies on the deep structure of the renormalization group. The outstanding question is whether this feature is specific to d = 2 space-time dimensions or it holds in higher dimensions, too. As of January 2014, our consensus is that there is no known example of scale invariant but non-conformal field theories in d = 4 space-time dimensions under the assumptions of (1) unitarity, (2) Poincaré invariance (causality), (3) discrete spectrum in scaling dimensions, (4) existence of scale current and (5) unbroken scale invariance in the vacuum. We have a perturbative proof of the enhancement of conformal invariance from scale invariance based on the higher dimensional analogue of Zamolodchikov's c-theorem, but the non-perturbative proof is yet to come. As a reference we have tried to collect as many interesting examples of scale invariance in relativistic quantum field theories as possible in this article. We give a complementary holographic argument based on the energy-condition of the gravitational system and the space-time diffeomorphism in order to support the claim of the symmetry enhancement. We believe that the possible enhancement of conformal invariance from scale invariance reveals the sublime nature of the renormalization group and space-time with holography. This review is based on a lecture note on scale invariance vs conformal invariance, on which the author gave lectures at Taiwan Central University for the 5th Taiwan School on Strings and

  19. Local Pauli stabilizers of symmetric hypergraph states

    NASA Astrophysics Data System (ADS)

    Lyons, David W.; Gibbons, Nathaniel P.; Peters, Mark A.; Upchurch, Daniel J.; Walck, Scott N.; Wertz, Ezekiel W.

    2017-06-01

    Hypergraph states of many quantum bits share the rich interplay between simple combinatorial description and nontrivial entanglement properties enjoyed by the graph states that they generalize. In this paper, we consider hypergraph states that are also permutationally invariant. We characterize the states in this class that have nontrivial local Pauli stabilizers and give applications to nonlocality and error correction.

  20. Testing local position and fundamental constant invariance due to periodic gravitational and boost using long-term comparison of the SYRTE atomic fountains and H-masers

    NASA Astrophysics Data System (ADS)

    Tobar, M. E.; Stanwix, P. L.; McFerran, J. J.; Guéna, J.; Abgrall, M.; Bize, S.; Clairon, A.; Laurent, Ph.; Rosenbusch, P.; Rovera, D.; Santarelli, G.

    2013-06-01

    The frequencies of three separate Cs fountain clocks and one Rb fountain clock have been compared to various hydrogen masers to search for periodic changes correlated with the changing solar gravitational potential at the Earth and boost with respect to the cosmic microwave background rest frame. The data sets span over more than 8 yr. The main sources of long-term noise in such experiments are the offsets and linear drifts associated with the various H-masers. The drift can vary from nearly immeasurable to as high as 1.3×10-15 per day. To circumvent these effects, we apply a numerical derivative to the data, which significantly reduces the standard error when searching for periodic signals. We determine a standard error for the putative local position invariance coefficient with respect to gravity for a Cs-fountain H-maser comparison of |βH-βCs|≤4.8×10-6 and |βH-βRb|≤10-5 for a Rb-Fountain H-maser comparison. From the same data, the putative boost local position invariance coefficients were measured to a precision of up to parts in 1011 with respect to the cosmic microwave background rest frame. By combining these boost invariance experiments to a cryogenic sapphire oscillator vs H-maser comparison, independent limits on all nine coefficients of the boost-violation vector with respect to fundamental constant invariance, Bα, Be, and Bq (fine structure constant, electron mass, and quark mass, respectively), were determined to a precision of parts up to 1010.

  1. Prediction of alkane enthalpies by means of correlation weighting of Morgan extended connectivity in molecular graphs

    NASA Astrophysics Data System (ADS)

    Toropov, A. A.; Toropova, A. P.; Nesterova, A. I.; Nabiev, O. M.

    2004-01-01

    Labeled hydrogen-filled graphs (LHFGs) together with graphs of atomic orbitals (GAOs) have been used to represent the molecular structure of alkanes. The GAO is an attempt at taking into account the structures of atoms (i.e., atomic orbitals such as, 1s 1, 2p 2, 3d 10) for QSPR/QSAR analyses. As a method of alkane enthalpies modeling, optimization of correlation weights of local invariants (OCWLI) of the LHFGs and the GAOs has been used. Statistical characteristics of such models based on the OCWLI of the GAO are better than those based on the OCWLI of the LHFGs.

  2. Potential energy surface fitting by a statistically localized, permutationally invariant, local interpolating moving least squares method for the many-body potential: Method and application to N{sub 4}

    SciTech Connect

    Bender, Jason D.; Doraiswamy, Sriram; Candler, Graham V. E-mail: candler@aem.umn.edu; Truhlar, Donald G. E-mail: candler@aem.umn.edu

    2014-02-07

    Fitting potential energy surfaces to analytic forms is an important first step for efficient molecular dynamics simulations. Here, we present an improved version of the local interpolating moving least squares method (L-IMLS) for such fitting. Our method has three key improvements. First, pairwise interactions are modeled separately from many-body interactions. Second, permutational invariance is incorporated in the basis functions, using permutationally invariant polynomials in Morse variables, and in the weight functions. Third, computational cost is reduced by statistical localization, in which we statistically correlate the cutoff radius with data point density. We motivate our discussion in this paper with a review of global and local least-squares-based fitting methods in one dimension. Then, we develop our method in six dimensions, and we note that it allows the analytic evaluation of gradients, a feature that is important for molecular dynamics. The approach, which we call statistically localized, permutationally invariant, local interpolating moving least squares fitting of the many-body potential (SL-PI-L-IMLS-MP, or, more simply, L-IMLS-G2), is used to fit a potential energy surface to an electronic structure dataset for N{sub 4}. We discuss its performance on the dataset and give directions for further research, including applications to trajectory calculations.

  3. Graph partitions and cluster synchronization in networks of oscillators

    PubMed Central

    Schaub, Michael T.; O’Clery, Neave; Billeh, Yazan N.; Delvenne, Jean-Charles; Lambiotte, Renaud; Barahona, Mauricio

    2017-01-01

    Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable Partitions of the network graph and their associated quotient graphs. We exploit this graph-theoretical concept to study the phenomenon of cluster synchronization, in which different groups of nodes converge to distinct behaviors. We derive conditions and properties of networks in which such clustered behavior emerges, and show that the ensuing dynamics is the result of the localization of the eigenvectors of the associated graph Laplacians linked to the existence of invariant subspaces. The framework is applied to both linear and non-linear models, first for the standard case of networks with positive edges, before being generalized to the case of signed networks with both positive and negative interactions. We illustrate our results with examples of both signed and unsigned graphs for consensus dynamics and for partial synchronization of oscillator networks under the master stability function as well as Kuramoto oscillators. PMID:27781454

  4. Index statistical properties of sparse random graphs

    NASA Astrophysics Data System (ADS)

    Metz, F. L.; Stariolo, Daniel A.

    2015-10-01

    Using the replica method, we develop an analytical approach to compute the characteristic function for the probability PN(K ,λ ) that a large N ×N adjacency matrix of sparse random graphs has K eigenvalues below a threshold λ . The method allows to determine, in principle, all moments of PN(K ,λ ) , from which the typical sample-to-sample fluctuations can be fully characterized. For random graph models with localized eigenvectors, we show that the index variance scales linearly with N ≫1 for |λ |>0 , with a model-dependent prefactor that can be exactly calculated. Explicit results are discussed for Erdös-Rényi and regular random graphs, both exhibiting a prefactor with a nonmonotonic behavior as a function of λ . These results contrast with rotationally invariant random matrices, where the index variance scales only as lnN , with an universal prefactor that is independent of λ . Numerical diagonalization results confirm the exactness of our approach and, in addition, strongly support the Gaussian nature of the index fluctuations.

  5. (Ad/f,g/), (ad/fg/) and locally (ad/f,g/) invariant and controllability distributions

    NASA Technical Reports Server (NTRS)

    Krener, A. J.

    1985-01-01

    Over the past decade, it has been found that concepts from differential topology such as foliation and invariant distribution play a crucial role in the study of nonlinear systems. These concepts were first employed in studies of nonlinear controllability and observability. More recently, they have occurred in the study of decoupling and linearization via feedback. In connection with the widening area of application, requirements for a greater precision have arisen. The present paper represents an attempt to provide that precision. In this paper, an introduction is given of the basic concepts which are needed for an understanding of controllability, observability, and decoupling of nonlinear systems. Attention is given to mathematical preliminaries, aspects of invariance, nonlinear controllability and observability, disturbance decoupling, and controllability distributions.

  6. Graph Structure-Based Simultaneous Localization and Mapping Using a Hybrid Method of 2D Laser Scan and Monocular Camera Image in Environments with Laser Scan Ambiguity

    PubMed Central

    Oh, Taekjun; Lee, Donghwa; Kim, Hyungjin; Myung, Hyun

    2015-01-01

    Localization is an essential issue for robot navigation, allowing the robot to perform tasks autonomously. However, in environments with laser scan ambiguity, such as long corridors, the conventional SLAM (simultaneous localization and mapping) algorithms exploiting a laser scanner may not estimate the robot pose robustly. To resolve this problem, we propose a novel localization approach based on a hybrid method incorporating a 2D laser scanner and a monocular camera in the framework of a graph structure-based SLAM. 3D coordinates of image feature points are acquired through the hybrid method, with the assumption that the wall is normal to the ground and vertically flat. However, this assumption can be relieved, because the subsequent feature matching process rejects the outliers on an inclined or non-flat wall. Through graph optimization with constraints generated by the hybrid method, the final robot pose is estimated. To verify the effectiveness of the proposed method, real experiments were conducted in an indoor environment with a long corridor. The experimental results were compared with those of the conventional GMappingapproach. The results demonstrate that it is possible to localize the robot in environments with laser scan ambiguity in real time, and the performance of the proposed method is superior to that of the conventional approach. PMID:26151203

  7. Graph Structure-Based Simultaneous Localization and Mapping Using a Hybrid Method of 2D Laser Scan and Monocular Camera Image in Environments with Laser Scan Ambiguity.

    PubMed

    Oh, Taekjun; Lee, Donghwa; Kim, Hyungjin; Myung, Hyun

    2015-07-03

    Localization is an essential issue for robot navigation, allowing the robot to perform tasks autonomously. However, in environments with laser scan ambiguity, such as long corridors, the conventional SLAM (simultaneous localization and mapping) algorithms exploiting a laser scanner may not estimate the robot pose robustly. To resolve this problem, we propose a novel localization approach based on a hybrid method incorporating a 2D laser scanner and a monocular camera in the framework of a graph structure-based SLAM. 3D coordinates of image feature points are acquired through the hybrid method, with the assumption that the wall is normal to the ground and vertically flat. However, this assumption can be relieved, because the subsequent feature matching process rejects the outliers on an inclined or non-flat wall. Through graph optimization with constraints generated by the hybrid method, the final robot pose is estimated. To verify the effectiveness of the proposed method, real experiments were conducted in an indoor environment with a long corridor. The experimental results were compared with those of the conventional GMappingapproach. The results demonstrate that it is possible to localize the robot in environments with laser scan ambiguity in real time, and the performance of the proposed method is superior to that of the conventional approach.

  8. Graphing Predictions

    ERIC Educational Resources Information Center

    Connery, Keely Flynn

    2007-01-01

    Graphing predictions is especially important in classes where relationships between variables need to be explored and derived. In this article, the author describes how his students sketch the graphs of their predictions before they begin their investigations on two laboratory activities: Distance Versus Time Cart Race Lab and Resistance; and…

  9. Graphing Predictions

    ERIC Educational Resources Information Center

    Connery, Keely Flynn

    2007-01-01

    Graphing predictions is especially important in classes where relationships between variables need to be explored and derived. In this article, the author describes how his students sketch the graphs of their predictions before they begin their investigations on two laboratory activities: Distance Versus Time Cart Race Lab and Resistance; and…

  10. Continuous Active Sonar for Undersea Vehicles Final Report: Input of Factor Graphs into the Detection, Classification, and Localization Chain and Continuous Active SONAR in Undersea Vehicles

    DTIC Science & Technology

    2015-12-31

    distribution is unlimited" ES 14. ABSTRACT This report examines the application of factor graphs (graph-based architectures utilizing message passing) to...Research Laboratory The Pennsylvania State University Abstract: This report examines the application of factor graphs (graph-based architectures ...on Particle filtering and Smoothing: Fifteen years later. Tokyo, Japan . Duda, R ., Hart, P ., & Stork, D. (2001). Introduction. In Pattern

  11. A notion of graph likelihood and an infinite monkey theorem

    NASA Astrophysics Data System (ADS)

    Banerji, Christopher R. S.; Mansour, Toufik; Severini, Simone

    2014-01-01

    We play with a graph-theoretic analogue of the folklore infinite monkey theorem. We define a notion of graph likelihood as the probability that a given graph is constructed by a monkey in a number of time steps equal to the number of vertices. We present an algorithm to compute this graph invariant and closed formulas for some infinite classes. We have to leave the computational complexity of the likelihood as an open problem.

  12. Local and nonlocal advected invariants and helicities in magnetohydrodynamics and gas dynamics: II. Noether's theorems and Casimirs

    NASA Astrophysics Data System (ADS)

    Webb, G. M.; Dasgupta, B.; McKenzie, J. F.; Hu, Q.; Zank, G. P.

    2014-03-01

    Conservation laws in ideal gas dynamics and magnetohydrodynamics (MHD) associated with fluid relabeling symmetries are derived using Noether's first and second theorems. Lie dragged invariants are discussed in terms of the MHD Casimirs. A nonlocal conservation law for fluid helicity applicable for a non-barotropic fluid involving Clebsch variables is derived using Noether's theorem, in conjunction with a fluid relabeling symmetry and a gauge transformation. A nonlocal cross helicity conservation law involving Clebsch potentials, and the MHD energy conservation law are derived by the same method. An Euler-Poincaré variational approach is also used to derive conservation laws associated with fluid relabeling symmetries using Noether's second theorem.

  13. Scenario Graphs and Attack Graphs

    DTIC Science & Technology

    2004-04-14

    46 6.1 Vulnerability Analysis of a Network . . . . . . . . . . . . . . . . . . . . . . . . . 53 6.2 Sandia Red Team Attack Graph...asymptotic bound. The test machine was a 1Ghz Pentium III with 1GB of RAM, running Red Hat Linux 7.3. Figure 4.1(a) plots running time of the implemen...host scanning tools network information vulnerability Attack Graph network Red

  14. Invariant perfect tensors

    NASA Astrophysics Data System (ADS)

    Li, Youning; Han, Muxin; Grassl, Markus; Zeng, Bei

    2017-06-01

    Invariant tensors are states in the SU(2) tensor product representation that are invariant under SU(2) action. They play an important role in the study of loop quantum gravity. On the other hand, perfect tensors are highly entangled many-body quantum states with local density matrices maximally mixed. Recently, the notion of perfect tensors has attracted a lot of attention in the fields of quantum information theory, condensed matter theory, and quantum gravity. In this work, we introduce the concept of an invariant perfect tensor (IPT), which is an n-valent tensor that is both invariant and perfect. We discuss the existence and construction of IPTs. For bivalent tensors, the IPT is the unique singlet state for each local dimension. The trivalent IPT also exists and is uniquely given by Wigner’s 3j symbol. However, we show that, surprisingly, 4-valent IPTs do not exist for any identical local dimension d. On the contrary, when the dimension is large, almost all invariant tensors are asymptotically perfect, which is a consequence of the phenomenon of the concentration of measure for multipartite quantum states.

  15. Graph Theory

    SciTech Connect

    Sanfilippo, Antonio P.

    2005-12-27

    Graph theory is a branch of discrete combinatorial mathematics that studies the properties of graphs. The theory was pioneered by the Swiss mathematician Leonhard Euler in the 18th century, commenced its formal development during the second half of the 19th century, and has witnessed substantial growth during the last seventy years, with applications in areas as diverse as engineering, computer science, physics, sociology, chemistry and biology. Graph theory has also had a strong impact in computational linguistics by providing the foundations for the theory of features structures that has emerged as one of the most widely used frameworks for the representation of grammar formalisms.

  16. Generalized scale invariant theories

    NASA Astrophysics Data System (ADS)

    Padilla, Antonio; Stefanyszyn, David; Tsoukalas, Minas

    2014-03-01

    We present the most general actions of a single scalar field and two scalar fields coupled to gravity, consistent with second-order field equations in four dimensions, possessing local scale invariance. We apply two different methods to arrive at our results. One method, Ricci gauging, was known to the literature and we find this to produce the same result for the case of one scalar field as a more efficient method presented here. However, we also find our more efficient method to be much more general when we consider two scalar fields. Locally scale invariant actions are also presented for theories with more than two scalar fields coupled to gravity and we explain how one could construct the most general actions for any number of scalar fields. Our generalized scale invariant actions have obvious applications to early Universe cosmology and include, for example, the Bezrukov-Shaposhnikov action as a subset.

  17. Algebraic distance on graphs.

    SciTech Connect

    Chen, J.; Safro, I.

    2011-01-01

    Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.

  18. Invariant death.

    PubMed

    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.

  19. Invariant death

    PubMed Central

    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. PMID:27785361

  20. On 3d bulk geometry of Virasoro coadjoint orbits: orbit invariant charges and Virasoro hair on locally AdS_3 geometries

    NASA Astrophysics Data System (ADS)

    Sheikh-Jabbari, M. M.; Yavartanoo, H.

    2016-09-01

    Expanding upon [arXiv:1404.4472, arXiv:1511.06079], we provide a further detailed analysis of Bañados geometries, the most general solutions to the AdS_3 Einstein gravity with Brown-Henneaux boundary conditions. We analyze in some detail the causal, horizon, and boundary structure, and the geodesic motion on these geometries, as well as the two classes of symplectic charges one can associate with these geometries: charges associated with the exact symmetries and the Virasoro charges. We elaborate on the one-to-one relation between the coadjoint orbits of two copies of the Virasoro group and Bañados geometries. We discuss that the information as regards the Bañados goemetries falls into two categories: "orbit invariant" information and "Virasoro hairs". The former concerns geometric quantities, while the latter are specified by the non-local surface integrals. We elaborate on multi-BTZ geometries which have a number of disconnected pieces at the horizon bifurcation curve. We study multi-BTZ black hole thermodynamics and discuss that the thermodynamic quantities are orbit invariants. We also comment on the implications of our analysis for a 2d CFT dual which could possibly be dual to AdS_3 Einstein gravity.

  1. Chromatic polynomials of random graphs

    NASA Astrophysics Data System (ADS)

    Van Bussel, Frank; Ehrlich, Christoph; Fliegner, Denny; Stolzenberg, Sebastian; Timme, Marc

    2010-04-01

    Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.

  2. Adjusting protein graphs based on graph entropy.

    PubMed

    Peng, Sheng-Lung; Tsay, Yu-Wei

    2014-01-01

    Measuring protein structural similarity attempts to establish a relationship of equivalence between polymer structures based on their conformations. In several recent studies, researchers have explored protein-graph remodeling, instead of looking a minimum superimposition for pairwise proteins. When graphs are used to represent structured objects, the problem of measuring object similarity become one of computing the similarity between graphs. Graph theory provides an alternative perspective as well as efficiency. Once a protein graph has been created, its structural stability must be verified. Therefore, a criterion is needed to determine if a protein graph can be used for structural comparison. In this paper, we propose a measurement for protein graph remodeling based on graph entropy. We extend the concept of graph entropy to determine whether a graph is suitable for representing a protein. The experimental results suggest that when applied, graph entropy helps a conformational on protein graph modeling. Furthermore, it indirectly contributes to protein structural comparison if a protein graph is solid.

  3. Test of Graphing and Graph Interpretation Skills.

    ERIC Educational Resources Information Center

    Hermann, J.

    This monograph is a test of graphing and graph interpretation skills which assesses performance on all the skills of graphing which are contained in the AAAS program, Science - A Process Approach. The testing includes construction of bar graphs, interpreting information on graphs, the use of the Cartesian coordinate system, making predictions from…

  4. Translation Invariant Extensions of Finite Volume Measures

    NASA Astrophysics Data System (ADS)

    Goldstein, S.; Kuna, T.; Lebowitz, J. L.; Speer, E. R.

    2017-02-01

    We investigate the following questions: Given a measure μ _Λ on configurations on a subset Λ of a lattice L, where a configuration is an element of Ω ^Λ for some fixed set Ω , does there exist a measure μ on configurations on all of L, invariant under some specified symmetry group of L, such that μ _Λ is its marginal on configurations on Λ ? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which L=Z^d and the symmetries are the translations. For the case in which Λ is an interval in Z we give a simple necessary and sufficient condition, local translation invariance ( LTI), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which L is the Bethe lattice. On Z we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When Λ subset Z is not an interval, or when Λ subset Z^d with d>1, the LTI condition is necessary but not sufficient for extendibility. For Z^d with d>1, extendibility is in some sense undecidable.

  5. Claw-Free Maximal Planar Graphs

    DTIC Science & Technology

    1989-01-01

    0, 1,2 and 3 points of degree 6 respectively.) Now suppose G,. has no claws for 3 < r < i and consider graph G ,+,. Graph G,+ 1 is obtained from Gr by...adjacent to a point v by N(v) and call the induced subgraph GiN(v)] the neighborhood graph of v in G . Graph G is said to be locally n-connected if for all

  6. Inverse scattering problem for quantum graph vertices

    SciTech Connect

    Cheon, Taksu; Turek, Ondrej; Exner, Pavel

    2011-06-15

    We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of the Hermitian unitary matrix when the vertex coupling is of the scale-invariant (or Fueloep-Tsutsui) form. This enables the construction of quantum graphs with desired properties in a tailor-made fashion. The procedure is illustrated on the example of quantum vertices with equal transmission probabilities.

  7. Graphing Reality

    NASA Astrophysics Data System (ADS)

    Beeken, Paul

    2014-11-01

    Graphing is an essential skill that forms the foundation of any physical science.1 Understanding the relationships between measurements ultimately determines which modeling equations are successful in predicting observations.2 Over the years, science and math teachers have approached teaching this skill with a variety of techniques. For secondary school instruction, the job of graphing skills falls heavily on physics teachers. By virtue of the nature of the topics we cover, it is our mission to develop this skill to the fine art that it is.

  8. Grasp Invariance

    DTIC Science & Technology

    2010-01-01

    principle’s application to many common devices from jar wrenches to rock-climbing cams. 1 Introduction What principles should guide the design of...this paper we explore the possible role of the fingers in adapting to variations in object shape and pose. One common design approach is to adapt to...several fingers, the job of gracefully adapting to shape and pose variations may fall on the finger form. This work explores grasp invariance over shape and

  9. Threshold Graph Limits and Random Threshold Graphs

    PubMed Central

    Diaconis, Persi; Holmes, Susan; Janson, Svante

    2010-01-01

    We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits. PMID:20811581

  10. Tractors, mass, and Weyl invariance

    NASA Astrophysics Data System (ADS)

    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.

  11. Graphing Reality

    ERIC Educational Resources Information Center

    Beeken, Paul

    2014-01-01

    Graphing is an essential skill that forms the foundation of any physical science. Understanding the relationships between measurements ultimately determines which modeling equations are successful in predicting observations. Over the years, science and math teachers have approached teaching this skill with a variety of techniques. For secondary…

  12. Graphing Reality

    ERIC Educational Resources Information Center

    Beeken, Paul

    2014-01-01

    Graphing is an essential skill that forms the foundation of any physical science. Understanding the relationships between measurements ultimately determines which modeling equations are successful in predicting observations. Over the years, science and math teachers have approached teaching this skill with a variety of techniques. For secondary…

  13. GraphBench

    SciTech Connect

    Sukumar, Sreenivas R.; Hong, Seokyong; Lee, Sangkeun; Lim, Seung-Hwan

    2016-06-01

    GraphBench is a benchmark suite for graph pattern mining and graph analysis systems. The benchmark suite is a significant addition to conducting apples-apples comparison of graph analysis software (databases, in-memory tools, triple stores, etc.)

  14. Tight Lower Bound for Percolation Threshold on an Infinite Graph

    NASA Astrophysics Data System (ADS)

    Hamilton, Kathleen E.; Pryadko, Leonid P.

    2014-11-01

    We construct a tight lower bound for the site percolation threshold on an infinite graph, which becomes exact for an infinite tree. The bound is given by the inverse of the maximal eigenvalue of the Hashimoto matrix used to count nonbacktracking walks on the original graph. Our bound always exceeds the inverse spectral radius of the graph's adjacency matrix, and it is also generally tighter than the existing bound in terms of the maximum degree. We give a constructive proof for existence of such an eigenvalue in the case of a connected infinite quasitransitive graph, a graph-theoretic analog of a translationally invariant system.

  15. The F-coindex of some graph operations.

    PubMed

    De, Nilanjan; Nayeem, Sk Md Abu; Pal, Anita

    2016-01-01

    The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. In this paper, we introduce a new invariant which is named as F-coindex. Here, we study basic mathematical properties and the behavior of the newly introduced F-coindex under several graph operations such as union, join, Cartesian product, composition, tensor product, strong product, corona product, disjunction, symmetric difference of graphs and hence apply our results to find the F-coindex of different chemically interesting molecular graphs and nano-structures.

  16. Line graphs for fractals

    NASA Astrophysics Data System (ADS)

    Warchalowski, Wiktor; Krawczyk, Malgorzata J.

    2017-03-01

    We found the Lindenmayer systems for line graphs built on selected fractals. We show that the fractal dimension of such obtained graphs in all analysed cases is the same as for their original graphs. Both for the original graphs and for their line graphs we identified classes of nodes which reflect symmetry of the graph.

  17. Sequential motif profile of natural visibility graphs

    NASA Astrophysics Data System (ADS)

    Iacovacci, Jacopo; Lacasa, Lucas

    2016-11-01

    The concept of sequential visibility graph motifs—subgraphs appearing with characteristic frequencies in the visibility graphs associated to time series—has been advanced recently along with a theoretical framework to compute analytically the motif profiles associated to horizontal visibility graphs (HVGs). Here we develop a theory to compute the profile of sequential visibility graph motifs in the context of natural visibility graphs (VGs). This theory gives exact results for deterministic aperiodic processes with a smooth invariant density or stochastic processes that fulfill the Markov property and have a continuous marginal distribution. The framework also allows for a linear time numerical estimation in the case of empirical time series. A comparison between the HVG and the VG case (including evaluation of their robustness for short series polluted with measurement noise) is also presented.

  18. Sequential motif profile of natural visibility graphs.

    PubMed

    Iacovacci, Jacopo; Lacasa, Lucas

    2016-11-01

    The concept of sequential visibility graph motifs-subgraphs appearing with characteristic frequencies in the visibility graphs associated to time series-has been advanced recently along with a theoretical framework to compute analytically the motif profiles associated to horizontal visibility graphs (HVGs). Here we develop a theory to compute the profile of sequential visibility graph motifs in the context of natural visibility graphs (VGs). This theory gives exact results for deterministic aperiodic processes with a smooth invariant density or stochastic processes that fulfill the Markov property and have a continuous marginal distribution. The framework also allows for a linear time numerical estimation in the case of empirical time series. A comparison between the HVG and the VG case (including evaluation of their robustness for short series polluted with measurement noise) is also presented.

  19. Evolutionary games on networks and payoff invariance under replicator dynamics.

    PubMed

    Luthi, Leslie; Tomassini, Marco; Pestelacci, Enea

    2009-06-01

    The commonly used accumulated payoff scheme is not invariant with respect to shifts of payoff values when applied locally in degree-inhomogeneous population structures. We propose a suitably modified payoff scheme and we show both formally and by numerical simulation, that it leaves the replicator dynamics invariant with respect to affine transformations of the game payoff matrix. We then show empirically that, using the modified payoff scheme, an interesting amount of cooperation can be reached in three paradigmatic non-cooperative two-person games in populations that are structured according to graphs that have a marked degree inhomogeneity, similar to actual graphs found in society. The three games are the Prisoner's Dilemma, the Hawks-Doves and the Stag-Hunt. This confirms previous important observations that, under certain conditions, cooperation may emerge in such network-structured populations, even though standard replicator dynamics for mixing populations prescribes equilibria in which cooperation is totally absent in the Prisoner's Dilemma, and it is less widespread in the other two games.

  20. Approximate Graph Edit Distance in Quadratic Time.

    PubMed

    Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst

    2015-09-14

    Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.

  1. Generalized graph states based on Hadamard matrices

    SciTech Connect

    Cui, Shawn X.; Yu, Nengkun; Zeng, Bei

    2015-07-15

    Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a stabilizer group or an encoding circuit, both can be directly given by the graph. To generalize graph states, whose stabilizer groups are abelian subgroups of the Pauli group, one approach taken is to study non-abelian stabilizers. In this work, we propose to generalize graph states based on the encoding circuit, which is completely determined by the graph and a Hadamard matrix. We study the entanglement structures of these generalized graph states and show that they are all maximally mixed locally. We also explore the relationship between the equivalence of Hadamard matrices and local equivalence of the corresponding generalized graph states. This leads to a natural generalization of the Pauli (X, Z) pairs, which characterizes the local symmetries of these generalized graph states. Our approach is also naturally generalized to construct graph quantum codes which are beyond stabilizer codes.

  2. Proof of the local mass-angular momenta inequality for U{(1)}^{2} invariant black holes

    NASA Astrophysics Data System (ADS)

    Alaee, Aghil; Kunduri, Hari K.

    2015-08-01

    We consider initial data for extreme vacuum asymptotically flat black holes with {{R}}× U{(1)}2 symmetry. Such geometries are critical points of a mass functional defined for a wide class of asymptotically flat, ‘(t-{φ }i)’ symmetric maximal initial data for the vacuum Einstein equations. We prove that the above extreme geometries are local minima of mass among nearby initial data (with the same interval structure) with fixed angular momenta. Thus the ADM mass of nearby data m≥slant f({J}1,{J}2) for some function f depending on the interval structure. The proof requires that the initial data of the critical points satisfy certain conditions that are satisfied by the extreme Myers-Perry and extreme black ring data.

  3. Constrained Markovian Dynamics of Random Graphs

    NASA Astrophysics Data System (ADS)

    Coolen, A. C. C.; de Martino, A.; Annibale, A.

    2009-09-01

    We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the `mobility' (the number of allowed moves for any given graph). As an application of the general theory we analyze the properties of degree-preserving Markov chains based on elementary edge switchings. We give an exact yet simple formula for the mobility in terms of the graph's adjacency matrix and its spectrum. This formula allows us to define acceptance probabilities for edge switchings, such that the Markov chains become controlled Glauber-type detailed balance processes, designed to evolve to any required invariant measure (representing the asymptotic frequencies with which the allowed graphs are visited during the process). As a corollary we also derive a condition in terms of simple degree statistics, sufficient to guarantee that, in the limit where the number of nodes diverges, even for state-independent acceptance probabilities of proposed moves the invariant measure of the process will be uniform. We test our theory on synthetic graphs and on realistic larger graphs as studied in cellular biology, showing explicitly that, for instances where the simple edge swap dynamics fails to converge to the uniform measure, a suitably modified Markov chain instead generates the correct phase space sampling.

  4. A Novel Multi-Purpose Matching Representation of Local 3D Surfaces: A Rotationally Invariant, Efficient, and Highly Discriminative Approach With an Adjustable Sensitivity.

    PubMed

    Al-Osaimi, Faisal R

    2016-02-01

    In this paper, a novel approach to local 3D surface matching representation suitable for a range of 3D vision applications is introduced. Local 3D surface patches around key points on the 3D surface are represented by 2D images such that the representing 2D images enjoy certain characteristics which positively impact the matching accuracy, robustness, and speed. First, the proposed representation is complete, in the sense, there is no information loss during their computation. Second, the 3DoF 2D representations are strictly invariant to all the 3DoF rotations. To optimally avail surface information, the sensitivity of the representations to surface information is adjustable. This also provides the proposed matching representation with the means to optimally adjust to a particular class of problems/applications or an acquisition technology. Each 2D matching representation is a sequence of adjustable integral kernels, where each kernel is efficiently computed from a triple of precise 3D curves (profiles) formed by intersecting three concentric spheres with the 3D surface. Robust techniques for sampling the profiles and establishing correspondences among them were devised. Based on the proposed matching representation, two techniques for the detection of key points were presented. The first is suitable for static images, while the second is suitable for 3D videos. The approach was tested on the face recognition grand challenge v2.0, the 3D twins expression challenge, and the Bosphorus data sets, and a superior face recognition performance was achieved. In addition, the proposed approach was used in object class recognition and tested on a Kinect data set.

  5. Segmentation of 3-D High-Frequency Ultrasound Images of Human Lymph Nodes Using Graph Cut With Energy Functional Adapted to Local Intensity Distribution.

    PubMed

    Kuo, Jen-Wei; Mamou, Jonathan; Wang, Yao; Saegusa-Beecroft, Emi; Machi, Junji; Feleppa, Ernest J

    2017-10-01

    Previous studies by our group have shown that 3-D high-frequency quantitative ultrasound (QUS) methods have the potential to differentiate metastatic lymph nodes (LNs) from cancer-free LNs dissected from human cancer patients. To successfully perform these methods inside the LN parenchyma (LNP), an automatic segmentation method is highly desired to exclude the surrounding thin layer of fat from QUS processing and accurately correct for ultrasound attenuation. In high-frequency ultrasound images of LNs, the intensity distribution of LNP and fat varies spatially because of acoustic attenuation and focusing effects. Thus, the intensity contrast between two object regions (e.g., LNP and fat) is also spatially varying. In our previous work, nested graph cut (GC) demonstrated its ability to simultaneously segment LNP, fat, and the outer phosphate-buffered saline bath even when some boundaries are lost because of acoustic attenuation and focusing effects. This paper describes a novel approach called GC with locally adaptive energy to further deal with spatially varying distributions of LNP and fat caused by inhomogeneous acoustic attenuation. The proposed method achieved Dice similarity coefficients of 0.937±0.035 when compared with expert manual segmentation on a representative data set consisting of 115 3-D LN images obtained from colorectal cancer patients.

  6. Graph anomalies in cyber communications

    SciTech Connect

    Vander Wiel, Scott A; Storlie, Curtis B; Sandine, Gary; Hagberg, Aric A; Fisk, Michael

    2011-01-11

    Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail.

  7. Adjusting protein graphs based on graph entropy

    PubMed Central

    2014-01-01

    Measuring protein structural similarity attempts to establish a relationship of equivalence between polymer structures based on their conformations. In several recent studies, researchers have explored protein-graph remodeling, instead of looking a minimum superimposition for pairwise proteins. When graphs are used to represent structured objects, the problem of measuring object similarity become one of computing the similarity between graphs. Graph theory provides an alternative perspective as well as efficiency. Once a protein graph has been created, its structural stability must be verified. Therefore, a criterion is needed to determine if a protein graph can be used for structural comparison. In this paper, we propose a measurement for protein graph remodeling based on graph entropy. We extend the concept of graph entropy to determine whether a graph is suitable for representing a protein. The experimental results suggest that when applied, graph entropy helps a conformational on protein graph modeling. Furthermore, it indirectly contributes to protein structural comparison if a protein graph is solid. PMID:25474347

  8. Cayley Bipolar Fuzzy Graphs

    PubMed Central

    Alshehri, Noura O.

    2013-01-01

    We introduce the concept of Cayley bipolar fuzzy graphs and investigate some of their properties. We present some interesting properties of bipolar fuzzy graphs in terms of algebraic structures. We also discuss connectedness in Cayley bipolar fuzzy graphs. PMID:24453797

  9. Invariants of broken discrete symmetries.

    PubMed

    Kalozoumis, P A; Morfonios, C; Diakonos, F K; Schmelcher, P

    2014-08-01

    The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

  10. Invariants of Broken Discrete Symmetries

    NASA Astrophysics Data System (ADS)

    Kalozoumis, P. A.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.

    2014-08-01

    The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

  11. Factorized Graph Matching.

    PubMed

    Zhou, Feng; de la Torre, Fernando

    2015-11-19

    Graph matching (GM) is a fundamental problem in computer science, and it plays a central role to solve correspondence problems in computer vision. GM problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem (QAP). Although widely used, solving the correspondence problem through GM has two main limitations: (1) the QAP is NP-hard and difficult to approximate; (2) GM algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems. To address aforementioned problems, this paper proposes factorized graph matching (FGM). FGM factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges. Four are the benefits that follow from this factorization: (1) There is no need to compute the costly (in space and time) pairwise affinity matrix; (2) The factorization allows the use of a path-following optimization algorithm, that leads to improved optimization strategies and matching performance; (3) Given the factorization, it becomes straight-forward to incorporate geometric transformations (rigid and non-rigid) to the GM problem. (4) Using a matrix formulation for the GM problem and the factorization, it is easy to reveal commonalities and differences between different GM methods. The factorization also provides a clean connection with other matching algorithms such as iterative closest point; Experimental results on synthetic and real databases illustrate how FGM outperforms state-of-the-art algorithms for GM. The code is available at http://humansensing.cs.cmu.edu/fgm.

  12. Possible universal quantum algorithms for generalized Turaev-Viro invariants

    NASA Astrophysics Data System (ADS)

    Vélez, Mario; Ospina, Juan

    2011-05-01

    An emergent trend in quantum computation is the topological quantum computation (TQC). Briefly, TQC results from the application of quantum computation with the aim to solve the problems of quantum topology such as topological invariants for knots and links (Jones polynomials, HOMFLY polynomials, Khovanov polynomials); topological invariants for graphs (Tutte polynomial and Bollobás-Riordan polynomial); topological invariants for 3-manifolds (Reshetiskin-Turaev, Turaev-Viro and Turaer-Viro-Ocneanu invariants) and topological invariants for 4-manifolds( Crane-Yetter invariants). In a few words, TQC is concerned with the formulation of quantum algorithms for the computation of these topological invariants in quantum topology. Given that one of the fundamental achievements of quantum topology was the discovery of strong connections between monoidal categories and 3-dimensional manifolds, in TQC is possible and necessary to exploit such connections with the purpose to formulate universal quantum algorithms for topological invariants of 3-manifolds. In the present work we make an exploration of such possibilities. Specifically we search for universal quantum algorithms for generalized Turaev-Viro invariants of 3-manifolds such as the Turaev-Viro-Ocneanu invariants, the Kashaev-Baseilhac-Benedetti invariants of 3-manifolds with links and the Geer-Kashaev-Turaev invariants of 3-manifolds with a link and a principal bundle. We also look for physical systems (three dimensional topological insulators and three-dimensional gravity) over which implement the resulting universal topological quantum algorithms.

  13. Graphing Polar Curves

    ERIC Educational Resources Information Center

    Lawes, Jonathan F.

    2013-01-01

    Graphing polar curves typically involves a combination of three traditional techniques, all of which can be time-consuming and tedious. However, an alternative method--graphing the polar function on a rectangular plane--simplifies graphing, increases student understanding of the polar coordinate system, and reinforces graphing techniques learned…

  14. Ensembles of physical states and random quantum circuits on graphs

    NASA Astrophysics Data System (ADS)

    Hamma, Alioscia; Santra, Siddhartha; Zanardi, Paolo

    2012-11-01

    In this paper we continue and extend the investigations of the ensembles of random physical states introduced in Hamma [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.109.040502 109, 040502 (2012)]. These ensembles are constructed by finite-length random quantum circuits (RQC) acting on the (hyper)edges of an underlying (hyper)graph structure. The latter encodes for the locality structure associated with finite-time quantum evolutions generated by physical, i.e., local, Hamiltonians. Our goal is to analyze physical properties of typical states in these ensembles; in particular here we focus on proxies of quantum entanglement as purity and α-Renyi entropies. The problem is formulated in terms of matrix elements of superoperators which depend on the graph structure, choice of probability measure over the local unitaries, and circuit length. In the α=2 case these superoperators act on a restricted multiqubit space generated by permutation operators associated to the subsets of vertices of the graph. For permutationally invariant interactions the dynamics can be further restricted to an exponentially smaller subspace. We consider different families of RQCs and study their typical entanglement properties for finite time as well as their asymptotic behavior. We find that area law holds in average and that the volume law is a typical property (that is, it holds in average and the fluctuations around the average are vanishing for the large system) of physical states. The area law arises when the evolution time is O(1) with respect to the size L of the system, while the volume law arises as is typical when the evolution time scales like O(L).

  15. Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.

    PubMed

    Shang, Yilun

    2015-01-01

    Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.

  16. Classification and predictions of RNA pseudoknots based on topological invariants

    NASA Astrophysics Data System (ADS)

    Vernizzi, Graziano; Orland, Henri; Zee, A.

    2016-10-01

    We propose a new topological characterization of ribonucleic acid (RNA) secondary structures with pseudoknots based on two topological invariants. Starting from the classic arc representation of RNA secondary structures, we consider a model that couples both (i) the topological genus of the graph and (ii) the number of crossing arcs of the corresponding primitive graph. We add a term proportional to these topological invariants to the standard free energy of the RNA molecule, thus obtaining a novel free-energy parametrization that takes into account the abundance of topologies of RNA pseudoknots observed in RNA databases.

  17. Gauge invariance of quantum gravity in the causal approach

    NASA Astrophysics Data System (ADS)

    Schorn, Ivo

    1997-03-01

    We investigate gauge invariance of perturbative quantum gravity without matter fields in the causal Epstein - Glaser approach. This approach uses free fields only so that all objects of the theory are mathematically well defined. The first-order graviton self-couplings are obtained from the Einstein - Hilbert Lagrangian written in terms of Goldberg variables and expanded to lowest order on the flat Minkowski background metric (linearized Einstein theory). Similar to Yang - Mills theory, gauge invariance to first order requires an additional coupling to fermionic ghost fields. For second-order tree graphs, gauge invariance generates four-graviton normalization terms, which agree exactly with the next order of the expansion of the Einstein - Hilbert Lagrangian. Gauge invariance of the ghost sector is then examined in detail. It is stressed that, despite some formal similarities, the concept of operator gauge invariance used in the causal method is different from the conventional BRS-invariance commonly used in the literature.

  18. Unsupervised spectral mesh segmentation driven by heterogeneous graphs.

    PubMed

    Theologou, Panagiotis; Pratikakis, Ioannis; Theoharis, Theoharis

    2016-03-21

    A fully automatic mesh segmentation scheme using heterogeneous graphs is presented. We introduce a spectral framework where local geometry affinities are coupled with surface patch affinities. A heterogeneous graph is constructed combining two distinct graphs: a weighted graph based on adjacency of patches of an initial over-segmentation, and the weighted dual mesh graph. The partitioning relies on processing each eigenvector of the heterogeneous graph Laplacian individually, taking into account the nodal set and nodal domain theory. Experiments on standard datasets show that the proposed unsupervised approach outperforms the state-of-the-art unsupervised methodologies and is comparable to the best supervised approaches.

  19. Unsupervised Spectral Mesh Segmentation Driven by Heterogeneous Graphs.

    PubMed

    Theologou, Panagiotis; Pratikakis, Ioannis; Theoharis, Theoharis

    2017-02-01

    A fully automatic mesh segmentation scheme using heterogeneous graphs is presented. We introduce a spectral framework where local geometry affinities are coupled with surface patch affinities. A heterogeneous graph is constructed combining two distinct graphs: a weighted graph based on adjacency of patches of an initial over-segmentation, and the weighted dual mesh graph. The partitioning relies on processing each eigenvector of the heterogeneous graph Laplacian individually, taking into account the nodal set and nodal domain theory. Experiments on standard datasets show that the proposed unsupervised approach outperforms the state-of-the-art unsupervised methodologies and is comparable to the best supervised approaches.

  20. Multipartite invariant states. I. Unitary symmetry

    SciTech Connect

    Chruscinski, Dariusz; Kossakowski, Andrzej

    2006-06-15

    We propose a natural generalization of bipartite Werner and isotropic states to multipartite systems consisting of an arbitrary even number of d-dimensional subsystems (qudits). These generalized states are invariant under the action of local unitary operations. We study basic properties of multipartite invariant states and present necessary and sufficient separability criteria.

  1. Quantum graph as a quantum spectral filter

    NASA Astrophysics Data System (ADS)

    Turek, Ondřej; Cheon, Taksu

    2013-03-01

    We study the transmission of a quantum particle along a straight input-output line to which a graph Γ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant coupling with a coupling parameter α. We show that the probability of transmission along the line as a function of the particle energy tends to the indicator function of the energy spectrum of Γ as α → ∞. This effect can be used for a spectral analysis of the given graph Γ. Its applications include a control of a transmission along the line and spectral filtering. The result is illustrated with an example where Γ is a loop exposed to a magnetic field. Two more quantum devices are designed using other special scale-invariant vertex couplings. They can serve as a band-stop filter and as a spectral separator, respectively.

  2. Quantum graph as a quantum spectral filter

    SciTech Connect

    Turek, Ondrej; Cheon, Taksu

    2013-03-15

    We study the transmission of a quantum particle along a straight input-output line to which a graph {Gamma} is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant coupling with a coupling parameter {alpha}. We show that the probability of transmission along the line as a function of the particle energy tends to the indicator function of the energy spectrum of {Gamma} as {alpha}{yields}{infinity}. This effect can be used for a spectral analysis of the given graph {Gamma}. Its applications include a control of a transmission along the line and spectral filtering. The result is illustrated with an example where {Gamma} is a loop exposed to a magnetic field. Two more quantum devices are designed using other special scale-invariant vertex couplings. They can serve as a band-stop filter and as a spectral separator, respectively.

  3. Principal Graph and Structure Learning Based on Reversed Graph Embedding.

    PubMed

    Mao, Qi; Wang, Li; Tsang, Ivor; Sun, Yijun

    2016-12-05

    Many scientific datasets are of high dimension, and the analysis usually requires retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing methods work only for data with structures that are mathematically formulated by curves, which is quite restrictive for real applications. A few methods can overcome the above problem, but they either require complicated human-made rules for a specific task with lack of adaption flexibility to different tasks, or cannot obtain explicit structures of data. To address these issues, we develop a novel principal graph and structure learning framework that captures the local information of the underlying graph structure based on reversed graph embedding. As showcases, models that can learn a spanning tree or a weighted undirected `1 graph are proposed, and a new learning algorithm is developed that learns a set of principal points and a graph structure from data, simultaneously. The new algorithm is simple with guaranteed convergence. We then extend the proposed framework to deal with large-scale data. Experimental results on various synthetic and six real world datasets show that the proposed method compares favorably with baselines and can uncover the underlying structure correctly.

  4. Intrinsic graph structure estimation using graph Laplacian.

    PubMed

    Noda, Atsushi; Hino, Hideitsu; Tatsuno, Masami; Akaho, Shotaro; Murata, Noboru

    2014-07-01

    A graph is a mathematical representation of a set of variables where some pairs of the variables are connected by edges. Common examples of graphs are railroads, the Internet, and neural networks. It is both theoretically and practically important to estimate the intensity of direct connections between variables. In this study, a problem of estimating the intrinsic graph structure from observed data is considered. The observed data in this study are a matrix with elements representing dependency between nodes in the graph. The dependency represents more than direct connections because it includes influences of various paths. For example, each element of the observed matrix represents a co-occurrence of events at two nodes or a correlation of variables corresponding to two nodes. In this setting, spurious correlations make the estimation of direct connection difficult. To alleviate this difficulty, a digraph Laplacian is used for characterizing a graph. A generative model of this observed matrix is proposed, and a parameter estimation algorithm for the model is also introduced. The notable advantage of the proposed method is its ability to deal with directed graphs, while conventional graph structure estimation methods such as covariance selections are applicable only to undirected graphs. The algorithm is experimentally shown to be able to identify the intrinsic graph structure.

  5. Khovanov homology of links and graphs

    NASA Astrophysics Data System (ADS)

    Stosic, Marko

    2006-05-01

    In this thesis we work with Khovanov homology of links and its generalizations, as well as with the homology of graphs. Khovanov homology of links consists of graded chain complexes which are link invariants, up to chain homotopy, with graded Euler characteristic equal to the Jones polynomial of the link. Hence, it can be regarded as the "categorification" of the Jones polynomial. We prove that the first homology group of positive braid knots is trivial. Futhermore, we prove that non-alternating torus knots are homologically thick. In addition, we show that we can decrease the number of full twists of torus knots without changing low-degree homology and consequently that there exists stable homology for torus knots. We also prove most of the above properties for Khovanov-Rozansky homology. Concerning graph homology, we categorify the dichromatic (and consequently Tutte) polynomial for graphs, by categorifying an infinite set of its one-variable specializations. We categorify explicitly the one-variable specialization that is an analog of the Jones polynomial of an alternating link corresponding to the initial graph. Also, we categorify explicitly the whole two-variable dichromatic polynomial of graphs by using Koszul complexes. textbf{Key-words:} Khovanov homology, Jones polynomial, link, torus knot, graph, dichromatic polynomial

  6. Interval Graph Limits

    PubMed Central

    Diaconis, Persi; Holmes, Susan; Janson, Svante

    2015-01-01

    We work out a graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function W (x, y) on the unit square, with x and y uniform on the interval (0, 1). Instead, we fix a W and change the underlying distribution of the coordinates x and y. We find choices such that our limits are continuous. Connections to random interval graphs are given, including some examples. We also show a continuity result for the chromatic number and clique number of interval graphs. Some results on uniqueness of the limit description are given for general graph limits. PMID:26405368

  7. Quantum snake walk on graphs

    SciTech Connect

    Rosmanis, Ansis

    2011-02-15

    I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.

  8. Bandlimited graph signal reconstruction by diffusion operator

    NASA Astrophysics Data System (ADS)

    Yang, Lishan; You, Kangyong; Guo, Wenbin

    2016-12-01

    Signal processing on graphs extends signal processing concepts and methodologies from the classical signal processing theory to data indexed by general graphs. For a bandlimited graph signal, the unknown data associated with unsampled vertices can be reconstructed from the sampled data by exploiting the spatial relationship of graph signal. In this paper, we propose a generalized analytical framework of unsampled graph signal and introduce a concept of diffusion operator which consists of local-mean and global-bias diffusion operator. Then, a diffusion operator-based iterative algorithm is proposed to reconstruct bandlimited graph signal from sampled data. In each iteration, the reconstructed residuals associated with the sampled vertices are diffused to all the unsampled vertices for accelerating the convergence. We then prove that the proposed reconstruction strategy converges to the original graph signal. The simulation results demonstrate the effectiveness of the proposed reconstruction strategy with various downsampling patterns, fluctuation of graph cut-off frequency, robustness on the classic graph structures, and noisy scenarios.

  9. Universality in spectral statistics of open quantum graphs.

    PubMed

    Gutkin, B; Osipov, V Al

    2015-06-01

    The quantum evolution maps of closed chaotic quantum graphs are unitary and known to have universal spectral correlations matching predictions of random matrix theory. In chaotic graphs with absorption the quantum maps become nonunitary. We show that their spectral statistics exhibit universality at the soft edges of the spectrum. The same spectral behavior is observed in many classical nonunitary ensembles of random matrices with rotationally invariant measures.

  10. Universality in spectral statistics of open quantum graphs

    NASA Astrophysics Data System (ADS)

    Gutkin, B.; Osipov, V. Al.

    2015-06-01

    The quantum evolution maps of closed chaotic quantum graphs are unitary and known to have universal spectral correlations matching predictions of random matrix theory. In chaotic graphs with absorption the quantum maps become nonunitary. We show that their spectral statistics exhibit universality at the soft edges of the spectrum. The same spectral behavior is observed in many classical nonunitary ensembles of random matrices with rotationally invariant measures.

  11. Generalizing twisted gauge invariance

    SciTech Connect

    Duenas-Vidal, Alvaro; Vazquez-Mozo, Miguel A.

    2009-05-01

    We discuss the twisting of gauge symmetry in noncommutative gauge theories and show how this can be generalized to a whole continuous family of twisted gauge invariances. The physical relevance of these twisted invariances is discussed.

  12. The Oriented Graph Complexes

    NASA Astrophysics Data System (ADS)

    Willwacher, Thomas

    2015-03-01

    The oriented graph complexes are complexes of directed graphs without directed cycles. They govern, for example, the quantization of Lie bialgebras and infinite dimensional deformation quantization. Similar to the ordinary graph complexes GC n introduced by Kontsevich they come in two essentially different versions, depending on the parity of n. It is shown that, surprisingly, the oriented graph complex is quasi-isomorphic to the ordinary commutative graph complex of opposite parity GC n-1, up to some known classes. This yields in particular a combinatorial description of the action of on Lie bialgebras, and shows that a cycle-free formality morphism in the sense of Shoikhet can be constructed rationally without reference to configuration space integrals. Curiously, the obstruction class in the oriented graph complex found by Shoikhet corresponds to the well known theta graph in the ordinary graph complex.

  13. On molecular graph comparison.

    PubMed

    Melo, Jenny A; Daza, Edgar

    2011-06-01

    Since the last half of the nineteenth century, molecular graphs have been present in several branches of chemistry. When used for molecular structure representation, they have been compared after mapping the corresponding graphs into mathematical objects. However, direct molecular comparison of molecular graphs is a research field less explored. The goal of this mini-review is to show some distance and similarity coefficients which were proposed to directly compare molecular graphs or which could be useful to do so.

  14. Graph-Plotting Routine

    NASA Technical Reports Server (NTRS)

    Kantak, Anil V.

    1987-01-01

    Plotter routine for IBM PC (AKPLOT) designed for engineers and scientists who use graphs as integral parts of their documentation. Allows user to generate graph and edit its appearance on cathode-ray tube. Graph may undergo many interactive alterations before finally dumped from screen to be plotted by printer. Written in BASIC.

  15. Graphs in Scientific Publications.

    ERIC Educational Resources Information Center

    Cleveland, William S.

    Two surveys were carried out to help increase knowledge of current graph usage in science. A detailed analysis of all graphs in one volume of the journal "Science" revealed that 30 percent had errors. Graphs are used more in some disciplines than in others; a survey of 57 journals revealed natural science journals use far more graphs…

  16. Graphing Inequalities, Connecting Meaning

    ERIC Educational Resources Information Center

    Switzer, J. Matt

    2014-01-01

    Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…

  17. Are Graphs Finally Surfacing?

    ERIC Educational Resources Information Center

    Beineke, Lowell W.

    1989-01-01

    Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)

  18. Graphing Inequalities, Connecting Meaning

    ERIC Educational Resources Information Center

    Switzer, J. Matt

    2014-01-01

    Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…

  19. Graphing Important People

    ERIC Educational Resources Information Center

    Reading Teacher, 2012

    2012-01-01

    The "Toolbox" column features content adapted from ReadWriteThink.org lesson plans and provides practical tools for classroom teachers. This issue's column features a lesson plan adapted from "Graphing Plot and Character in a Novel" by Lisa Storm Fink and "Bio-graph: Graphing Life Events" by Susan Spangler. Students retell biographic events…

  20. Graphing Important People

    ERIC Educational Resources Information Center

    Reading Teacher, 2012

    2012-01-01

    The "Toolbox" column features content adapted from ReadWriteThink.org lesson plans and provides practical tools for classroom teachers. This issue's column features a lesson plan adapted from "Graphing Plot and Character in a Novel" by Lisa Storm Fink and "Bio-graph: Graphing Life Events" by Susan Spangler. Students retell biographic events…

  1. Experimental Study of Quantum Graphs with Microwave Networks

    NASA Astrophysics Data System (ADS)

    Fu, Ziyuan; Koch, Trystan; Antonsen, Thomas; Ott, Edward; Anlage, Steven; Wave Chaos Team

    An experimental setup consisting of microwave networks is used to simulate quantum graphs. The networks are constructed from coaxial cables connected by T junctions. The networks are built for operation both at room temperature and superconducting versions that operate at cryogenic temperatures. In the experiments, a phase shifter is connected to one of the network bonds to generate an ensemble of quantum graphs by varying the phase delay. The eigenvalue spectrum is found from S-parameter measurements on one-port graphs. With the experimental data, the nearest-neighbor spacing statistics and the impedance statistics of the graphs are examined. It is also demonstrated that time-reversal invariance for microwave propagation in the graphs can be broken without increasing dissipation significantly by making nodes with circulators. Random matrix theory (RMT) successfully describes universal statistical properties of the system. We acknowledge support under contract AFOSR COE Grant FA9550-15-1-0171.

  2. GraphVar: a user-friendly toolbox for comprehensive graph analyses of functional brain connectivity.

    PubMed

    Kruschwitz, J D; List, D; Waller, L; Rubinov, M; Walter, H

    2015-04-30

    Graph theory provides a powerful and comprehensive formalism of global and local topological network properties of complex structural or functional brain connectivity. Software packages such as the Brain-Connectivity-Toolbox have contributed to graph theory's increasing popularity for characterization of brain networks. However, comparably comprehensive packages are command-line based and require programming experience; this precludes their use by users without a computational background, whose research would otherwise benefit from graph-theoretical methods. "GraphVar" is a user-friendly GUI-based toolbox for comprehensive graph-theoretical analyses of brain connectivity, including network construction and characterization, statistical analysis on network topological measures, network based statistics, and interactive exploration of results. GraphVar provides a comprehensive collection of graph analysis routines for analyses of functional brain connectivity in one single toolbox by combining features across multiple currently available toolboxes, such as the Brain Connectivity Toolbox, the Graph Analysis Toolbox, and the Network Based Statistic Toolbox (BCT, Rubinov and Sporns, 2010; GAT, Hosseini et al., 2012; NBS, Zalesky et al., 2010). GraphVar was developed under the GNU General Public License v3.0 and can be downloaded at www.rfmri.org/graphvar or www.nitrc.org/projects/graphvar. By combining together features across multiple toolboxes, GraphVar will allow comprehensive graph-theoretical analyses in one single toolbox without resorting to code. GraphVar will make graph theoretical methods more accessible for a broader audience of neuroimaging researchers. Copyright © 2015 Elsevier B.V. All rights reserved.

  3. Methods of visualizing graphs

    DOEpatents

    Wong, Pak C.; Mackey, Patrick S.; Perrine, Kenneth A.; Foote, Harlan P.; Thomas, James J.

    2008-12-23

    Methods for visualizing a graph by automatically drawing elements of the graph as labels are disclosed. In one embodiment, the method comprises receiving node information and edge information from an input device and/or communication interface, constructing a graph layout based at least in part on that information, wherein the edges are automatically drawn as labels, and displaying the graph on a display device according to the graph layout. In some embodiments, the nodes are automatically drawn as labels instead of, or in addition to, the label-edges.

  4. Horizontal visibility graphs generated by type-I intermittency.

    PubMed

    Núñez, Ángel M; Luque, Bartolo; Lacasa, Lucas; Gómez, Jose Patricio; Robledo, Alberto

    2013-05-01

    The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associated HV graphs. We show how the alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics. We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

  5. Horizontal visibility graphs generated by type-I intermittency

    NASA Astrophysics Data System (ADS)

    Núñez, Ángel M.; Luque, Bartolo; Lacasa, Lucas; Gómez, Jose Patricio; Robledo, Alberto

    2013-05-01

    The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associated HV graphs. We show how the alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics. We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

  6. Hyperbolic graph generator

    NASA Astrophysics Data System (ADS)

    Aldecoa, Rodrigo; Orsini, Chiara; Krioukov, Dmitri

    2015-11-01

    Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks can be adequately modeled as random geometric graphs in hyperbolic spaces. In this paper, we present a computer program to generate such graphs. Besides real-world-like networks, the program can generate random graphs from other well-known graph ensembles, such as the soft configuration model, random geometric graphs on a circle, or Erdős-Rényi random graphs. The simulations show a good match between the expected values of different network structural properties and the corresponding empirical values measured in generated graphs, confirming the accurate behavior of the program.

  7. Knot Invariants and Cellular Automata

    DTIC Science & Technology

    1993-05-04

    lattice gases. Since our approach equates the spacetime evolution of a dynamical system with an equilibrium configuration of a statistical mechanics...model in one higher dimension, a model of ’t Hooft for two dimensional spacetime with discrete local coordinate invariance was a natural inspiration [5...thermodynamic equilibrium, as well as demonstrating the efficacy of constructing and analyzing lattice gas automata according to ( spacetime ) symmetry principles

  8. Graphing trillions of triangles

    PubMed Central

    Burkhardt, Paul

    2016-01-01

    The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed. PMID:28690426

  9. Advances in Rotation-Invariant Texture Analysis

    NASA Astrophysics Data System (ADS)

    Estudillo-Romero, Alfonso; Escalante-Ramirez, Boris

    Robust rotation invariance has been a matter of great interest in many applications which use low-level features such as textures. In this paper, we propose a method to analyze and capture visual patterns from textures regardless their orientation. In order to achieve rotation invariance, visual texture patterns are locally described as one-dimensional patterns by appropriately steering the Cartesian Hermite coefficients. Experiments with two datasets from the Brodatz album were performed to evaluate orientation invariance. High average precision and recall rates were achieved by the proposed method.

  10. Nested Tracking Graphs

    DOE PAGES

    Lukasczyk, Jonas; Weber, Gunther; Maciejewski, Ross; ...

    2017-06-01

    Tracking graphs are a well established tool in topological analysis to visualize the evolution of components and their properties over time, i.e., when components appear, disappear, merge, and split. However, tracking graphs are limited to a single level threshold and the graphs may vary substantially even under small changes to the threshold. To examine the evolution of features for varying levels, users have to compare multiple tracking graphs without a direct visual link between them. We propose a novel, interactive, nested graph visualization based on the fact that the tracked superlevel set components for different levels are related to eachmore » other through their nesting hierarchy. This approach allows us to set multiple tracking graphs in context to each other and enables users to effectively follow the evolution of components for different levels simultaneously. We show the effectiveness of our approach on datasets from finite pointset methods, computational fluid dynamics, and cosmology simulations.« less

  11. Topologies on directed graphs

    NASA Technical Reports Server (NTRS)

    Lieberman, R. N.

    1972-01-01

    Given a directed graph, a natural topology is defined and relationships between standard topological properties and graph theoretical concepts are studied. In particular, the properties of connectivity and separatedness are investigated. A metric is introduced which is shown to be related to separatedness. The topological notions of continuity and homeomorphism. A class of maps is studied which preserve both graph and topological properties. Applications involving strong maps and contractions are also presented.

  12. Online dynamic graph drawing.

    PubMed

    Frishman, Yaniv; Tal, Ayellet

    2008-01-01

    This paper presents an algorithm for drawing a sequence of graphs online. The algorithm strives to maintain the global structure of the graph and thus the user's mental map, while allowing arbitrary modifications between consecutive layouts. The algorithm works online and uses various execution culling methods in order to reduce the layout time and handle large dynamic graphs. Techniques for representing graphs on the GPU allow a speedup by a factor of up to 17 compared to the CPU implementation. The scalability of the algorithm across GPU generations is demonstrated. Applications of the algorithm to the visualization of discussion threads in Internet sites and to the visualization of social networks are provided.

  13. Graph Generator Survey

    SciTech Connect

    Lothian, Josh; Powers, Sarah S; Sullivan, Blair D; Baker, Matthew B; Schrock, Jonathan; Poole, Stephen W

    2013-12-01

    The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of dierent application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.

  14. Recognition of Probe Ptolemaic Graphs

    NASA Astrophysics Data System (ADS)

    Chang, Maw-Shang; Hung, Ling-Ju

    Let G denote a graph class. An undirected graph G is called a probe G graph if one can make G a graph in G by adding edges between vertices in some independent set of G. By definition graph class G is a subclass of probe G graphs. Ptolemaic graphs are chordal and induced gem free. They form a subclass of both chordal graphs and distance-hereditary graphs. Many problems NP-hard on chordal graphs can be solved in polynomial time on ptolemaic graphs. We proposed an O(nm)-time algorithm to recognize probe ptolemaic graphs where n and m are the numbers of vertices and edges of the input graph respectively.

  15. Graph-Based Inter-Subject Pattern Analysis of fMRI Data

    PubMed Central

    Takerkart, Sylvain; Auzias, Guillaume; Thirion, Bertrand; Ralaivola, Liva

    2014-01-01

    In brain imaging, solving learning problems in multi-subjects settings is difficult because of the differences that exist across individuals. Here we introduce a novel classification framework based on group-invariant graphical representations, allowing to overcome the inter-subject variability present in functional magnetic resonance imaging (fMRI) data and to perform multivariate pattern analysis across subjects. Our contribution is twofold: first, we propose an unsupervised representation learning scheme that encodes all relevant characteristics of distributed fMRI patterns into attributed graphs; second, we introduce a custom-designed graph kernel that exploits all these characteristics and makes it possible to perform supervised learning (here, classification) directly in graph space. The well-foundedness of our technique and the robustness of the performance to the parameter setting are demonstrated through inter-subject classification experiments conducted on both artificial data and a real fMRI experiment aimed at characterizing local cortical representations. Our results show that our framework produces accurate inter-subject predictions and that it outperforms a wide range of state-of-the-art vector- and parcel-based classification methods. Moreover, the genericity of our method makes it is easily adaptable to a wide range of potential applications. The dataset used in this study and an implementation of our framework are available at http://dx.doi.org/10.6084/m9.figshare.1086317. PMID:25127129

  16. Large Deviation Function for the Number of Eigenvalues of Sparse Random Graphs Inside an Interval

    NASA Astrophysics Data System (ADS)

    Metz, Fernando L.; Pérez Castillo, Isaac

    2016-09-01

    We present a general method to obtain the exact rate function Ψ[a ,b ](k ) controlling the large deviation probability Prob[IN[a ,b ]=k N ]≍e-N Ψ[a ,b ](k ) that an N ×N sparse random matrix has IN[a ,b ]=k N eigenvalues inside the interval [a ,b ]. The method is applied to study the eigenvalue statistics in two distinct examples: (i) the shifted index number of eigenvalues for an ensemble of Erdös-Rényi graphs and (ii) the number of eigenvalues within a bounded region of the spectrum for the Anderson model on regular random graphs. A salient feature of the rate function in both cases is that, unlike rotationally invariant random matrices, it is asymmetric with respect to its minimum. The asymmetric character depends on the disorder in a way that is compatible with the distinct eigenvalue statistics corresponding to localized and delocalized eigenstates. The results also show that the level compressibility κ2/κ1 for the Anderson model on a regular graph satisfies 0 <κ2/κ1<1 in the bulk regime, in contrast with the behavior found in Gaussian random matrices. Our theoretical findings are thoroughly compared to numerical diagonalization in both cases, showing a reasonable good agreement.

  17. Large Deviation Function for the Number of Eigenvalues of Sparse Random Graphs Inside an Interval.

    PubMed

    Metz, Fernando L; Pérez Castillo, Isaac

    2016-09-02

    We present a general method to obtain the exact rate function Ψ_{[a,b]}(k) controlling the large deviation probability Prob[I_{N}[a,b]=kN]≍e^{-NΨ_{[a,b]}(k)} that an N×N sparse random matrix has I_{N}[a,b]=kN eigenvalues inside the interval [a,b]. The method is applied to study the eigenvalue statistics in two distinct examples: (i) the shifted index number of eigenvalues for an ensemble of Erdös-Rényi graphs and (ii) the number of eigenvalues within a bounded region of the spectrum for the Anderson model on regular random graphs. A salient feature of the rate function in both cases is that, unlike rotationally invariant random matrices, it is asymmetric with respect to its minimum. The asymmetric character depends on the disorder in a way that is compatible with the distinct eigenvalue statistics corresponding to localized and delocalized eigenstates. The results also show that the level compressibility κ_{2}/κ_{1} for the Anderson model on a regular graph satisfies 0<κ_{2}/κ_{1}<1 in the bulk regime, in contrast with the behavior found in Gaussian random matrices. Our theoretical findings are thoroughly compared to numerical diagonalization in both cases, showing a reasonable good agreement.

  18. Permutation centralizer algebras and multimatrix invariants

    NASA Astrophysics Data System (ADS)

    Mattioli, Paolo; Ramgoolam, Sanjaye

    2016-03-01

    We introduce a class of permutation centralizer algebras which underly the combinatorics of multimatrix gauge-invariant observables. One family of such noncommutative algebras is parametrized by two integers. Its Wedderburn-Artin decomposition explains the counting of restricted Schur operators, which were introduced in the physics literature to describe open strings attached to giant gravitons and were subsequently used to diagonalize the Gaussian inner product for gauge invariants of two-matrix models. The structure of the algebra, notably its dimension, its center and its maximally commuting subalgebra, is related to Littlewood-Richardson numbers for composing Young diagrams. It gives a precise characterization of the minimal set of charges needed to distinguish arbitrary matrix gauge invariants, which are related to enhanced symmetries in gauge theory. The algebra also gives a star product for matrix invariants. The center of the algebra allows efficient computation of a sector of multimatrix correlators. These generate the counting of a certain class of bicoloured ribbon graphs with arbitrary genus.

  19. Graphs, matrices, and the GraphBLAS: Seven good reasons

    DOE PAGES

    Kepner, Jeremy; Bader, David; Buluç, Aydın; ...

    2015-01-01

    The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istcbigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implementmore » a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.« less

  20. Graphs, matrices, and the GraphBLAS: Seven good reasons

    SciTech Connect

    Kepner, Jeremy; Bader, David; Buluç, Aydın; Gilbert, John; Mattson, Timothy; Meyerhenke, Henning

    2015-01-01

    The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istcbigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.

  1. Proton spin: A topological invariant

    NASA Astrophysics Data System (ADS)

    Tiwari, S. C.

    2016-11-01

    Proton spin problem is given a new perspective with the proposition that spin is a topological invariant represented by a de Rham 3-period. The idea is developed generalizing Finkelstein-Rubinstein theory for Skyrmions/kinks to topological defects, and using non-Abelian de Rham theorems. Two kinds of de Rham theorems are discussed applicable to matrix-valued differential forms, and traces. Physical and mathematical interpretations of de Rham periods are presented. It is suggested that Wilson lines and loop operators probe the local properties of the topology, and spin as a topological invariant in pDIS measurements could appear with any value from 0 to ℏ 2, i.e. proton spin decomposition has no meaning in this approach.

  2. Fault-tolerant dynamic task graph scheduling

    SciTech Connect

    Kurt, Mehmet C.; Krishnamoorthy, Sriram; Agrawal, Kunal; Agrawal, Gagan

    2014-11-16

    In this paper, we present an approach to fault tolerant execution of dynamic task graphs scheduled using work stealing. In particular, we focus on selective and localized recovery of tasks in the presence of soft faults. We elicit from the user the basic task graph structure in terms of successor and predecessor relationships. The work stealing-based algorithm to schedule such a task graph is augmented to enable recovery when the data and meta-data associated with a task get corrupted. We use this redundancy, and the knowledge of the task graph structure, to selectively recover from faults with low space and time overheads. We show that the fault tolerant design retains the essential properties of the underlying work stealing-based task scheduling algorithm, and that the fault tolerant execution is asymptotically optimal when task re-execution is taken into account. Experimental evaluation demonstrates the low cost of recovery under various fault scenarios.

  3. Invariants of Boundary Link Cobordism

    NASA Astrophysics Data System (ADS)

    Sheiham, Desmond

    2001-10-01

    An n-dimensional μ-component boundary link is a codimension 2 embedding of spheres L=bigsqcup_{μ}S^n subset S^{n+2} such that there exist μ disjoint oriented embedded (n+1)-manifolds which span the components of L. An F_μ-link is a boundary link together with a cobordism class of such spanning manifolds. The F_μ-link cobordism group C_n(F_μ) is known to be trivial when n is even but not finitely generated when n is odd. Our main result is an algorithm to decide whether two odd-dimensional F_μ-links represent the same cobordism class in C_{2q-1}(F_μ) assuming q>1. We proceed to compute the isomorphism class of C_{2q-1}(F_μ), generalizing Levine's computation of the knot cobordism group C_{2q-1}(F_1). Our starting point is the algebraic formulation of Levine, Ko and Mio who identify C_{2q-1}(F_μ) with a surgery obstruction group, the Witt group G^{(-1)^q,μ}(Z) of μ-component Seifert matrices. We obtain a complete set of torsion-free invariants by passing from integer coefficients to complex coefficients and by applying the algebraic machinery of Quebbemann, Scharlau and Schulte. Signatures correspond to `algebraically integral' simple self-dual representations of a certain quiver (directed graph with loops). These representations, in turn, correspond to algebraic integers on an infinite disjoint union of real affine varieties. To distinguish torsion classes, we consider rational coefficients in place of complex coefficients, expressing G^{(-1)^q,μ}(Q) as an infinite direct sum of Witt groups of finite-dimensional division Q-algebras with involution. Numerical invariants of such Witt groups are available in the literature.

  4. Real World Graph Connectivity

    ERIC Educational Resources Information Center

    Lind, Joy; Narayan, Darren

    2009-01-01

    We present the topic of graph connectivity along with a famous theorem of Menger in the real-world setting of the national computer network infrastructure of "National LambdaRail". We include a set of exercises where students reinforce their understanding of graph connectivity by analysing the "National LambdaRail" network. Finally, we give…

  5. Graphing from Everyday Experience.

    ERIC Educational Resources Information Center

    Carraher, David; Schliemann, Analucia; Nemirousky, Ricardo

    1995-01-01

    Discusses the importance of teaching grounded in the everyday experiences and concerns of the learners. Studies how people with limited school experience can understand graphs and concludes that individuals with limited academic education can clarify the role of everyday experiences in learning about graphs. (ASK)

  6. Making "Photo" Graphs

    ERIC Educational Resources Information Center

    Doto, Julianne; Golbeck, Susan

    2007-01-01

    Collecting data and analyzing the results of experiments is difficult for children. The authors found a surprising way to help their third graders make graphs and draw conclusions from their data: digital photographs. The pictures bridged the gap between an abstract graph and the plants it represented. With the support of the photos, students…

  7. Learning graph matching.

    PubMed

    Caetano, Tibério S; McAuley, Julian J; Cheng, Li; Le, Quoc V; Smola, Alex J

    2009-06-01

    As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the 'labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.

  8. Walking Out Graphs

    ERIC Educational Resources Information Center

    Shen, Ji

    2009-01-01

    In the Walking Out Graphs Lesson described here, students experience several types of representations used to describe motion, including words, sentences, equations, graphs, data tables, and actions. The most important theme of this lesson is that students have to understand the consistency among these representations and form the habit of…

  9. Using Specialized Graph Paper.

    ERIC Educational Resources Information Center

    James, C.

    1988-01-01

    Discusses the use of logarithm and reciprocal graphs in the college physics classroom. Provides examples, such as electrical conductivity, reliability function in the Weibull model, and the Clausius-Clapeyron equation for latent heat of vaporation. Shows graphs with weighting of points. (YP)

  10. ACTIVITIES: Graphs and Games

    ERIC Educational Resources Information Center

    Hirsch, Christian R.

    1975-01-01

    Using a set of worksheets, students will discover and apply Euler's formula regarding connected planar graphs and play and analyze the game of Sprouts. One sheet leads to the discovery of Euler's formula; another concerns traversability of a graph; another gives an example and a game involving these ideas. (Author/KM)

  11. Reflections on "The Graph"

    ERIC Educational Resources Information Center

    Petrosino, Anthony

    2012-01-01

    This article responds to arguments by Skidmore and Thompson (this issue of "Educational Researcher") that a graph published more than 10 years ago was erroneously reproduced and "gratuitously damaged" perceptions of the quality of education research. After describing the purpose of the original graph, the author counters assertions that the graph…

  12. Real World Graph Connectivity

    ERIC Educational Resources Information Center

    Lind, Joy; Narayan, Darren

    2009-01-01

    We present the topic of graph connectivity along with a famous theorem of Menger in the real-world setting of the national computer network infrastructure of "National LambdaRail". We include a set of exercises where students reinforce their understanding of graph connectivity by analysing the "National LambdaRail" network. Finally, we give…

  13. Exploring Graphs: WYSIWYG.

    ERIC Educational Resources Information Center

    Johnson, Millie

    1997-01-01

    Graphs from media sources and questions developed from them can be used in the middle school mathematics classroom. Graphs depict storage temperature on a milk carton; air pressure measurements on a package of shock absorbers; sleep-wake patterns of an infant; a dog's breathing patterns; and the angle, velocity, and radius of a leaning bicyclist…

  14. ACTIVITIES: Graphs and Games

    ERIC Educational Resources Information Center

    Hirsch, Christian R.

    1975-01-01

    Using a set of worksheets, students will discover and apply Euler's formula regarding connected planar graphs and play and analyze the game of Sprouts. One sheet leads to the discovery of Euler's formula; another concerns traversability of a graph; another gives an example and a game involving these ideas. (Author/KM)

  15. Exploring Graphs: WYSIWYG.

    ERIC Educational Resources Information Center

    Johnson, Millie

    1997-01-01

    Graphs from media sources and questions developed from them can be used in the middle school mathematics classroom. Graphs depict storage temperature on a milk carton; air pressure measurements on a package of shock absorbers; sleep-wake patterns of an infant; a dog's breathing patterns; and the angle, velocity, and radius of a leaning bicyclist…

  16. Making "Photo" Graphs

    ERIC Educational Resources Information Center

    Doto, Julianne; Golbeck, Susan

    2007-01-01

    Collecting data and analyzing the results of experiments is difficult for children. The authors found a surprising way to help their third graders make graphs and draw conclusions from their data: digital photographs. The pictures bridged the gap between an abstract graph and the plants it represented. With the support of the photos, students…

  17. Evolutionary stability on graphs.

    PubMed

    Ohtsuki, Hisashi; Nowak, Martin A

    2008-04-21

    Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs. We obtain analytical conditions for regular graphs of degree k > 2. Those theoretical predictions are compared with computer simulations for random regular graphs and for lattices. We study three different update rules: birth-death (BD), death-birth (DB), and imitation (IM) updating. Evolutionary stability on sparse graphs does not imply evolutionary stability in a well-mixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs.

  18. Evolutionary stability on graphs

    PubMed Central

    Ohtsuki, Hisashi; Nowak, Martin A.

    2008-01-01

    Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs. We obtain analytical conditions for regular graphs of degree k > 2. Those theoretical predictions are compared with computer simulations for random regular graphs and for lattices. We study three different update rules: birth-death (BD), death-birth (DB), and imitation (IM) updating. Evolutionary stability on sparse graphs does not imply evolutionary stability in a well-mixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs. PMID:18295801

  19. Reproducibility of graph metrics in FMRI networks.

    PubMed

    Telesford, Qawi K; Morgan, Ashley R; Hayasaka, Satoru; Simpson, Sean L; Barret, William; Kraft, Robert A; Mozolic, Jennifer L; Laurienti, Paul J

    2010-01-01

    The reliability of graph metrics calculated in network analysis is essential to the interpretation of complex network organization. These graph metrics are used to deduce the small-world properties in networks. In this study, we investigated the test-retest reliability of graph metrics from functional magnetic resonance imaging data collected for two runs in 45 healthy older adults. Graph metrics were calculated on data for both runs and compared using intraclass correlation coefficient (ICC) statistics and Bland-Altman (BA) plots. ICC scores describe the level of absolute agreement between two measurements and provide a measure of reproducibility. For mean graph metrics, ICC scores were high for clustering coefficient (ICC = 0.86), global efficiency (ICC = 0.83), path length (ICC = 0.79), and local efficiency (ICC = 0.75); the ICC score for degree was found to be low (ICC = 0.29). ICC scores were also used to generate reproducibility maps in brain space to test voxel-wise reproducibility for unsmoothed and smoothed data. Reproducibility was uniform across the brain for global efficiency and path length, but was only high in network hubs for clustering coefficient, local efficiency, and degree. BA plots were used to test the measurement repeatability of all graph metrics. All graph metrics fell within the limits for repeatability. Together, these results suggest that with exception of degree, mean graph metrics are reproducible and suitable for clinical studies. Further exploration is warranted to better understand reproducibility across the brain on a voxel-wise basis.

  20. Watson-Crick pairing, the Heisenberg group and Milnor invariants.

    PubMed

    Gadgil, Siddhartha

    2009-07-01

    We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.

  1. Cosmological disformal invariance

    SciTech Connect

    Domènech, Guillem; Sasaki, Misao; Naruko, Atsushi E-mail: naruko@th.phys.titech.ac.jp

    2015-10-01

    The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a disformal transformation is made.

  2. Cosmological disformal invariance

    NASA Astrophysics Data System (ADS)

    Domènech, Guillem; Naruko, Atsushi; Sasaki, Misao

    2015-10-01

    The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a disformal transformation is made.

  3. Invariants of polarization transformations.

    PubMed

    Sadjadi, Firooz A

    2007-05-20

    The use of polarization-sensitive sensors is being explored in a variety of applications. Polarization diversity has been shown to improve the performance of the automatic target detection and recognition in a significant way. However, it also brings out the problems associated with processing and storing more data and the problem of polarization distortion during transmission. We present a technique for extracting attributes that are invariant under polarization transformations. The polarimetric signatures are represented in terms of the components of the Stokes vectors. Invariant algebra is then used to extract a set of signature-related attributes that are invariant under linear transformation of the Stokes vectors. Experimental results using polarimetric infrared signatures of a number of manmade and natural objects undergoing systematic linear transformations support the invariancy of these attributes.

  4. Rotational Invariant Dimensionality Reduction Algorithms.

    PubMed

    Lai, Zhihui; Xu, Yong; Yang, Jian; Shen, Linlin; Zhang, David

    2016-06-30

    A common intrinsic limitation of the traditional subspace learning methods is the sensitivity to the outliers and the image variations of the object since they use the L₂ norm as the metric. In this paper, a series of methods based on the L₂,₁-norm are proposed for linear dimensionality reduction. Since the L₂,₁-norm based objective function is robust to the image variations, the proposed algorithms can perform robust image feature extraction for classification. We use different ideas to design different algorithms and obtain a unified rotational invariant (RI) dimensionality reduction framework, which extends the well-known graph embedding algorithm framework to a more generalized form. We provide the comprehensive analyses to show the essential properties of the proposed algorithm framework. This paper indicates that the optimization problems have global optimal solutions when all the orthogonal projections of the data space are computed and used. Experimental results on popular image datasets indicate that the proposed RI dimensionality reduction algorithms can obtain competitive performance compared with the previous L₂ norm based subspace learning algorithms.

  5. Invariance Under Quasi-isometries of Subcritical and Supercritical Behavior in the Boolean Model of Percolation

    NASA Astrophysics Data System (ADS)

    Coletti, Cristian F.; Miranda, Daniel; Mussini, Filipe

    2016-02-01

    In this work we study the Poisson Boolean model of percolation in locally compact Polish metric spaces and we prove the invariance of subcritical and supercritical phases under mm-quasi-isometries. More precisely, we prove that if a metric space M is mm-quasi-isometric to another metric space N and the Poisson Boolean model in M exhibits any of the following: (a) a subcritical phase; (b) a supercritical phase; or (c) a phase transition, then respectively so does the Poisson Boolean model of percolation in N. Then we use these results in order to understand the phase transition phenomenon in a large family of metric spaces. Indeed, we study the Poisson Boolean model of percolation in the context of Riemannian manifolds, in a large family of nilpotent Lie groups and in Cayley graphs. Also, we prove the existence of a subcritical phase in Gromov spaces with bounded growth at some scale.

  6. Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?

    ERIC Educational Resources Information Center

    Öçal, Mehmet Fatih

    2017-01-01

    Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students' learning during graphing functions. However, the display of graphs of functions that students sketched by hand may…

  7. The Effect of Using Graphing Calculators in Complex Function Graphs

    ERIC Educational Resources Information Center

    Ocak, Mehmet Akif

    2008-01-01

    This study investigates the role of graphing calculators in multiple representations for knowledge transfer and the omission of oversimplification in complex function graphs. The main aim is to examine whether graphing calculators were used efficiently to see different cases and multiple perspectives among complex function graphs, or whether…

  8. Explicit Krawtchouk moment invariants for invariant image recognition

    NASA Astrophysics Data System (ADS)

    Xiao, Bin; Zhang, Yanhong; Li, Linping; Li, Weisheng; Wang, Guoyin

    2016-03-01

    The existing Krawtchouk moment invariants are derived by a linear combination of geometric moment invariants. This indirect method cannot achieve perfect performance in rotation, scale, and translation (RST) invariant image recognition since the derivation of these invariants are not built on Krawtchouk polynomials. A direct method to derive RST invariants from Krawtchouk moments, named explicit Krawtchouk moment invariants, is proposed. The proposed method drives Krawtchouk moment invariants by algebraically eliminating the distorted (i.e., rotated, scaled, and translated) factor contained in the Krawtchouk moments of distorted image. Experimental results show that, compared with the indirect methods, the proposed approach can significantly improve the performance in terms of recognition accuracy and noise robustness.

  9. Quadratic Generalized Scale Invariance

    NASA Astrophysics Data System (ADS)

    Lovejoy, S.; Schertzer, D.; Addor, J. B.

    Nearly twenty years ago, two of us argued that in order to account for the scaling strat- ification of the atmosphere, that an anisotropic "unified scaling model" of the atmo- sphere was required with elliptical dimension 23/9=2.555... "in between" the standard 3-D (small scale) and 2-D large scale model. This model was based on the formal- ism of generalized scale invariance (GSI). Physically, GSI is justified by arguing that various conserved fluxes (energy, buoyancy force variance etc.) should define the ap- propriate notion of scale. In a recent large scale satellite cloud image analysis, we directly confirmed this model by studying the isotropic (angle averaged) horizontal cloud statistics. Mathematically, GSI is based on a a group of scale changing opera- tors and their generators but to date, both analyses (primarily of cloud images) and nu- merical (multifractal) simulations, have been limited to the special case of linear GSI. This has shown that cloud texture can plausibly be associated with local linearizations. However realistic morphologies involve spatially avarying textures; the full non linear GSI is clearly necessary. In this talk, we first show that the observed angle averaged (multi)scaling statistics only give a realtively weak constraint on the nonlinear gner- ator: that the latter can be expressed by self-similar (isotropic) part, and a deviatoric part described (in two dimensions) by an arbitrary scalar potential which contains all the information about the cloud morphology. We then show (using a theorem due to Poincaré) how to reduce nonlinear GSI to linear GSI plus a nonlinear coordinate trans- formation numerically, using this to take multifractal GSI modelling to the next level of approximation: quadratic GSI. We show many examples of the coresponding simu- lations which include transitions from various morphologies (including cyclones) and we discuss the results in relation to satellite cloud images.

  10. Tailored Random Graph Ensembles

    NASA Astrophysics Data System (ADS)

    Roberts, E. S.; Annibale, A.; Coolen, A. C. C.

    2013-02-01

    Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.

  11. Reaction spreading on graphs.

    PubMed

    Burioni, Raffaella; Chibbaro, Sergio; Vergni, Davide; Vulpiani, Angelo

    2012-11-01

    We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e., on the time evolution of the reaction product M(t). At variance with pure diffusive processes, characterized by the spectral dimension d{s}, the important quantity for reaction spreading is found to be the connectivity dimension d{l}. Numerical data, in agreement with analytical estimates based on the features of n independent random walkers on the graph, show that M(t)∼t{d{l}}. In the case of Erdös-Renyi random graphs, the reaction product is characterized by an exponential growth M(t)e{αt} with α proportional to ln(k), where (k) is the average degree of the graph.

  12. Radiative-recoil corrections in muonium. Selection of graphs

    SciTech Connect

    Karshenboim, S.G.; Shelyuto, V.A.; Eides, M.I.

    1988-09-01

    A study is made of all graphs containing radiative insertions in the electron line which lead to corrections of the orders ..cap alpha..(Z..cap alpha..)E/sub F/ and ..cap alpha..(Z..cap alpha..)(m/M)E/sub F/ to the hyperfine splitting in muonium. A simple gauge-invariant set of graphs corresponding to these corrections is obtained, a procedure for calculating them is studied, and it is shown that the anomalous magnetic moment does not lead to such corrections.

  13. A Semantic Graph Query Language

    SciTech Connect

    Kaplan, I L

    2006-10-16

    Semantic graphs can be used to organize large amounts of information from a number of sources into one unified structure. A semantic query language provides a foundation for extracting information from the semantic graph. The graph query language described here provides a simple, powerful method for querying semantic graphs.

  14. Assortativity of complementary graphs

    NASA Astrophysics Data System (ADS)

    Wang, H.; Winterbach, W.; van Mieghem, P.

    2011-09-01

    Newman's measure for (dis)assortativity, the linear degree correlationρD, is widely studied although analytic insight into the assortativity of an arbitrary network remains far from well understood. In this paper, we derive the general relation (2), (3) and Theorem 1 between the assortativity ρD(G) of a graph G and the assortativityρD(Gc) of its complement Gc. Both ρD(G) and ρD(Gc) are linearly related by the degree distribution in G. When the graph G(N,p) possesses a binomial degree distribution as in the Erdős-Rényi random graphs Gp(N), its complementary graph Gpc(N) = G1-p(N) follows a binomial degree distribution as in the Erdős-Rényi random graphs G1-p(N). We prove that the maximum and minimum assortativity of a class of graphs with a binomial distribution are asymptotically antisymmetric: ρmax(N,p) = -ρmin(N,p) for N → ∞. The general relation (3) nicely leads to (a) the relation (10) and (16) between the assortativity range ρmax(G)-ρmin(G) of a graph with a given degree distribution and the range ρmax(Gc)-ρmin(Gc) of its complementary graph and (b) new bounds (6) and (15) of the assortativity. These results together with our numerical experiments in over 30 real-world complex networks illustrate that the assortativity range ρmax-ρmin is generally large in sparse networks, which underlines the importance of assortativity as a network characterizer.

  15. Commuting projections on graphs

    SciTech Connect

    Vassilevski, Panayot S.; Zikatanov, Ludmil T.

    2013-02-19

    For a given (connected) graph, we consider vector spaces of (discrete) functions defined on its vertices and its edges. These two spaces are related by a discrete gradient operator, Grad and its adjoint, ₋Div, referred to as (negative) discrete divergence. We also consider a coarse graph obtained by aggregation of vertices of the original one. Then a coarse vertex space is identified with the subspace of piecewise constant functions over the aggregates. We consider the ℓ2-projection QH onto the space of these piecewise constants. In the present paper, our main result is the construction of a projection π H from the original edge-space onto a properly constructed coarse edge-space associated with the edges of the coarse graph. The projections π H and QH commute with the discrete divergence operator, i.e., we have div π H = QH div. The respective pair of coarse edge-space and coarse vertexspace offer the potential to construct two-level, and by recursion, multilevel methods for the mixed formulation of the graph Laplacian which utilizes the discrete divergence operator. The performance of one two-level method with overlapping Schwarz smoothing and correction based on the constructed coarse spaces for solving such mixed graph Laplacian systems is illustrated on a number of graph examples.

  16. Clique graphs and overlapping communities

    NASA Astrophysics Data System (ADS)

    Evans, T. S.

    2010-12-01

    It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of communities or clusters is used to illustrate how a clique graph may be exploited. In particular a benchmark network is shown where clique graphs find the overlapping communities accurately while vertex partition methods fail.

  17. A new, analytic, non-perturbative, gauge-invariant formulation of realistic QCD

    NASA Astrophysics Data System (ADS)

    Fried, H. M.; Grandou, T.; Gabellini, Y.; Sheu, Y.-M.

    2012-09-01

    This Formulation [1], [2], [3] is New, in the sense that it is less than 3 years old. But it could have been done decades ago, since the input information existed, but was overlooked. It is Analytic in the sense that physically-reasonable approximations can be estimated with paper and pencil; and exact amplitudes can be calculated as Meijer G-functions of various orders. It is Non-Perturbative in the sense that sums over all possible gluon exchanges between any pair of quarks and/or antiquarks, including cubic and quartic gluon interactions, are exactly performed. These multiple gluon exchanges combine into "Gluon Bundles" (GBs), as sums over Feynman graphs with finite numbers of exchanged gluons are replaced by "Bundle Graphs". In effect, gluons disappear from the formalism, and GBs remain as the effective carrier of all interactions between quark lines. A simple re-arrangement of the Schwinger/Symanzik functional solution for the Generating Functional of QCD - a rearrangement possible in QCD but not in QED - produces a formal statement of Gauge-Invariance, even though the formulation contains gauge-dependent gluon propagators. After the non-perturbative sums produce GBs, one sees explicit cancelation of all gauge-dependent gluon propagators; gauge-invariance is achieved as gauge-independence. A new insight into Realistic QCD appears in the non-perturbative domain, because quarks do not have individual asymptotic states; they are always asymptotically bound, and their transverse coordinates cannot, in principle, be measured exactly. "Transverse Imprecision" is introduced into the basic Lagrangian, and quark-binding potentials for the construction of mesons and nucleons can then be defined and evaluated. And the greatest surprise of all: A new, non-perturbative property appears, called Effective Locality, with the result that all functional integrals reduce to (a few) sets of ordinary integrals, easy to estimate approximately, or calculate on a desk-top computer. A

  18. A new, analytic, non-perturbative, gauge-invariant formulation of realistic QCD

    SciTech Connect

    Fried, H. M.; Grandou, T.; Gabellini, Y.; Sheu, Y.-M.

    2012-09-26

    This Formulation [1], [2], [3] is New, in the sense that it is less than 3 years old. But it could have been done decades ago, since the input information existed, but was overlooked. It is Analytic in the sense that physically-reasonable approximations can be estimated with paper and pencil; and exact amplitudes can be calculated as Meijer G-functions of various orders. It is Non-Perturbative in the sense that sums over all possible gluon exchanges between any pair of quarks and/or antiquarks, including cubic and quartic gluon interactions, are exactly performed. These multiple gluon exchanges combine into 'Gluon Bundles' (GBs), as sums over Feynman graphs with finite numbers of exchanged gluons are replaced by {sup B}undle Graphs{sup .} In effect, gluons disappear from the formalism, and GBs remain as the effective carrier of all interactions between quark lines. A simple re-arrangement of the Schwinger/Symanzik functional solution for the Generating Functional of QCD - a rearrangement possible in QCD but not in QED - produces a formal statement of Gauge-Invariance, even though the formulation contains gauge-dependent gluon propagators. After the non-perturbative sums produce GBs, one sees explicit cancelation of all gauge-dependent gluon propagators; gauge-invariance is achieved as gauge-independence. A new insight into Realistic QCD appears in the non-perturbative domain, because quarks do not have individual asymptotic states; they are always asymptotically bound, and their transverse coordinates cannot, in principle, be measured exactly. 'Transverse Imprecision' is introduced into the basic Lagrangian, and quark-binding potentials for the construction of mesons and nucleons can then be defined and evaluated. And the greatest surprise of all: A new, non-perturbative property appears, called Effective Locality, with the result that all functional integrals reduce to (a few) sets of ordinary integrals, easy to estimate approximately, or calculate on a desk

  19. Proxy Graph: Visual Quality Metrics of Big Graph Sampling.

    PubMed

    Nguyen, Quan-Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra

    2017-02-24

    Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.

  20. Invariance in vowel systems.

    PubMed

    Funabashi, Masatoshi

    2015-05-01

    This study applies information geometry of normal distribution to model Japanese vowels on the basis of the first and second formants. The distribution of Kullback-Leibler (KL) divergence and its decomposed components were investigated to reveal the statistical invariance in the vowel system. The results suggest that although significant variability exists in individual KL divergence distributions, the population distribution tends to converge into a specific log-normal distribution. This distribution can be considered as an invariant distribution for the standard-Japanese speaking population. Furthermore, it was revealed that the mean and variance components of KL divergence are linearly related in the population distribution. The significance of these invariant features is discussed.

  1. Lattice invariants for knots

    SciTech Connect

    Janse Van Rensburg, E.J.

    1996-12-31

    The geometry of polygonal knots in the cubic lattice may be used to define some knot invariants. One such invariant is the minimal edge number, which is the minimum number of edges necessary (and sufficient) to construct a lattice knot of given type. In addition, one may also define the minimal (unfolded) surface number, and the minimal (unfolded) boundary number; these are the minimum number of 2-cells necessary to construct an unfolded lattice Seifert surface of a given knot type in the lattice, and the minimum number of edges necessary in a lattice knot to guarantee the existence of an unfolded lattice Seifert surface. In addition, I derive some relations amongst these invariants. 8 refs., 5 figs., 2 tabs.

  2. Reparametrization invariant collinear operators

    SciTech Connect

    Marcantonini, Claudio; Stewart, Iain W.

    2009-03-15

    In constructing collinear operators, which describe the production of energetic jets or energetic hadrons, important constraints are provided by reparametrization invariance (RPI). RPI encodes Lorentz invariance in a power expansion about a collinear direction, and connects the Wilson coefficients of operators at different orders in this expansion to all orders in {alpha}{sub s}. We construct reparametrization invariant collinear objects. The expansion of operators built from these objects provides an efficient way of deriving RPI relations and finding a minimal basis of operators, particularly when one has an observable with multiple collinear directions and/or soft particles. Complete basis of operators is constructed for pure glue currents at twist-4, and for operators with multiple collinear directions, including those appearing in e{sup +}e{sup -}{yields}3 jets, and for pp{yields}2 jets initiated via gluon fusion.

  3. GraphPrints: Towards a Graph Analytic Method for Network Anomaly Detection

    SciTech Connect

    Harshaw, Chris R; Bridges, Robert A; Iannacone, Michael D; Reed, Joel W; Goodall, John R

    2016-01-01

    This paper introduces a novel graph-analytic approach for detecting anomalies in network flow data called \\textit{GraphPrints}. Building on foundational network-mining techniques, our method represents time slices of traffic as a graph, then counts graphlets\\textemdash small induced subgraphs that describe local topology. By performing outlier detection on the sequence of graphlet counts, anomalous intervals of traffic are identified, and furthermore, individual IPs experiencing abnormal behavior are singled-out. Initial testing of GraphPrints is performed on real network data with an implanted anomaly. Evaluation shows false positive rates bounded by 2.84\\% at the time-interval level, and 0.05\\% at the IP-level with 100\\% true positive rates at both.

  4. Supersymmetric invariant theories

    NASA Astrophysics Data System (ADS)

    Esipova, S. R.; Lavrov, P. M.; Radchenko, O. V.

    2014-04-01

    We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is a direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.

  5. Multipartite invariant states. II. Orthogonal symmetry

    SciTech Connect

    Chruscinski, Dariusz; Kossakowski, Andrzej

    2006-06-15

    We construct a class of multipartite states possessing orthogonal symmetry. This new class contains multipartite states which are invariant under the action of local unitary operations introduced in our preceding paper [Phys. Rev. A 73, 062314 (2006)]. We study basic properties of multipartite symmetric states: separability criteria and multi-PPT conditions.

  6. A new approach to analytic, non-perturbative and gauge-invariant QCD

    SciTech Connect

    Fried, H.M.; Grandou, T.; Sheu, Y.-M.

    2012-11-15

    Following a previous calculation of quark scattering in eikonal approximation, this paper presents a new, analytic and rigorous approach to the calculation of QCD phenomena. In this formulation a basic distinction between the conventional 'idealistic' description of QCD and a more 'realistic' description is brought into focus by a non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of the exact Fradkin representations of Green's functional G{sub c}(x,y|A) and the vacuum functional L[A]. Because quarks exist asymptotically only in bound states, their transverse coordinates can never be measured with arbitrary precision; the non-perturbative neglect of this statement leads to obstructions that are easily corrected by invoking in the basic Lagrangian a probability amplitude which describes such transverse imprecision. The second result of this non-perturbative analysis is the appearance of a new and simplifying output called 'Effective Locality', in which the interactions between quarks by the exchange of a 'gluon bundle'-which 'bundle' contains an infinite number of gluons, including cubic and quartic gluon interactions-display an exact locality property that reduces the several functional integrals of the formulation down to a set of ordinary integrals. It should be emphasized that 'non-perturbative' here refers to the effective summation of all gluons between a pair of quark lines-which may be the same quark line, as in a self-energy graph-but does not (yet) include a summation over all closed-quark loops which are tied by gluon-bundle exchange to the rest of the 'Bundle Diagram'. As an example of the power of these methods we offer as a first analytic calculation the quark-antiquark binding potential of a pion, and the corresponding three-quark binding potential of a nucleon, obtained in a simple way from relevant eikonal scattering approximations. A second calculation, analytic, non-perturbative and

  7. Internet topology: connectivity of IP graphs

    NASA Astrophysics Data System (ADS)

    Broido, Andre; claffy, kc

    2001-07-01

    In this paper we introduce a framework for analyzing local properties of Internet connectivity. We compare BGP and probed topology data, finding that currently probed topology data yields much denser coverage of AS-level connectivity. We describe data acquisition and construction of several IP- level graphs derived from a collection of 220 M skitter traceroutes. We find that a graph consisting of IP nodes and links contains 90.5% of its 629 K nodes in the acyclic subgraph. In particular, 55% of the IP nodes are in trees. Full bidirectional connectivity is observed for a giant component containing 8.3% of IP nodes.

  8. Optimized Graph Search Using Multi-Level Graph Clustering

    NASA Astrophysics Data System (ADS)

    Kala, Rahul; Shukla, Anupam; Tiwari, Ritu

    Graphs find a variety of use in numerous domains especially because of their capability to model common problems. The social networking graphs that are used for social networking analysis, a feature given by various social networking sites are an example of this. Graphs can also be visualized in the search engines to carry search operations and provide results. Various searching algorithms have been developed for searching in graphs. In this paper we propose that the entire network graph be clustered. The larger graphs are clustered to make smaller graphs. These smaller graphs can again be clustered to further reduce the size of graph. The search is performed on the smallest graph to identify the general path, which may be further build up to actual nodes by working on the individual clusters involved. Since many searches are carried out on the same graph, clustering may be done once and the data may be used for multiple searches over the time. If the graph changes considerably, only then we may re-cluster the graph.

  9. Filtering Random Graph Processes Over Random Time-Varying Graphs

    NASA Astrophysics Data System (ADS)

    Isufi, Elvin; Loukas, Andreas; Simonetto, Andrea; Leus, Geert

    2017-08-01

    Graph filters play a key role in processing the graph spectra of signals supported on the vertices of a graph. However, despite their widespread use, graph filters have been analyzed only in the deterministic setting, ignoring the impact of stochastic- ity in both the graph topology as well as the signal itself. To bridge this gap, we examine the statistical behavior of the two key filter types, finite impulse response (FIR) and autoregressive moving average (ARMA) graph filters, when operating on random time- varying graph signals (or random graph processes) over random time-varying graphs. Our analysis shows that (i) in expectation, the filters behave as the same deterministic filters operating on a deterministic graph, being the expected graph, having as input signal a deterministic signal, being the expected signal, and (ii) there are meaningful upper bounds for the variance of the filter output. We conclude the paper by proposing two novel ways of exploiting randomness to improve (joint graph-time) noise cancellation, as well as to reduce the computational complexity of graph filtering. As demonstrated by numerical results, these methods outperform the disjoint average and denoise algorithm, and yield a (up to) four times complexity redution, with very little difference from the optimal solution.

  10. Metric Ranking of Invariant Networks with Belief Propagation

    SciTech Connect

    Tao, Changxia; Ge, Yong; Song, Qinbao; Ge, Yuan; Omitaomu, Olufemi A

    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.

  11. Riemann quasi-invariants

    SciTech Connect

    Pokhozhaev, Stanislav I

    2011-06-30

    The notion of Riemann quasi-invariants is introduced and their applications to several conservation laws are considered. The case of nonisentropic flow of an ideal polytropic gas is analysed in detail. Sufficient conditions for gradient catastrophes are obtained. Bibliography: 16 titles.

  12. Modular invariant inflation

    SciTech Connect

    Kobayashi, Tatsuo; Nitta, Daisuke; Urakawa, Yuko

    2016-08-08

    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{sub ht}, but it also has a non-negligible deviation from V{sub ht}. 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.

  13. Modular invariant gaugino condensation

    SciTech Connect

    Gaillard, M.K.

    1991-05-09

    The construction of effective supergravity lagrangians for gaugino condensation is reviewed and recent results are presented that are consistent with modular invariance and yield a positive definite potential of the noscale type. Possible implications for phenomenology are briefly discussed. 29 refs.

  14. Modular invariant inflation

    NASA Astrophysics Data System (ADS)

    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.

  15. Integral Invariant Signatures

    DTIC Science & Technology

    2004-05-01

    change under the various nui- sances of image formation and viewing geometry was appealing; it held potential for application to recognition...Springer, 1990. 29. S. Z. Li. Shape matching based on invariants. In O. M. Omidvar (ed.), editor, Progress in Neural Networks : Shape Recognition, volume 6

  16. Idiographic Measurement Invariance?

    ERIC Educational Resources Information Center

    Willoughby, Michael T.; Sideris, John

    2007-01-01

    In this article, the authors comment on Nesselroade, Gerstorf, Hardy, and Ram's efforts (this issue) to grapple with the challenge of accommodating idiographic assessment as it pertains to measurement invariance (MI). Although the authors are in complete agreement with the motivation for Nesselroade et al.'s work, the authors have concerns about…

  17. Equivariant K3 invariants

    SciTech Connect

    Cheng, Miranda C. N.; Duncan, John F. R.; Harrison, Sarah M.; Kachru, Shamit

    2017-01-01

    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–Hohenegger–Volpato, and one may consider corresponding equivariant refined K3 Gopakumar–Vafa invariants. The same symmetries naturally arise in the auxiliary CFT state space, affording a suggestive alternative view of the same computation. We comment on a lift of this story to the generating function of elliptic genera of symmetric products of K3 surfaces.

  18. Equivariant K3 invariants

    DOE PAGES

    Cheng, Miranda C. N.; Duncan, John F. R.; Harrison, Sarah M.; ...

    2017-01-01

    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 ofmore » 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–Hohenegger–Volpato, and one may consider corresponding equivariant refined K3 Gopakumar–Vafa invariants. The same symmetries naturally arise in the auxiliary CFT state space, affording a suggestive alternative view of the same computation. We comment on a lift of this story to the generating function of elliptic genera of symmetric products of K3 surfaces.« less

  19. The order of a homotopy invariant in the stable case

    NASA Astrophysics Data System (ADS)

    Podkorytov, Semen S.

    2011-08-01

    Let X, Y be cell complexes, let U be an Abelian group, and let f\\colon \\lbrack X,Y \\rbrack \\to U be a homotopy invariant. By definition, the invariant f has order at most r if the characteristic function of the rth Cartesian power of the graph of a continuous map a\\colon X\\to Y determines the value f( \\lbrack a \\rbrack ) {Z}-linearly. It is proved that, in the stable case (that is, when \\operatorname{dim} X<2n-1, and Y is (n-1)-connected for some natural number n), for a finite cell complex X the order of the invariant f is equal to its degree with respect to the Curtis filtration of the group \\lbrack X,Y \\rbrack . Bibliography: 9 titles.

  20. Invariant measures on multimode quantum Gaussian states

    SciTech Connect

    Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.

    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.

  1. Invariant measures on multimode quantum Gaussian states

    NASA Astrophysics Data System (ADS)

    Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.

    2012-12-01

    We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

  2. Subdominant pseudoultrametric on graphs

    SciTech Connect

    Dovgoshei, A A; Petrov, E A

    2013-08-31

    Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.

  3. Quantum ergodicity on graphs.

    PubMed

    Gnutzmann, S; Keating, J P; Piotet, F

    2008-12-31

    We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for large well-connected graphs. We use an exact field-theoretic expression in terms of a variant of the supersymmetric nonlinear sigma model. Our estimate is based on a saddle-point analysis of this expression and leads to a criterion for when equidistribution emerges asymptotically in the limit of large graphs. Our theory predicts a rate of convergence that is a significant refinement of previous estimates, long assumed to be valid for quantum chaotic systems, agreeing with them in some situations but not all. We discuss specific examples for which the theory is tested numerically.

  4. Quantum Ergodicity on Graphs

    SciTech Connect

    Gnutzmann, S.; Keating, J. P.; Piotet, F.

    2008-12-31

    We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for large well-connected graphs. We use an exact field-theoretic expression in terms of a variant of the supersymmetric nonlinear {sigma} model. Our estimate is based on a saddle-point analysis of this expression and leads to a criterion for when equidistribution emerges asymptotically in the limit of large graphs. Our theory predicts a rate of convergence that is a significant refinement of previous estimates, long assumed to be valid for quantum chaotic systems, agreeing with them in some situations but not all. We discuss specific examples for which the theory is tested numerically.

  5. Heuristic Traversal Of A Free Space Graph

    NASA Astrophysics Data System (ADS)

    Holmes, Peter D.; Jungert, Erland

    1989-01-01

    In order to plan paths within a physical working space, effective data structures must be used for spatial representation. A free space graph is a data structure derived from a systematic decomposition of the unobstructed portions of the working space. For the two-dimensional case, this work describes an heuristic method for traversal and search of one particular type of free space graph. The focus herein regards the "dialogue" between an A* search process and an inference engine whose rules employ spatial operators for classification of local topologies within the free space graph. This knowledge-based technique is used to generate plans which describe admissible sequences of movement between selected start and goal configurations.

  6. Computing Role Assignments of Proper Interval Graphs in Polynomial Time

    NASA Astrophysics Data System (ADS)

    Heggernes, Pinar; van't Hof, Pim; Paulusma, Daniël

    A homomorphism from a graph G to a graph R is locally surjective if its restriction to the neighborhood of each vertex of G is surjective. Such a homomorphism is also called an R-role assignment of G. Role assignments have applications in distributed computing, social network theory, and topological graph theory. The Role Assignment problem has as input a pair of graphs (G,R) and asks whether G has an R-role assignment. This problem is NP-complete already on input pairs (G,R) where R is a path on three vertices. So far, the only known non-trivial tractable case consists of input pairs (G,R) where G is a tree. We present a polynomial time algorithm that solves Role Assignment on all input pairs (G,R) where G is a proper interval graph. Thus we identify the first graph class other than trees on which the problem is tractable. As a complementary result, we show that the problem is Graph Isomorphism-hard on chordal graphs, a superclass of proper interval graphs and trees.

  7. Graphing Calculator Mini Course

    NASA Technical Reports Server (NTRS)

    Karnawat, Sunil R.

    1996-01-01

    The "Graphing Calculator Mini Course" project provided a mathematically-intensive technologically-based summer enrichment workshop for teachers of American Indian students on the Turtle Mountain Indian Reservation. Eleven such teachers participated in the six-day workshop in summer of 1996 and three Sunday workshops in the academic year. The project aimed to improve science and mathematics education on the reservation by showing teachers effective ways to use high-end graphing calculators as teaching and learning tools in science and mathematics courses at all levels. In particular, the workshop concentrated on applying TI-82's user-friendly features to understand the various mathematical and scientific concepts.

  8. Invariant object recognition based on extended fragments.

    PubMed

    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.

  9. Measurement Invariance versus Selection Invariance: Is Fair Selection Possible?

    ERIC Educational Resources Information Center

    Borsman, 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 instrument is used and group differences are present in…

  10. Measurement Invariance versus Selection Invariance: Is Fair Selection Possible?

    ERIC Educational Resources Information Center

    Borsman, 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 instrument is used and group differences are present in…

  11. Gauge-Invariant Formulation of Circular Dichroism.

    PubMed

    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.

  12. Robust deformable and occluded object tracking with dynamic graph.

    PubMed

    Cai, Zhaowei; Wen, Longyin; Lei, Zhen; Vasconcelos, Nuno; Li, Stan Z

    2014-12-01

    While some efforts have been paid to handle deformation and occlusion in visual tracking, they are still great challenges. In this paper, a dynamic graph-based tracker (DGT) is proposed to address these two challenges in a unified framework. In the dynamic target graph, nodes are the target local parts encoding appearance information, and edges are the interactions between nodes encoding inner geometric structure information. This graph representation provides much more information for tracking in the presence of deformation and occlusion. The target tracking is then formulated as tracking this dynamic undirected graph, which is also a matching problem between the target graph and the candidate graph. The local parts within the candidate graph are separated from the background with Markov random field, and spectral clustering is used to solve the graph matching. The final target state is determined through a weighted voting procedure according to the reliability of part correspondence, and refined with recourse to a foreground/background segmentation. An effective online updating mechanism is proposed to update the model, allowing DGT to robustly adapt to variations of target structure. Experimental results show improved performance over several state-of-the-art trackers, in various challenging scenarios.

  13. Dimensionless, Scale Invariant, Edge Weight Metric for the Study of Complex Structural Networks.

    PubMed

    Colon-Perez, Luis M; Spindler, Caitlin; Goicochea, Shelby; Triplett, William; Parekh, Mansi; Montie, Eric; Carney, Paul R; Price, Catherine; Mareci, Thomas H

    2015-01-01

    High spatial and angular resolution diffusion weighted imaging (DWI) with network analysis provides a unique framework for the study of brain structure in vivo. DWI-derived brain connectivity patterns are best characterized with graph theory using an edge weight to quantify the strength of white matter connections between gray matter nodes. Here a dimensionless, scale-invariant edge weight is introduced to measure node connectivity. This edge weight metric provides reasonable and consistent values over any size scale (e.g. rodents to humans) used to quantify the strength of connection. Firstly, simulations were used to assess the effects of tractography seed point density and random errors in the estimated fiber orientations; with sufficient signal-to-noise ratio (SNR), edge weight estimates improve as the seed density increases. Secondly to evaluate the application of the edge weight in the human brain, ten repeated measures of DWI in the same healthy human subject were analyzed. Mean edge weight values within the cingulum and corpus callosum were consistent and showed low variability. Thirdly, using excised rat brains to study the effects of spatial resolution, the weight of edges connecting major structures in the temporal lobe were used to characterize connectivity in this local network. The results indicate that with adequate resolution and SNR, connections between network nodes are characterized well by this edge weight metric. Therefore this new dimensionless, scale-invariant edge weight metric provides a robust measure of network connectivity that can be applied in any size regime.

  14. Dimensionless, Scale Invariant, Edge Weight Metric for the Study of Complex Structural Networks

    PubMed Central

    Colon-Perez, Luis M.; Spindler, Caitlin; Goicochea, Shelby; Triplett, William; Parekh, Mansi; Montie, Eric; Carney, Paul R.; Price, Catherine; Mareci, Thomas H.

    2015-01-01

    High spatial and angular resolution diffusion weighted imaging (DWI) with network analysis provides a unique framework for the study of brain structure in vivo. DWI-derived brain connectivity patterns are best characterized with graph theory using an edge weight to quantify the strength of white matter connections between gray matter nodes. Here a dimensionless, scale-invariant edge weight is introduced to measure node connectivity. This edge weight metric provides reasonable and consistent values over any size scale (e.g. rodents to humans) used to quantify the strength of connection. Firstly, simulations were used to assess the effects of tractography seed point density and random errors in the estimated fiber orientations; with sufficient signal-to-noise ratio (SNR), edge weight estimates improve as the seed density increases. Secondly to evaluate the application of the edge weight in the human brain, ten repeated measures of DWI in the same healthy human subject were analyzed. Mean edge weight values within the cingulum and corpus callosum were consistent and showed low variability. Thirdly, using excised rat brains to study the effects of spatial resolution, the weight of edges connecting major structures in the temporal lobe were used to characterize connectivity in this local network. The results indicate that with adequate resolution and SNR, connections between network nodes are characterized well by this edge weight metric. Therefore this new dimensionless, scale-invariant edge weight metric provides a robust measure of network connectivity that can be applied in any size regime. PMID:26173147

  15. Markov invariants, plethysms, and phylogenetics.

    PubMed

    Sumner, J G; Charleston, M A; Jermiin, L S; Jarvis, P D

    2008-08-07

    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 analyzing 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.

  16. Graph ensemble boosting for imbalanced noisy graph stream classification.

    PubMed

    Pan, Shirui; Wu, Jia; Zhu, Xingquan; Zhang, Chengqi

    2015-05-01

    Many applications involve stream data with structural dependency, graph representations, and continuously increasing volumes. For these applications, it is very common that their class distributions are imbalanced with minority (or positive) samples being only a small portion of the population, which imposes significant challenges for learning models to accurately identify minority samples. This problem is further complicated with the presence of noise, because they are similar to minority samples and any treatment for the class imbalance may falsely focus on the noise and result in deterioration of accuracy. In this paper, we propose a classification model to tackle imbalanced graph streams with noise. Our method, graph ensemble boosting, employs an ensemble-based framework to partition graph stream into chunks each containing a number of noisy graphs with imbalanced class distributions. For each individual chunk, we propose a boosting algorithm to combine discriminative subgraph pattern selection and model learning as a unified framework for graph classification. To tackle concept drifting in graph streams, an instance level weighting mechanism is used to dynamically adjust the instance weight, through which the boosting framework can emphasize on difficult graph samples. The classifiers built from different graph chunks form an ensemble for graph stream classification. Experiments on real-life imbalanced graph streams demonstrate clear benefits of our boosting design for handling imbalanced noisy graph stream.

  17. Ancestral recombinations graph: a reconstructability perspective using random-graphs framework.

    PubMed

    Parida, Laxmi

    2010-10-01

    We present a random graphs framework to study pedigree history in an ideal (Wright Fisher) population. This framework correlates the underlying mathematical objects in, for example, pedigree graph, mtDNA or NRY Chr tree, ARG (Ancestral Recombinations Graph), and HUD used in literature, into a single unified random graph framework. It also gives a natural definition, based solely on the topology, of an ARG, one of the most interesting as well as useful mathematical objects in this area. The random graphs framework gives an alternative parametrization of the ARG that does not use the recombination rate q and instead uses a parameter M based on the (estimate of ) the number of non-mixing segments in the extant units. This seems more natural in a setting that attempts to tease apart the population dynamics from the biology of the units. This framework also gives a purely topological definition of GMRCA, analogous to MRCA on trees (which has a purely topological description i.e., it is a root, graph-theoretically speaking, of a tree). Secondly, with a natural extension of the ideas from random-graphs we present a sampling (simulation) algorithm to construct random instances of ARG/unilinear transmission graph. This is the first (to the best of the author's knowledge) algorithm that guarantees uniform sampling of the space of ARG instances, reflecting the ideal population model. Finally, using a measure of reconstructability of the past historical events given a collection of extant sequences, we conclude for a given set of extant sequences, the joint history of local segments along a chromosome is reconstructible.

  18. Line Graph Learning

    ERIC Educational Resources Information Center

    Pitts Bannister, Vanessa R.; Jamar, Idorenyin; Mutegi, Jomo W.

    2007-01-01

    In this article, the learning progress of one fifth-grade student is examined with regard to the development of her graph interpretation skills as she participated in the Junior Science Institute (JSI), a two-week, science intensive summer camp in which participants engaged in microbiology research and application. By showcasing the student's…

  19. Cookies and Graphs

    ERIC Educational Resources Information Center

    Cooper, Carol

    1975-01-01

    Teachers of an integrated elementary classroom used cookie-sharing time as a learning experience for students. Responsible for dividing varying amounts of cookies daily, the students learned to translate their experiences to graphs of differing sophistication and analyses. Further interpretation and application were done by individual students…

  20. Body Motion and Graphing.

    ERIC Educational Resources Information Center

    Nemirovsky, Ricardo; Tierney, Cornelia; Wright, Tracy

    1998-01-01

    Analyzed two children's use of a computer-based motion detector to make sense of symbolic expressions (Cartesian graphs). Found three themes: (1) tool perspectives, efforts to understand graphical responses to body motion; (2) fusion, emergent ways of talking and behaving that merge symbols and referents; and (3) graphical spaces, when changing…

  1. Straight Line Graphs

    ERIC Educational Resources Information Center

    Krueger, Tom

    2010-01-01

    In this article, the author shares one effective lesson idea on straight line graphs that he applied in his lower ability Y9 class. The author wanted something interesting for his class to do, something that was fun and engaging with direct feedback, and something that worked because someone else had tried it before. In a word, the author admits…

  2. Hidden Behavior in Graphs.

    ERIC Educational Resources Information Center

    Donley, H. Edward; George, Elizabeth Ann

    1993-01-01

    Demonstrates how to construct rational, exponential, and sinusoidal functions that appear normal on one scale but exhibit interesting hidden behavior when viewed on another scale. By exploring these examples, students learn the importance of scale, window size, and resolution effects in computer and calculator graphing. (MAZ)

  3. Line Graph Learning

    ERIC Educational Resources Information Center

    Pitts Bannister, Vanessa R.; Jamar, Idorenyin; Mutegi, Jomo W.

    2007-01-01

    In this article, the learning progress of one fifth-grade student is examined with regard to the development of her graph interpretation skills as she participated in the Junior Science Institute (JSI), a two-week, science intensive summer camp in which participants engaged in microbiology research and application. By showcasing the student's…

  4. GraphLib

    SciTech Connect

    2013-02-19

    This library is used in several LLNL projects, including STAT (the Stack Trace Analysis Tool for scalable debugging) and some modules in P^nMPI (a tool MPI tool infrastructure). It can also be used standalone for creating and manipulationg graphs, but its API is primarily tuned to support these other projects

  5. Graph-theoretical exorcism

    SciTech Connect

    Simmons, G.J.

    1985-01-01

    Given a graph G and an ordering phi of the vertices, V(G), we define a parsimonious proper coloring (PPC) of V(G) under phi to be a proper coloring of V(G) in the order phi, where a new color is introduced only when a vertex cannot be properly colored in its order with any of the colors already used.

  6. Coloring geographical threshold graphs

    SciTech Connect

    Bradonjic, Milan; Percus, Allon; Muller, Tobias

    2008-01-01

    We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.

  7. Introduction to Graphing.

    ERIC Educational Resources Information Center

    Sokol, William

    In this autoinstructional packet, the student is given an experimental situation which introduces him to the process of graphing. The lesson is presented for secondary school students in chemistry. Algebra I and a Del Mod System program (indicated as SE 018 020) are suggested prerequisites for the use of this program. Behavioral objectives are…

  8. Straight Line Graphs

    ERIC Educational Resources Information Center

    Krueger, Tom

    2010-01-01

    In this article, the author shares one effective lesson idea on straight line graphs that he applied in his lower ability Y9 class. The author wanted something interesting for his class to do, something that was fun and engaging with direct feedback, and something that worked because someone else had tried it before. In a word, the author admits…

  9. Feature Tracking Using Reeb Graphs

    SciTech Connect

    Weber, Gunther H.; Bremer, Peer-Timo; Day, Marcus S.; Bell, John B.; Pascucci, Valerio

    2010-08-02

    Tracking features and exploring their temporal dynamics can aid scientists in identifying interesting time intervals in a simulation and serve as basis for performing quantitative analyses of temporal phenomena. In this paper, we develop a novel approach for tracking subsets of isosurfaces, such as burning regions in simulated flames, which are defined as areas of high fuel consumption on a temperature isosurface. Tracking such regions as they merge and split over time can provide important insights into the impact of turbulence on the combustion process. However, the convoluted nature of the temperature isosurface and its rapid movement make this analysis particularly challenging. Our approach tracks burning regions by extracting a temperature isovolume from the four-dimensional space-time temperature field. It then obtains isosurfaces for the original simulation time steps and labels individual connected 'burning' regions based on the local fuel consumption value. Based on this information, a boundary surface between burning and non-burning regions is constructed. The Reeb graph of this boundary surface is the tracking graph for burning regions.

  10. Multithreaded Algorithms for Graph Coloring

    SciTech Connect

    Catalyurek, Umit V.; Feo, John T.; Gebremedhin, Assefaw H.; Halappanavar, Mahantesh; Pothen, Alex

    2012-10-21

    Graph algorithms are challenging to parallelize when high performance and scalability are primary goals. Low concurrency, poor data locality, irregular access pattern, and high data access to computation ratio are among the chief reasons for the challenge. The performance implication of these features is exasperated on distributed memory machines. More success is being achieved on shared-memory, multi-core architectures supporting multithreading. We consider a prototypical graph problem, coloring, and show how a greedy algorithm for solving it can be e*ectively parallelized on multithreaded architectures. We present in particular two di*erent parallel algorithms. The first relies on speculation and iteration, and is suitable for any shared-memory, multithreaded system. The second uses data ow principles and is targeted at the massively multithreaded Cray XMT system. We benchmark the algorithms on three di*erent platforms and demonstrate scalable runtime performance. In terms of quality of solution, both algorithms use nearly the same number of colors as the serial algorithm.

  11. Quantum walks on quotient graphs

    SciTech Connect

    Krovi, Hari; Brun, Todd A.

    2007-06-15

    A discrete-time quantum walk on a graph {gamma} is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup.

  12. Temporal Representation in Semantic Graphs

    SciTech Connect

    Levandoski, J J; Abdulla, G M

    2007-08-07

    A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.

  13. Invariance and Objectivity

    NASA Astrophysics Data System (ADS)

    Vollmer, Gerhard

    2010-10-01

    Scientific knowledge should not only be true, it should be as objective as possible. It should refer to a reality independent of any subject. What can we use as a criterion of objectivity? Intersubjectivity (i.e., intersubjective understandability and intersubjective testability) is necessary, but not sufficient. Other criteria are: independence of reference system, independence of method, non-conventionality. Is there some common trait? Yes, there is: invariance under some specified transformations. Thus, we say: A proposition is objective only if its truth is invariant against a change in the conditions under which it was formulated. We give illustrations from geometry, perception, neurobiology, relativity theory, and quantum theory. Such an objectivist position has many advantages.

  14. A Complete Set of Invariants for LU-Equivalence of Density Operators

    NASA Astrophysics Data System (ADS)

    Turner, Jacob; Morton, Jason

    2017-05-01

    We show that two density operators of mixed quantum states are in the same local unitary orbit if and only if they agree on polynomial invariants in a certain Noetherian ring for which degree bounds are known in the literature. This implicitly gives a finite complete set of invariants for local unitary equivalence. This is done by showing that local unitary equivalence of density operators is equivalent to local GL equivalence and then using techniques from algebraic geometry and geometric invariant theory. We also classify the SLOCC polynomial invariants and give a degree bound for generators of the invariant ring in the case of n-qubit pure states. Of course it is well known that polynomial invariants are not a complete set of invariants for SLOCC.

  15. A Clustering Graph Generator

    SciTech Connect

    Winlaw, Manda; De Sterck, Hans; Sanders, Geoffrey

    2015-10-26

    In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.

  16. Quantum groups with invariant integrals

    PubMed Central

    Van Daele, Alfons

    2000-01-01

    Quantum groups have been studied intensively for the last two decades from various points of view. The underlying mathematical structure is that of an algebra with a coproduct. Compact quantum groups admit Haar measures. However, if we want to have a Haar measure also in the noncompact case, we are forced to work with algebras without identity, and the notion of a coproduct has to be adapted. These considerations lead to the theory of multiplier Hopf algebras, which provides the mathematical tool for studying noncompact quantum groups with Haar measures. I will concentrate on the *-algebra case and assume positivity of the invariant integral. Doing so, I create an algebraic framework that serves as a model for the operator algebra approach to quantum groups. Indeed, the theory of locally compact quantum groups can be seen as the topological version of the theory of quantum groups as they are developed here in a purely algebraic context. PMID:10639115

  17. Mining and Indexing Graph Databases

    ERIC Educational Resources Information Center

    Yuan, Dayu

    2013-01-01

    Graphs are widely used to model structures and relationships of objects in various scientific and commercial fields. Chemical molecules, proteins, malware system-call dependencies and three-dimensional mechanical parts are all modeled as graphs. In this dissertation, we propose to mine and index those graph data to enable fast and scalable search.…

  18. Recursive Feature Extraction in Graphs

    SciTech Connect

    2014-08-14

    ReFeX extracts recursive topological features from graph data. The input is a graph as a csv file and the output is a csv file containing feature values for each node in the graph. The features are based on topological counts in the neighborhoods of each nodes, as well as recursive summaries of neighbors' features.

  19. Mining and Indexing Graph Databases

    ERIC Educational Resources Information Center

    Yuan, Dayu

    2013-01-01

    Graphs are widely used to model structures and relationships of objects in various scientific and commercial fields. Chemical molecules, proteins, malware system-call dependencies and three-dimensional mechanical parts are all modeled as graphs. In this dissertation, we propose to mine and index those graph data to enable fast and scalable search.…

  20. Topic Model for Graph Mining.

    PubMed

    Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Luo, Xiangfeng

    2015-12-01

    Graph mining has been a popular research area because of its numerous application scenarios. Many unstructured and structured data can be represented as graphs, such as, documents, chemical molecular structures, and images. However, an issue in relation to current research on graphs is that they cannot adequately discover the topics hidden in graph-structured data which can be beneficial for both the unsupervised learning and supervised learning of the graphs. Although topic models have proved to be very successful in discovering latent topics, the standard topic models cannot be directly applied to graph-structured data due to the "bag-of-word" assumption. In this paper, an innovative graph topic model (GTM) is proposed to address this issue, which uses Bernoulli distributions to model the edges between nodes in a graph. It can, therefore, make the edges in a graph contribute to latent topic discovery and further improve the accuracy of the supervised and unsupervised learning of graphs. The experimental results on two different types of graph datasets show that the proposed GTM outperforms the latent Dirichlet allocation on classification by using the unveiled topics of these two models to represent graphs.

  1. Kevin Bacon and Graph Theory

    ERIC Educational Resources Information Center

    Hopkins, Brian

    2004-01-01

    The interconnected world of actors and movies is a familiar, rich example for graph theory. This paper gives the history of the "Kevin Bacon Game" and makes extensive use of a Web site to analyze the underlying graph. The main content is the classroom development of the weighted average to determine the best choice of "center" for the graph. The…

  2. A Note on Hamiltonian Graphs

    ERIC Educational Resources Information Center

    Skurnick, Ronald; Davi, Charles; Skurnick, Mia

    2005-01-01

    Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…

  3. A Note on Hamiltonian Graphs

    ERIC Educational Resources Information Center

    Skurnick, Ronald; Davi, Charles; Skurnick, Mia

    2005-01-01

    Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…

  4. Kevin Bacon and Graph Theory

    ERIC Educational Resources Information Center

    Hopkins, Brian

    2004-01-01

    The interconnected world of actors and movies is a familiar, rich example for graph theory. This paper gives the history of the "Kevin Bacon Game" and makes extensive use of a Web site to analyze the underlying graph. The main content is the classroom development of the weighted average to determine the best choice of "center" for the graph. The…

  5. View Invariant Gait Recognition

    NASA Astrophysics Data System (ADS)

    Seely, Richard D.; Goffredo, Michela; Carter, John N.; Nixon, Mark S.

    Recognition by gait is of particular interest since it is the biometric that is available at the lowest resolution, or when other biometrics are (intentionally) obscured. Gait as a biometric has now shown increasing recognition capability. There are many approaches and these show that recognition can achieve excellent performance on current large databases. The majority of these approaches are planar 2D, largely since the early large databases featured subjects walking in a plane normal to the camera view. To extend deployment capability, we need viewpoint invariant gait biometrics. We describe approaches where viewpoint invariance is achieved by 3D approaches or in 2D. In the first group, the identification relies on parameters extracted from the 3D body deformation during walking. These methods use several video cameras and the 3D reconstruction is achieved after a camera calibration process. On the other hand, the 2D gait biometric approaches use a single camera, usually positioned perpendicular to the subject’s walking direction. Because in real surveillance scenarios a system that operates in an unconstrained environment is necessary, many of the recent gait analysis approaches are orientated toward view-invariant gait recognition.

  6. Fitness landscapes, memetic algorithms, and greedy operators for graph bipartitioning.

    PubMed

    Merz, P; Freisleben, B

    2000-01-01

    The fitness landscape of the graph bipartitioning problem is investigated by performing a search space analysis for several types of graphs. The analysis shows that the structure of the search space is significantly different for the types of instances studied. Moreover, with increasing epistasis, the amount of gene interactions in the representation of a solution in an evolutionary algorithm, the number of local minima for one type of instance decreases and, thus, the search becomes easier. We suggest that other characteristics besides high epistasis might have greater influence on the hardness of a problem. To understand these characteristics, the notion of a dependency graph describing gene interactions is introduced. In particular, the local structure and the regularity of the dependency graph seems to be important for the performance of an algorithm, and in fact, algorithms that exploit these properties perform significantly better than others which do not. It will be shown that a simple hybrid multi-start local search exploiting locality in the structure of the graphs is able to find optimum or near optimum solutions very quickly. However, if the problem size increases or the graphs become unstructured, a memetic algorithm (a genetic algorithm incorporating local search) is shown to be much more effective.

  7. Data Structures and Algorithms for Graph Based Remote Sensed Image Content Storage and Retrieval

    SciTech Connect

    Grant, C W

    2004-06-24

    The Image Content Engine (ICE) project at Lawrence Livermore National Laboratory (LLNL) extracts, stores and allows queries of image content on multiple levels. ICE is designed for multiple application domains. The domain explored in this work is aerial and satellite surveillance imagery. The highest level of semantic information used in ICE is graph based. After objects are detected and classified, they are grouped based in their interrelations. The graph representing a locally related set of objects is called a 'graphlet'. Graphlets are interconnected into a larger graph which covers an entire set of images. Queries based on graph properties are notoriously difficult due the inherent complexity of the graph isomorphism and sub-graph isomorphism problems. ICE exploits limitations in graph and query structure and uses a set of auxiliary data structures to quickly process a useful set of graph based queries. These queries could not be processed using semantically lower level (tile and object based) queries.

  8. What is a complex graph?

    NASA Astrophysics Data System (ADS)

    Kim, Jongkwang; Wilhelm, Thomas

    2008-04-01

    Many papers published in recent years show that real-world graphs G(n,m) ( n nodes, m edges) are more or less “complex” in the sense that different topological features deviate from random graphs. Here we narrow the definition of graph complexity and argue that a complex graph contains many different subgraphs. We present different measures that quantify this complexity, for instance C1e, the relative number of non-isomorphic one-edge-deleted subgraphs (i.e. DECK size). However, because these different subgraph measures are computationally demanding, we also study simpler complexity measures focussing on slightly different aspects of graph complexity. We consider heuristically defined “product measures”, the products of two quantities which are zero in the extreme cases of a path and clique, and “entropy measures” quantifying the diversity of different topological features. The previously defined network/graph complexity measures Medium Articulation and Offdiagonal complexity ( OdC) belong to these two classes. We study OdC measures in some detail and compare it with our new measures. For all measures, the most complex graph G has a medium number of edges, between the edge numbers of the minimum and the maximum connected graph n-1graph complexity measures are characterized with the help of different example graphs. For all measures the corresponding time complexity is given. Finally, we discuss the complexity of 33 real-world graphs of different biological, social and economic systems with the six computationally most simple measures (including OdC). The complexities of the real graphs are compared with average complexities of two different random graph versions: complete random graphs (just fixed n,m) and rewired graphs with fixed node degrees.

  9. Reproducibility of graph metrics of human brain structural networks.

    PubMed

    Duda, Jeffrey T; Cook, Philip A; Gee, James C

    2014-01-01

    Recent interest in human brain connectivity has led to the application of graph theoretical analysis to human brain structural networks, in particular white matter connectivity inferred from diffusion imaging and fiber tractography. While these methods have been used to study a variety of patient populations, there has been less examination of the reproducibility of these methods. A number of tractography algorithms exist and many of these are known to be sensitive to user-selected parameters. The methods used to derive a connectivity matrix from fiber tractography output may also influence the resulting graph metrics. Here we examine how these algorithm and parameter choices influence the reproducibility of proposed graph metrics on a publicly available test-retest dataset consisting of 21 healthy adults. The dice coefficient is used to examine topological similarity of constant density subgraphs both within and between subjects. Seven graph metrics are examined here: mean clustering coefficient, characteristic path length, largest connected component size, assortativity, global efficiency, local efficiency, and rich club coefficient. The reproducibility of these network summary measures is examined using the intraclass correlation coefficient (ICC). Graph curves are created by treating the graph metrics as functions of a parameter such as graph density. Functional data analysis techniques are used to examine differences in graph measures that result from the choice of fiber tracking algorithm. The graph metrics consistently showed good levels of reproducibility as measured with ICC, with the exception of some instability at low graph density levels. The global and local efficiency measures were the most robust to the choice of fiber tracking algorithm.

  10. Orthocomplemented complete lattices and graphs

    NASA Astrophysics Data System (ADS)

    Ollech, Astrid

    1995-08-01

    The problem I consider originates from Dörfler, who found a construction to assign an Orthocomplemented lattice H(G) to a graph G. By Dörfler it is known that for every finite Orthocomplemented lattice L there exists a graph G such that H(G)=L. Unfortunately, we can find more than one graph G with this property, i.e., orthocomplemented lattices which belong to different graphs can be isomorphic. I show some conditions under which two graphs have the same orthocomplemented lattice.

  11. Spectral fluctuations of quantum graphs

    SciTech Connect

    Pluhař, Z.; Weidenmüller, H. A.

    2014-10-15

    We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry.

  12. Quantification of Graph Complexity Based on the Edge Weight Distribution Balance: Application to Brain Networks.

    PubMed

    Gomez-Pilar, Javier; Poza, Jesús; Bachiller, Alejandro; Gómez, Carlos; Núñez, Pablo; Lubeiro, Alba; Molina, Vicente; Hornero, Roberto

    2017-05-23

    The aim of this study was to introduce a novel global measure of graph complexity: Shannon graph complexity (SGC). This measure was specifically developed for weighted graphs, but it can also be applied to binary graphs. The proposed complexity measure was designed to capture the interplay between two properties of a system: the 'information' (calculated by means of Shannon entropy) and the 'order' of the system (estimated by means of a disequilibrium measure). SGC is based on the concept that complex graphs should maintain an equilibrium between the aforementioned two properties, which can be measured by means of the edge weight distribution. In this study, SGC was assessed using four synthetic graph datasets and a real dataset, formed by electroencephalographic (EEG) recordings from controls and schizophrenia patients. SGC was compared with graph density (GD), a classical measure used to evaluate graph complexity. Our results showed that SGC is invariant with respect to GD and independent of node degree distribution. Furthermore, its variation with graph size [Formula: see text] is close to zero for [Formula: see text]. Results from the real dataset showed an increment in the weight distribution balance during the cognitive processing for both controls and schizophrenia patients, although these changes are more relevant for controls. Our findings revealed that SGC does not need a comparison with null-hypothesis networks constructed by a surrogate process. In addition, SGC results on the real dataset suggest that schizophrenia is associated with a deficit in the brain dynamic reorganization related to secondary pathways of the brain network.

  13. Scaling Semantic Graph Databases in Size and Performance

    SciTech Connect

    Morari, Alessandro; Castellana, Vito G.; Villa, Oreste; Tumeo, Antonino; Weaver, Jesse R.; Haglin, David J.; Choudhury, Sutanay; Feo, John T.

    2014-08-06

    In this paper we present SGEM, a full software system for accelerating large-scale semantic graph databases on commodity clusters. Unlike current approaches, SGEM addresses semantic graph databases by only employing graph methods at all the levels of the stack. On one hand, this allows exploiting the space efficiency of graph data structures and the inherent parallelism of graph algorithms. These features adapt well to the increasing system memory and core counts of modern commodity clusters. On the other hand, however, these systems are optimized for regular computation and batched data transfers, while graph methods usually are irregular and generate fine-grained data accesses with poor spatial and temporal locality. Our framework comprises a SPARQL to data parallel C compiler, a library of parallel graph methods and a custom, multithreaded runtime system. We introduce our stack, motivate its advantages with respect to other solutions and show how we solved the challenges posed by irregular behaviors. We present the result of our software stack on the Berlin SPARQL benchmarks with datasets up to 10 billion triples (a triple corresponds to a graph edge), demonstrating scaling in dataset size and in performance as more nodes are added to the cluster.

  14. Constructing splits graphs.

    PubMed

    Dress, Andreas W M; Huson, Daniel H

    2004-01-01

    Phylogenetic trees correspond one-to-one to compatible systems of splits and so splits play an important role in theoretical and computational aspects of phylogeny. Whereas any tree reconstruction method can be thought of as producing a compatible system of splits, an increasing number of phylogenetic algorithms are available that compute split systems that are not necessarily compatible and, thus, cannot always be represented by a tree. Such methods include the split decomposition, Neighbor-Net, consensus networks, and the Z-closure method. A more general split system of this kind can be represented graphically by a so-called splits graph, which generalizes the concept of a phylogenetic tree. This paper addresses the problem of computing a splits graph for a given set of splits. We have implemented all presented algorithms in a new program called SplitsTree4.

  15. An Unusual Exponential Graph

    ERIC Educational Resources Information Center

    Syed, M. Qasim; Lovatt, Ian

    2014-01-01

    This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…

  16. Optical tomography on graphs

    NASA Astrophysics Data System (ADS)

    Chung, Francis J.; Gilbert, Anna C.; Hoskins, Jeremy G.; Schotland, John C.

    2017-05-01

    We present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving estimates characterizing the domain of convergence, approximation errors, and stability of our approach. We also present a modification which allows additional information on the structure of the potential to be incorporated, facilitating recovery for a broader class of problems.

  17. An Unusual Exponential Graph

    ERIC Educational Resources Information Center

    Syed, M. Qasim; Lovatt, Ian

    2014-01-01

    This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…

  18. A Novel Graph Constructor for Semisupervised Discriminant Analysis: Combined Low-Rank and k-Nearest Neighbor Graph

    PubMed Central

    Pan, Yongke; Niu, Wenjia

    2017-01-01

    Semisupervised Discriminant Analysis (SDA) is a semisupervised dimensionality reduction algorithm, which can easily resolve the out-of-sample problem. Relative works usually focus on the geometric relationships of data points, which are not obvious, to enhance the performance of SDA. Different from these relative works, the regularized graph construction is researched here, which is important in the graph-based semisupervised learning methods. In this paper, we propose a novel graph for Semisupervised Discriminant Analysis, which is called combined low-rank and k-nearest neighbor (LRKNN) graph. In our LRKNN graph, we map the data to the LR feature space and then the kNN is adopted to satisfy the algorithmic requirements of SDA. Since the low-rank representation can capture the global structure and the k-nearest neighbor algorithm can maximally preserve the local geometrical structure of the data, the LRKNN graph can significantly improve the performance of SDA. Extensive experiments on several real-world databases show that the proposed LRKNN graph is an efficient graph constructor, which can largely outperform other commonly used baselines. PMID:28316616

  19. A Novel Graph Constructor for Semisupervised Discriminant Analysis: Combined Low-Rank and k-Nearest Neighbor Graph.

    PubMed

    Zu, Baokai; Xia, Kewen; Pan, Yongke; Niu, Wenjia

    2017-01-01

    Semisupervised Discriminant Analysis (SDA) is a semisupervised dimensionality reduction algorithm, which can easily resolve the out-of-sample problem. Relative works usually focus on the geometric relationships of data points, which are not obvious, to enhance the performance of SDA. Different from these relative works, the regularized graph construction is researched here, which is important in the graph-based semisupervised learning methods. In this paper, we propose a novel graph for Semisupervised Discriminant Analysis, which is called combined low-rank and k-nearest neighbor (LRKNN) graph. In our LRKNN graph, we map the data to the LR feature space and then the kNN is adopted to satisfy the algorithmic requirements of SDA. Since the low-rank representation can capture the global structure and the k-nearest neighbor algorithm can maximally preserve the local geometrical structure of the data, the LRKNN graph can significantly improve the performance of SDA. Extensive experiments on several real-world databases show that the proposed LRKNN graph is an efficient graph constructor, which can largely outperform other commonly used baselines.

  20. Perspective Projection Invariants,

    DTIC Science & Technology

    1986-02-01

    ORGANIZATION NAME ANC ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK Artificial Inteligence Laboratory AREA & WORK UNIT NUMBERSO 545 Technology Square dCambridge...AD-AI67 793 PERSPECTIVE PROJECTION INVARIANTS(U) MASSACHUSETTS INST 1/1~ OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB VERRI ET AL, FEB 86 AI-M-832...0R020I4 661 SEC R TVC PAGE fjSr .W IlIII UI A 8 gT@OFTNS21 07 1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY ARTIFICIAL INTELLIGENCE LABORATORY and CENTER

  1. How to Use Spanning Trees to Navigate in Graphs

    NASA Astrophysics Data System (ADS)

    Dragan, Feodor F.; Xiang, Yang

    In this paper, we investigate three strategies of how to use a spanning tree T of a graph G to navigate in G, i.e., to move from a current vertex x towards a destination vertex y via a path that is close to optimal. In each strategy, each vertex v has full knowledge of its neighborhood N G [v] in G (or, k-neighborhood D k (v,G), where k is a small integer) and uses a small piece of global information from spanning tree T (e.g., distance or ancestry information in T), available locally at v, to navigate in G. We investigate advantages and limitations of these strategies on particular families of graphs such as graphs with locally connected spanning trees, graphs with bounded length of largest induced cycle, graphs with bounded tree-length, graphs with bounded hyperbolicity. For most of these families of graphs, the ancestry information from a BFS-tree guarantees short enough routing paths. In many cases, the obtained results are optimal up to a constant factor.

  2. The Graph Laplacian and the Dynamics of Complex Networks

    SciTech Connect

    Thulasidasan, Sunil

    2012-06-11

    In this talk, we explore the structure of networks from a spectral graph-theoretic perspective by analyzing the properties of the Laplacian matrix associated with the graph induced by a network. We will see how the eigenvalues of the graph Laplacian relate to the underlying network structure and dynamics and provides insight into a phenomenon frequently observed in real world networks - the emergence of collective behavior from purely local interactions seen in the coordinated motion of animals and phase transitions in biological networks, to name a few.

  3. Statistics of Gaussian packets on metric and decorated graphs

    PubMed Central

    Chernyshev, V. L.; Shafarevich, A. I.

    2014-01-01

    We study a semiclassical asymptotics of the Cauchy problem for a time-dependent Schrödinger equation on metric and decorated graphs with a localized initial function. A decorated graph is a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds. The main term of an asymptotic solution at an arbitrary finite time is a sum of Gaussian packets and generalized Gaussian packets (localized near a certain set of codimension one). We study the number of packets as time tends to infinity. We prove that under certain assumptions this number grows in time as a polynomial and packets fill the graph uniformly. We discuss a simple example of the opposite situation: in this case, a numerical experiment shows a subexponential growth. PMID:24344346

  4. Statistics of Gaussian packets on metric and decorated graphs.

    PubMed

    Chernyshev, V L; Shafarevich, A I

    2014-01-28

    We study a semiclassical asymptotics of the Cauchy problem for a time-dependent Schrödinger equation on metric and decorated graphs with a localized initial function. A decorated graph is a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds. The main term of an asymptotic solution at an arbitrary finite time is a sum of Gaussian packets and generalized Gaussian packets (localized near a certain set of codimension one). We study the number of packets as time tends to infinity. We prove that under certain assumptions this number grows in time as a polynomial and packets fill the graph uniformly. We discuss a simple example of the opposite situation: in this case, a numerical experiment shows a subexponential growth.

  5. Drawing Large Graphs by Multilevel Maxent-Stress Optimization.

    PubMed

    Meyerhenke, Henning; Nollenburg, Martin; Schulz, Christian

    2017-03-29

    Drawing large graphs appropriately is an important step for the visual analysis of data from real-world networks. Here we present a novel multilevel algorithm to compute a graph layout with respect to the maxent-stress metric proposed by Gansner et al. (2013) that combines layout stress and entropy. As opposed to previous work, we do not solve the resulting linear systems of the maxent-stress metric with a typical numerical solver. Instead we use a simple local iterative scheme within a multilevel approach. To accelerate local optimization, we approximate long-range forces and use shared-memory parallelism. Our experiments validate the high potential of our approach, which is particularly appealing for dynamic graphs. In comparison to the previously best maxent-stress optimizer, which is sequential, our parallel implementation is on average 30 times faster already for static graphs (and still faster if executed on a single thread) while producing a comparable solution quality.

  6. Invariant measures for singular hyperbolic attractors

    SciTech Connect

    Sataev, Evgueni A

    2010-05-11

    This paper continues the author's previous paper, where strong unstable spaces were constructed for a singular hyperbolic attractor. In this paper the existence of local strongly unstable manifolds and invariant measures of Sinai-Bowen-Ruelle type is established. The properties of such measures are studied. It is proved that the number of ergodic components is finite and the set of periodic trajectories is dense. Bibliography: 34 titles.

  7. Graph pyramids for protein function prediction

    PubMed Central

    2015-01-01

    Background Uncovering the hidden organizational characteristics and regularities among biological sequences is the key issue for detailed understanding of an underlying biological phenomenon. Thus pattern recognition from nucleic acid sequences is an important affair for protein function prediction. As proteins from the same family exhibit similar characteristics, homology based approaches predict protein functions via protein classification. But conventional classification approaches mostly rely on the global features by considering only strong protein similarity matches. This leads to significant loss of prediction accuracy. Methods Here we construct the Protein-Protein Similarity (PPS) network, which captures the subtle properties of protein families. The proposed method considers the local as well as the global features, by examining the interactions among 'weakly interacting proteins' in the PPS network and by using hierarchical graph analysis via the graph pyramid. Different underlying properties of the protein families are uncovered by operating the proposed graph based features at various pyramid levels. Results Experimental results on benchmark data sets show that the proposed hierarchical voting algorithm using graph pyramid helps to improve computational efficiency as well the protein classification accuracy. Quantitatively, among 14,086 test sequences, on an average the proposed method misclassified only 21.1 sequences whereas baseline BLAST score based global feature matching method misclassified 362.9 sequences. With each correctly classified test sequence, the fast incremental learning ability of the proposed method further enhances the training model. Thus it has achieved more than 96% protein classification accuracy using only 20% per class training data. PMID:26044522

  8. Graph pyramids for protein function prediction.

    PubMed

    Sandhan, Tushar; Yoo, Youngjun; Choi, Jin; Kim, Sun

    2015-01-01

    Uncovering the hidden organizational characteristics and regularities among biological sequences is the key issue for detailed understanding of an underlying biological phenomenon. Thus pattern recognition from nucleic acid sequences is an important affair for protein function prediction. As proteins from the same family exhibit similar characteristics, homology based approaches predict protein functions via protein classification. But conventional classification approaches mostly rely on the global features by considering only strong protein similarity matches. This leads to significant loss of prediction accuracy. Here we construct the Protein-Protein Similarity (PPS) network, which captures the subtle properties of protein families. The proposed method considers the local as well as the global features, by examining the interactions among 'weakly interacting proteins' in the PPS network and by using hierarchical graph analysis via the graph pyramid. Different underlying properties of the protein families are uncovered by operating the proposed graph based features at various pyramid levels. Experimental results on benchmark data sets show that the proposed hierarchical voting algorithm using graph pyramid helps to improve computational efficiency as well the protein classification accuracy. Quantitatively, among 14,086 test sequences, on an average the proposed method misclassified only 21.1 sequences whereas baseline BLAST score based global feature matching method misclassified 362.9 sequences. With each correctly classified test sequence, the fast incremental learning ability of the proposed method further enhances the training model. Thus it has achieved more than 96% protein classification accuracy using only 20% per class training data.

  9. Figure-Ground Segmentation Using Factor Graphs.

    PubMed

    Shen, Huiying; Coughlan, James; Ivanchenko, Volodymyr

    2009-06-04

    Foreground-background segmentation has recently been applied [26,12] to the detection and segmentation of specific objects or structures of interest from the background as an efficient alternative to techniques such as deformable templates [27]. We introduce a graphical model (i.e. Markov random field)-based formulation of structure-specific figure-ground segmentation based on simple geometric features extracted from an image, such as local configurations of linear features, that are characteristic of the desired figure structure. Our formulation is novel in that it is based on factor graphs, which are graphical models that encode interactions among arbitrary numbers of random variables. The ability of factor graphs to express interactions higher than pairwise order (the highest order encountered in most graphical models used in computer vision) is useful for modeling a variety of pattern recognition problems. In particular, we show how this property makes factor graphs a natural framework for performing grouping and segmentation, and demonstrate that the factor graph framework emerges naturally from a simple maximum entropy model of figure-ground segmentation.We cast our approach in a learning framework, in which the contributions of multiple grouping cues are learned from training data, and apply our framework to the problem of finding printed text in natural scenes. Experimental results are described, including a performance analysis that demonstrates the feasibility of the approach.

  10. Lung segmentation with graph cuts: Graph size versus performance

    NASA Astrophysics Data System (ADS)

    Pazokifard, Banafsheh; Sowmya, Arcot

    2013-10-01

    The effect of graph size on segmentation performance and speed is investigated, where segmentation is based on the graph cuts algorithm. The study is performed on lung extraction in 50 complete multi detector computed tomography (MDCT) datasets, and a fully automatic procedure. The experiments were performed on different graph sizes for both 2-D (4 and 8 neighbours) and 3-D (6 and 26 neighbours) graphs. Five slices from each segmented dataset were compared to the reference delineation provided by a radiologist. Our evaluations highlight the fact that when medical image segmentation is performed using graph cuts, increasing graph and neighbourhood connection size does not necessarily improve the segmentation performance, but also increase the running time dramatically.

  11. Entanglement, Invariants, and Phylogenetics

    NASA Astrophysics Data System (ADS)

    Sumner, J. G.

    2007-10-01

    This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units from biomolecular sequence data. The techniques of mathematical physics are plethora and have been developed for some time. The Markov model of phylogenetics and its analysis is a relatively new technique where most progress to date has been achieved by using discrete mathematics. This thesis takes a group theoretical approach to the problem by beginning with a remarkable mathematical parallel to the process of scattering in particle physics. This is shown to equate to branching events in the evolutionary history of molecular units. The major technical result of this thesis is the derivation of existence proofs and computational techniques for calculating polynomial group invariant functions on a multi-linear space where the group action is that relevant to a Markovian time evolution. The practical results of this thesis are an extended analysis of the use of invariant functions in distance based methods and the presentation of a new reconstruction technique for quartet trees which is consistent with the most general Markov model of sequence evolution.

  12. Evaluation of Graph Pattern Matching Workloads in Graph Analysis Systems

    SciTech Connect

    Hong, Seokyong; Lee, Sangkeun; Lim, Seung-Hwan; Sukumar, Sreenivas Rangan; Vatsavai, Raju

    2016-01-01

    Graph analysis has emerged as a powerful method for data scientists to represent, integrate, query, and explore heterogeneous data sources. As a result, graph data management and mining became a popular area of research, and led to the development of plethora of systems in recent years. Unfortunately, the number of emerging graph analysis systems and the wide range of applications, coupled with a lack of apples-to-apples comparisons, make it difficult to understand the trade-offs between different systems and the graph operations for which they are designed. A fair comparison of these systems is a challenging task for the following reasons: multiple data models, non-standardized serialization formats, various query interfaces to users, and diverse environments they operate in. To address these key challenges, in this paper we present a new benchmark suite by extending the Lehigh University Benchmark (LUBM) to cover the most common capabilities of various graph analysis systems. We provide the design process of the benchmark, which generalizes the workflow for data scientists to conduct the desired graph analysis on different graph analysis systems. Equipped with this extended benchmark suite, we present performance comparison for nine subgraph pattern retrieval operations over six graph analysis systems, namely NetworkX, Neo4j, Jena, Titan, GraphX, and uRiKA. Through the proposed benchmark suite, this study reveals both quantitative and qualitative findings in (1) implications in loading data into each system; (2) challenges in describing graph patterns for each query interface; and (3) different sensitivity of each system to query selectivity. We envision that this study will pave the road for: (i) data scientists to select the suitable graph analysis systems, and (ii) data management system designers to advance graph analysis systems.

  13. Boundary cue invariance in cortical orientation maps.

    PubMed

    Zhan, Chang'an A; Baker, Curtis L

    2006-06-01

    We effortlessly perceive oriented boundaries defined by either luminance changes ('first-order' cues) or texture variations ('second-order' cues). Many neurons in mammalian visual cortex show orientation preference to both types of boundaries, but it is uncertain how they contribute to perceptual orientation cue-invariance at the neuronal population level. Using optical imaging in cat A 18, we observed highly similar orientation preference maps to first-order and a variety of second-order visual stimuli. Thus the neuronal representation of coarse-scale boundary orientation appears to be invariant to the characteristics (including local orientation) of the fine-scale textures by which those boundaries are defined. A common feature of second-order visual stimuli is that modulation shifts their Fourier energy for boundary orientation to the higher spatial frequencies of their constituent textures - our results suggest a common neural mechanism (demodulation) mediating visual processing of many kinds of texture boundary. The similarity between orientation maps to different stimuli implies that second-order responsive neurons are homogeneously distributed across the cortical surface. Such homogeneously cue-invariant orientation representation could provide a neural substrate for perceptual form-cue invariance, and reflect an optimal organization for encoding orientation information in natural scenes.

  14. Highly Asynchronous VisitOr Queue Graph Toolkit

    SciTech Connect

    Pearce, R.

    2012-10-01

    HAVOQGT is a C++ framework that can be used to create highly parallel graph traversal algorithms. The framework stores the graph and algorithmic data structures on external memory that is typically mapped to high performance locally attached NAND FLASH arrays. The framework supports a vertex-centered visitor programming model. The frameworkd has been used to implement breadth first search, connected components, and single source shortest path.

  15. Automated Program Recognition by Graph Parsing

    DTIC Science & Technology

    1992-07-01

    programs are represented as attributed dataflow graphs and a library of clichis is encoded as an attributed graph grammar . Graph parsing is used to...recognition. Second, we investigate the expressiveness of our graph grammar formalism for capturing pro- gramming cliches. Third, we empirically and...library of cliches is encoded as an attributed graph grammar . Graph parsing is used to recognize clich6s in the code. We demonstrate that this graph

  16. Graph Coarsening for Path Finding in Cybersecurity Graphs

    SciTech Connect

    Hogan, Emilie A.; Johnson, John R.; Halappanavar, Mahantesh

    2013-01-01

    n the pass-the-hash attack, hackers repeatedly steal password hashes and move through a computer network with the goal of reaching a computer with high level administrative privileges. In this paper we apply graph coarsening in network graphs for the purpose of detecting hackers using this attack or assessing the risk level of the network's current state. We repeatedly take graph minors, which preserve the existence of paths in the graph, and take powers of the adjacency matrix to count the paths. This allows us to detect the existence of paths as well as find paths that have high risk of being used by adversaries.

  17. Invariants from classical field theory

    SciTech Connect

    Diaz, Rafael; Leal, Lorenzo

    2008-06-15

    We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.

  18. On Edge Exchangeable Random Graphs

    NASA Astrophysics Data System (ADS)

    Janson, Svante

    2017-06-01

    We study a recent model for edge exchangeable random graphs introduced by Crane and Dempsey; in particular we study asymptotic properties of the random simple graph obtained by merging multiple edges. We study a number of examples, and show that the model can produce dense, sparse and extremely sparse random graphs. One example yields a power-law degree distribution. We give some examples where the random graph is dense and converges a.s. in the sense of graph limit theory, but also an example where a.s. every graph limit is the limit of some subsequence. Another example is sparse and yields convergence to a non-integrable generalized graphon defined on (0,∞).

  19. Potts model and graph theory

    NASA Astrophysics Data System (ADS)

    Wu, F. Y.

    1988-07-01

    Elementary exposition is given of some recent developments in studies of graphtheoretic aspects of the Potts model. Topics discussed include graphical expansions of the Potts partition function and correlation functions and their relationships with the chromatic, dichromatic, and flow polynomials occurring in graph theory. It is also shown that the Potts model realization of these classic graph-theoretic problems provides alternate and direct proofs of properties established heretofore only in the context of formal graph theory.

  20. The scale invariant generator technique for quantifying anisotropic scale invariance

    NASA Astrophysics Data System (ADS)

    Lewis, G. M.; Lovejoy, S.; Schertzer, D.; Pecknold, S.

    1999-11-01

    Scale invariance is rapidly becoming a new paradigm for geophysics. However, little attention has been paid to the anisotropy that is invariably present in geophysical fields in the form of differential stratification and rotation, texture and morphology. In order to account for scaling anisotropy, the formalism of generalized scale invariance (GSI) was developed. Until now there has existed only a single fairly ad hoc GSI analysis technique valid for studying differential rotation. In this paper, we use a two-dimensional representation of the linear approximation to generalized scale invariance, to obtain a much improved technique for quantifying anisotropic scale invariance called the scale invariant generator technique (SIG). The accuracy of the technique is tested using anisotropic multifractal simulations and error estimates are provided for the geophysically relevant range of parameters. It is found that the technique yields reasonable estimates for simulations with a diversity of anisotropic and statistical characteristics. The scale invariant generator technique can profitably be applied to the scale invariant study of vertical/horizontal and space/time cross-sections of geophysical fields as well as to the study of the texture/morphology of fields.

  1. Bifurcation from an invariant to a non-invariant attractor

    NASA Astrophysics Data System (ADS)

    Mandal, D.

    2016-12-01

    Switching dynamical systems are very common in many areas of physics and engineering. We consider a piecewise linear map that periodically switches between more than one different functional forms. We show that in such systems it is possible to have a border collision bifurcation where the system transits from an invariant attractor to a non-invariant attractor.

  2. A classical theory of continuous spin and hidden gauge invariance

    SciTech Connect

    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.

  3. A classical theory of continuous spin and hidden gauge invariance

    SciTech Connect

    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.

  4. Generalized invariance principles and the theory of stability.

    NASA Technical Reports Server (NTRS)

    Lasalle, J. P.

    1971-01-01

    Description of some recent extensions of the invariance principle to more generalized dynamical systems where the state space is not locally compact and the flow is unique only in the forward direction of time. A sufficient condition for asymptotic stability of an invariant set is obtained which does not require that the Liapunov function be positive-definite. A recently developed generalized invariance principle is described which is applicable to functional differential equations, partial differential equations, and, in particular, to certain stability problems arising in thermoelasticity, viscoelasticity, and distributed nonlinear networks.

  5. Integrability and Dynamics of Quadratic Three-Dimensional Differential Systems Having an Invariant Paraboloid

    NASA Astrophysics Data System (ADS)

    Messias, Marcelo; Reinol, Alisson C.

    Invariant algebraic surfaces are commonly observed in differential systems arising in mathematical modeling of natural phenomena. In this paper, we study the integrability and dynamics of quadratic polynomial differential systems defined in ℝ3 having an elliptic paraboloid as an invariant algebraic surface. We obtain the normal form for these kind of systems and, by using the invariant paraboloid, we prove the existence of first integrals, exponential factors, Darboux invariants and inverse Jacobi multipliers, for suitable choices of parameter values. We characterize all the possible configurations of invariant parallels and invariant meridians on the invariant paraboloid and give necessary conditions for the invariant parallel to be a limit cycle and for the invariant meridian to have two orbits heteroclinic to a point at infinity. We also study the dynamics of a particular class of the quadratic polynomial differential systems having an invariant paraboloid, giving information about localization and local stability of finite singular points and, by using the Poincaré compactification, we study their dynamics on the Poincaré sphere (at infinity). Finally, we study the well-known Rabinovich system in the case of invariant paraboloids, performing a detailed study of its dynamics restricted to these invariant algebraic surfaces.

  6. Contact Graph Routing

    NASA Technical Reports Server (NTRS)

    Burleigh, Scott C.

    2011-01-01

    Contact Graph Routing (CGR) is a dynamic routing system that computes routes through a time-varying topology of scheduled communication contacts in a network based on the DTN (Delay-Tolerant Networking) architecture. It is designed to enable dynamic selection of data transmission routes in a space network based on DTN. This dynamic responsiveness in route computation should be significantly more effective and less expensive than static routing, increasing total data return while at the same time reducing mission operations cost and risk. The basic strategy of CGR is to take advantage of the fact that, since flight mission communication operations are planned in detail, the communication routes between any pair of bundle agents in a population of nodes that have all been informed of one another's plans can be inferred from those plans rather than discovered via dialogue (which is impractical over long one-way-light-time space links). Messages that convey this planning information are used to construct contact graphs (time-varying models of network connectivity) from which CGR automatically computes efficient routes for bundles. Automatic route selection increases the flexibility and resilience of the space network, simplifying cross-support and reducing mission management costs. Note that there are no routing tables in Contact Graph Routing. The best route for a bundle destined for a given node may routinely be different from the best route for a different bundle destined for the same node, depending on bundle priority, bundle expiration time, and changes in the current lengths of transmission queues for neighboring nodes; routes must be computed individually for each bundle, from the Bundle Protocol agent's current network connectivity model for the bundle s destination node (the contact graph). Clearly this places a premium on optimizing the implementation of the route computation algorithm. The scalability of CGR to very large networks remains a research topic

  7. Eigensolutions of dodecahedron graphs

    NASA Astrophysics Data System (ADS)

    Ghosh, Piyali; Karmakar, Somnath; Mandal, Bholanath

    2014-02-01

    Eigensolutions of 20-vertex cage (i.e. dodecahedron) have been determined with the use of fivefold rotational symmetry. For homo-dodecahedron the eigensolutions become analytical but for the hetero-dodecahedron having two different types of atoms ((C,N),(C,B),(B,N)) the eigensolutions are found to be factored out into five 4-degree polynomials with one corresponding to nondegenerate and other four corresponding to two degenerate eigensolutions. Eigenspectra and total π-electron energies of homo- and hetero-dodecahedron graphs have been calculated.

  8. Strongly Regular Graphs,

    DTIC Science & Technology

    1973-10-01

    The theory of strongly regular graphs was introduced by Bose r7 1 in 1963, in connection with partial geometries and 2 class association schemes. One...non adjacent vertices is constant and equal to ~. We shall denote by ~(p) (reap.r(p)) the set of vertices adjacent (resp.non adjacent) to a vertex p...is the complement of .2’ if the set of vertices of ~ is the set of vertices of .2’ and if two vertices in .2’ are adjacent if and only if they were

  9. Graph Theory of Tower Tasks

    PubMed Central

    Hinz, Andreas M.

    2012-01-01

    The appropriate mathematical model for the problem space of tower transformation tasks is the state graph representing positions of discs or balls and their moves. Graph theoretical quantities like distance, eccentricities or degrees of vertices and symmetries of graphs support the choice of problems, the selection of tasks and the analysis of performance of subjects whose solution paths can be projected onto the graph. The mathematical model is also at the base of a computerized test tool to administer various types of tower tasks. PMID:22207419

  10. Noncommutative Riemannian geometry on graphs

    NASA Astrophysics Data System (ADS)

    Majid, Shahn

    2013-07-01

    We show that arising out of noncommutative geometry is a natural family of edge Laplacians on the edges of a graph. The family includes a canonical edge Laplacian associated to the graph, extending the usual graph Laplacian on vertices, and we find its spectrum. We show that for a connected graph its eigenvalues are strictly positive aside from one mandatory zero mode, and include all the vertex degrees. Our edge Laplacian is not the graph Laplacian on the line graph but rather it arises as the noncommutative Laplace-Beltrami operator on differential 1-forms, where we use the language of differential algebras to functorially interpret a graph as providing a 'finite manifold structure' on the set of vertices. We equip any graph with a canonical 'Euclidean metric' and a canonical bimodule connection, and in the case of a Cayley graph we construct a metric compatible connection for the Euclidean metric. We make use of results on bimodule connections on inner calculi on algebras, which we prove, including a general relation between zero curvature and the braid relations.

  11. Spectral partitioning in equitable graphs

    NASA Astrophysics Data System (ADS)

    Barucca, Paolo

    2017-06-01

    Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e., random graphs with a block-regular structure, is studied, for which analytical results can be obtained. In particular, the spectral density of this ensemble is computed exactly for a modular and bipartite structure. Kesten-McKay's law for random regular graphs is found analytically to apply also for modular and bipartite structures when blocks are homogeneous. An exact solution to graph partitioning for two equal-sized communities is proposed and verified numerically, and a conjecture on the absence of an efficient recovery detectability transition in equitable graphs is suggested. A final discussion summarizes results and outlines their relevance for the solution of graph partitioning problems in other graph ensembles, in particular for the study of detectability thresholds and resolution limits in stochastic block models.

  12. BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.

    PubMed

    Vorburger, Robert S; Reischauer, Carolin; Boesiger, Peter

    2013-02-01

    Bootstrap methods have recently been introduced to diffusion-weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model. These methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain. Thereby, the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms. Graph based approaches have been proposed to overcome this drawback of streamline techniques. For this reason, the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method, called BootGraph. The acquired data set is thereby converted into a weighted, undirected graph by defining a vertex in each voxel and edges between adjacent vertices. By means of the cone of uncertainty, which is derived using the wild bootstrap, a weight is thereafter assigned to each edge. Two path finding algorithms are subsequently applied to derive connection probabilities. While the first algorithm is based on the shortest path approach, the second algorithm takes all existing paths between two vertices into consideration. Tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm. The BootGraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints, such as a curvature threshold. By inheriting the advantages of the bootstrap method and graph theory, the BootGraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of

  13. Light-bending tests of Lorentz invariance

    SciTech Connect

    Tso, Rhondale; Bailey, Quentin G.

    2011-10-15

    Classical light-bending is investigated for weak gravitational fields in the presence of hypothetical local Lorentz violation. Using an effective field theory framework that describes general deviations from local Lorentz invariance, we derive a modified deflection angle for light passing near a massive body. The results include anisotropic effects not present for spherical sources in General Relativity as well as Weak Equivalence Principle violation. We develop an expression for the relative deflection of two distant stars that can be used to analyze data in past and future solar-system observations. The measurement sensitivities of such tests to coefficients for Lorentz violation are discussed.

  14. Parabolic Refined Invariants and Macdonald Polynomials

    NASA Astrophysics Data System (ADS)

    Chuang, Wu-yen; Diaconescu, Duiliu-Emanuel; Donagi, Ron; Pantev, Tony

    2015-05-01

    A string theoretic derivation is given for the conjecture of Hausel, Letellier and Rodriguez-Villegas on the cohomology of character varieties with marked points. Their formula is identified with a refined BPS expansion in the stable pair theory of a local root stack, generalizing previous work of the first two authors in collaboration with Pan. Haiman's geometric construction for Macdonald polynomials is shown to emerge naturally in this context via geometric engineering. In particular this yields a new conjectural relation between Macdonald polynomials and refined local orbifold curve counting invariants. The string theoretic approach also leads to a new spectral cover construction for parabolic Higgs bundles in terms of holomorphic symplectic orbifolds.

  15. Differential invariants of self-dual conformal structures

    NASA Astrophysics Data System (ADS)

    Kruglikov, Boris; Schneider, Eivind

    2017-03-01

    We compute the quotient of the self-duality equation for conformal metrics by the action of the diffeomorphism group. We also determine Hilbert polynomial, counting the number of independent scalar differential invariants depending on the jet-order, and the corresponding Poincaré function. We describe the field of rational differential invariants separating generic orbits of the diffeomorphism pseudogroup action, resolving the local recognition problem for self-dual conformal structures.

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

    SciTech Connect

    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. Neural network for graphs: a contextual constructive approach.

    PubMed

    Micheli, Alessio

    2009-03-01

    This paper presents a new approach for learning in structured domains (SDs) using a constructive neural network for graphs (NN4G). The new model allows the extension of the input domain for supervised neural networks to a general class of graphs including both acyclic/cyclic, directed/undirected labeled graphs. In particular, the model can realize adaptive contextual transductions, learning the mapping from graphs for both classification and regression tasks. In contrast to previous neural networks for structures that had a recursive dynamics, NN4G is based on a constructive feedforward architecture with state variables that uses neurons with no feedback connections. The neurons are applied to the input graphs by a general traversal process that relaxes the constraints of previous approaches derived by the causality assumption over hierarchical input data. Moreover, the incremental approach eliminates the need to introduce cyclic dependencies in the definition of the system state variables. In the traversal process, the NN4G units exploit (local) contextual information of the graphs vertices. In spite of the simplicity of the approach, we show that, through the compositionality of the contextual information developed by the learning, the model can deal with contextual information that is incrementally extended according to the graphs topology. The effectiveness and the generality of the new approach are investigated by analyzing its theoretical properties and providing experimental results.

  18. Graph Visualization for RDF Graphs with SPARQL-EndPoints

    SciTech Connect

    Sukumar, Sreenivas R; Bond, Nathaniel

    2014-07-11

    RDF graphs are hard to visualize as triples. This software module is a web interface that connects to a SPARQL endpoint and retrieves graph data that the user can explore interactively and seamlessly. The software written in python and JavaScript has been tested to work on screens as little as the smart phones to large screens such as EVEREST.

  19. Encoding protein-ligand interaction patterns in fingerprints and graphs.

    PubMed

    Desaphy, Jérémy; Raimbaud, Eric; Ducrot, Pierre; Rognan, Didier

    2013-03-25

    We herewith present a novel and universal method to convert protein-ligand coordinates into a simple fingerprint of 210 integers registering the corresponding molecular interaction pattern. Each interaction (hydrophobic, aromatic, hydrogen bond, ionic bond, metal complexation) is detected on the fly and physically described by a pseudoatom centered either on the interacting ligand atom, the interacting protein atom, or the geometric center of both interacting atoms. Counting all possible triplets of interaction pseudoatoms within six distance ranges, and pruning the full integer vector to keep the most frequent triplets enables the definition of a simple (210 integers) and coordinate frame-invariant interaction pattern descriptor (TIFP) that can be applied to compare any pair of protein-ligand complexes. TIFP fingerprints have been calculated for ca. 10,000 druggable protein-ligand complexes therefore enabling a wide comparison of relationships between interaction pattern similarity and ligand or binding site pairwise similarity. We notably show that interaction pattern similarity strongly depends on binding site similarity. In addition to the TIFP fingerprint which registers intermolecular interactions between a ligand and its target protein, we developed two tools (Ishape, Grim) to align protein-ligand complexes from their interaction patterns. Ishape is based on the overlap of interaction pseudoatoms using a smooth Gaussian function, whereas Grim utilizes a standard clique detection algorithm to match interaction pattern graphs. Both tools are complementary and enable protein-ligand complex alignments capitalizing on both global and local pattern similarities. The new fingerprint and companion alignment tools have been successfully used in three scenarios: (i) interaction-biased alignment of protein-ligand complexes, (ii) postprocessing docking poses according to known interaction patterns for a particular target, and (iii) virtual screening for bioisosteric

  20. Quantum Graph Analysis

    SciTech Connect

    Maunz, Peter Lukas Wilhelm; Sterk, Jonathan David; Lobser, Daniel; Parekh, Ojas D.; Ryan-Anderson, Ciaran

    2016-01-01

    In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.

  1. Comparing pedigree graphs.

    PubMed

    Kirkpatrick, Bonnie; Reshef, Yakir; Finucane, Hilary; Jiang, Haitao; Zhu, Binhai; Karp, Richard M

    2012-09-01

    Pedigree graphs, or family trees, are typically constructed by an expensive process of examining genealogical records to determine which pairs of individuals are parent and child. New methods to automate this process take as input genetic data from a set of extant individuals and reconstruct ancestral individuals. There is a great need to evaluate the quality of these methods by comparing the estimated pedigree to the true pedigree. In this article, we consider two main pedigree comparison problems. The first is the pedigree isomorphism problem, for which we present a linear-time algorithm for leaf-labeled pedigrees. The second is the pedigree edit distance problem, for which we present (1) several algorithms that are fast and exact in various special cases, and (2) a general, randomized heuristic algorithm. In the negative direction, we first prove that the pedigree isomorphism problem is as hard as the general graph isomorphism problem, and that the sub-pedigree isomorphism problem is NP-hard. We then show that the pedigree edit distance problem is APX-hard in general and NP-hard on leaf-labeled pedigrees. We use simulated pedigrees to compare our edit-distance algorithms to each other as well as to a branch-and-bound algorithm that always finds an optimal solution.

  2. Quantization of gauge fields, graph polynomials and graph homology

    SciTech Connect

    Kreimer, Dirk; Sars, Matthias; Suijlekom, Walter D. van

    2013-09-15

    We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials. The transition to the full gauge theory amplitude is obtained by the use of a third, new, graph polynomial, the corolla polynomial. This implies effectively a covariant quantization without ghosts, where all the relevant signs of the ghost sector are incorporated in a double complex furnished by the corolla polynomial–we call it cycle homology–and by graph homology. -- Highlights: •We derive gauge theory Feynman from scalar field theory with 3-valent vertices. •We clarify the role of graph homology and cycle homology. •We use parametric renormalization and the new corolla polynomial.

  3. Invariant Measures for Cherry Flows

    NASA Astrophysics Data System (ADS)

    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.

  4. The asymptotics of large constrained graphs

    NASA Astrophysics Data System (ADS)

    Radin, Charles; Ren, Kui; Sadun, Lorenzo

    2014-05-01

    We show, through local estimates and simulation, that if one constrains simple graphs by their densities ɛ of edges and τ of triangles, then asymptotically (in the number of vertices) for over 95% of the possible range of those densities there is a well-defined typical graph, and it has a very simple structure: the vertices are decomposed into two subsets V1 and V2 of fixed relative size c and 1 - c, and there are well-defined probabilities of edges, gjk, between vj ∈ Vj, and vk ∈ Vk. Furthermore the four parameters c, g11, g22 and g12 are smooth functions of (ɛ, τ) except at two smooth ‘phase transition’ curves.

  5. Spectral graph optimization for instance reduction.

    PubMed

    Nikolaidis, Konstantinos; Rodriguez-Martinez, Eduardo; Goulermas, John Yannis; Wu, Q H

    2012-07-01

    The operation of instance-based learning algorithms is based on storing a large set of prototypes in the system's database. However, such systems often experience issues with storage requirements, sensitivity to noise, and computational complexity, which result in high search and response times. In this brief, we introduce a novel framework that employs spectral graph theory to efficiently partition the dataset to border and internal instances. This is achieved by using a diverse set of border-discriminating features that capture the local friend and enemy profiles of the samples. The fused information from these features is then used via graph-cut modeling approach to generate the final dataset partitions of border and nonborder samples. The proposed method is referred to as the spectral instance reduction (SIR) algorithm. Experiments with a large number of datasets show that SIR performs competitively compared to many other reduction algorithms, in terms of both objectives of classification accuracy and data condensation.

  6. Crunching Large Graphs with Commodity Processors

    SciTech Connect

    Nelson, Jacob E; Myers, Brandon D; Hunter, Andrew H; Briggs, Preston; Ceze, Luis; Ebeling, William C; Grossman, Dan; Kahan, Simon H; Oskin, Mark

    2011-05-26

    Crunching large graphs is the basis of many emerging appli- cations, such as social network analysis and bioinformatics. Graph analytics algorithms exhibit little locality and therefore present significant performance challenges. Hardware multi- threading systems (e.g, Cray XMT) show that with enough concurrency, we can tolerate long latencies. Unfortunately, this solution is not available with commodity parts. Our goal is to develop a latency-tolerant system built out of commodity parts and mostly in software. The proposed system includes a runtime that supports a large number of lightweight contexts, full-bit synchronization and a memory manager that provides a high-latency but high-bandwidth global shared memory. This paper lays out the vision for our system, and justifies its feasibility with a performance analysis of the run- time for latency tolerance.

  7. Remarks on holography with broken Lorentz invariance

    NASA Astrophysics Data System (ADS)

    Gordeli, Ivan; Koroteev, Peter

    2009-12-01

    Recently a family of solutions of Einstein equations in backgrounds with broken Lorentz invariance was found. We show that the gravitational solution recently obtained by Kachru et al. is a part of the former solution which was derived earlier in the framework of extra-dimensional theories. We show how the energy-momentum and Einstein tensors are related and establish a correspondence between parameters which govern Lorentz invariance violation. Then we demonstrate that scaling behavior of two point correlation functions of local operators in scalar field theory is reproduced correctly for two cases with critical values of scaling parameters. Therefore, we complete the dictionary of “tree-level” duality for all known solutions of the bulk theory. In the end we speculate on relations between renormalization group flow of a boundary theory and asymptotic behavior of gravitational solutions in the bulk.

  8. Fast forward to the classical adiabatic invariant

    NASA Astrophysics Data System (ADS)

    Jarzynski, Christopher; Deffner, Sebastian; Patra, Ayoti; Subaşı, Yiǧit

    2017-03-01

    We show how the classical action, an adiabatic invariant, can be preserved under nonadiabatic conditions. Specifically, for a time-dependent Hamiltonian H =p2/2 m +U (q ,t ) in one degree of freedom, and for an arbitrary choice of action I0, we construct a so-called fast-forward potential energy function VFF(q ,t ) that, when added to H , guides all trajectories with initial action I0 to end with the same value of action. We use this result to construct a local dynamical invariant J (q ,p ,t ) whose value remains constant along these trajectories. We illustrate our results with numerical simulations. Finally, we sketch how our classical results may be used to design approximate quantum shortcuts to adiabaticity.

  9. Physical Invariants of Intelligence

    NASA Technical Reports Server (NTRS)

    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

  10. STRUCTURAL ANNOTATION OF EM IMAGES BY GRAPH CUT

    SciTech Connect

    Chang, Hang; Auer, Manfred; Parvin, Bahram

    2009-05-08

    Biological images have the potential to reveal complex signatures that may not be amenable to morphological modeling in terms of shape, location, texture, and color. An effective analytical method is to characterize the composition of a specimen based on user-defined patterns of texture and contrast formation. However, such a simple requirement demands an improved model for stability and robustness. Here, an interactive computational model is introduced for learning patterns of interest by example. The learned patterns bound an active contour model in which the traditional gradient descent optimization is replaced by the more efficient optimization of the graph cut methods. First, the energy function is defined according to the curve evolution. Next, a graph is constructed with weighted edges on the energy function and is optimized with the graph cut algorithm. As a result, the method combines the advantages of the level set method and graph cut algorithm, i.e.,"topological" invariance and computational efficiency. The technique is extended to the multi-phase segmentation problem; the method is validated on synthetic images and then applied to specimens imaged by transmission electron microscopy(TEM).

  11. Fracture and Fragmentation of Simplicial Finite Elements Meshes using Graphs

    SciTech Connect

    Mota, A; Knap, J; Ortiz, M

    2006-10-18

    An approach for the topological representation of simplicial finite element meshes as graphs is presented. It is shown that by using a graph, the topological changes induced by fracture reduce to a few, local kernel operations. The performance of the graph representation is demonstrated and analyzed, using as reference the 3D fracture algorithm by Pandolfi and Ortiz [22]. It is shown that the graph representation initializes in O(N{sub E}{sup 1.1}) time and fractures in O(N{sub I}{sup 1.0}) time, while the reference implementation requires O(N{sub E}{sup 2.1}) time to initialize and O(N{sub I}{sup 1.9}) time to fracture, where NE is the number of elements in the mesh and N{sub I} is the number of interfaces to fracture.

  12. Open-system dynamics of graph-state entanglement.

    PubMed

    Cavalcanti, Daniel; Chaves, Rafael; Aolita, Leandro; Davidovich, Luiz; Acín, Antonio

    2009-07-17

    We consider graph states of an arbitrary number of particles undergoing generic decoherence. We present methods to obtain lower and upper bounds for the system's entanglement in terms of that of considerably smaller subsystems. For an important class of noisy channels, namely, the Pauli maps, these bounds coincide and thus provide the exact analytical expression for the entanglement evolution. All of the results apply also to (mixed) graph-diagonal states and hold true for any convex entanglement monotone. Since any state can be locally depolarized to some graph-diagonal state, our method provides a lower bound for the entanglement decay of any arbitrary state. Finally, this formalism also allows for the direct identification of the robustness under size scaling of graph states in the presence of decoherence, merely by inspection of their connectivities.

  13. South Pole Lorentz Invariance Test

    NASA Astrophysics Data System (ADS)

    Hedges, Morgan; Smiciklas, Marc; Romalis, Michael

    2015-05-01

    Searches for Lorentz and CPT violation play an important role in testing current theories of space-time. To test one of the consequences of local Lorentz invariance we have performed a precision test of spatial isotropy at the Amundsen-Scott station near the geographic South Pole. This location provides the most isotropic environment available on Earth. The experiment is a rotating atomic-spin co-magnetometer which compares energy levels of 21Ne and Rubidium atoms as a function of direction. The experimental sensitivity obtained is more than an order of magnitude better than in previous such measurements, known as Hughes-Drever experiments. By operating the experiment at the Pole we are able to eliminate background signals due to the gyroscopic interactions of spins with Earth's rotation as well as diurnal environmental effects. Here we will present final results from the experiment's 2-year data collection period. This is the first precision atomic physics experiment performed at the Pole, and we will discuss the potential for future such measurements.

  14. South Pole Lorentz Invariance Test

    NASA Astrophysics Data System (ADS)

    Hedges, Morgan; Smiciklas, Marc; Romalis, Michael

    2015-04-01

    Tests of Lorentz and CPT symmetries are important because they form a cornerstone of quantum field theory and general relativity. To test one of the consequences of local Lorentz invariance we have performed a precision test of spatial isotropy at the Amundsen-Scott station near the geographic South Pole. This location provides the most isotropic environment available on Earth. We use an atomic spin co-magnetometer to compare energy levels in 21 Ne and Rubidium atoms as the apparatus rotates with respect to the cosmos. Our experimental sensitivity is more than an order of magnitude greater than in previous such measurements, known as Hughes-Drever experiments. By operating at the South Pole we eliminate background signals due to the gyroscopic interactions of spins with Earth's rotation as well as diurnal environmental effects. The experiment has finished a 2-year data collection period and we expect to present the final results at the meeting. This is the first precision atomic physics experiment performed at the Pole and we will discuss the potential for future such measurements.

  15. Network reconstruction via graph blending

    NASA Astrophysics Data System (ADS)

    Estrada, Rolando

    2016-05-01

    Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.

  16. Graphs as Statements of Belief.

    ERIC Educational Resources Information Center

    Lake, David

    2002-01-01

    Identifies points where beliefs are important when making decisions about how graphs are drawn. Describes a simple case of the reaction between 'bicarb soda' and orange or lemon juice and discusses how drawing a graph becomes a statement of belief. (KHR)

  17. Graphs and Zero-Divisors

    ERIC Educational Resources Information Center

    Axtell, M.; Stickles, J.

    2010-01-01

    The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings--by professional mathematicians "and" undergraduates. The objective is to find algebraic information within the geometry of these graphs. This topic is approachable by anyone with one or two semesters of abstract algebra. This article gives the…

  18. Blind Identification of Graph Filters

    NASA Astrophysics Data System (ADS)

    Segarra, Santiago; Mateos, Gonzalo; Marques, Antonio G.; Ribeiro, Alejandro

    2017-03-01

    Network processes are often represented as signals defined on the vertices of a graph. To untangle the latent structure of such signals, one can view them as outputs of linear graph filters modeling underlying network dynamics. This paper deals with the problem of joint identification of a graph filter and its input signal, thus broadening the scope of classical blind deconvolution of temporal and spatial signals to the less-structured graph domain. Given a graph signal $\\mathbf{y}$ modeled as the output of a graph filter, the goal is to recover the vector of filter coefficients $\\mathbf{h}$, and the input signal $\\mathbf{x}$ which is assumed to be sparse. While $\\mathbf{y}$ is a bilinear function of $\\mathbf{x}$ and $\\mathbf{h}$, the filtered graph signal is also a linear combination of the entries of the lifted rank-one, row-sparse matrix $\\mathbf{x} \\mathbf{h}^T$. The blind graph-filter identification problem can thus be tackled via rank and sparsity minimization subject to linear constraints, an inverse problem amenable to convex relaxations offering provable recovery guarantees under simplifying assumptions. Numerical tests using both synthetic and real-world networks illustrate the merits of the proposed algorithms, as well as the benefits of leveraging multiple signals to aid the blind identification task.

  19. Graphs and Zero-Divisors

    ERIC Educational Resources Information Center

    Axtell, M.; Stickles, J.

    2010-01-01

    The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings--by professional mathematicians "and" undergraduates. The objective is to find algebraic information within the geometry of these graphs. This topic is approachable by anyone with one or two semesters of abstract algebra. This article gives the…

  20. Graphs as Statements of Belief.

    ERIC Educational Resources Information Center

    Lake, David

    2002-01-01

    Identifies points where beliefs are important when making decisions about how graphs are drawn. Describes a simple case of the reaction between 'bicarb soda' and orange or lemon juice and discusses how drawing a graph becomes a statement of belief. (KHR)

  1. A PVS Graph Theory Library

    NASA Technical Reports Server (NTRS)

    Butler, Ricky W.; Sjogren, Jon A.

    1998-01-01

    This paper documents the NASA Langley PVS graph theory library. The library provides fundamental definitions for graphs, subgraphs, walks, paths, subgraphs generated by walks, trees, cycles, degree, separating sets, and four notions of connectedness. Theorems provided include Ramsey's and Menger's and the equivalence of all four notions of connectedness.

  2. Graph theoretical model of a sensorimotor connectome in zebrafish.

    PubMed

    Stobb, Michael; Peterson, Joshua M; Mazzag, Borbala; Gahtan, Ethan

    2012-01-01

    Mapping the detailed connectivity patterns (connectomes) of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron) varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome.

  3. Graph Theoretical Model of a Sensorimotor Connectome in Zebrafish

    PubMed Central

    Stobb, Michael; Peterson, Joshua M.; Mazzag, Borbala; Gahtan, Ethan

    2012-01-01

    Mapping the detailed connectivity patterns (connectomes) of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron) varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome. PMID:22624008

  4. A Collection of Features for Semantic Graphs

    SciTech Connect

    Eliassi-Rad, T; Fodor, I K; Gallagher, B

    2007-05-02

    Semantic graphs are commonly used to represent data from one or more data sources. Such graphs extend traditional graphs by imposing types on both nodes and links. This type information defines permissible links among specified nodes and can be represented as a graph commonly referred to as an ontology or schema graph. Figure 1 depicts an ontology graph for data from National Association of Securities Dealers. Each node type and link type may also have a list of attributes. To capture the increased complexity of semantic graphs, concepts derived for standard graphs have to be extended. This document explains briefly features commonly used to characterize graphs, and their extensions to semantic graphs. This document is divided into two sections. Section 2 contains the feature descriptions for static graphs. Section 3 extends the features for semantic graphs that vary over time.

  5. Scale-invariant gauge theories of gravity: Theoretical foundations

    NASA Astrophysics Data System (ADS)

    Lasenby, A. N.; Hobson, M. P.

    2016-09-01

    We consider the construction of gauge theories of gravity, focussing in particular on the extension of local Poincaré invariance to include invariance under local changes of scale. We work exclusively in terms of finite transformations, which allow for a more transparent interpretation of such theories in terms of gauge fields in Minkowski spacetime. Our approach therefore differs from the usual geometrical description of locally scale-invariant Poincaré gauge theory (PGT) and Weyl gauge theory (WGT) in terms of Riemann-Cartan and Weyl-Cartan spacetimes, respectively. In particular, we reconsider the interpretation of the Einstein gauge and also the equations of motion of matter fields and test particles in these theories. Inspired by the observation that the PGT and WGT matter actions for the Dirac field and electromagnetic field have more general invariance properties than those imposed by construction, we go on to present a novel alternative to WGT by considering an "extended" form for the transformation law of the rotational gauge field under local dilations, which includes its "normal" transformation law in WGT as a special case. The resulting "extended" Weyl gauge theory (eWGT) has a number of interesting features that we describe in detail. In particular, we present a new scale-invariant gauge theory of gravity that accommodates ordinary matter and is defined by the most general parity-invariant eWGT Lagrangian that is at most quadratic in the eWGT field strengths, and we derive its field equations. We also consider the construction of PGTs that are invariant under local dilations assuming either the "normal" or "extended" transformation law for the rotational gauge field, but show that they are special cases of WGT and eWGT, respectively.

  6. Possible universal quantum algorithms for generalized Khovanov homology and the Rasmussen's invariant

    NASA Astrophysics Data System (ADS)

    Vélez, Mario; Ospina, Juan

    2012-06-01

    Possible quantum algorithms for generalized Khovanov homology and the Rasmussen's invariant are proposed. Such algorithms are resulting from adaptations of the recently proposed Kauffman's algorithm for the standard Khovanov homology. The method that was applied consists in to write the relevant quantum invariant as the trace of a certain unitary operator and then to compute the trace using the Hadamard test. We apply such method to the quantum computation of the Jones polynomial, HOMFLY polynomial, Chromatic polynomial, Tutte polynomial and Bollobàs- Riordan polynomial. These polynomials are quantum topological invariants for knots, links, graphs and ribbon graphs respectively. The Jones polynomial is categorified by the standard Khovanov homology and the others polynomials are categorified by generalized Khovanov homologies, such as the Khovanov-Rozansky homology and the graph homologies. The algorithm for the Rasmussen's invariant is obtained using the gauge theory; and the recently introduced program of homotopyfication is linked with the super-symmetric quantum mechanics. It is claimed that a new program of analytification could be development from the homotopyfication using the celebrated Atiyah-Singer theorem and its super-symmetric interpretations. It is hoped that the super-symmetric quantum mechanics provides the hardware for the implementation of the proposed quantum algorithms.

  7. Semi-Markov Graph Dynamics

    PubMed Central

    Raberto, Marco; Rapallo, Fabio; Scalas, Enrico

    2011-01-01

    In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs. PMID:21887245

  8. Path similarity skeleton graph matching.

    PubMed

    Bai, Xiang; Latecki, Longin Jan

    2008-07-01

    This paper presents a novel framework to for shape recognition based on object silhouettes. The main idea is to match skeleton graphs by comparing the shortest paths between skeleton endpoints. In contrast to typical tree or graph matching methods, we completely ignore the topological graph structure. Our approach is motivated by the fact that visually similar skeleton graphs may have completely different topological structures. The proposed comparison of shortest paths between endpoints of skeleton graphs yields correct matching results in such cases. The skeletons are pruned by contour partitioning with Discrete Curve Evolution, which implies that the endpoints of skeleton branches correspond to visual parts of the objects. The experimental results demonstrate that our method is able to produce correct results in the presence of articulations, stretching, and occlusion.

  9. Quantum Ergodicity on Regular Graphs

    NASA Astrophysics Data System (ADS)

    Anantharaman, Nalini

    2017-07-01

    We give three different proofs of the main result of Anantharaman and Le Masson (Duke Math J 164(4):723-765, 2015), establishing quantum ergodicity—a form of delocalization—for eigenfunctions of the laplacian on large regular graphs of fixed degree. These three proofs are much shorter than the original one, quite different from one another, and we feel that each of the four proofs sheds a different light on the problem. The goal of this exploration is to find a proof that could be adapted for other models of interest in mathematical physics, such as the Anderson model on large regular graphs, regular graphs with weighted edges, or possibly certain models of non-regular graphs. A source of optimism in this direction is that we are able to extend the last proof to the case of anisotropic random walks on large regular graphs.

  10. Effect of Graph Scale on Risky Choice: Evidence from Preference and Process in Decision-Making

    PubMed Central

    Sun, Yan; Li, Shu; Bonini, Nicolao; Liu, Yang

    2016-01-01

    We investigate the effect of graph scale on risky choices. By (de)compressing the scale, we manipulate the relative physical distance between options on a given attribute in a coordinate graphical context. In Experiment 1, the risky choice changes as a function of the scale in the graph. In Experiment 2, we show that the type of graph scale also affects decision times. In Experiment 3, we examine the graph scale effect by using real money among students who have taken statistics courses. Consequently, the scale effects still appear even when we control the variations in calculation ability and increase the gravity with which participants view the consequence of their decisions. This finding is inconsistent with descriptive invariance of preference. The theoretical implications and practical applications of the findings are discussed. PMID:26771530

  11. Uncorrelated and discriminative graph embedding for face recognition

    NASA Astrophysics Data System (ADS)

    Peng, Chengyu; Li, Jianwei; Huang, Hong

    2011-07-01

    We present a novel feature extraction algorithm for face recognition called the uncorrelated and discriminative graph embedding (UDGE) algorithm, which incorporates graph embedding and local scaling method and obtains uncorrelated discriminative vectors in the projected subspace. An optimization objective function is herein defined to make the discriminative projections preserve the intrinsic neighborhood geometry of the within-class samples while enlarging the margins of between-class samples near to the class boundaries. UDGE efficiently dispenses with a prespecified parameter which is data-dependent to balance the objective of the within-class locality and the between-class locality in comparison with the linear extension of graph embedding in a face recognition scenario. Moreover, it can address the small sample-size problem, and its classification accuracy is not sensitive to neighbor samples size and weight value, as well. Extensive experiments on extended YaleB, CMU PIE, and Indian face databases demonstrate the effectiveness of UDGE.

  12. Graph-theoretic independence as a predictor of fullerene stability

    NASA Astrophysics Data System (ADS)

    Fajtlowicz, S.; Larson, C. E.

    2003-08-01

    The independence number of the graph of a fullerene, the size of the largest set of vertices such that no two are adjacent (corresponding to the largest set of atoms of the molecule, no pair of which are bonded), appears to be a useful selector in identifying stable fullerene isomers. The experimentally characterized isomers with 60, 70 and 76 atoms uniquely minimize this number among the classes of possible structures with, respectively, 60, 70 and 76 atoms. Other experimentally characterized isomers also rank extremely low with respect to this invariant. These findings were initiated by a conjecture of the computer program Graffiti.

  13. Completeness and regularity of generalized fuzzy graphs.

    PubMed

    Samanta, Sovan; Sarkar, Biswajit; Shin, Dongmin; Pal, Madhumangal

    2016-01-01

    Fuzzy graphs are the backbone of many real systems like networks, image, scheduling, etc. But, due to some restriction on edges, fuzzy graphs are limited to represent for some systems. Generalized fuzzy graphs are appropriate to avoid such restrictions. In this study generalized fuzzy graphs are introduced. In this study, matrix representation of generalized fuzzy graphs is described. Completeness and regularity are two important parameters of graph theory. Here, regular and complete generalized fuzzy graphs are introduced. Some properties of them are discussed. After that, effective regular graphs are exemplified.

  14. Comparison and enumeration of chemical graphs.

    PubMed

    Akutsu, Tatsuya; Nagamochi, Hiroshi

    2013-01-01

    Chemical compounds are usually represented as graph structured data in computers. In this review article, we overview several graph classes relevant to chemical compounds and the computational complexities of several fundamental problems for these graph classes. In particular, we consider the following problems: determining whether two chemical graphs are identical, determining whether one input chemical graph is a part of the other input chemical graph, finding a maximum common part of two input graphs, finding a reaction atom mapping, enumerating possible chemical graphs, and enumerating stereoisomers. We also discuss the relationship between the fifth problem and kernel functions for chemical compounds.

  15. Comparison and Enumeration of Chemical Graphs

    PubMed Central

    Akutsu, Tatsuya; Nagamochi, Hiroshi

    2013-01-01

    Chemical compounds are usually represented as graph structured data in computers. In this review article, we overview several graph classes relevant to chemical compounds and the computational complexities of several fundamental problems for these graph classes. In particular, we consider the following problems: determining whether two chemical graphs are identical, determining whether one input chemical graph is a part of the other input chemical graph, finding a maximum common part of two input graphs, finding a reaction atom mapping, enumerating possible chemical graphs, and enumerating stereoisomers. We also discuss the relationship between the fifth problem and kernel functions for chemical compounds. PMID:24688697

  16. GRAPH III: a digitizing and graph plotting program

    SciTech Connect

    Selleck, C.B.

    1986-03-01

    GRAPH is an interactive program that allows the user to perform two functions. The first is to plot two dimensional graphs and the second is to digitize graphs or plots to create data files of points. The program is designed to allow the user to get results quickly and easily. It is written in RATIV (a FORTRAN preprocessor) and is currently in use at Sandia under VMS on a VAX computer and CTSS on a Cray supercomputer. The program provides graphical output through all of the Sandia Virtual Device Interface (VDI) graphics devices. 2 refs., 3 figs., 3 tabs.

  17. Shape Invariance in Deformation Quantization

    NASA Astrophysics Data System (ADS)

    Rasinariu, Constantin

    2013-03-01

    Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this work explores the implications of the supersymmetric quantum mechanics and shape invariance techniques to the phase space formalism. We show that shape invariance induces a new set of relations between the Wigner functions of the system, that allows for their direct calculation, once we know one of them. The simple harmonic oscillator and the Morse potential are presented as examples. I would like to acknowledge a sabbatical leave and grant from Columbia College Chicago that made this work possible.

  18. Shape invariance through Crum transformation

    SciTech Connect

    Organista, Jose Orlando; Nowakowski, Marek; Rosu, H. C.

    2006-12-15

    We show in a rigorous way that Crum's result regarding the equal eigenvalue spectrum of Sturm-Liouville problems can be obtained iteratively by successive Darboux transformations. Furthermore, it can be shown that all neighboring Darboux-transformed potentials of higher order, u{sub k} and u{sub k+1}, satisfy the condition of shape invariance provided the original potential u does so. Based on this result, we prove that under the condition of shape invariance, the nth iteration of the original Sturm-Liouville problem defined solely through the shape invariance is equal to the nth Crum transformation.

  19. Bayesian tests of measurement invariance.

    PubMed

    Verhagen, A J; Fox, J P

    2013-11-01

    Random item effects models provide a natural framework for the exploration of violations of measurement invariance without the need for anchor items. Within the random item effects modelling framework, Bayesian tests (Bayes factor, deviance information criterion) are proposed which enable multiple marginal invariance hypotheses to be tested simultaneously. The performance of the tests is evaluated with a simulation study which shows that the tests have high power and low Type I error rate. Data from the European Social Survey are used to test for measurement invariance of attitude towards immigrant items and to show that background information can be used to explain cross-national variation in item functioning.

  20. Entanglement classification and invariant-based entanglement measures

    NASA Astrophysics Data System (ADS)

    Li, Xiangrong; Li, Dafa

    2015-01-01

    We propose a method of classifying n -qubit states into stochastic local operations and classical communication inequivalent families in terms of the rank of the square matrix C (iσy) ⊗kCT , where C is the rectangular coefficient matrix of the state and σy is the Pauli operator. The rank of the square matrix C (iσy) ⊗kCT is capable of distinguishing between n -qubit Greenberger-Horne-Zeilinger and W states. The determinant of the matrix gives rise to a family of polynomial invariants for n qubits which include as special cases well-known polynomial invariants in the literature. In addition, explicit expressions can be given for these polynomial invariants and this allows us to investigate the properties of entanglement measures built upon the absolute values of polynomial invariants for product states.

  1. Permutation-invariant distance between atomic configurations.

    PubMed

    Ferré, Grégoire; Maillet, Jean-Bernard; Stoltz, Gabriel

    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.

  2. Permutation-invariant distance between atomic configurations

    SciTech Connect

    Ferré, Grégoire; Maillet, Jean-Bernard; Stoltz, Gabriel

    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.

  3. Invariant measures in brain dynamics

    NASA Astrophysics Data System (ADS)

    Boyarsky, Abraham; Góra, Paweł

    2006-10-01

    This note concerns brain activity at the level of neural ensembles and uses ideas from ergodic dynamical systems to model and characterize chaotic patterns among these ensembles during conscious mental activity. Central to our model is the definition of a space of neural ensembles and the assumption of discrete time ensemble dynamics. We argue that continuous invariant measures draw the attention of deeper brain processes, engendering emergent properties such as consciousness. Invariant measures supported on a finite set of ensembles reflect periodic behavior, whereas the existence of continuous invariant measures reflect the dynamics of nonrepeating ensemble patterns that elicit the interest of deeper mental processes. We shall consider two different ways to achieve continuous invariant measures on the space of neural ensembles: (1) via quantum jitters, and (2) via sensory input accompanied by inner thought processes which engender a “folding” property on the space of ensembles.

  4. Flying through Graphs: An Introduction to Graph Theory.

    ERIC Educational Resources Information Center

    McDuffie, Amy Roth

    2001-01-01

    Presents an activity incorporating basic terminology, concepts, and solution methods of graph theory in the context of solving problems related to air travel. Discusses prerequisite knowledge and resources and includes a teacher's guide with a student worksheet. (KHR)

  5. Flying through Graphs: An Introduction to Graph Theory.

    ERIC Educational Resources Information Center

    McDuffie, Amy Roth

    2001-01-01

    Presents an activity incorporating basic terminology, concepts, and solution methods of graph theory in the context of solving problems related to air travel. Discusses prerequisite knowledge and resources and includes a teacher's guide with a student worksheet. (KHR)

  6. DNA Rearrangements through Spatial Graphs

    NASA Astrophysics Data System (ADS)

    Jonoska, Nataša; Saito, Masahico

    The paper is a short overview of a recent model of homologous DNA recombination events guided by RNA templates that have been observed in certain species of ciliates. This model uses spatial graphs to describe DNA rearrangements and show how gene recombination can be modeled as topological braiding of the DNA. We show that a graph structure, which we refer to as an assembly graph, containing only 1- and 4-valent rigid vertices can provide a physical representation of the DNA at the time of recombination. With this representation, 4-valent vertices correspond to the alignment of the recombination sites, and we model the actual recombination event as smoothing of these vertices.

  7. Multigraph: Reusable Interactive Data Graphs

    NASA Astrophysics Data System (ADS)

    Phillips, M. B.

    2010-12-01

    There are surprisingly few good software tools available for presenting time series data on the internet. The most common practice is to use a desktop program such as Excel or Matlab to save a graph as an image which can be included in a web page like any other image. This disconnects the graph from the data in a way that makes updating a graph with new data a cumbersome manual process, and it limits the user to one particular view of the data. The Multigraph project defines an XML format for describing interactive data graphs, and software tools for creating and rendering those graphs in web pages and other internet connected applications. Viewing a Multigraph graph is extremely simple and intuitive, and requires no instructions; the user can pan and zoom by clicking and dragging, in a familiar "Google Maps" kind of way. Creating a new graph for inclusion in a web page involves writing a simple XML configuration file. Multigraph can read data in a variety of formats, and can display data from a web service, allowing users to "surf" through large data sets, downloading only those the parts of the data that are needed for display. The Multigraph XML format, or "MUGL" for short, provides a concise description of the visual properties of a graph, such as axes, plot styles, data sources, labels, etc, as well as interactivity properties such as how and whether the user can pan or zoom along each axis. Multigraph reads a file in this format, draws the described graph, and allows the user to interact with it. Multigraph software currently includes a Flash application for embedding graphs in web pages, a Flex component for embedding graphs in larger Flex/Flash applications, and a plugin for creating graphs in the WordPress content management system. Plans for the future include a Java version for desktop viewing and editing, a command line version for batch and server side rendering, and possibly Android and iPhone versions. Multigraph is currently in use on several web

  8. Orthosymplectically invariant functions in superspace

    NASA Astrophysics Data System (ADS)

    Coulembier, K.; De Bie, H.; Sommen, F.

    2010-08-01

    The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically symmetric functions can be used to solve orthosymplectically invariant Schrödinger equations in superspace, such as the (an)harmonic oscillator or the Kepler problem. Finally, the obtained machinery is used to prove the Funk-Hecke theorem and Bochner's relations in superspace.

  9. Graphle: Interactive exploration of large, dense graphs

    PubMed Central

    2009-01-01

    Background A wide variety of biological data can be modeled as network structures, including experimental results (e.g. protein-protein interactions), computational predictions (e.g. functional interaction networks), or curated structures (e.g. the Gene Ontology). While several tools exist for visualizing large graphs at a global level or small graphs in detail, previous systems have generally not allowed interactive analysis of dense networks containing thousands of vertices at a level of detail useful for biologists. Investigators often wish to explore specific portions of such networks from a detailed, gene-specific perspective, and balancing this requirement with the networks' large size, complex structure, and rich metadata is a substantial computational challenge. Results Graphle is an online interface to large collections of arbitrary undirected, weighted graphs, each possibly containing tens of thousands of vertices (e.g. genes) and hundreds of millions of edges (e.g. interactions). These are stored on a centralized server and accessed efficiently through an interactive Java applet. The Graphle applet allows a user to examine specific portions of a graph, retrieving the relevant neighborhood around a set of query vertices (genes). This neighborhood can then be refined and modified interactively, and the results can be saved either as publication-quality images or as raw data for further analysis. The Graphle web site currently includes several hundred biological networks representing predicted functional relationships from three heterogeneous data integration systems: S. cerevisiae data from bioPIXIE, E. coli data using MEFIT, and H. sapiens data from HEFalMp. Conclusions Graphle serves as a search and visualization engine for biological networks, which can be managed locally (simplifying collaborative data sharing) and investigated remotely. The Graphle framework is freely downloadable and easily installed on new servers, allowing any lab to quickly set up

  10. OSRI: a rotationally invariant binary descriptor.

    PubMed

    Xu, Xianwei; Tian, Lu; Feng, Jianjiang; Zhou, Jie

    2014-07-01

    Binary descriptors are becoming widely used in computer vision field because of their high matching efficiency and low memory requirements. Since conventional approaches, which first compute a floating-point descriptor then binarize it, are computationally expensive, some recent efforts have focused on directly computing binary descriptors from local image patches. Although these binary descriptors enable a significant speedup in processing time, their performances usually drop a lot due to orientation estimation errors and limited description abilities. To address these issues, we propose a novel binary descriptor based on the ordinal and spatial information of regional invariants (OSRIs) over a rotation invariant sampling pattern. Our main contributions are twofold: 1) each bit in OSRI is computed based on difference tests of regional invariants over pairwise sampling-regions instead of difference tests of pixel intensities commonly used in existing binary descriptors, which can significantly enhance the discriminative ability and 2) rotation and illumination changes are handled well by ordering pixels according to their intensities and gradient orientations, meanwhile, which is also more reliable than those methods that resort to a reference orientation for rotation invariance. Besides, a statistical analysis of discriminative abilities of different parts in the descriptor is conducted to design a cascade filter which can reject nonmatching descriptors at early stages by comparing just a small portion of the whole descriptor, further reducing the matching time. Extensive experiments on four challenging data sets (Oxford, 53 Objects, ZuBuD, and Kentucky) show that OSRI significantly outperforms two state-of-the-art binary descriptors (FREAK and ORB). The matching performance of OSRI with only 512 bits is also better than the well-known floating-point descriptor SIFT (4K bits) and is comparable with the state-of-the-art floating-point descriptor MROGH (6K bits

  11. Hidden scale invariance of metals

    NASA Astrophysics Data System (ADS)

    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.

  12. Nonclassicality Invariant of General Two-Mode Gaussian States

    PubMed Central

    Arkhipov, Ievgen I.; Peřina Jr., Jan; Svozilík, Jiří; Miranowicz, Adam

    2016-01-01

    We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. The invariant naturally splits into an entanglement monotone and local-nonclassicality quantifiers applied to the reduced states. This shows how entanglement can be converted into local squeezing and vice versa. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light. An extension of this approach to pure three-mode Gaussian states is given. PMID:27210547

  13. Collaborative mining of graph patterns from multiple sources

    NASA Astrophysics Data System (ADS)

    Levchuk, Georgiy; Colonna-Romanoa, John

    2016-05-01

    Intelligence analysts require automated tools to mine multi-source data, including answering queries, learning patterns of life, and discovering malicious or anomalous activities. Graph mining algorithms have recently attracted significant attention in intelligence community, because the text-derived knowledge can be efficiently represented as graphs of entities and relationships. However, graph mining models are limited to use-cases involving collocated data, and often make restrictive assumptions about the types of patterns that need to be discovered, the relationships between individual sources, and availability of accurate data segmentation. In this paper we present a model to learn the graph patterns from multiple relational data sources, when each source might have only a fragment (or subgraph) of the knowledge that needs to be discovered, and segmentation of data into training or testing instances is not available. Our model is based on distributed collaborative graph learning, and is effective in situations when the data is kept locally and cannot be moved to a centralized location. Our experiments show that proposed collaborative learning achieves learning quality better than aggregated centralized graph learning, and has learning time comparable to traditional distributed learning in which a knowledge of data segmentation is needed.

  14. Evolutionary Dynamics on Degree-Heterogeneous Graphs

    NASA Astrophysics Data System (ADS)

    Antal, T.; Redner, S.; Sood, V.

    2006-05-01

    The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model dynamics) or by an individual giving birth to an offspring that takes over a random neighbor node (invasion process dynamics). The fixation probability for one species to take over a population of N individuals depends crucially on the dynamics and on the local environment. Starting with a single fitter mutant at a node of degree k, the fixation probability is proportional to k for voter model dynamics and to 1/k for invasion process dynamics.

  15. Multitask linear discriminant analysis for view invariant action recognition.

    PubMed

    Yan, Yan; Ricci, Elisa; Subramanian, Ramanathan; Liu, Gaowen; Sebe, Nicu

    2014-12-01

    Robust action recognition under viewpoint changes has received considerable attention recently. To this end, self-similarity matrices (SSMs) have been found to be effective view-invariant action descriptors. To enhance the performance of SSM-based methods, we propose multitask linear discriminant analysis (LDA), a novel multitask learning framework for multiview action recognition that allows for the sharing of discriminative SSM features among different views (i.e., tasks). Inspired by the mathematical connection between multivariate linear regression and LDA, we model multitask multiclass LDA as a single optimization problem by choosing an appropriate class indicator matrix. In particular, we propose two variants of graph-guided multitask LDA: 1) where the graph weights specifying view dependencies are fixed a priori and 2) where graph weights are flexibly learnt from the training data. We evaluate the proposed methods extensively on multiview RGB and RGBD video data sets, and experimental results confirm that the proposed approaches compare favorably with the state-of-the-art.

  16. Multibody graph transformations and analysis

    PubMed Central

    2013-01-01

    This two-part paper uses graph transformation methods to develop methods for partitioning, aggregating, and constraint embedding for multibody systems. This first part focuses on tree-topology systems and reviews the key notion of spatial kernel operator (SKO) models for such systems. It develops systematic and rigorous techniques for partitioning SKO models in terms of the SKO models of the component subsystems based on the path-induced property of the component subgraphs. It shows that the sparsity structure of key matrix operators and the mass matrix for the multibody system can be described using partitioning transformations. Subsequently, the notions of node contractions and subgraph aggregation and their role in coarsening graphs are discussed. It is shown that the tree property of a graph is preserved after subgraph aggregation if and only if the subgraph satisfies an aggregation condition. These graph theory ideas are used to develop SKO models for the aggregated tree multibody systems. PMID:24288438

  17. Decision net, directed graph, and neural net processing of imaging spectrometer data

    NASA Technical Reports Server (NTRS)

    Casasent, David; Liu, Shiaw-Dong; Yoneyama, Hideyuki; Barnard, Etienne

    1989-01-01

    A decision-net solution involving a novel hierarchical classifier and a set of multiple directed graphs, as well as a neural-net solution, are respectively presented for large-class problem and mixture problem treatments of imaging spectrometer data. The clustering method for hierarchical classifier design, when used with multiple directed graphs, yields an efficient decision net. New directed-graph rules for reducing local maxima as well as the number of perturbations required, and the new starting-node rules for extending the reachability and reducing the search time of the graphs, are noted to yield superior results, as indicated by an illustrative 500-class imaging spectrometer problem.

  18. Constructing Dense Graphs with Unique Hamiltonian Cycles

    ERIC Educational Resources Information Center

    Lynch, Mark A. M.

    2012-01-01

    It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

  19. Alzheimer's disease: connecting findings from graph theoretical studies of brain networks.

    PubMed

    Tijms, Betty M; Wink, Alle Meije; de Haan, Willem; van der Flier, Wiesje M; Stam, Cornelis J; Scheltens, Philip; Barkhof, Frederik

    2013-08-01

    The interrelationships between pathological processes and emerging clinical phenotypes in Alzheimer's disease (AD) are important yet complicated to study, because the brain is a complex network where local disruptions can have widespread effects. Recently, properties in brain networks obtained with neuroimaging techniques have been studied in AD with tools from graph theory. However, the interpretation of graph alterations remains unclear, because the definition of connectivity depends on the imaging modality used. Here we examined which graph properties have been consistently reported to be disturbed in AD studies, using a heuristically defined "graph space" to investigate which theoretical models can best explain graph alterations in AD. Findings from structural and functional graphs point to a loss of highly connected areas in AD. However, studies showed considerable variability in reported group differences of most graph properties. This suggests that brain graphs might not be isometric, which complicates the interpretation of graph measurements. We highlight confounding factors such as differences in graph construction methods and provide recommendations for future research.

  20. CUDA Enabled Graph Subset Examiner

    SciTech Connect

    Johnston, Jeremy T.

    2016-12-22

    Finding Godsil-McKay switching sets in graphs is one way to demonstrate that a specific graph is not determined by its spectrum--the eigenvalues of its adjacency matrix. An important area of active research in pure mathematics is determining which graphs are determined by their spectra, i.e. when the spectrum of the adjacency matrix uniquely determines the underlying graph. We are interested in exploring the spectra of graphs in the Johnson scheme and specifically seek to determine which of these graphs are determined by their spectra. Given a graph G, a Godsil-McKay switching set is an induced subgraph H on 2k vertices with the following properties: I) H is regular, ii) every vertex in G/H is adjacent to either 0, k, or 2k vertices of H, and iii) at least one vertex in G/H is adjacent to k vertices in H. The software package examines each subset of a user specified size to determine whether or not it satisfies those 3 conditions. The software makes use of the massive parallel processing power of CUDA enabled GPUs. It also exploits the vertex transitivity of graphs in the Johnson scheme by reasoning that if G has a Godsil-McKay switching set, then it has a switching set which includes vertex 1. While the code (in its current state) is tuned to this specific problem, the method of examining each induced subgraph of G can be easily re-written to check for any user specified conditions on the subgraphs and can therefore be used much more broadly.

  1. Weyl invariance with a nontrivial mass scale

    SciTech Connect

    Álvarez, Enrique; González-Martín, Sergio

    2016-09-07

    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.

  2. CPT violation implies violation of Lorentz invariance.

    PubMed

    Greenberg, O W

    2002-12-02

    A interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.

  3. Robust (semi) nonnegative graph embedding.

    PubMed

    Zhang, Hanwang; Zha, Zheng-Jun; Yang, Yang; Yan, Shuicheng; Chua, Tat-Seng

    2014-07-01

    Nonnegative matrix factorization (NMF) has received considerable attention in image processing, computer vision, and patter recognition. An important variant of NMF is nonnegative graph embedding (NGE), which encodes the statistical or geometric information of data in the process of matrix factorization. The NGE offers a general framework for unsupervised/supervised settings. However, NGE-like algorithms often suffer from noisy data, unreliable graphs, and noisy labels, which are commonly encountered in real-world applications. To address these issues, in this paper, we first propose a robust nonnegative graph embedding (RNGE) framework, where the joint sparsity in both graph embedding and data reconstruction endues robustness to undesirable noises. Next, we present a robust seminonnegative graph embedding (RsNGE) framework, which only constrains the coefficient matrix to be nonnegative while places no constraint on the base matrix. This extends the applicable range of RNGE to data which are not nonnegative and endows more discriminative power of the learnt base matrix. The RNGE/RsNGE provides a general formulation such that all the algorithms unified within the graph embedding framework can be easily extended to obtain their robust nonnegative/seminonnegative solutions. Further, we develop elegant multiplicative updating solutions that can solve RNGE/RsNGE efficiently and offer a rigorous convergence analysis. We conduct extensive experiments on four real-world data sets and compare the proposed RNGE/RsNGE to other representative NMF variants and data factorization methods. The experimental results demonstrate the robustness and effectiveness of the proposed approaches.

  4. Clinical correlates of graph theory findings in temporal lobe epilepsy.

    PubMed

    Haneef, Zulfi; Chiang, Sharon

    2014-11-01

    Temporal lobe epilepsy (TLE) is considered a brain network disorder, additionally representing the most common form of pharmaco-resistant epilepsy in adults. There is increasing evidence that seizures in TLE arise from abnormal epileptogenic networks, which extend beyond the clinico-radiologically determined epileptogenic zone and may contribute to the failure rate of 30-50% following epilepsy surgery. Graph theory allows for a network-based representation of TLE brain networks using several neuroimaging and electrophysiologic modalities, and has potential to provide clinicians with clinically useful biomarkers for diagnostic and prognostic purposes. We performed a review of the current state of graph theory findings in TLE as they pertain to localization of the epileptogenic zone, prediction of pre- and post-surgical seizure frequency and cognitive performance, and monitoring cognitive decline in TLE. Although different neuroimaging and electrophysiologic modalities have yielded occasionally conflicting results, several potential biomarkers have been characterized for identifying the epileptogenic zone, pre-/post-surgical seizure prediction, and assessing cognitive performance. For localization, graph theory measures of centrality have shown the most potential, including betweenness centrality, outdegree, and graph index complexity, whereas for prediction of seizure frequency, measures of synchronizability have shown the most potential. The utility of clustering coefficient and characteristic path length for assessing cognitive performance in TLE is also discussed. Future studies integrating data from multiple modalities and testing predictive models are needed to clarify findings and develop graph theory for its clinical utility. Copyright © 2014 British Epilepsy Association. Published by Elsevier Ltd. All rights reserved.

  5. Clinical correlates of graph theory findings in temporal lobe epilepsy

    PubMed Central

    Haneef, Zulfi; Chiang, Sharon

    2014-01-01

    Purpose Temporal lobe epilepsy (TLE) is considered a brain network disorder, additionally representing the most common form of pharmaco-resistant epilepsy in adults. There is increasing evidence that seizures in TLE arise from abnormal epileptogenic networks, which extend beyond the clinico-radiologically determined epileptogenic zone and may contribute to the failure rate of 30–50% following epilepsy surgery. Graph theory allows for a network-based representation of TLE brain networks using several neuroimaging and electrophysiologic modalities, and has potential to provide clinicians with clinically useful biomarkers for diagnostic and prognostic purposes. Methods We performed a review of the current state of graph theory findings in TLE as they pertain to localization of the epileptogenic zone, prediction of pre- and post-surgical seizure frequency and cognitive performance, and monitoring cognitive decline in TLE. Results Although different neuroimaging and electrophysiologic modalities have yielded occasionally conflicting results, several potential biomarkers have been characterized for identifying the epileptogenic zone, pre-/post-surgical seizure prediction, and assessing cognitive performance. For localization, graph theory measures of centrality have shown the most potential, including betweenness centrality, outdegree, and graph index complexity, whereas for prediction of seizure frequency, measures of synchronizability have shown the most potential. The utility of clustering coefficient and characteristic path length for assessing cognitive performance in TLE is also discussed. Conclusions Future studies integrating data from multiple modalities and testing predictive models are needed to clarify findings and develop graph theory for its clinical utility. PMID:25127370

  6. Community-local homology of force chains in granular materials

    NASA Astrophysics Data System (ADS)

    Giusti, Chad; Owens, Eli; Daniels, Karen; Bassett, Danielle

    2015-03-01

    The development of robust quantitative measurements of the structure of force chains in granular materials remains an open problem. Recent work of Bassett, et. al. applies community detection algorithms to extract subnetworks of strongly interacting particles, and then computes geometric measures of these networks to characterize local branching. Separately, Kramar, et. al. apply persistent homology to extract robust global signatures of chains in terms of their Betti numbers. Here, we investigate a hybrid of these two approaches, computing low-dimensional persistent homology of the clique complexes of communities in force-chain graphs. Such invariants measure the tendency of core chain sections to branch while remaining insensitive to the presence of tightly-packed collections of particles, thus making them natural candidates for both local and global stability analysis.

  7. Scale invariance and invariant scaling in a mixed hierarchical system.

    PubMed

    Shnirman, M G; Blanter, E M

    1999-11-01

    We consider a mixed hierarchical model with heterogeneous and monotone conditions of destruction. We investigate how scaling properties of defects in the model are related with heterogeneity of rules of destruction, determined by concentration of the mixture. The system demonstrates different kinds of criticality as a general form of system behavior. The following forms of critical behavior are obtained: stability, catastrophe, scale invariance, and invariant scaling. Different slopes of the magnitude-frequency relation are realized in areas of critical stability and catastrophe. A simple relation between the slope of magnitude-frequency relation and parameters of the mixture is established.

  8. Private Graphs - Access Rights on Graphs for Seamless Navigation

    NASA Astrophysics Data System (ADS)

    Dorner, W.; Hau, F.; Pagany, R.

    2016-06-01

    After the success of GNSS (Global Navigational Satellite Systems) and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS - Real Time Locating Services (e.g. WIFI) and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites), but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.

  9. GraphMeta: Managing HPC Rich Metadata in Graphs

    SciTech Connect

    Dai, Dong; Chen, Yong; Carns, Philip; Jenkins, John; Zhang, Wei; Ross, Robert

    2016-01-01

    High-performance computing (HPC) systems face increasingly critical metadata management challenges, especially in the approaching exascale era. These challenges arise not only from exploding metadata volumes, but also from increasingly diverse metadata, which contains data provenance and arbitrary user-defined attributes in addition to traditional POSIX metadata. This ‘rich’ metadata is becoming critical to supporting advanced data management functionality such as data auditing and validation. In our prior work, we identified a graph-based model as a promising solution to uniformly manage HPC rich metadata due to its flexibility and generality. However, at the same time, graph-based HPC rich metadata anagement also introduces significant challenges to the underlying infrastructure. In this study, we first identify the challenges on the underlying infrastructure to support scalable, high-performance rich metadata management. Based on that, we introduce GraphMeta, a graphbased engine designed for this use case. It achieves performance scalability by introducing a new graph partitioning algorithm and a write-optimal storage engine. We evaluate GraphMeta under both synthetic and real HPC metadata workloads, compare it with other approaches, and demonstrate its advantages in terms of efficiency and usability for rich metadata management in HPC systems.

  10. A class of finite symmetric graphs with 2-arc transitive quotients

    NASA Astrophysics Data System (ADS)

    Li, Cai Heng; Praeger, Cheryl E.; Zhou, Sanming

    2000-07-01

    Let [Gamma] be a finite G-symmetric graph whose vertex set admits a non-trivial G-invariant partition [script B] with block size v. A framework for studying such graphs [Gamma] was developed by Gardiner and Praeger which involved an analysis of the quotient graph [Gamma][script B] relative to [script B], the bipartite subgraph [Gamma][B, C] of [Gamma] induced by adjacent blocks B, C of [Gamma][script B] and a certain 1-design [script D](B) induced by a block B [set membership] [script B]. The present paper studies the case where the size k of the blocks of [script D](B) satisfies k = v [minus sign] 1. In the general case, where k = v [minus sign] 1 [gt-or-equal, slanted] 2, the setwise stabilizer GB is doubly transitive on B and G is faithful on [script B]. We prove that [script D](B) contains no repeated blocks if and only if [Gamma][script B] is (G, 2)-arc transitive and give a method for constructing such a graph from a 2-arc transitive graph with a self-paired orbit on 3-arcs. We show further that each such graph may be constructed by this method. In particular every 3-arc transitive graph, and every 2-arc transitive graph of even valency, may occur as [Gamma][script B] for some graph [Gamma] with these properties. We prove further that [Gamma][B, C] [congruent with] Kv[minus sign]1,v[minus sign]1 if and only if [Gamma][script B] is (G, 3)-arc transitive.

  11. A comparative study of theoretical graph models for characterizing structural networks of human brain.

    PubMed

    Li, Xiaojin; Hu, Xintao; Jin, Changfeng; Han, Junwei; Liu, Tianming; Guo, Lei; Hao, Wei; Li, Lingjiang

    2013-01-01

    Previous studies have investigated both structural and functional brain networks via graph-theoretical methods. However, there is an important issue that has not been adequately discussed before: what is the optimal theoretical graph model for describing the structural networks of human brain? In this paper, we perform a comparative study to address this problem. Firstly, large-scale cortical regions of interest (ROIs) are localized by recently developed and validated brain reference system named Dense Individualized Common Connectivity-based Cortical Landmarks (DICCCOL) to address the limitations in the identification of the brain network ROIs in previous studies. Then, we construct structural brain networks based on diffusion tensor imaging (DTI) data. Afterwards, the global and local graph properties of the constructed structural brain networks are measured using the state-of-the-art graph analysis algorithms and tools and are further compared with seven popular theoretical graph models. In addition, we compare the topological properties between two graph models, namely, stickiness-index-based model (STICKY) and scale-free gene duplication model (SF-GD), that have higher similarity with the real structural brain networks in terms of global and local graph properties. Our experimental results suggest that among the seven theoretical graph models compared in this study, STICKY and SF-GD models have better performances in characterizing the structural human brain network.

  12. Abelian link invariants and homology

    SciTech Connect

    Guadagnini, Enore; Mancarella, Francesco

    2010-06-15

    We consider the link invariants defined by the quantum Chern-Simons field theory with compact gauge group U(1) in a closed oriented 3-manifold M. The relation of the Abelian link invariants with the homology group of the complement of the links is discussed. We prove that, when M is a homology sphere or when a link--in a generic manifold M--is homologically trivial, the associated observables coincide with the observables of the sphere S{sup 3}. Finally, we show that the U(1) Reshetikhin-Turaev surgery invariant of the manifold M is not a function of the homology group only, nor a function of the homotopy type of M alone.

  13. Invariance concepts in spectral analysis

    NASA Astrophysics Data System (ADS)

    Schaum, Alan

    2017-05-01

    Methods are developed for insuring robust discrimination performance in detection problems with epistemic unknowns. The problem is first solved for the class of problems exhibiting some symmetry, as expressed by invariances to some group of feature space transformations. The determination of whether a problem admits a uniformly most powerful invariant (UMPI) solution (and how to derive it) is solved with a new and simple procedure. This motivates an approach for solving problems where a symmetry is gracefully broken, which leads in turn to a general approach for producing robust detectors. This introduces a new category of detector, the UMPIC (UMPI constrained). Finally, principles of UMPIC construction are shown to apply to problems exhibiting no invariances.

  14. Test of charge conjugation invariance.

    PubMed

    Nefkens, B M K; Prakhov, S; Gårdestig, A; Allgower, C E; Bekrenev, V; Briscoe, W J; Clajus, M; Comfort, J R; Craig, K; Grosnick, D; Isenhower, D; Knecht, N; Koetke, D; Koulbardis, A; Kozlenko, N; Kruglov, S; Lolos, G; Lopatin, I; Manley, D M; Manweiler, R; Marusić, A; McDonald, S; Olmsted, J; Papandreou, Z; Peaslee, D; Phaisangittisakul, N; Price, J W; Ramirez, A F; Sadler, M; Shafi, A; Spinka, H; Stanislaus, T D S; Starostin, A; Staudenmaier, H M; Supek, I; Tippens, W B

    2005-02-04

    We report on the first determination of upper limits on the branching ratio (BR) of eta decay to pi0pi0gamma and to pi0pi0pi0gamma. Both decay modes are strictly forbidden by charge conjugation (C) invariance. Using the Crystal Ball multiphoton detector, we obtained BR(eta-->pi0pi0gamma)<5 x 10(-4) at the 90% confidence level, in support of C invariance of isoscalar electromagnetic interactions of the light quarks. We have also measured BR(eta-->pi0pi0pi0gamma)<6 x 10(-5) at the 90% confidence level, in support of C invariance of isovector electromagnetic interactions.

  15. Energy Invariance in Capillary Systems.

    PubMed

    Ruiz-Gutiérrez, Élfego; Guan, Jian H; Xu, Ben; McHale, Glen; Wells, Gary G; Ledesma-Aguilar, Rodrigo

    2017-05-26

    We demonstrate the continuous translational invariance of the energy of a capillary surface in contact with reconfigurable solid boundaries. We present a theoretical approach to find the energy-invariant equilibria of spherical capillary surfaces in contact with solid boundaries of arbitrary shape and examine the implications of dynamic frictional forces upon a reconfiguration of the boundaries. Experimentally, we realize our ideas by manipulating the position of a droplet in a wedge geometry using lubricant-impregnated solid surfaces, which eliminate the contact-angle hysteresis and provide a test bed for quantifying dissipative losses out of equilibrium. Our experiments show that dissipative energy losses for an otherwise energy-invariant reconfiguration are relatively small, provided that the actuation time scale is longer than the typical relaxation time scale of the capillary surface. We discuss the wider applicability of our ideas as a pathway for liquid manipulation at no potential energy cost in low-pinning, low-friction situations.

  16. Energy Invariance in Capillary Systems

    NASA Astrophysics Data System (ADS)

    Ruiz-Gutiérrez, Élfego; Guan, Jian H.; Xu, Ben; McHale, Glen; Wells, Gary G.; Ledesma-Aguilar, Rodrigo

    2017-05-01

    We demonstrate the continuous translational invariance of the energy of a capillary surface in contact with reconfigurable solid boundaries. We present a theoretical approach to find the energy-invariant equilibria of spherical capillary surfaces in contact with solid boundaries of arbitrary shape and examine the implications of dynamic frictional forces upon a reconfiguration of the boundaries. Experimentally, we realize our ideas by manipulating the position of a droplet in a wedge geometry using lubricant-impregnated solid surfaces, which eliminate the contact-angle hysteresis and provide a test bed for quantifying dissipative losses out of equilibrium. Our experiments show that dissipative energy losses for an otherwise energy-invariant reconfiguration are relatively small, provided that the actuation time scale is longer than the typical relaxation time scale of the capillary surface. We discuss the wider applicability of our ideas as a pathway for liquid manipulation at no potential energy cost in low-pinning, low-friction situations.

  17. Sharing Teaching Ideas: Graphing Families of Curves Using Transformations of Reference Graphs

    ERIC Educational Resources Information Center

    Kukla, David

    2007-01-01

    This article provides for a fast extremely accurate approach to graphing functions that is based on learning function reference graphs and then applying algebraic transformations to these reference graphs.

  18. Graph theory data for topological quantum chemistry

    NASA Astrophysics Data System (ADS)

    Vergniory, M. G.; Elcoro, L.; Wang, Zhijun; Cano, Jennifer; Felser, C.; Aroyo, M. I.; Bernevig, B. Andrei; Bradlyn, Barry

    2017-08-01

    Topological phases of noninteracting particles are distinguished by the global properties of their band structure and eigenfunctions in momentum space. On the other hand, group theory as conventionally applied to solid-state physics focuses only on properties that are local (at high-symmetry points, lines, and planes) in the Brillouin zone. To bridge this gap, we have previously [Bradlyn et al., Nature (London) 547, 298 (2017), 10.1038/nature23268] mapped the problem of constructing global band structures out of local data to a graph construction problem. In this paper, we provide the explicit data and formulate the necessary algorithms to produce all topologically distinct graphs. Furthermore, we show how to apply these algorithms to certain "elementary" band structures highlighted in the aforementioned reference, and thus we identified and tabulated all orbital types and lattices that can give rise to topologically disconnected band structures. Finally, we show how to use the newly developed bandrep program on the Bilbao Crystallographic Server to access the results of our computation.

  19. Graph theory data for topological quantum chemistry.

    PubMed

    Vergniory, M G; Elcoro, L; Wang, Zhijun; Cano, Jennifer; Felser, C; Aroyo, M I; Bernevig, B Andrei; Bradlyn, Barry

    2017-08-01

    Topological phases of noninteracting particles are distinguished by the global properties of their band structure and eigenfunctions in momentum space. On the other hand, group theory as conventionally applied to solid-state physics focuses only on properties that are local (at high-symmetry points, lines, and planes) in the Brillouin zone. To bridge this gap, we have previously [Bradlyn et al., Nature (London) 547, 298 (2017)NATUAS0028-083610.1038/nature23268] mapped the problem of constructing global band structures out of local data to a graph construction problem. In this paper, we provide the explicit data and formulate the necessary algorithms to produce all topologically distinct graphs. Furthermore, we show how to apply these algorithms to certain "elementary" band structures highlighted in the aforementioned reference, and thus we identified and tabulated all orbital types and lattices that can give rise to topologically disconnected band structures. Finally, we show how to use the newly developed bandrep program on the Bilbao Crystallographic Server to access the results of our computation.

  20. Monadic structures over an ordered universal random graph and finite automata

    NASA Astrophysics Data System (ADS)

    Dudakov, Sergey M.

    2011-10-01

    We continue the investigation of the expressive power of the language of predicate logic for finite algebraic systems embedded in infinite systems. This investigation stems from papers of M. A. Taitslin, M. Benedikt and L. Libkin, among others. We study the properties of a finite monadic system which can be expressed by formulae if such a system is embedded in a random graph that is totally ordered in an arbitrary way. The Büchi representation is used to connect monadic structures and formal languages. It is shown that, if one restricts attention to formulae that are -invariant in totally ordered random graphs, then these formulae correspond to finite automata. We show that =-invariant formulae expressing the properties of the embedded system itself can express only Boolean combinations of properties of the form `the cardinality of an intersection of one-place predicates belongs to one of finitely many fixed finite or infinite arithmetic progressions'.