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Sample records for local graph invariants

  1. Scale-invariant geometric random graphs.

    PubMed

    Xie, Zheng; Rogers, Tim

    2016-03-01

    We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to influence zones that depend on node position in space and time, mimicking the heterogeneity and increased specialization found in growing networks. Through calculations and numerical simulations we explore the consequences of scale invariance for geometric random graphs generated this way. Our analysis reveals a dichotomy between scale-free and Poisson distributions of in- and out-degree, the existence of a random number of hub nodes, high clustering, and unusual percolation behavior. These properties are similar to those of empirically observed web graphs. PMID:27078369

  2. The uniqueness of DMAX-matrix graph invariants.

    PubMed

    Dehmer, Matthias; Shi, Yongtang

    2014-01-01

    In this paper, we examine the uniqueness (discrimination power) of a newly proposed graph invariant based on the matrix DMAX defined by Randić et al. In order to do so, we use exhaustively generated graphs instead of special graph classes such as trees only. Using these graph classes allow us to generalize the findings towards complex networks as they usually do not possess any structural constraints. We obtain that the uniqueness of this newly proposed graph invariant is approximately as low as the uniqueness of the Balaban J index on exhaustively generated (general) graphs. PMID:24392099

  3. A Local Galilean Invariant Thermostat.

    PubMed

    Groot, Robert D

    2006-05-01

    The thermostat introduced recently by Stoyanov and Groot (J. Chem. Phys. 2005, 122, 114112) is analyzed for inhomogeneous systems. This thermostat has one global feature, because the mean temperature used to drive the system toward equilibrium is a global average. The consequence is that the thermostat locally conserves energy rather than temperature. Thus, local temperature variations can be long-lived, although they do average out by thermal diffusion. To obtain a faster local temperature equilibration, a truly local thermostat must be introduced. To conserve momentum and, hence, to simulate hydrodynamic interactions, the thermostat must be Galilean invariant. Such a local Galilean invariant thermostat is studied here. It is shown that, by defining a local temperature on each particle, the ensemble is locally isothermal. The local temperature is obtained from a local square velocity average around each particle. Simulations on the ideal gas show that this local Nosé-Hoover algorithm has a similar artifact as dissipative particle dynamics:  the ideal gas pair correlation function is slightly distorted. This is attributed to the fact that the thermostat compensates fluctuations that are natural within a small cluster of particles. When the cutoff range rc for the square velocity average is increased, systematic errors decrease proportionally to rc(-)(3/2); hence, the systematic error can be made arbitrary small.

  4. Compact set of invariants characterizing graph states of up to eight qubits

    NASA Astrophysics Data System (ADS)

    Cabello, Adán; López-Tarrida, Antonio J.; Moreno, Pilar; Portillo, José R.

    2009-07-01

    The set of entanglement measures proposed by Hein, Eisert, and Briegel for n -qubit graph states [Phys. Rev. A 69, 062311 (2004)] fails to distinguish between inequivalent classes under local Clifford operations if n≥7 . On the other hand, the set of invariants proposed by van den Nest, Dehaene, and De Moor (VDD) [Phys. Rev. A 72, 014307 (2005)] distinguishes between inequivalent classes, but contains too many invariants (more than 2×1036 for n=7 ) to be practical. Here we solve the problem of deciding which entanglement class a graph state of n≤8 qubits belongs to by calculating some of the state’s intrinsic properties. We show that four invariants related to those proposed by VDD are enough for distinguishing between all inequivalent classes with n≤8 qubits.

  5. Invariant feature extraction for color image mosaic by graph card processing

    NASA Astrophysics Data System (ADS)

    Liu, Jin; Chen, Lin; Li, Deren

    2009-10-01

    Image mosaic can be widely used in remote measuring, scout in battlefield and Panasonic image demonstration. In this project, we find a general method for video (or sequence images) mosaic by techniques, such as extracting invariant features, gpu processing, multi-color feature selection, ransac algorithm for homograph matching. In order to match the image sequence automatically without influence of rotation, scale and contrast transform, local invariant feature descriptor have been extracted by graph card unit. The gpu mosaic algorithm performs very well that can be compare to slow CPU version of mosaic program with little cost time.

  6. 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.

  7. Localized, partially space-invariant filtering

    NASA Astrophysics Data System (ADS)

    Zalevsky, Zeev; Mendlovic, David; Caulfield, John H.

    1997-02-01

    In cases in which the image-to-image spatial variability of the input pattern changes with the spatial location, a localized-filtering method should be used for pattern recognition. Localized space-invariant filtering is investigated, and its improved recognition abilities are demonstrated with the recognition of fingerprints. The motivation for the investigated implementation is related to the fact that a person never presses his finger on a surface with equal pressure. This variation results in different amounts of spatial shifting being required from the optical processor in different regions of the fingerprint. A two-region mathematical model for representing the human finger is presented and investigated by use of localized space-invariant filtering by means of a computer.

  8. 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.

  9. 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.

  10. 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.

  11. Percolation in invariant Poisson graphs with i.i.d. degrees

    NASA Astrophysics Data System (ADS)

    Deijfen, Maria; Häggström, Olle; Holroyd, Alexander E.

    2012-04-01

    Let each point of a homogeneous Poisson process in ℝ d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution μ on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution μ. Leaving aside degenerate cases, we prove that for any μ there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme which is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on μ for the absence and presence of infinite components.

  12. 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.

  13. 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.

  14. Comparison of image patches using local moment invariants.

    PubMed

    Sit, Atilla; Kihara, Daisuke

    2014-05-01

    We propose a new set of moment invariants based on Krawtchouk polynomials for comparison of local patches in 2D images. Being computed from discrete functions, these moments do not carry the error due to discretization. Unlike many orthogonal moments, which usually capture global features, Krawtchouk moments can be used to compute local descriptors from a region-of-interest in an image. This can be achieved by changing two parameters, and hence shifting the center of interest region horizontally or vertically or both. This property enables comparison of two arbitrary local regions. We show that Krawtchouk moments can be written as a linear combination of geometric moments, so easily converted to rotation, size, and position independent invariants. We also construct local Hu-based invariants using Hu invariants and utilizing them on images localized by the weight function given in the definition of Krawtchouk polynomials. We give the formulation of local Krawtchouk-based and Hu-based invariants, and evaluate their discriminative performance on local comparison of artificially generated test images.

  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. 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

  18. 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.

  19. Structural information content of networks: graph entropy based on local vertex functionals.

    PubMed

    Dehmer, Matthias; Emmert-Streib, Frank

    2008-04-01

    In this paper we define the structural information content of graphs as their corresponding graph entropy. This definition is based on local vertex functionals obtained by calculating j-spheres via the algorithm of Dijkstra. We prove that the graph entropy and, hence, the local vertex functionals can be computed with polynomial time complexity enabling the application of our measure for large graphs. In this paper we present numerical results for the graph entropy of chemical graphs and discuss resulting properties. PMID:18243802

  20. Preserving local gauge invariance with t -channel Regge exchange

    NASA Astrophysics Data System (ADS)

    Haberzettl, Helmut; Wang, Xiao-Yun; He, Jun

    2015-11-01

    Considering single-meson photo- and electroproduction off a baryon, it is shown how to restore local gauge invariance that was broken by replacing standard Feynman-type meson exchange in the t channel by exchange of a Regge trajectory. This is achieved by constructing a contact current whose four-divergence cancels the gauge-invariance-violating contributions resulting from all states above the base state on the Regge trajectory. To illustrate the procedure, modifications necessary for the process γ +p →K++Σ*0 are discussed in some detail. We also provide the general expression for the contact current for an arbitrary reaction.

  1. Invariant current approach to wave propagation in locally symmetric structures

    NASA Astrophysics Data System (ADS)

    Zampetakis, V. E.; Diakonou, M. K.; Morfonios, C. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.

    2016-05-01

    A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of the stationary Schrödinger equation. The local symmetries of the potential are encoded into corresponding local basis vectors in terms of symmetry-induced two-point invariant currents which map the basis amplitudes between symmetry-related points. A universal wavefunction structure in locally symmetric potentials is revealed, independently of the physical boundary conditions, by using special local bases which are adapted to the existing local symmetries. The local symmetry bases enable efficient computation of spatially resolved wave amplitudes in systems with arbitrary combinations of local inversion and translation symmetries. The approach opens the perspective of a flexible analysis and control of wave localization in structurally complex systems.

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

    NASA Astrophysics Data System (ADS)

    Haah, Jeongwan

    2016-03-01

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

  3. 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

  4. 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.

  5. 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

  6. 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. PMID:22164016

  7. Image retrieval based on local grey-level invariants

    NASA Astrophysics Data System (ADS)

    Bordeaux, Eva; Shrikhande, Neelima

    2005-10-01

    During past decades, the enormous growth of image archives has significantly increased the demand for research efforts aimed at efficiently finding specific images within large databases. This paper investigates matching of images of buildings, architectural designs, blueprints and sketches. Their geometrical constrains lead to the proposed approach: the use of local grey-level invariants based on internal contours of the object. The problem involves three key phases: object recognition in image data, matching two images and searching the database of images. The emphasis of this paper is on object recognition based on internal contours of image data. In her master's thesis, M.M. Kulkarni described a technique for image retrieval by contour analysis implemented on external contours of an object in an image data. This is used to define the category of a building (tower, dome, flat, etc). Integration of these results with local grey-level invariant analysis creates a more robust image retrieval system. Thus, the best match result is the intersection of the results of contour analysis and grey-level invariants analysis. Experiments conducted for the database of architectural buildings have shown robustness w.r.t. to image rotation, translation, small view-point variations, partial visibility and extraneous features. The recognition rate is above 99% for a variety of tested images taken under different conditions.

  8. 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.

  9. f(T) gravity and local Lorentz invariance

    SciTech Connect

    Li Baojiu; Sotiriou, Thomas P.; Barrow, John D.

    2011-03-15

    We show that in theories of generalized teleparallel gravity, whose Lagrangians are algebraic functions of the usual teleparallel Lagrangian, the action and the field equations are not invariant under local Lorentz transformations. We also argue that these theories appear to have extra degrees of freedom with respect to general relativity. The usual teleparallel Lagrangian, which has been extensively studied and leads to a theory dynamically equivalent to general relativity, is an exception. Both of these facts appear to have been overlooked in the recent literature on f(T) gravity, but are crucial for assessing the viability of these theories as alternative explanations for the acceleration of the Universe.

  10. Nonergodicity and localization of invariant measure for two colliding masses

    NASA Astrophysics Data System (ADS)

    Wang, Jiao; Casati, Giulio; Prosen, Tomaž

    2014-04-01

    We show evidence, based on extensive and carefully performed numerical experiments, that the system of two elastic hard-point masses in one dimension is not ergodic for a generic mass ratio and consequently does not follow the principle of energy equipartition. This system is equivalent to a right triangular billiard. Remarkably, following the time-dependent probability distribution in a suitably chosen velocity direction space, we find evidence of exponential localization of invariant measure. For nongeneric mass ratios which correspond to billiard angles which are rational, or weak irrational multiples of π, the system is ergodic, consistent with existing rigorous results.

  11. 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

  12. 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. PMID:25608306

  13. Fermions in gravity with local spin-base invariance

    NASA Astrophysics Data System (ADS)

    Gies, Holger; Lippoldt, Stefan

    2014-03-01

    We study a formulation of Dirac fermions in curved spacetime that respects general coordinate invariance as well as invariance under local spin-base transformations. The natural variables for this formulation are spacetime-dependent Dirac matrices subject to the Clifford-algebra constraint. In particular, a coframe, i.e. vierbein field is not required. The corresponding affine spin connection consists of a canonical part that is completely fixed in terms of the Dirac matrices and a free part that can be interpreted as spin torsion. A general variation of the Dirac matrices naturally induces a spinorial Lie derivative which coincides with the known Kosmann-Lie derivative in the absence of torsion. Using this formulation for building a field theory of quantized gravity and matter fields, we show that it suffices to quantize the metric and the matter fields. This observation is of particular relevance for field theory approaches to quantum gravity, as it can serve for a purely metric-based quantization scheme for gravity even in the presence of fermions.

  14. 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.

  15. Localized structural health monitoring via transmission zero invariance

    NASA Astrophysics Data System (ADS)

    Reich, Gregory William

    2000-11-01

    This thesis presents a method of localized health monitoring based on an invariance property of transmission zeros of substructural frequency response functions. The proposed method has several desirable characteristics which make it attractive for use in damage detection applications. These are the independence from initial parameter estimates, the determination of a unique damage location, and the fact that the method is particularly suited for structural continuum applications where other methods perform poorly. The proposed method is based on a substructuring technique for structural mechanics. The structural equations of motion are cast in a variational framework and are mathematically decomposed into substructures using Lagrange multipliers as boundary constraints. The global dynamics of the system are then written in terms of the independent dynamics of each substructure plus the inter-element dynamics. The frequency response functions of the localized form represent the energy transfer between unique input forces which are derived from the total global force input and output variables which exist independently on a substructure. Because transmission zeros are highly dependent on the input and output of the system under consideration, they exhibit different characteristics in the local form versus the global form. If damage is limited to a change in flexibility, then it can be shown that the transmission zeros of a partition of the full transfer function matrix corresponding to a damaged substructure are invariant to the damage. Transmission zeros of partitions of the transfer function matrix corresponding to healthy substructures likewise can be shown to vary with the damage. Identification of the substructure whose zeros exhibit the least amount of variation between tests results in identification of the damage location. Analytical and experimental examples are used to demonstrate the theory and abilities of the proposed method. In each example, the system

  16. 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.

  17. 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.

  18. 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. PMID:25910105

  19. Shannon's, mutual, conditional and joint entropy information indices: generalization of global indices defined from local vertex invariants.

    PubMed

    Barigye, Stephen J; Marrero-Ponce, Yovani; Santiago, Oscar Martinez; López, Yoan Martinez; Pérez-Giménez, Facundo; Torrens, Francisco

    2013-06-01

    A new mathematical approach is proposed in the definition of molecular descriptors (MDs) based on the application of information theory concepts. This approach stems from a new matrix representation of a molecular graph (G) which is derived from the generalization of an incidence matrix whose row entries correspond to connected subgraphs of a given G, and the calculation of the Shannon's entropy, the negentropy and the standardized information content, plus for the first time, the mutual, conditional and joint entropy-based MDs associated with G. We also define strategies that generalize the definition of global or local invariants from atomic contributions (local vertex invariants, LOVIs), introducing related metrics (norms), means and statistical invariants. These invariants are applied to a vector whose components express the atomic information content calculated using the Shannon's, mutual, conditional and joint entropybased atomic information indices. The novel information indices (IFIs) are implemented in the program TOMOCOMDCARDD. A principal component analysis reveals that the novel IFIs are capable of capturing structural information not codified by IFIs implemented in the software DRAGON. A comparative study of the different parameters (e.g. subgraph orders and/or types, invariants and class of MDs) used in the definition of these IFIs reveals several interesting results. The mutual entropy-based indices give the best correlation results in modeling of a physicochemical property, namely the partition coefficient of the 34 derivatives of 2-furylethylenes, among the classes of indices investigated in this study. In a comparison with classical MDs it is demonstrated that the new IFIs give good results for various QSPR models.

  20. 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

  1. Discrete spectrum for quantum graph with local disturbance of the periodicity

    NASA Astrophysics Data System (ADS)

    Popov, Igor Yu; Blinova, Irina V.; Popov, Anton I.

    2015-12-01

    The problem of discrete spectrum for quantum graph with local disturbance of the periodicity is described. The Hamiltonian is determined as 1D Schrödinger operator on each edge and some boundary conditions at each vertex. The spectral analysis of the quantum graph having the form of branching strips with hexagonal (honeycomb) structure is considered in more details.

  2. 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.

  3. Localization Computation of One-Point Disk Invariants of Projective Calabi-Yau Complete Intersections

    NASA Astrophysics Data System (ADS)

    Popa, Alexandra

    2014-12-01

    We define one-point disk invariants of a smooth projective Calabi-Yau complete intersection in the presence of an anti-holomorphic involution via localization. We show that these invariants are rational numbers and obtain a formula for them which confirms, in particular, a conjecture by Jinzenji-Shimizu [(Int J Geom Method M 11(1):1456005, 2014), Conjecture 1].

  4. Invariant conserved currents in gravity theories: Diffeomorphisms and local gauge symmetries

    NASA Astrophysics Data System (ADS)

    Obukhov, Yuri N.; Rubilar, Guillermo F.

    2007-12-01

    Previously, we developed a general method to construct invariant conserved currents and charges in gravitational theories with Lagrangians that are invariant under spacetime diffeomorphisms and local Lorentz transformations. This approach is now generalized to the case when the local Lorentz group is replaced by an arbitrary local gauge group. The particular examples include the Maxwell and Yang-Mills fields coupled to gravity with Abelian and non-Abelian local internal symmetries and the metric-affine gravity in which the local Lorentz spacetime group is extended to the local general linear group.

  5. 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.

  6. Spectral properties of microwave graphs with local absorption.

    PubMed

    Allgaier, Markus; Gehler, Stefan; Barkhofen, Sonja; Stöckmann, H-J; Kuhl, Ulrich

    2014-02-01

    The influence of absorption on the spectra of microwave graphs has been studied experimentally. The microwave networks were made up of coaxial cables and T junctions. First, absorption was introduced by attaching a 50Ω load to an additional vertex for graphs with and without time-reversal symmetry. The resulting level-spacing distributions were compared with a generalization of the Wigner surmise in the presence of open channels proposed recently by Poli et al. [Phys. Rev. Lett. 108, 174101 (2012)]. Good agreement was found using an effective coupling parameter. Second, absorption was introduced along one individual bond via a variable microwave attenuator, and the influence of absorption on the length spectrum was studied. The peak heights in the length spectra corresponding to orbits avoiding the absorber were found to be independent of the attenuation, whereas, the heights of the peaks belonging to orbits passing the absorber once or twice showed the expected decrease with increasing attenuation.

  7. A fast Monte Carlo algorithm for source localization on graphs

    NASA Astrophysics Data System (ADS)

    Agaskar, Ameya; Lu, Yue M.

    2013-09-01

    Epidemic models on networks have long been studied by biologists and social sciences to determine the steady state levels of an infection on a network. Recently, however, several authors have begun considering the more difficult problem of estimating the source of an infection given information about its behavior some time after the initial infection. In this paper, we describe a technique to estimate the source of an infection on a general graph based on observations from a small set of observers during a fixed time window at some unknown time after the initial infection. We describe an alternate representation for the susceptible-infected (SI) infection model based on geodesic distances on a randomly-weighted version of the graph; this representation allows us to exploit fast algorithms to compute geodesic distances to estimate the marginal distributions for each observer and compute a pseudo-likelihood function that is maximized to find the source.

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

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

    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.

  9. Global Positioning System test of the local position invariance of Planck's constant.

    PubMed

    Kentosh, J; Mohageg, M

    2012-03-16

    Publicly available clock correction data from the Global Positioning System was analyzed and used in combination with the results of terrestrial clock comparison experiments to confirm the local position invariance (LPI) of Planck's constant within the context of general relativity. The results indicate that h is invariant within a limit of |β(h)|<0.007, where β(h) is a dimensionless parameter that represents the extent of LPI violation.

  10. Feature-based affine-Invariant localization of faces.

    PubMed

    Hamouz, M; Kittler, J; Kamarainen, J K; Paalanen, P; Kälviäinen, H; Matas, J

    2005-09-01

    We present a novel method for localizing faces in person identification scenarios. Such scenarios involve high resolution images of frontal faces. The proposed algorithm does not require color, copes well in cluttered backgrounds, and accurately localizes faces including eye centers. An extensive analysis and a performance evaluation on the XM2VTS database and on the realistic BioID and BANCA face databases is presented. We show that the algorithm has precision superior to reference methods.

  11. Local graph alignment and motif search in biological networks

    NASA Astrophysics Data System (ADS)

    Berg, Johannes; Lässig, Michael

    2004-10-01

    Interaction networks are of central importance in postgenomic molecular biology, with increasing amounts of data becoming available by high-throughput methods. Examples are gene regulatory networks or protein interaction maps. The main challenge in the analysis of these data is to read off biological functions from the topology of the network. Topological motifs, i.e., patterns occurring repeatedly at different positions in the network, have recently been identified as basic modules of molecular information processing. In this article, we discuss motifs derived from families of mutually similar but not necessarily identical patterns. We establish a statistical model for the occurrence of such motifs, from which we derive a scoring function for their statistical significance. Based on this scoring function, we develop a search algorithm for topological motifs called graph alignment, a procedure with some analogies to sequence alignment. The algorithm is applied to the gene regulation network of Escherichia coli.

  12. 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.

  13. 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.

  14. 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

  15. Locally linear regression for pose-invariant face recognition.

    PubMed

    Chai, Xiujuan; Shan, Shiguang; Chen, Xilin; Gao, Wen

    2007-07-01

    The variation of facial appearance due to the viewpoint (/pose) degrades face recognition systems considerably, which is one of the bottlenecks in face recognition. One of the possible solutions is generating virtual frontal view from any given nonfrontal view to obtain a virtual gallery/probe face. Following this idea, this paper proposes a simple, but efficient, novel locally linear regression (LLR) method, which generates the virtual frontal view from a given nonfrontal face image. We first justify the basic assumption of the paper that there exists an approximate linear mapping between a nonfrontal face image and its frontal counterpart. Then, by formulating the estimation of the linear mapping as a prediction problem, we present the regression-based solution, i.e., globally linear regression. To improve the prediction accuracy in the case of coarse alignment, LLR is further proposed. In LLR, we first perform dense sampling in the nonfrontal face image to obtain many overlapped local patches. Then, the linear regression technique is applied to each small patch for the prediction of its virtual frontal patch. Through the combination of all these patches, the virtual frontal view is generated. The experimental results on the CMU PIE database show distinct advantage of the proposed method over Eigen light-field method.

  16. Local and BRST-invariant Yang-Mills theory within the Gribov horizon

    NASA Astrophysics Data System (ADS)

    Capri, M. A. L.; Dudal, D.; Fiorentini, D.; Guimaraes, M. S.; Justo, I. F.; Pereira, A. D.; Mintz, B. W.; Palhares, L. F.; Sobreiro, R. F.; Sorella, S. P.

    2016-07-01

    We present a local setup for the recently introduced BRST-invariant formulation of Yang-Mills theories for linear covariant gauges that takes into account the existence of gauge copies à la Gribov and Zwanziger. Through the convenient use of auxiliary fields, including one of the Stueckelberg type, it is shown that both the action and the associated nilpotent BRST operator can be put in local form. Direct consequences of this fully local and BRST-symmetric framework are drawn from its Ward identities: (i) an exact prediction for the longitudinal part of the gluon propagator in linear covariant gauges that is compatible with recent lattice results and (ii) a proof of the gauge-parameter itxndependence of all correlation functions of local BRST-invariant operators.

  17. Locality preserving non-negative basis learning with graph embedding.

    PubMed

    Ghanbari, Yasser; Herrington, John; Gur, Ruben C; Schultz, Robert T; Verma, Ragini

    2013-01-01

    The high dimensionality of connectivity networks necessitates the development of methods identifying the connectivity building blocks that not only characterize the patterns of brain pathology but also reveal representative population patterns. In this paper, we present a non-negative component analysis framework for learning localized and sparse sub-network patterns of connectivity matrices by decomposing them into two sets of discriminative and reconstructive bases. In order to obtain components that are designed towards extracting population differences, we exploit the geometry of the population by using a graphtheoretical scheme that imposes locality-preserving properties as well as maintaining the underlying distance between distant nodes in the original and the projected space. The effectiveness of the proposed framework is demonstrated by applying it to two clinical studies using connectivity matrices derived from DTI to study a population of subjects with ASD, as well as a developmental study of structural brain connectivity that extracts gender differences. PMID:24683979

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

    NASA Astrophysics Data System (ADS)

    Tian, David Wenjie

    2016-08-01

    For a large class of scalar-tensor-like gravity whose action contains nonminimal couplings between a scalar field φ (x^α ) and generic curvature invariants R beyond the Ricci scalar R=R^α _{α }, we prove the covariant invariance of its field equation and confirm/prove the local energy-momentum conservation. These φ (x^α )- R coupling terms break the symmetry of diffeomorphism invariance under an active transformation, which implies that the solutions to the field equation should satisfy the consistency condition R ≡ 0 when φ (x^α ) is nondynamical and massless. Following this fact and based on the accelerated expansion of the observable Universe, we propose a primary test to check the viability of the modified gravity to be an effective dark energy, and a simplest example passing the test is the "Weyl/conformal dark energy".

  19. The problem of deficiency indices for discrete Schroedinger operators on locally finite graphs

    SciTech Connect

    Golenia, Sylvain

    2011-06-15

    The number of self-adjoint extensions of a symmetric operator acting on a complex Hilbert space is characterized by its deficiency indices. Given a locally finite unoriented simple tree, we prove that the deficiency indices of any discrete Schroedinger operator are either null or infinite. We also prove that all deterministic discrete Schroedinger operators which act on a random tree are almost surely self-adjoint. Furthermore, we provide several criteria of essential self-adjointness. We also address some importance to the case of the adjacency matrix and conjecture that, given a locally finite unoriented simple graph, its deficiency indices are either null or infinite. Besides that, we consider some generalizations of trees and weighted graphs.

  20. 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. PMID:27255799

  1. Locally gauge-invariant spin response of 3He-B films with Majorana surface states

    NASA Astrophysics Data System (ADS)

    Taylor, Edward; Berlinsky, A. John; Kallin, Catherine

    2015-04-01

    A locally gauge-invariant theory of the spin response of a thin film of 3He-B film is given that describes fluctuation effects arising from the coupled dynamics of the superconducting order parameter (the collective mode) and in-gap Majorana surface states. In contrast to a mean-field calculation of the spin response, which predicts a nonzero imaginary longitudinal spin susceptibility at frequencies inside the bulk gap due to absorption from the Majorana states, our gauge-invariant theory shows that this response is strongly suppressed above the collective mode frequency and vanishes if dipole-dipole interactions are neglected. In the presence of dipole-dipole interactions, in sufficiently thin films, and at ultralow temperatures, the Majorana states lead to a distinctive magnetic-field- and temperature-dependent damping of the collective mode, a feature that may be observable in longitudinal NMR experiments.

  2. Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry

    SciTech Connect

    Obukhov, Yuri N.; Rubilar, Guillermo F.

    2006-09-15

    We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in many covariant and noncovariant(ly looking) ways. An interesting mathematical fact underlies such a diversity: there is a certain ambiguity in a definition of the (Lorentz-) covariant generalization of the usual Lie derivative. Using this freedom, we develop a general approach to the construction of invariant conserved currents generated by an arbitrary vector field on the spacetime. This is done in any dimension, for any Lagrangian of the gravitational field and of a (minimally or nonminimally) coupled matter field. A development of the ''regularization via relocalization'' scheme is used to obtain finite conserved quantities for asymptotically nonflat solutions. We illustrate how our formalism works by some explicit examples.

  3. A graph-based approach for local and global panorama imaging in cystoscopy

    NASA Astrophysics Data System (ADS)

    Bergen, Tobias; Wittenberg, Thomas; Münzenmayer, Christian; Chen, Chi Chiung Grace; Hager, Gregory D.

    2013-03-01

    Inspection of the urinary bladder with an endoscope (cystoscope) is the usual procedure for early detection of bladder cancer. The very limited field of view provided by the endoscope makes it challenging to ensure, that the interior bladder wall has been examined completely. Panorama imaging techniques can be used to assist the surgeon and provide a larger view field. Different approaches have been proposed, but generating a panorama image of the entire bladder from real patient data is still a challenging research topic. We propose a graph-based and hierarchical approach to assess this problem to first generate several local panorama images, followed by a global textured three-dimensional reconstruction of the organ. In this contribution, we address details of the first level of the approach including a graph-based algorithm to deal with the challenging condition of in-vivo data. This graph strategy gives rise to a robust relocalization strategy in case of tracking failure, an effective keyframe selection process as well as the concept of building locally optimized sub-maps, which lay the ground for a global optimization process. Our results show the successful application of the method to four in-vivo data sets.

  4. Universal Quantum Graphs

    NASA Astrophysics Data System (ADS)

    Pluhař, Z.; Weidenmüller, H. A.

    2014-04-01

    For time-reversal invariant graphs we prove the Bohigas-Giannoni-Schmit conjecture in its most general form: For graphs that are mixing in the classical limit, all spectral correlation functions coincide with those of the Gaussian orthogonal ensemble of random matrices. For open graphs, we derive the analogous identities for all S-matrix correlation functions.

  5. Underground localization using dual magnetic field sequence measurement and pose graph SLAM for directional drilling

    NASA Astrophysics Data System (ADS)

    Park, Byeolteo; Myung, Hyun

    2014-12-01

    With the development of unconventional gas, the technology of directional drilling has become more advanced. Underground localization is the key technique of directional drilling for real-time path following and system control. However, there are problems such as vibration, disconnection with external infrastructure, and magnetic field distortion. Conventional methods cannot solve these problems in real time or in various environments. In this paper, a novel underground localization algorithm using a re-measurement of the sequence of the magnetic field and pose graph SLAM (simultaneous localization and mapping) is introduced. The proposed algorithm exploits the property of the drilling system that the body passes through the previous pass. By comparing the recorded measurement from one magnetic sensor and the current re-measurement from another magnetic sensor, the proposed algorithm predicts the pose of the drilling system. The performance of the algorithm is validated through simulations and experiments.

  6. 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.

  7. 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. PMID:24702346

  8. 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.

  9. 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

  10. 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

  11. The mixed two qutrit system: local unitary invariants, entanglement monotones, and the SLOCC group SL(3,{ {C}})

    NASA Astrophysics Data System (ADS)

    Jarvis, P. D.

    2014-05-01

    We consider local unitary invariants and entanglement monotones for the mixed two qutrit system. Character methods for the local SU(3) × SU(3) transformation group are used to establish the count of algebraically independent polynomial invariants up to degree 5 in the components of the density operator. These are identified up to quartic degree in the standard basis of Gell-Mann matrices, with the help of the calculus of f and d coefficients. Next, investigating local measurement operations, we study a SLOCC qutrit group, which plays the role of a ‘relativistic’ transformation group analogous to that of the Lorentz group SL(2,{ {C}})_{ {R}}\\simeq SO(3,1) for the qubit case. This is the group SL(3,{ {C}})_{ {R}}, presented as a group of real 9 × 9 matrices acting linearly on the nine-dimensional space of projective coordinates for the qutrit density matrix. The counterpart, for qutrits, of the invariant 4 × 4 Minkowski metric of the qubit case, proves to be a certain 9 × 9 × 9 totally symmetric three-fold tensor generalizing the Gell-Mann d coefficient. Using this structure, we provide a count of the corresponding local special linear polynomial invariants using group character methods. Finally, we give an explicit construction of the lowest degree quantity (the cubic invariant) and its expansion in terms of SU(3) × SU(3) invariants, and we indicate how to construct higher degree analogues. These quantities are proven to yield entanglement monotones. This work generalizes and partly extends the paper of King et al (2007 J. Phys. A: Math. Theor. 40 10083) on the mixed two qubit system, which is reviewed in an appendix.

  12. 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.

  13. GraphClust: alignment-free structural clustering of local RNA secondary structures

    PubMed Central

    Rose, Dominic; Backofen, Rolf

    2012-01-01

    Motivation: Clustering according to sequence–structure similarity has now become a generally accepted scheme for ncRNA annotation. Its application to complete genomic sequences as well as whole transcriptomes is therefore desirable but hindered by extremely high computational costs. Results: We present a novel linear-time, alignment-free method for comparing and clustering RNAs according to sequence and structure. The approach scales to datasets of hundreds of thousands of sequences. The quality of the retrieved clusters has been benchmarked against known ncRNA datasets and is comparable to state-of-the-art sequence–structure methods although achieving speedups of several orders of magnitude. A selection of applications aiming at the detection of novel structural ncRNAs are presented. Exemplarily, we predicted local structural elements specific to lincRNAs likely functionally associating involved transcripts to vital processes of the human nervous system. In total, we predicted 349 local structural RNA elements. Availability: The GraphClust pipeline is available on request. Contact: backofen@informatik.uni-freiburg.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:22689765

  14. Improved tests of local position invariance using 87Rb and 133Cs fountains.

    PubMed

    Guéna, J; Abgrall, M; Rovera, D; Rosenbusch, P; Tobar, M E; Laurent, Ph; Clairon, A; Bize, S

    2012-08-24

    We report tests of local position invariance based on measurements of the ratio of the ground state hyperfine frequencies of 133Cs and 87Rb in laser-cooled atomic fountain clocks. Measurements extending over 14 years set a stringent limit to a possible variation with time of this ratio: d ln(ν(Rb)/ν(Cs))/dt=(-1.39±0.91)×10(-16) yr(-1). This improves by a factor of 7.7 over our previous report [H. Marion et al., Phys. Rev. Lett. 90, 150801 (2003)]. Our measurements also set the first limit to a fractional variation of the Rb/Cs frequency ratio with gravitational potential at the level of c(2)d ln(ν(Rb)/ν(Cs))/dU=(0.11±1.04)×10(-6), providing a new stringent differential redshift test. The above limits equivalently apply to the fractional variation of the quantity α(-0.49)(g(Rb)/g(Cs)), which involves the fine-structure constant α and the ratio of the nuclear g-factors of the two alkalis. The link with variations of the light quark mass is also presented together with a global analysis combining other available highly accurate clock comparisons. PMID:23002732

  15. 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.

  16. Contact-Free Palm-Vein Recognition Based on Local Invariant Features

    PubMed Central

    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. PMID:24866176

  17. 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.

  18. Stable standing waves for a NLS on star graphs as local minimizers of the constrained energy

    NASA Astrophysics Data System (ADS)

    Adami, Riccardo; Cacciapuoti, Claudio; Finco, Domenico; Noja, Diego

    2016-05-01

    On a star graph made of N ≥ 3 halflines (edges) we consider a Schrödinger equation with a subcritical power-type nonlinearity and an attractive delta interaction located at the vertex. From previous works it is known that there exists a family of standing waves, symmetric with respect to the exchange of edges, that can be parametrized by the mass (or L2-norm) of its elements. Furthermore, if the mass is small enough, then the corresponding symmetric standing wave is a ground state and, consequently, it is orbitally stable. On the other hand, if the mass is above a threshold value, then the system has no ground state. Here we prove that orbital stability holds for every value of the mass, even if the corresponding symmetric standing wave is not a ground state, since it is anyway a local minimizer of the energy among functions with the same mass. The proof is based on a new technique that allows to restrict the analysis to functions made of pieces of soliton, reducing the problem to a finite-dimensional one. In such a way, we do not need to use direct methods of Calculus of Variations, nor linearization procedures.

  19. 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.

  20. 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.

  1. Relaxing Lorentz invariance in general perturbative anomalies

    SciTech Connect

    Salvio, A.

    2008-10-15

    We analyze the role of Lorentz symmetry in the perturbative nongravitational anomalies for a single family of fermions. The theory is assumed to be translational-invariant, power-counting renormalizable and based on a local action, but is allowed to have general Lorentz violating operators. We study the conservation of global and gauge currents associated with general internal symmetry groups and find, by using a perturbative approach, that Lorentz symmetry does not participate in the clash of symmetries that leads to the anomalies. We first analyze the triangle graphs and prove that there are regulators for which the anomalous part of the Ward identities exactly reproduces the Lorentz-invariant case. Then we show, by means of a regulator independent argument, that the anomaly cancellation conditions derived in Lorentz-invariant theories remain necessary ingredients for anomaly freedom.

  2. 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.

  3. Closely Spaced MEG Source Localization and Functional Connectivity Analysis Using a New Prewhitening Invariance of Noise Space Algorithm.

    PubMed

    Zhang, Junpeng; Cui, Yuan; Deng, Lihua; He, Ling; Zhang, Junran; Zhang, Jing; Zhou, Qun; Liu, Qi; Zhang, Zhiguo

    2016-01-01

    This paper proposed a prewhitening invariance of noise space (PW-INN) as a new magnetoencephalography (MEG) source analysis method, which is particularly suitable for localizing closely spaced and highly correlated cortical sources under real MEG noise. Conventional source localization methods, such as sLORETA and beamformer, cannot distinguish closely spaced cortical sources, especially under strong intersource correlation. Our previous work proposed an invariance of noise space (INN) method to resolve closely spaced sources, but its performance is seriously degraded under correlated noise between MEG sensors. The proposed PW-INN method largely mitigates the adverse influence of correlated MEG noise by projecting MEG data to a new space defined by the orthogonal complement of dominant eigenvectors of correlated MEG noise. Simulation results showed that PW-INN is superior to INN, sLORETA, and beamformer in terms of localization accuracy for closely spaced and highly correlated sources. Lastly, source connectivity between closely spaced sources can be satisfactorily constructed from source time courses estimated by PW-INN but not from results of other conventional methods. Therefore, the proposed PW-INN method is a promising MEG source analysis to provide a high spatial-temporal characterization of cortical activity and connectivity, which is crucial for basic and clinical research of neural plasticity.

  4. Closely Spaced MEG Source Localization and Functional Connectivity Analysis Using a New Prewhitening Invariance of Noise Space Algorithm

    PubMed Central

    Zhang, Junpeng; Cui, Yuan; Deng, Lihua; He, Ling; Zhang, Junran; Zhang, Jing; Zhou, Qun; Liu, Qi; Zhang, Zhiguo

    2016-01-01

    This paper proposed a prewhitening invariance of noise space (PW-INN) as a new magnetoencephalography (MEG) source analysis method, which is particularly suitable for localizing closely spaced and highly correlated cortical sources under real MEG noise. Conventional source localization methods, such as sLORETA and beamformer, cannot distinguish closely spaced cortical sources, especially under strong intersource correlation. Our previous work proposed an invariance of noise space (INN) method to resolve closely spaced sources, but its performance is seriously degraded under correlated noise between MEG sensors. The proposed PW-INN method largely mitigates the adverse influence of correlated MEG noise by projecting MEG data to a new space defined by the orthogonal complement of dominant eigenvectors of correlated MEG noise. Simulation results showed that PW-INN is superior to INN, sLORETA, and beamformer in terms of localization accuracy for closely spaced and highly correlated sources. Lastly, source connectivity between closely spaced sources can be satisfactorily constructed from source time courses estimated by PW-INN but not from results of other conventional methods. Therefore, the proposed PW-INN method is a promising MEG source analysis to provide a high spatial-temporal characterization of cortical activity and connectivity, which is crucial for basic and clinical research of neural plasticity. PMID:26819768

  5. 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

    2016-07-01

    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.

  6. Hyperspectral target detection using graph theory models and manifold geometry via an adaptive implementation of locally linear embedding

    NASA Astrophysics Data System (ADS)

    Ziemann, Amanda K.; Messinger, David W.

    2014-06-01

    Hyperspectral images comprise, by design, high dimensional image data. However, research has shown that for a d-dimensional hyperspectral image, it is typical for the data to inherently occupy an m-dimensional space, with m << d. In the remote sensing community, this has led to a recent increase in the use of non-linear manifold learning, which aims to characterize the embedded lower-dimensional, non-linear manifold upon which the hyperspectral data inherently lie. Classic hyperspectral data models include statistical, linear subspace, and linear mixture models, but these can place restrictive assumptions on the distribution of the data. With graph theory and manifold learning based models, the only assumption is that the data reside on an underlying manifold. In previous publications, we have shown that manifold coordinate approximation using locally linear embedding (LLE) is a viable pre-processing step for target detection with the Adaptive Cosine/Coherence Estimator (ACE) algorithm. Here, we improve upon that methodology using a more rigorous, data-driven implementation of LLE that incorporates the injection of a cloud" of target pixels and the Spectral Angle Mapper (SAM) detector. The LLE algorithm, which holds that the data is locally linear, is typically governed by a user defined parameter k, indicating the number of nearest neighbors to use in the initial graph model. We use an adaptive approach to building the graph that is governed by the data itself and does not rely upon user input. This implementation of LLE can yield greater separation between the target pixels and the background pixels in the manifold space. We present an analysis of target detection performance in the manifold coordinates using scene-derived target spectra and laboratory-measured target spectra across two different data sets.

  7. Context-Invariant and Local Quasi Hidden Variable (qHV) Modelling Versus Contextual and Nonlocal HV Modelling

    NASA Astrophysics Data System (ADS)

    Loubenets, Elena R.

    2015-07-01

    For the probabilistic description of all the joint von Neumann measurements on a D-dimensional quantum system, we present the specific example of a context-invariant quasi hidden variable (qHV) model, proved in Loubenets (J Math Phys 56:032201, 2015) to exist for each Hilbert space. In this model, a quantum observable X is represented by a variety of random variables satisfying the functional condition required in quantum foundations but, in contrast to a contextual model, each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. This, in particular, implies the specific local qHV (LqHV) model for an N-qudit state and allows us to derive the new exact upper bound on the maximal violation of 22-setting Bell-type inequalities of any type (either on correlation functions or on joint probabilities) under N-partite joint von Neumann measurements on an N-qudit state. For d = 2, this new upper bound coincides with the maximal violation by an N-qubit state of the Mermin-Klyshko inequality. Based on our results, we discuss the conceptual and mathematical advantages of context-invariant and local qHV modelling.

  8. 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.

  9. Graph characterization via Ihara coefficients.

    PubMed

    Ren, Peng; Wilson, Richard C; Hancock, Edwin R

    2011-02-01

    The novel contributions of this paper are twofold. First, we demonstrate how to characterize unweighted graphs in a permutation-invariant manner using the polynomial coefficients from the Ihara zeta function, i.e., the Ihara coefficients. Second, we generalize the definition of the Ihara coefficients to edge-weighted graphs. For an unweighted graph, the Ihara zeta function is the reciprocal of a quasi characteristic polynomial of the adjacency matrix of the associated oriented line graph. Since the Ihara zeta function has poles that give rise to infinities, the most convenient numerically stable representation is to work with the coefficients of the quasi characteristic polynomial. Moreover, the polynomial coefficients are invariant to vertex order permutations and also convey information concerning the cycle structure of the graph. To generalize the representation to edge-weighted graphs, we make use of the reduced Bartholdi zeta function. We prove that the computation of the Ihara coefficients for unweighted graphs is a special case of our proposed method for unit edge weights. We also present a spectral analysis of the Ihara coefficients and indicate their advantages over other graph spectral methods. We apply the proposed graph characterization method to capturing graph-class structure and clustering graphs. Experimental results reveal that the Ihara coefficients are more effective than methods based on Laplacian spectra.

  10. 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)

  11. 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

  12. The emergence of gauge invariance: The stay-at-home gauge versus local-global duality

    NASA Astrophysics Data System (ADS)

    Zaanen, J.; Beekman, A. J.

    2012-04-01

    In condensed matter physics, gauge symmetries other than the U(1) of electromagnetism are of an emergent nature. Two emergence mechanisms for gauge symmetry are well established: the way in which it arises in Kramers-Wannier type local-global dualities, and the way in which local constraints encountered in (doped) Mott insulators are encoded. We demonstrate that these gauge structures are closely related, and appear as counterparts in the canonical and field-theoretical languages. The restoration of symmetry in a disorder phase transition is due to having the original local variables subjected to a coherent superposition of all possible topological defect configurations, with the effect that correlation functions are no longer well-defined. This is completely equivalent to assigning gauge freedom to those variables. Two cases are considered explicitly: the well-known vortex duality in bosonic Mott insulators serves to illustrate the principle; and the acquired wisdom is then applied to the less familiar context of dualities in quantum elasticity, where we elucidate the relation between the quantum nematic and linearized gravity. We reflect on some deeper implications for the emergence of gauge symmetry in general.

  13. 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. PMID:27106344

  14. 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.

  15. 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

  16. 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

  17. 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

  18. Modulation of propagation-invariant Localized Waves for FSO communication systems.

    PubMed

    Salem, Mohamed A; Bağcı, Hakan

    2012-07-01

    The novel concept of spatio-temporal modulation of Nyquist pulses is introduced, and the resulting wave-packets are termed Nyquist Localized Waves (LWs). Ideal Nyquist LWs belong to the generic family of LW solutions and can propagate indefinitely in unbounded media without attenuation or chromatic dispersion. The possibility of modulating Nyquist LWs for free-space optical (FSO) communication systems is demonstrated using two different modulation techniques. The first technique is on-off keying (OOK) with alternate mark inversion (AMI) coding for 1-bit per symbol transmission, and the second one is 16-ary quadrature amplitude modulation (16-QAM) for 4-bits per symbol transmission. Aspects related to the performance, detection and generation of the spatio-temporally coupled wave-packets are discussed and future research directions are outlined.

  19. Graph Library

    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 abilitymore » to export graphs into various open formats such as DOT and GML.« less

  20. 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.

  1. 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

  2. Campaign graphs

    SciTech Connect

    Simmons, G.J.

    1988-01-01

    We define a class of geometrical constructions in the plane in which each (unextended) line lies on (precisely) k points, and every point is an endpoint of (precisely) one line. We will refer to any construction satisfying these conditions as a campaign graph, or as a k-campaign graph if the value of k isn't clear from the context. A k-campaign graph, G, is said to be critical if no subgraph of G is also a k-campaign graph. 11 figs.

  3. [Local population of Eritrichium caucasicum as an object of mathematical modelling. I. Life cycle graph and a nonautonomous matrix model].

    PubMed

    Logofet, D O; Belova, I N; Kazantseva, E S; Onipchenko, V G

    2016-01-01

    For the plant species, which is considered a short-lived perennial, we have composed a scale of ontogenetic stages and the life cycle graph (LCG) according to annual observations on permanent sample plots in an Alpine lichen heath during the 2009-2014 period. The LCG that reflects seed reproduction has been reduced to the one that avoids the stage of soil seed bank, yet preserves the arcs of annual recruitment. The corresponding matrix model of stage-structured population dynamics has four stages: juvenile plants (including seedlings), virginal, generative, and 'terminally generative' (the plants die after seed production). Model calibration reduces to directly calculating the rates of transition between stages and those of delays within stages from the data of only one time step, while keeping the two reproduction rates uncertain, yet confined to the quantitative bounds of observed recruitment. This has enabled us to determine a feasible range for the dominant eigenvalue of the model matrix, i.e., the quantitative bounds for the measure of how the local population adapts to its environment, at each of the five time steps, resulting in aformally nonautonomous model. To obtain 'age-specific parameters' from a stage-classified model, we have applied the technique that constructs a virtual absorbing Markov chain and calculates its fundamental matrix. In a nonautonomous model, the estimates of life expectancy also depend on the time of observation (that fixes certain environmental conditions), and vary from two to nearly seven years. The estimates reveal how specifically short lives the short-lived perennial, while their range motivates the task to average the model matrices over the whole period of observation. The model indicates that Eritrichium caucasicum plants spend the most part of their life span in the virginal stage under each of the environment conditions observed, thus revealing the place retention strategy by C. K6rner (2003), or the delayed

  4. [Local population of Eritrichium caucasicum as an object of mathematical modelling. I. Life cycle graph and a nonautonomous matrix model].

    PubMed

    Logofet, D O; Belova, I N; Kazantseva, E S; Onipchenko, V G

    2016-01-01

    For the plant species, which is considered a short-lived perennial, we have composed a scale of ontogenetic stages and the life cycle graph (LCG) according to annual observations on permanent sample plots in an Alpine lichen heath during the 2009-2014 period. The LCG that reflects seed reproduction has been reduced to the one that avoids the stage of soil seed bank, yet preserves the arcs of annual recruitment. The corresponding matrix model of stage-structured population dynamics has four stages: juvenile plants (including seedlings), virginal, generative, and 'terminally generative' (the plants die after seed production). Model calibration reduces to directly calculating the rates of transition between stages and those of delays within stages from the data of only one time step, while keeping the two reproduction rates uncertain, yet confined to the quantitative bounds of observed recruitment. This has enabled us to determine a feasible range for the dominant eigenvalue of the model matrix, i.e., the quantitative bounds for the measure of how the local population adapts to its environment, at each of the five time steps, resulting in aformally nonautonomous model. To obtain 'age-specific parameters' from a stage-classified model, we have applied the technique that constructs a virtual absorbing Markov chain and calculates its fundamental matrix. In a nonautonomous model, the estimates of life expectancy also depend on the time of observation (that fixes certain environmental conditions), and vary from two to nearly seven years. The estimates reveal how specifically short lives the short-lived perennial, while their range motivates the task to average the model matrices over the whole period of observation. The model indicates that Eritrichium caucasicum plants spend the most part of their life span in the virginal stage under each of the environment conditions observed, thus revealing the place retention strategy by C. K6rner (2003), or the delayed

  5. 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.

  6. 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.

  7. Graph partitions and cluster synchronization in networks of oscillators

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

    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.

  8. 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

  9. 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

    2015-01-01

    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

  10. 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.

  11. 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…

  12. Identification of human protein complexes from local sub-graphs of protein-protein interaction network based on random forest with topological structure features.

    PubMed

    Li, Zhan-Chao; Lai, Yan-Hua; Chen, Li-Li; Zhou, Xuan; Dai, Zong; Zou, Xiao-Yong

    2012-03-01

    In the post-genomic era, one of the most important and challenging tasks is to identify protein complexes and further elucidate its molecular mechanisms in specific biological processes. Previous computational approaches usually identify protein complexes from protein interaction network based on dense sub-graphs and incomplete priori information. Additionally, the computational approaches have little concern about the biological properties of proteins and there is no a common evaluation metric to evaluate the performance. So, it is necessary to construct novel method for identifying protein complexes and elucidating the function of protein complexes. In this study, a novel approach is proposed to identify protein complexes using random forest and topological structure. Each protein complex is represented by a graph of interactions, where descriptor of the protein primary structure is used to characterize biological properties of protein and vertex is weighted by the descriptor. The topological structure features are developed and used to characterize protein complexes. Random forest algorithm is utilized to build prediction model and identify protein complexes from local sub-graphs instead of dense sub-graphs. As a demonstration, the proposed approach is applied to protein interaction data in human, and the satisfied results are obtained with accuracy of 80.24%, sensitivity of 81.94%, specificity of 80.07%, and Matthew's correlation coefficient of 0.4087 in 10-fold cross-validation test. Some new protein complexes are identified, and analysis based on Gene Ontology shows that the complexes are likely to be true complexes and play important roles in the pathogenesis of some diseases. PCI-RFTS, a corresponding executable program for protein complexes identification, can be acquired freely on request from the authors.

  13. 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.

  14. 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.

  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. Semantic graphs and associative memories.

    PubMed

    Pomi, Andrés; Mizraji, Eduardo

    2004-12-01

    Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.

  17. Semantic graphs and associative memories

    NASA Astrophysics Data System (ADS)

    Pomi, Andrés; Mizraji, Eduardo

    2004-12-01

    Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.

  18. 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.

  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. 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.

  2. Automatic detection and segmentation of bovine corpora lutea in ultrasonographic ovarian images using genetic programming and rotation invariant local binary patterns.

    PubMed

    Dong, Meng; Eramian, Mark G; Ludwig, Simone A; Pierson, Roger A

    2013-04-01

    In this study, we propose a fully automatic algorithm to detect and segment corpora lutea (CL) using genetic programming and rotationally invariant local binary patterns. Detection and segmentation experiments were conducted and evaluated on 30 images containing a CL and 30 images with no CL. The detection algorithm correctly determined the presence or absence of a CL in 93.33 % of the images. The segmentation algorithm achieved a mean (±standard deviation) sensitivity and specificity of 0.8693 ± 0.1371 and 0.9136 ± 0.0503, respectively, over the 30 CL images. The mean root mean squared distance of the segmented boundary from the true boundary was 1.12 ± 0.463 mm and the mean maximum deviation (Hausdorff distance) was 3.39 ± 2.00 mm. The success of these algorithms demonstrates that similar algorithms designed for the analysis of in vivo human ovaries are likely viable.

  3. 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…

  4. 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.

  5. 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.

  6. The Role of Hepatic Invariant (I)NKT Cells in Systemic/Local Inflammation and Mortality During Polymicrobial Septic Shock1

    PubMed Central

    Hu, Caroline K.; Venet, Fabienne; Heffernan, David S.; Wang, Yvonne L.; Horner, Brian; Huang, Xin; Chung, Chun-Shiang; Gregory, Stephen H.; Ayala, Alfred

    2009-01-01

    Natural killer T (NKT)4 cells have been described as “innate regulatory cells” because of their rapid response to conserved glycolipids presented on CD1d via their invariant TCR. However, little is known about the contribution of the hepatic NKT cell to the development of a local and/or systemic immune response to acute septic challenge (cecal ligation & puncture; CLP). We found not only that mice deficient in invariant [i] NKT cells (Jα18 -/-) had a marked attenuation in CLP induced mortality, but also exhibited an oblation of the systemic inflammatory response (with little effect on splenic/ peritoneal immune responsiveness). Flow cytometric data indicated that following CLP, there was a marked decline in the % of CD3+αGalCer-CD1d-tetramer+ cells in the mouse C57BL/6J and Balb/c liver non-parenchymal cell population. This was associated with the marked activation of these cells (increased expression of CD69 and CD25) as well as a rise in the frequency of NKT cells positive for both Th1 and Th2 intracellular cytokines. In this respect, when mice were pre-treated in vivo with anti-CD1d blocking antibody we observed not only that this inhibited the systemic rise of IL-6 and IL-10 levels in septic mice and improved overall septic survival, but that the CLP induced changes in liver macrophage IL-6 and IL-10 expressions were inversely effected by this treatment. Together, these findings suggest that the activation of hepatic iNKT cells plays a critical role in regulating the innate immune/ systemic inflammatory response and survival in a model of acute septic shock. PMID:19201902

  7. 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.

  8. 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.

  9. Yamabe type equations on graphs

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

    Let G = (V , E) be a locally finite graph, Ω ⊂ V be a bounded domain, Δ be the usual graph Laplacian, and λ1 (Ω) be the first eigenvalue of -Δ with respect to Dirichlet boundary condition. Using the mountain pass theorem due to Ambrosetti-Rabinowitz, we prove that if α <λ1 (Ω), then for any p > 2, there exists a positive solution to

  10. Understanding Graphs & Charts.

    ERIC Educational Resources Information Center

    Cleary, John J.; Gravely, Mary Liles

    Developed by educators from the Emily Griffith Opportunity School, this teacher's guide was developed for a 4-hour workshop to teach employees how to read the charts and graphs they need in the workplace. The unit covers four types of graphs: pictographs, bar graphs, line graphs, and circle graphs. The guide is divided into four sections: reading…

  11. 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. PMID:26513787

  12. 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.

  13. Subgraph-Based Filterbanks for Graph Signals

    NASA Astrophysics Data System (ADS)

    Tremblay, Nicolas; Borgnat, Pierre

    2016-08-01

    We design a critically-sampled compact-support biorthogonal transform for graph signals, via graph filterbanks. Instead of partitioning the nodes in two sets so as to remove one every two nodes in the filterbank downsampling operations, the design is based on a partition of the graph in connected subgraphs. Coarsening is achieved by defining one "supernode" for each subgraph and the edges for this coarsened graph derives from the connectivity between the subgraphs. Unlike the "one every two nodes" downsampling on bipartite graphs, this coarsening operation does not have an exact formulation in the graph Fourier domain. Instead, we rely on the local Fourier bases of each subgraph to define filtering operations. We apply successfully this method to decompose graph signals, and show promising performance on compression and denoising.

  14. 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.

  15. Ezekiel graphs

    SciTech Connect

    Simmons, G.J.

    1991-01-01

    In spite of the old adage that No finite sequence of symbols is random,'' there are many instances in which it is desirable to quantify how random'' a finite sequence is. Pseudorandom number generators and cryptographic key generators typically expand a short, randomly chosen, seed sequence into a much longer sequence which should appear random to anyone ignorant of the seed. Unique initiating signals chosen to minimize the likelihood of an accidental initiation of an important action should be random'' to lessen the chance of their natural occurrence, etc. Consequently, numerous tests for the randomness of finite sequences have been proposed. John Milnor argued that if a binary sequence is random then the fraction of 1's, r{sub 1}, should be very nearly 1/2 in it and in all of what he called its derivatives. Since every sequence has a unique derivative this defines a natural family of digraphs, G{sub n}, on 2{sup n} vertices in which vertices are labeled with n-bit binary sequences and an edge is directed from the vertex labeled with the sequence A to the vertex labeled with the sequence B if B is the derivative of A. Each component of G{sub n} is eventually cyclic. This paper is concerned with a special case in which the sequences in a cycle are all cyclic shifts of a single sequence -- hence the name of Ezekiel graphs. Surprising, there are Ezekiel graphs for which r{sub 1} is as close to 1/2 as is numerically possible, i.e., that satisfy Milnor's test for randomness as closely as it can be satisfied, even though the sequence of sequences are about as far from random as is conceivable. In this paper the existence and properties of Ezekiel sequences are investigated from an algebraic standpoint.

  16. Graph signatures for visual analytics.

    PubMed

    Wong, Pak Chung; Foote, Harlan; Chin, George; Mackey, Patrick; Perrine, Ken

    2006-01-01

    We present a visual analytics technique to explore graphs using the concept of a data signature. A data signature, in our context, is a multidimensional vector that captures the local topology information surrounding each graph node. Signature vectors extracted from a graph are projected onto a low-dimensional scatterplot through the use of scaling. The resultant scatterplot, which reflects the similarities of the vectors, allows analysts to examine the graph structures and their corresponding real-life interpretations through repeated use of brushing and linking between the two visualizations. The interpretation of the graph structures is based on the outcomes of multiple participatory analysis sessions with intelligence analysts conducted by the authors at the Pacific Northwest National Laboratory. The paper first uses three public domain data sets with either well-known or obvious features to explain the rationale of our design and illustrate its results. More advanced examples are then used in a customized usability study to evaluate the effectiveness and efficiency of our approach. The study results reveal not only the limitations and weaknesses of the traditional approach based solely on graph visualization, but also the advantages and strengths of our signature-guided approach presented in the paper.

  17. 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…

  18. Graphing for Any Grade.

    ERIC Educational Resources Information Center

    Nibbelink, William

    1982-01-01

    An instructional sequence for teaching graphing that has been extensively field tested in kindergarten through grade six is detailed. The material begins with point graphs, employs a movable y-axis to begin with minimal clutter, and has graphs constructed before reading graphs is required. (MP)

  19. Accurate Segmentation of Cervical Cytoplasm and Nuclei Based on Multiscale Convolutional Network and Graph Partitioning.

    PubMed

    Song, Youyi; Zhang, Ling; Chen, Siping; Ni, Dong; Lei, Baiying; Wang, Tianfu

    2015-10-01

    In this paper, a multiscale convolutional network (MSCN) and graph-partitioning-based method is proposed for accurate segmentation of cervical cytoplasm and nuclei. Specifically, deep learning via the MSCN is explored to extract scale invariant features, and then, segment regions centered at each pixel. The coarse segmentation is refined by an automated graph partitioning method based on the pretrained feature. The texture, shape, and contextual information of the target objects are learned to localize the appearance of distinctive boundary, which is also explored to generate markers to split the touching nuclei. For further refinement of the segmentation, a coarse-to-fine nucleus segmentation framework is developed. The computational complexity of the segmentation is reduced by using superpixel instead of raw pixels. Extensive experimental results demonstrate that the proposed cervical nucleus cell segmentation delivers promising results and outperforms existing methods.

  20. 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. PMID:25822506

  1. 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.

  2. Scale invariance and superfluid turbulence

    NASA Astrophysics Data System (ADS)

    Sen, Siddhartha; Ray, Koushik

    2013-11-01

    We construct a Schroedinger field theory invariant under local spatial scaling. It is shown to provide an effective theory of superfluid turbulence by deriving, analytically, the observed Kolmogorov 5/3 law and to lead to a Biot-Savart interaction between the observed filament excitations of the system as well.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. Multi-A Graph Patrolling and Partitioning

    NASA Astrophysics Data System (ADS)

    Elor, Y.; Bruckstein, A. M.

    2012-12-01

    We introduce a novel multi agent patrolling algorithm inspired by the behavior of gas filled balloons. Very low capability ant-like agents are considered with the task of patrolling an unknown area modeled as a graph. While executing the proposed algorithm, the agents dynamically partition the graph between them using simple local interactions, every agent assuming the responsibility for patrolling his subgraph. Balanced graph partition is an emergent behavior due to the local interactions between the agents in the swarm. Extensive simulations on various graphs (environments) showed that the average time to reach a balanced partition is linear with the graph size. The simulations yielded a convincing argument for conjecturing that if the graph being patrolled contains a balanced partition, the agents will find it. However, we could not prove this. Nevertheless, we have proved that if a balanced partition is reached, the maximum time lag between two successive visits to any vertex using the proposed strategy is at most twice the optimal so the patrol quality is at least half the optimal. In case of weighted graphs the patrol quality is at least (1)/(2){lmin}/{lmax} of the optimal where lmax (lmin) is the longest (shortest) edge in the graph.

  8. 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…

  9. 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.

  10. 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…

  11. Invariance and neural nets.

    PubMed

    Barnard, E; Casasent, D

    1991-01-01

    Application of neural nets to invariant pattern recognition is considered. The authors study various techniques for obtaining this invariance with neural net classifiers and identify the invariant-feature technique as the most suitable for current neural classifiers. A novel formulation of invariance in terms of constraints on the feature values leads to a general method for transforming any given feature space so that it becomes invariant to specified transformations. A case study using range imagery is used to exemplify these ideas, and good performance is obtained.

  12. Computation of Open Gromov-Witten Invariants for Toric Calabi-Yau 3-Folds by Topological Recursion, a Proof of the BKMP Conjecture

    NASA Astrophysics Data System (ADS)

    Eynard, B.; Orantin, N.

    2015-07-01

    The BKMP conjecture (2006-2008) proposed a new method to compute closed and open Gromov-Witten invariants for every toric Calabi-Yau 3-folds, through a topological recursion based on mirror symmetry. So far, this conjecture has been verified to low genus for several toric CY3folds, and proved to all genus only for . In this article we prove the general case. Our proof is based on the fact that both sides of the conjecture can be naturally written in terms of combinatorial sums of weighted graphs: on the A-model side this is the localization formula, and on the B-model side the graphs encode the recursive algorithm of the topological recursion. One can slightly reorganize the set of graphs obtained in the B-side, so that it coincides with the one obtained by localization in the A-model. Then it suffices to compare the weights of vertices and edges of graphs on each side, which is done in two steps: the weights coincide in the large radius limit, due to the fact that the toric graph is the tropical limit of the mirror curve. Then the derivatives with respect to Kähler radius coincide due to the special geometry property implied by the topological recursion.

  13. Graphing with "LogoWriter."

    ERIC Educational Resources Information Center

    Yoder, Sharon K.

    This book discusses four kinds of graphs that are taught in mathematics at the middle school level: pictographs, bar graphs, line graphs, and circle graphs. The chapters on each of these types of graphs contain information such as starting, scaling, drawing, labeling, and finishing the graphs using "LogoWriter." The final chapter of the book…

  14. Methods of visualizing graphs

    SciTech Connect

    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.

  15. Genome alignment with graph data structures: a comparison

    PubMed Central

    2014-01-01

    Background Recent advances in rapid, low-cost sequencing have opened up the opportunity to study complete genome sequences. The computational approach of multiple genome alignment allows investigation of evolutionarily related genomes in an integrated fashion, providing a basis for downstream analyses such as rearrangement studies and phylogenetic inference. Graphs have proven to be a powerful tool for coping with the complexity of genome-scale sequence alignments. The potential of graphs to intuitively represent all aspects of genome alignments led to the development of graph-based approaches for genome alignment. These approaches construct a graph from a set of local alignments, and derive a genome alignment through identification and removal of graph substructures that indicate errors in the alignment. Results We compare the structures of commonly used graphs in terms of their abilities to represent alignment information. We describe how the graphs can be transformed into each other, and identify and classify graph substructures common to one or more graphs. Based on previous approaches, we compile a list of modifications that remove these substructures. Conclusion We show that crucial pieces of alignment information, associated with inversions and duplications, are not visible in the structure of all graphs. If we neglect vertex or edge labels, the graphs differ in their information content. Still, many ideas are shared among all graph-based approaches. Based on these findings, we outline a conceptual framework for graph-based genome alignment that can assist in the development of future genome alignment tools. PMID:24712884

  16. 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.

  17. 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.

  18. Reconstruction of Graph Signals Through Percolation from Seeding Nodes

    NASA Astrophysics Data System (ADS)

    Segarra, Santiago; Marques, Antonio G.; Leus, Geert; Ribeiro, Alejandro

    2016-08-01

    New schemes to recover signals defined in the nodes of a graph are proposed. Our focus is on reconstructing bandlimited graph signals, which are signals that admit a sparse representation in a frequency domain related to the structure of the graph. Most existing formulations focus on estimating an unknown graph signal by observing its value on a subset of nodes. By contrast, in this paper, we study the problem of reconstructing a known graph signal using as input a graph signal that is non-zero only for a small subset of nodes (seeding nodes). The sparse signal is then percolated (interpolated) across the graph using a graph filter. Graph filters are a generalization of classical time-invariant systems and represent linear transformations that can be implemented distributedly across the nodes of the graph. Three setups are investigated. In the first one, a single simultaneous injection takes place on several nodes in the graph. In the second one, successive value injections take place on a single node. The third one is a generalization where multiple nodes inject multiple signal values. For noiseless settings, conditions under which perfect reconstruction is feasible are given, and the corresponding schemes to recover the desired signal are specified. Scenarios leading to imperfect reconstruction, either due to insufficient or noisy signal value injections, are also analyzed. Moreover, connections with classical interpolation in the time domain are discussed. The last part of the paper presents numerical experiments that illustrate the results developed through synthetic graph signals and two real-world signal reconstruction problems: influencing opinions in a social network and inducing a desired brain state in humans.

  19. Lorentz invariance with an invariant energy scale.

    PubMed

    Magueijo, João; Smolin, Lee

    2002-05-13

    We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.

  20. 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.

  1. 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.

  2. mpiGraph

    2007-05-22

    MpiGraph consists of an MPI application called mpiGraph written in C to measure message bandwidth and an associated crunch_mpiGraph script written in Perl to process the application output into an HTMO report. The mpiGraph application is designed to inspect the health and scalability of a high-performance interconnect while under heavy load. This is useful to detect hardware and software problems in a system, such as slow nodes, links, switches, or contention in switch routing. Itmore » is also useful to characterize how interconnect performance changes with different settings or how one interconnect type compares to another.« less

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

    DOE PAGESBeta

    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 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

  4. 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.

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

    PubMed

    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[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. PMID:27636476

  6. 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.

  7. 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

  8. Boosting Shift-Invariant Features

    NASA Astrophysics Data System (ADS)

    Hörnlein, Thomas; Jähne, Bernd

    This work presents a novel method for training shift-invariant features using a Boosting framework. Features performing local convolutions followed by subsampling are used to achieve shift-invariance. Other systems using this type of features, e.g. Convolutional Neural Networks, use complex feed-forward networks with multiple layers. In contrast, the proposed system adds features one at a time using smoothing spline base classifiers. Feature training optimizes base classifier costs. Boosting sample-reweighting ensures features to be both descriptive and independent. Our system has a lower number of design parameters as comparable systems, so adapting the system to new problems is simple. Also, the stage-wise training makes it very scalable. Experimental results show the competitiveness of our approach.

  9. 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…

  10. 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…

  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. 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…

  13. 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…

  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. 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)

  16. 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.

  17. Equitable random graphs

    NASA Astrophysics Data System (ADS)

    Newman, M. E. J.; Martin, Travis

    2014-11-01

    Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdős and Rényi, in particular, as well as the so-called configuration model, have served as the starting point for numerous calculations. In this paper we describe another large class of random graph models, which we call equitable random graphs and which are flexible enough to represent networks with diverse degree distributions and many nontrivial types of structure, including community structure, bipartite structure, degree correlations, stratification, and others, yet are exactly solvable for a wide range of properties in the limit of large graph size, including percolation properties, complete spectral density, and the behavior of homogeneous dynamical systems, such as coupled oscillators or epidemic models.

  18. 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.

  19. 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.

  20. Reaction spreading on graphs

    NASA Astrophysics Data System (ADS)

    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 ds, the important quantity for reaction spreading is found to be the connectivity dimension dl. Numerical data, in agreement with analytical estimates based on the features of n independent random walkers on the graph, show that M(t)˜tdl. In the case of Erdös-Renyi random graphs, the reaction product is characterized by an exponential growth M(t)˜eαt with α proportional to ln, where is the average degree of the graph.

  1. A study on vague graphs.

    PubMed

    Rashmanlou, Hossein; Samanta, Sovan; Pal, Madhumangal; Borzooei, R A

    2016-01-01

    The main purpose of this paper is to introduce the notion of vague h-morphism on vague graphs and regular vague graphs. The action of vague h-morphism on vague strong regular graphs are studied. Some elegant results on weak and co weak isomorphism are derived. Also, [Formula: see text]-complement of highly irregular vague graphs are defined. PMID:27536517

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. Deformed graph laplacian for semisupervised learning.

    PubMed

    Gong, Chen; Liu, Tongliang; Tao, Dacheng; Fu, Keren; Tu, Enmei; Yang, Jie

    2015-10-01

    Graph Laplacian has been widely exploited in traditional graph-based semisupervised learning (SSL) algorithms to regulate the labels of examples that vary smoothly on the graph. Although it achieves a promising performance in both transductive and inductive learning, it is not effective for handling ambiguous examples (shown in Fig. 1). This paper introduces deformed graph Laplacian (DGL) and presents label prediction via DGL (LPDGL) for SSL. The local smoothness term used in LPDGL, which regularizes examples and their neighbors locally, is able to improve classification accuracy by properly dealing with ambiguous examples. Theoretical studies reveal that LPDGL obtains the globally optimal decision function, and the free parameters are easy to tune. The generalization bound is derived based on the robustness analysis. Experiments on a variety of real-world data sets demonstrate that LPDGL achieves top-level performance on both transductive and inductive settings by comparing it with popular SSL algorithms, such as harmonic functions, AnchorGraph regularization, linear neighborhood propagation, Laplacian regularized least square, and Laplacian support vector machine.

  7. Scale invariance in biophysics

    NASA Astrophysics Data System (ADS)

    Stanley, H. Eugene

    2000-06-01

    In this general talk, we offer an overview of some problems of interest to biophysicists, medical physicists, and econophysicists. These include DNA sequences, brain plaques in Alzheimer patients, heartbeat intervals, and time series giving price fluctuations in economics. These problems have the common feature that they exhibit features that appear to be scale invariant. Particularly vexing is the problem that some of these scale invariant phenomena are not stationary-their statistical properties vary from one time interval to the next or form one position to the next. We will discuss methods, such as wavelet methods and multifractal methods, to cope with these problems. .

  8. 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.

  9. 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.

  10. From cognitive maps to cognitive graphs.

    PubMed

    Chrastil, Elizabeth R; Warren, William H

    2014-01-01

    We investigate the structure of spatial knowledge that spontaneously develops during free exploration of a novel environment. We present evidence that this structure is similar to a labeled graph: a network of topological connections between places, labeled with local metric information. In contrast to route knowledge, we find that the most frequent routes and detours to target locations had not been traveled during learning. Contrary to purely topological knowledge, participants typically traveled the shortest metric distance to a target, rather than topologically equivalent but longer paths. The results are consistent with the proposal that people learn a labeled graph of their environment.

  11. PolyGraph: a Polymer Visualization system

    NASA Astrophysics Data System (ADS)

    Cutkosky, Ashok; Tarazi, Najeeb; Lieberman Aiden, Erez

    2012-02-01

    Rapid advances in computational hardware and parallelization have made complex simulations of large polymers increasingly ubiquitous. However, visualizing such simulations remains a challenge. Here we present PolyGraph, a Blender-powered visualization system for complex polymer simulations. As a specific example, we study molecular dynamics simulations of condensing polymers. We illustrate our initial simulation results, suggesting that formation of local beads is an initial step in the condensation process. (This finding is consistent with earlier conjectures about polymer condensation.) PolyGraph makes it possible to create precise and visually appealing clips of polymer simulations. *contributed equally

  12. From Cognitive Maps to Cognitive Graphs

    PubMed Central

    Chrastil, Elizabeth R.; Warren, William H.

    2014-01-01

    We investigate the structure of spatial knowledge that spontaneously develops during free exploration of a novel environment. We present evidence that this structure is similar to a labeled graph: a network of topological connections between places, labeled with local metric information. In contrast to route knowledge, we find that the most frequent routes and detours to target locations had not been traveled during learning. Contrary to purely topological knowledge, participants typically traveled the shortest metric distance to a target, rather than topologically equivalent but longer paths. The results are consistent with the proposal that people learn a labeled graph of their environment. PMID:25389769

  13. 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.

  14. A Similarity Search Using Molecular Topological Graphs

    PubMed Central

    Fukunishi, Yoshifumi; Nakamura, Haruki

    2009-01-01

    A molecular similarity measure has been developed using molecular topological graphs and atomic partial charges. Two kinds of topological graphs were used. One is the ordinary adjacency matrix and the other is a matrix which represents the minimum path length between two atoms of the molecule. The ordinary adjacency matrix is suitable to compare the local structures of molecules such as functional groups, and the other matrix is suitable to compare the global structures of molecules. The combination of these two matrices gave a similarity measure. This method was applied to in silico drug screening, and the results showed that it was effective as a similarity measure. PMID:20037730

  15. 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.

  16. 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.

  17. 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.

  18. 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…

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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…

  4. Gauge-invariant massive BF models

    NASA Astrophysics Data System (ADS)

    Bizdadea, Constantin; Saliu, Solange-Odile

    2016-02-01

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

  5. 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. PMID:27295541

  6. 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.

  7. Robustness of random graphs based on graph spectra

    NASA Astrophysics Data System (ADS)

    Wu, Jun; Barahona, Mauricio; Tan, Yue-jin; Deng, Hong-zhong

    2012-12-01

    It has been recently proposed that the robustness of complex networks can be efficiently characterized through the natural connectivity, a spectral property of the graph which corresponds to the average Estrada index. The natural connectivity corresponds to an average eigenvalue calculated from the graph spectrum and can also be interpreted as the Helmholtz free energy of the network. In this article, we explore the use of this index to characterize the robustness of Erdős-Rényi (ER) random graphs, random regular graphs, and regular ring lattices. We show both analytically and numerically that the natural connectivity of ER random graphs increases linearly with the average degree. It is also shown that ER random graphs are more robust than the corresponding random regular graphs with the same number of vertices and edges. However, the relative robustness of ER random graphs and regular ring lattices depends on the average degree and graph size: there is a critical graph size above which regular ring lattices are more robust than random graphs. We use our analytical results to derive this critical graph size as a function of the average degree.

  8. 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.

  9. 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

  10. Graph for locked rotor current

    NASA Technical Reports Server (NTRS)

    Peck, R. R.

    1972-01-01

    Graph determines effect of stalled motor on a distribution system and eliminates hand calculation of amperage in emergencies. Graph is useful to any manufacturer, contractor, or maintenance department involved in electrical technology.

  11. GraphLib

    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

  12. 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…

  13. 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…

  14. 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…

  15. 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…

  16. Physics on Graphs

    NASA Astrophysics Data System (ADS)

    Schrader, Robert

    This is an extended version of the talk given at the Nato Advanced Research Workshop: New Challenges in Complex System Physics, May 20-24, 2013 in Samarkand (Uzbekistan). We report on results on three topics in joint work with V. Kostrykin (Mainz, Germany) and J. Potthoff (Mannheim, Germany): Propagation of waves on graphs,

  17. 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.

  18. 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.

  19. New Conic Graph Paper

    ERIC Educational Resources Information Center

    Rose, Kenneth

    1974-01-01

    Two new types of graph paper are described; focus-focus conic paper and focus-directrix paper. Both types make it easier to draw families of conics. Suggestions for further work are given as is a method for establishing a connection with other ways of looking at the conic sections. (LS)

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.…

  5. 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.

  6. Editing graphs for maximum effect

    SciTech Connect

    Murphy, P.W.; Rhiner, R.W.

    1991-01-08

    The paper contains over eighty rules for editing graphs, arranged under nine major headings in a logical sequence for editing all the graphs in a manuscript. It is excerpted from a monograph used at the Lawrence Livermore National Laboratory to train beginning technical editors in editing graphs; a corresponding Hypercard stack is also used in this training. 6 refs., 4 figs.

  7. 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…

  8. 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.

  9. Correlated Percolation, Fractal Structures, and Scale-Invariant Distribution of Clusters in Natural Images

    PubMed Central

    Saremi, Saeed; Sejnowski, Terrence J.

    2016-01-01

    Natural images are scale invariant with structures at all length scales. We formulated a geometric view of scale invariance in natural images using percolation theory, which describes the behavior of connected clusters on graphs. We map images to the percolation model by defining clusters on a binary representation for images. We show that critical percolating structures emerge in natural images and study their scaling properties by identifying fractal dimensions and exponents for the scale-invariant distributions of clusters. This formulation leads to a method for identifying clusters in images from underlying structures as a starting point for image segmentation. PMID:26415153

  10. 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.

  11. Spectral fluctuations of quantum graphs

    NASA Astrophysics Data System (ADS)

    Pluhař, Z.; Weidenmüller, H. A.

    2014-10-01

    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. 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.

  13. 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.

  14. 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.

  15. The Nakayama Automorphism of the Almost Calabi-Yau Algebras Associated to SU(3) Modular Invariants

    NASA Astrophysics Data System (ADS)

    Evans, David E.; Pugh, Mathew

    2012-05-01

    We determine the Nakayama automorphism of the almost Calabi-Yau algebra A associated to the braided subfactors or nimrep graphs associated to each SU(3) modular invariant. We use this to determine a resolution of A as an A- A bimodule, which will yield a projective resolution of A.

  16. 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.

  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. Gauge invariant quantum cosmology

    NASA Technical Reports Server (NTRS)

    Berger, Beverly K.

    1987-01-01

    The study of boundary conditions, the Hamiltonian constraint, reparameterization-invariance, and quantum dynamics, is presently approached by means of the path-integral quantization of minisuperspace models. The separation of the wave functions for expansion and contraction by the Feynman boundary conditions is such that there can be no interference between them. This is implemented by the choice of a contour in the complex plane, in order to define the phase of the square-root Arnowitt, Deser, and Misner (1960) Hamiltonian for expansion, collapse, and the classically forbidden region.

  19. Random graphs containing arbitrary distributions of subgraphs

    NASA Astrophysics Data System (ADS)

    Karrer, Brian; Newman, M. E. J.

    2010-12-01

    Traditional random graph models of networks generate networks that are locally treelike, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly nontreelike neighborhoods that contain short loops, cliques, or other biconnected subgraphs. In this paper we propose and analyze a class of random graph models that incorporates general subgraphs, allowing for nontreelike neighborhoods while still remaining solvable for many fundamental network properties. Among other things we give solutions for the size of the giant component, the position of the phase transition at which the giant component appears, and percolation properties for both site and bond percolation on networks generated by the model.

  20. 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.

  1. 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.

  2. Signals on Graphs: Uncertainty Principle and Sampling

    NASA Astrophysics Data System (ADS)

    Tsitsvero, Mikhail; Barbarossa, Sergio; Di Lorenzo, Paolo

    2016-09-01

    In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of graph signals that are maximally concentrated on the graph domain and on its dual. Then, building on this framework, we derive an uncertainty principle for graph signals and illustrate the conditions for the recovery of band-limited signals from a subset of samples. We show an interesting link between uncertainty principle and sampling and propose alternative signal recovery algorithms, including a generalization to frame-based reconstruction methods. After showing that the performance of signal recovery algorithms is significantly affected by the location of samples, we suggest and compare a few alternative sampling strategies. Finally, we provide the conditions for perfect recovery of a useful signal corrupted by sparse noise, showing that this problem is also intrinsically related to vertex-frequency localization properties.

  3. Nonequilibrium invariant measure under heat flow.

    PubMed

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

    2008-09-19

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

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

    SciTech Connect

    Hong, Seokyong; 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.

  5. Correlation functions in conformal invariant stochastic processes

    NASA Astrophysics Data System (ADS)

    Alcaraz, Francisco C.; Rittenberg, Vladimir

    2015-11-01

    We consider the problem of correlation functions in the stationary states of one-dimensional stochastic models having conformal invariance. If one considers the space dependence of the correlators, the novel aspect is that although one considers systems with periodic boundary conditions, the observables are described by boundary operators. From our experience with equilibrium problems one would have expected bulk operators. Boundary operators have correlators having critical exponents being half of those of bulk operators. If one studies the space-time dependence of the two-point function, one has to consider one boundary and one bulk operators. The Raise and Peel model has conformal invariance as can be shown in the spin 1/2 basis of the Hamiltonian which gives the time evolution of the system. This is an XXZ quantum chain with twisted boundary condition and local interactions. This Hamiltonian is integrable and the spectrum is known in the finite-size scaling limit. In the stochastic base in which the process is defined, the Hamiltonian is not local anymore. The mapping into an SOS model, helps to define new local operators. As a byproduct some new properties of the SOS model are conjectured. The predictions of conformal invariance are discussed in the new framework and compared with Monte Carlo simulations.

  6. 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.

  7. 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.

  8. 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.

  9. 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

  10. A graph theoretical approach to states and unitary operations

    NASA Astrophysics Data System (ADS)

    Dutta, Supriyo; Adhikari, Bibhas; Banerjee, Subhashish

    2016-05-01

    Building upon our previous work, on graphical representation of a quantum state by signless Laplacian matrix, we pose the following question. If a local unitary operation is applied to a quantum state, represented by a signless Laplacian matrix, what would be the corresponding graph and how does one implement local unitary transformations graphically? We answer this question by developing the notion of local unitary equivalent graphs. We illustrate our method by a few, well known, local unitary transformations implemented by single-qubit Pauli and Hadamard gates. We also show how graph switching can be used to implement the action of the C_NOT gate, resulting in a graphical description of Bell state generation.

  11. 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

  12. Detecting alternative graph clusterings.

    PubMed

    Mandala, Supreet; Kumara, Soundar; Yao, Tao

    2012-07-01

    The problem of graph clustering or community detection has enjoyed a lot of attention in complex networks literature. A quality function, modularity, quantifies the strength of clustering and on maximization yields sensible partitions. However, in most real world networks, there are an exponentially large number of near-optimal partitions with some being very different from each other. Therefore, picking an optimal clustering among the alternatives does not provide complete information about network topology. To tackle this problem, we propose a graph perturbation scheme which can be used to identify an ensemble of near-optimal and diverse clusterings. We establish analytical properties of modularity function under the perturbation which ensures diversity. Our approach is algorithm independent and therefore can leverage any of the existing modularity maximizing algorithms. We numerically show that our methodology can systematically identify very different partitions on several existing data sets. The knowledge of diverse partitions sheds more light into the topological organization and helps gain a more complete understanding of the underlying complex network.

  13. 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%.

  14. 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.

  15. Bulk-Boundary Duality, Gauge Invariance, and Quantum Error Corrections

    NASA Astrophysics Data System (ADS)

    Mintun, Eric; Polchinski, Joseph; Rosenhaus, Vladimir

    2015-10-01

    Recently, Almheiri, Dong, and Harlow have argued that the localization of bulk information in a boundary dual should be understood in terms of quantum error correction. We show that this structure appears naturally when the gauge invariance of the boundary theory is incorporated. This provides a new understanding of the nonuniqueness of the bulk fields (precursors). It suggests a close connection between gauge invariance and the emergence of spacetime.

  16. FAST TRACK COMMUNICATION: Lorentzian manifolds and scalar curvature invariants

    NASA Astrophysics Data System (ADS)

    Coley, Alan; Hervik, Sigbjørn; Pelavas, Nicos

    2010-05-01

    We discuss (arbitrary-dimensional) Lorentzian manifolds and the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. Recently, we have shown that in four dimensions a Lorentzian spacetime metric is either \\mathcal {I}-non-degenerate, and hence locally characterized by its scalar polynomial curvature invariants, or is a degenerate Kundt spacetime. We present a number of results that generalize these results to higher dimensions and discuss their consequences and potential physical applications.

  17. 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.

  18. A Discussion of Population Invariance

    ERIC Educational Resources Information Center

    Brennan, Robert L.

    2008-01-01

    The discussion here covers five articles that are linked in the sense that they all treat population invariance. This discussion of population invariance is a somewhat broader treatment of the subject than simply a discussion of these five articles. In particular, occasional reference is made to publications other than those in this issue. The…

  19. 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.

  20. 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

  1. 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.

  2. Intergroup networks as random threshold graphs

    NASA Astrophysics Data System (ADS)

    Saha, Sudipta; Ganguly, Niloy; Mukherjee, Animesh; Krueger, Tyll

    2014-04-01

    Similar-minded people tend to form social groups. Due to pluralistic homophily as well as a sort of heterophily, people also participate in a wide variety of groups. Thus, these groups generally overlap with each other; an overlap between two groups can be characterized by the number of common members. These common members can play a crucial role in the transmission of information between the groups. As a step towards understanding the information dissemination, we perceive the system as a pruned intergroup network and show that it maps to a very basic graph theoretic concept known as a threshold graph. We analyze several structural properties of this network such as degree distribution, largest component size, edge density, and local clustering coefficient. We compare the theoretical predictions with the results obtained from several online social networks (LiveJournal, Flickr, YouTube) and find a good match.

  3. Adiabatic invariance of oscillons/I -balls

    NASA Astrophysics Data System (ADS)

    Kawasaki, Masahiro; Takahashi, Fuminobu; Takeda, Naoyuki

    2015-11-01

    Real scalar fields are known to fragment into spatially localized and long-lived solitons called oscillons or I -balls. We prove the adiabatic invariance of the oscillons/I -balls for a potential that allows periodic motion even in the presence of non-negligible spatial gradient energy. We show that such a potential is uniquely determined to be the quadratic one with a logarithmic correction, for which the oscillons/I -balls are absolutely stable. For slightly different forms of the scalar potential dominated by the quadratic one, the oscillons/I -balls are only quasistable, because the adiabatic charge is only approximately conserved. We check the conservation of the adiabatic charge of the I -balls in numerical simulation by slowly varying the coefficient of logarithmic corrections. This unambiguously shows that the longevity of oscillons/I -balls is due to the adiabatic invariance.

  4. 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

  5. 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…

  6. 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.

  7. 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)

  8. 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.

  9. Generic quantum walks with memory on regular graphs

    NASA Astrophysics Data System (ADS)

    Li, Dan; Mc Gettrick, Michael; Gao, Fei; Xu, Jie; Wen, Qiao-Yan

    2016-04-01

    Quantum walks with memory (QWM) are a type of modified quantum walks that record the walker's latest path. As we know, only two kinds of QWM have been presented up to now. It is desired to design more QWM for research, so that we can explore the potential of QWM. In this work, by presenting the one-to-one correspondence between QWM on a regular graph and quantum walks without memory (QWoM) on a line digraph of the regular graph, we construct a generic model of QWM on regular graphs. This construction gives a general scheme for building all possible standard QWM on regular graphs and makes it possible to study properties of different kinds of QWM. Here, by taking the simplest example, which is QWM with one memory on the line, we analyze some properties of QWM, such as variance, occupancy rate, and localization.

  10. A random graph model of density thresholds in swarming cells.

    PubMed

    Jena, Siddhartha G

    2016-03-01

    Swarming behaviour is a type of bacterial motility that has been found to be dependent on reaching a local density threshold of cells. With this in mind, the process through which cell-to-cell interactions develop and how an assembly of cells reaches collective motility becomes increasingly important to understand. Additionally, populations of cells and organisms have been modelled through graphs to draw insightful conclusions about population dynamics on a spatial level. In the present study, we make use of analogous random graph structures to model the formation of large chain subgraphs, representing interactions between multiple cells, as a random graph Markov process. Using numerical simulations and analytical results on how quickly paths of certain lengths are reached in a random graph process, metrics for intercellular interaction dynamics at the swarm layer that may be experimentally evaluated are proposed. PMID:26893102

  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. 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).

  13. Graph Partitioning and Sequencing Software

    1995-09-19

    Graph partitioning is a fundemental problem in many scientific contexts. CHACO2.0 is a software package designed to partition and sequence graphs. CHACO2.0 allows for recursive application of several methods for finding small edge separators in weighted graphs. These methods include inertial, spectral, Kernighan Lin and multilevel methods in addition to several simpler strategies. Each of these approaches can be used to partition the graph into two, four, or eight pieces at each level of recursion.more » In addition, the Kernighan Lin method can be used to improve partitions generated by any of the other algorithms. CHACO2.0 can also be used to address various graph sequencing problems, with applications to scientific computing, database design, gene sequencing and other problems.« less

  14. 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

  15. 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.

  16. 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.

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

    PubMed

    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.

  18. 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

  19. Shaping propagation invariant laser beams

    NASA Astrophysics Data System (ADS)

    Soskind, Michael; Soskind, Rose; Soskind, Yakov

    2015-11-01

    Propagation-invariant structured laser beams possess several unique properties and play an important role in various photonics applications. The majority of propagation invariant beams are produced in the form of laser modes emanating from stable laser cavities. Therefore, their spatial structure is limited by the intracavity mode formation. We show that several types of anamorphic optical systems (AOSs) can be effectively employed to shape laser beams into a variety of propagation invariant structured fields with different shapes and phase distributions. We present a propagation matrix approach for designing AOSs and defining mode-matching conditions required for preserving propagation invariance of the output shaped fields. The propagation matrix approach was selected, as it provides a more straightforward approach in designing AOSs for shaping propagation-invariant laser beams than the alternative technique based on the Gouy phase evolution, especially in the case of multielement AOSs. Several practical configurations of optical systems that are suitable for shaping input laser beams into a diverse variety of structured propagation invariant laser beams are also presented. The laser beam shaping approach was applied by modeling propagation characteristics of several input laser beam types, including Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian structured field distributions. The influence of the Ince-Gaussian beam semifocal separation parameter and the azimuthal orientation between the input laser beams and the AOSs onto the resulting shape of the propagation invariant laser beams is presented as well.

  20. 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.

  1. Invariant manifolds and global bifurcations.

    PubMed

    Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M; Sandstede, Björn

    2015-09-01

    Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to global bifurcations. Bifurcation manifolds in the parameter spaces of multi-parameter families of dynamical systems also play a prominent role in dynamical systems theory. Much progress has been made in developing theory and computational methods for invariant manifolds during the past 25 years. This article highlights some of these achievements and remaining open problems. PMID:26428557

  2. Invariant manifolds and global bifurcations.

    PubMed

    Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M; Sandstede, Björn

    2015-09-01

    Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to global bifurcations. Bifurcation manifolds in the parameter spaces of multi-parameter families of dynamical systems also play a prominent role in dynamical systems theory. Much progress has been made in developing theory and computational methods for invariant manifolds during the past 25 years. This article highlights some of these achievements and remaining open problems.

  3. Invariant manifolds and global bifurcations

    NASA Astrophysics Data System (ADS)

    Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M.; Sandstede, Björn

    2015-09-01

    Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to global bifurcations. Bifurcation manifolds in the parameter spaces of multi-parameter families of dynamical systems also play a prominent role in dynamical systems theory. Much progress has been made in developing theory and computational methods for invariant manifolds during the past 25 years. This article highlights some of these achievements and remaining open problems.

  4. Generating maps, invariant manifolds, conjugacy

    NASA Astrophysics Data System (ADS)

    Chaperon, Marc

    2015-01-01

    The idea of generating functions and maps is presented, first in global symplectic geometry and then in the theory of invariant manifolds, as introduced by McGehee and Sander in 1996. Their result on the stable manifold theorem is generalised and simplified; the proofs no longer use any functional analysis. Then comes an original "non-autonomous" version of the previous results, yielding-besides Pesin's invariant laminations-seemingly unrelated results on invariant manifolds and conjugacies, presented in the end after a basic example.

  5. Asymptotic behavior of Laplacian-energy-like invariant of the 3.6.24 lattice with various boundary conditions.

    PubMed

    Liu, Jia-Bao; Cao, Jinde; Hayat, Tasawar; Alsaadi, Fuad E

    2016-01-01

    Let G be a connected graph of order n with Laplacian eigenvalues [Formula: see text]. The Laplacian-energy-like invariant of G, is defined as [Formula: see text]. In this paper, we investigate the asymptotic behavior of the 3.6.24 lattice in terms of Laplacian-energy-like invariant as m, n approach infinity. Additionally, we derive that [Formula: see text], [Formula: see text] and [Formula: see text] have the same asymptotic Laplacian-energy-like invariants. PMID:27625970

  6. 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.

  7. 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.

  8. 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

  9. 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

  10. 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.

  11. Nonclassicality Invariant of General Two-Mode Gaussian States

    NASA Astrophysics Data System (ADS)

    Arkhipov, Ievgen I.; Peřina, Jan, Jr.; Svozilík, Jiří; Miranowicz, Adam

    2016-05-01

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2011-09-01

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

  14. Multi-clues image retrieval based on improved color invariants

    NASA Astrophysics Data System (ADS)

    Liu, Liu; Li, Jian-Xun

    2012-05-01

    At present, image retrieval has a great progress in indexing efficiency and memory usage, which mainly benefits from the utilization of the text retrieval technology, such as the bag-of-features (BOF) model and the inverted-file structure. Meanwhile, because the robust local feature invariants are selected to establish BOF, the retrieval precision of BOF is enhanced, especially when it is applied to a large-scale database. However, these local feature invariants mainly consider the geometric variance of the objects in the images, and thus the color information of the objects fails to be made use of. Because of the development of the information technology and Internet, the majority of our retrieval objects is color images. Therefore, retrieval performance can be further improved through proper utilization of the color information. We propose an improved method through analyzing the flaw of shadow-shading quasi-invariant. The response and performance of shadow-shading quasi-invariant for the object edge with the variance of lighting are enhanced. The color descriptors of the invariant regions are extracted and integrated into BOF based on the local feature. The robustness of the algorithm and the improvement of the performance are verified in the final experiments.

  15. Invariant regularization of anomaly-free chiral theories

    NASA Astrophysics Data System (ADS)

    Chang, Lay Nam; Soo, Chopin

    1997-02-01

    We present a generalization of the Frolov-Slavnov invariant regularization scheme for chiral fermion theories in curved spacetimes. The Lagrangian level regularization is explicitly invariant under all the local gauge symmetries of the theory, including local Lorentz invariance. The perturbative scheme works for arbitrary representations which satisfy the chiral gauge anomaly and the mixed Lorentz-gauge anomaly cancellation conditions. Anomalous theories on the other hand manifest themselves by having divergent fermion loops which remain unregularized by the scheme. Since the invariant scheme is promoted to include also local Lorentz invariance, spectator fields which do not couple to gravity cannot be, and are not, introduced. Furthermore, the scheme is truly chiral (Weyl) in that all fields, including the regulators, are left handed; and only the left-handed spin connection is needed. The scheme is, therefore, well suited for the study of the interaction of matter with all four known forces in a completely chiral fashion. In contrast with the vectorlike formulation, the degeneracy between the Adler-Bell-Jackiw current and the fermion number current in the bare action is preserved by the chiral regularization scheme.

  16. 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…

  17. 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. PMID:25361507

  18. Local Toolkit

    SciTech Connect

    Lindstrom, P.; Yoon, S. E.; Isenburg, M.

    2007-05-31

    The LOCAL Toolkit contains tools and libraries developed under the LLNL LOCAL LDRD project for managing and processing large unstructured data sets primrily from parallel numerical simulations, such as triangular, tetrahedral, and hexahedral meshes, point sets, and graphs. The tools have three main functionalities: cache-coherent, linear ordering of multidimensional data; lossy and lossless data compression optimized for different data types; and an out-of-core streaming I/O library with simple processing modules for unstructed data.

  19. 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.

  20. N=2 gauge theories: Congruence subgroups, coset graphs, and modular surfaces

    NASA Astrophysics Data System (ADS)

    He, Yang-Hui; McKay, John

    2013-01-01

    We establish a correspondence between generalized quiver gauge theories in four dimensions and congruence subgroups of the modular group, hinging upon the trivalent graphs, which arise in both. The gauge theories and the graphs are enumerated and their numbers are compared. The correspondence is particularly striking for genus zero torsion-free congruence subgroups as exemplified by those which arise in Moonshine. We analyze in detail the case of index 24, where modular elliptic K3 surfaces emerge: here, the elliptic j-invariants can be recast as dessins d'enfant, which dictate the Seiberg-Witten curves.

  1. CPT violation implies violation of Lorentz invariance.

    PubMed

    Greenberg, O W

    2002-12-01

    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. PMID:12484997

  2. Weyl invariance with a nontrivial mass scale

    NASA Astrophysics Data System (ADS)

    Álvarez, Enrique; González-Martín, Sergio

    2016-09-01

    A theory with a mass scale and yet Weyl invariant is presented. The theory is not invariant under all diffeomorphisms but only under transverse ones. This is the reason why Weyl invariance does not imply scale invariance in a free falling frame. Physical implications of this framework are discussed.

  3. CPT violation implies violation of Lorentz invariance.

    PubMed

    Greenberg, O W

    2002-12-01

    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.

  4. 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

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

    NASA Astrophysics Data System (ADS)

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

    1988-09-01

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

  6. 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.

  7. Subvoxel accurate graph search using non-Euclidean graph space.

    PubMed

    Abràmoff, Michael D; Wu, Xiaodong; Lee, Kyungmoo; Tang, Li

    2014-01-01

    Graph search is attractive for the quantitative analysis of volumetric medical images, and especially for layered tissues, because it allows globally optimal solutions in low-order polynomial time. However, because nodes of graphs typically encode evenly distributed voxels of the volume with arcs connecting orthogonally sampled voxels in Euclidean space, segmentation cannot achieve greater precision than a single unit, i.e. the distance between two adjoining nodes, and partial volume effects are ignored. We generalize the graph to non-Euclidean space by allowing non-equidistant spacing between nodes, so that subvoxel accurate segmentation is achievable. Because the number of nodes and edges in the graph remains the same, running time and memory use are similar, while all the advantages of graph search, including global optimality and computational efficiency, are retained. A deformation field calculated from the volume data adaptively changes regional node density so that node density varies with the inverse of the expected cost. We validated our approach using optical coherence tomography (OCT) images of the retina and 3-D MR of the arterial wall, and achieved statistically significant increased accuracy. Our approach allows improved accuracy in volume data acquired with the same hardware, and also, preserved accuracy with lower resolution, more cost-effective, image acquisition equipment. The method is not limited to any specific imaging modality and readily extensible to higher dimensions.

  8. Graph-Facts: Trends in Alaska Education 1960-1971.

    ERIC Educational Resources Information Center

    Hagmeier, John

    Eleven graphs present information on status and trends in Alaska in terms of number of public high school graduates, statewide enrollment, expenditures per pupil, local assistance, pupil-staff ratio, transportation, rural school enrollment, correspondence study, school lunch programs, average salaries of professional school personnel, and…

  9. 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.

  10. Dark coupling and gauge invariance

    SciTech Connect

    Gavela, M.B.; Honorez, L. Lopez; Rigolin, S. E-mail: llopezho@ulb.ac.be E-mail: stefano.rigolin@pd.infn.it

    2010-11-01

    We study a coupled dark energy-dark matter model in which the energy-momentum exchange is proportional to the Hubble expansion rate. The inclusion of its perturbation is required by gauge invariance. We derive the linear perturbation equations for the gauge invariant energy density contrast and velocity of the coupled fluids, and we determine the initial conditions. The latter turn out to be adiabatic for dark energy, when assuming adiabatic initial conditions for all the standard fluids. We perform a full Monte Carlo Markov Chain likelihood analysis of the model, using WMAP 7-year data.

  11. Critical phenomena of invariant circles

    SciTech Connect

    Hu, B.; Shi, J. ); Kim, S. )

    1991-04-15

    Some novel critical phenomena are discovered in a class of nonanalytic twist maps. It is found that the degree of inflection {ital z} plays a role reminiscent of that of dimensionality in phase transitions with {ital z}=2 and 3 corresponding to the lower and upper critical dimensions, respectively. Moreover, recurrence of invariant circles has also been observed. An inverse residue criterion,'' complementary to the residue criterion'' for the determination of the disappearance point, is introduced to determine the reappearance point of invariant circles.

  12. Box graphs and resolutions I

    NASA Astrophysics Data System (ADS)

    Braun, Andreas P.; Schäfer-Nameki, Sakura

    2016-04-01

    Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial) toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU (5) by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.

  13. Gauge invariance and the sigma model for the heterotic string

    SciTech Connect

    Hamada, K.J.; Kodaira, J.; Saito, J.

    1987-06-01

    The authors consider the heterotic string in arbitrary background gauge fields. The full gauge Chern-Simmons terms are shown to be reproduced in the divergent terms of the corresponding sigma model to the two-loop order. The role of the Chern-Simmons terms is discussed from the viewpoint of the local gauge invariance.

  14. Invariant Measures for Monotone SPDEs with Multiplicative Noise Term

    SciTech Connect

    Es-Sarhir, Abdelhadi; Scheutzow, Michael Toelle, Jonas M.; Gaans, Onno van

    2013-10-15

    We study diffusion processes corresponding to infinite dimensional semilinear stochastic differential equations with local Lipschitz drift term and an arbitrary Lipschitz diffusion coefficient. We prove tightness and the Feller property of the solution to show existence of an invariant measure. As an application we discuss stochastic reaction diffusion equations.

  15. Multiple directed graph large-class multi-spectral processor

    NASA Technical Reports Server (NTRS)

    Casasent, David; Liu, Shiaw-Dong; Yoneyama, Hideyuki

    1988-01-01

    Numerical analysis techniques for the interpretation of high-resolution imaging-spectrometer data are described and demonstrated. The method proposed involves the use of (1) a hierarchical classifier with a tree structure generated automatically by a Fisher linear-discriminant-function algorithm and (2) a novel multiple-directed-graph scheme which reduces the local maxima and the number of perturbations required. Results for a 500-class test problem involving simulated imaging-spectrometer data are presented in tables and graphs; 100-percent-correct classification is achieved with an improvement factor of 5.

  16. Invariant Spatial Context Is Learned but Not Retrieved in Gaze-Contingent Tunnel-View Search

    ERIC Educational Resources Information Center

    Zang, Xuelian; Jia, Lina; Müller, Hermann J.; Shi, Zhuanghua

    2015-01-01

    Our visual brain is remarkable in extracting invariant properties from the noisy environment, guiding selection of where to look and what to identify. However, how the brain achieves this is still poorly understood. Here we explore interactions of local context and global structure in the long-term learning and retrieval of invariant display…

  17. Systematic Dimensionality Reduction for Quantum Walks: Optimal Spatial Search and Transport on Non-Regular Graphs

    PubMed Central

    Novo, Leonardo; Chakraborty, Shantanav; Mohseni, Masoud; Neven, Hartmut; Omar, Yasser

    2015-01-01

    Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that confine the dynamics to a smaller subspace of the full Hilbert space. In this work, we use invariant subspace methods, that can be computed systematically using the Lanczos algorithm, to obtain the reduced set of states that encompass the dynamics of the problem at hand without the specific knowledge of underlying symmetries. First, we apply this method to obtain new instances of graphs where the spatial quantum search algorithm is optimal: complete graphs with broken links and complete bipartite graphs, in particular, the star graph. These examples show that regularity and high-connectivity are not needed to achieve optimal spatial search. We also show that this method considerably simplifies the calculation of quantum transport efficiencies. Furthermore, we observe improved efficiencies by removing a few links from highly symmetric graphs. Finally, we show that this reduction method also allows us to obtain an upper bound for the fidelity of a single qubit transfer on an XY spin network. PMID:26330082

  18. Sequential visibility-graph motifs

    NASA Astrophysics Data System (ADS)

    Iacovacci, Jacopo; Lacasa, Lucas

    2016-04-01

    Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network science. In this work we introduce and study the concept of sequential visibility-graph motifs, smaller substructures of n consecutive nodes that appear with characteristic frequencies. We develop a theory to compute in an exact way the motif profiles associated with general classes of deterministic and stochastic dynamics. We find that this simple property is indeed a highly informative and computationally efficient feature capable of distinguishing among different dynamics and robust against noise contamination. We finally confirm that it can be used in practice to perform unsupervised learning, by extracting motif profiles from experimental heart-rate series and being able, accordingly, to disentangle meditative from other relaxation states. Applications of this general theory include the automatic classification and description of physical, biological, and financial time series.

  19. Algebraic connectivity and graph robustness.

    SciTech Connect

    Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.

    2009-07-01

    Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.

  20. The fragment assembly string graph.

    PubMed

    Myers, Eugene W

    2005-09-01

    We present a concept and formalism, the string graph, which represents all that is inferable about a DNA sequence from a collection of shotgun sequencing reads collected from it. We give time and space efficient algorithms for constructing a string graph given the collection of overlaps between the reads and, in particular, present a novel linear expected time algorithm for transitive reduction in this context. The result demonstrates that the decomposition of reads into kmers employed in the de Bruijn graph approach described earlier is not essential, and exposes its close connection to the unitig approach we developed at Celera. This paper is a preliminary piece giving the basic algorithm and results that demonstrate the efficiency and scalability of the method. These ideas are being used to build a next-generation whole genome assembler called BOA (Berkeley Open Assembler) that will easily scale to mammalian genomes.

  1. Graph Analytics for Signature Discovery

    SciTech Connect

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

    2013-06-01

    Within large amounts of seemingly unstructured data it can be diffcult to find signatures of events. In our work we transform unstructured data into a graph representation. By doing this we expose underlying structure in the data and can take advantage of existing graph analytics capabilities, as well as develop new capabilities. Currently we focus on applications in cybersecurity and communication domains. Within cybersecurity we aim to find signatures for perpetrators using the pass-the-hash attack, and in communications we look for emails or phone calls going up or down a chain of command. In both of these areas, and in many others, the signature we look for is a path with certain temporal properties. In this paper we discuss our methodology for finding these temporal paths within large graphs.

  2. Graph modeling systems and methods

    DOEpatents

    Neergaard, Mike

    2015-10-13

    An apparatus and a method for vulnerability and reliability modeling are provided. The method generally includes constructing a graph model of a physical network using a computer, the graph model including a plurality of terminating vertices to represent nodes in the physical network, a plurality of edges to represent transmission paths in the physical network, and a non-terminating vertex to represent a non-nodal vulnerability along a transmission path in the physical network. The method additionally includes evaluating the vulnerability and reliability of the physical network using the constructed graph model, wherein the vulnerability and reliability evaluation includes a determination of whether each terminating and non-terminating vertex represents a critical point of failure. The method can be utilized to evaluate wide variety of networks, including power grid infrastructures, communication network topologies, and fluid distribution systems.

  3. Finding One Community in a Sparse Graph

    NASA Astrophysics Data System (ADS)

    Montanari, Andrea

    2015-10-01

    We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still bounded). Given a realization of such graph, we aim at identifying the hidden subset of vertices. This can be regarded as a model for the problem of finding a tightly knitted community in a social network, or a cluster in a relational dataset. In this paper we present two sets of contributions: ( i) We use the cavity method from spin glass theory to derive an exact phase diagram for the reconstruction problem. In particular, as the difference in edge probability increases, the problem undergoes two phase transitions, a static phase transition and a dynamic one. ( ii) We establish rigorous bounds on the dynamic phase transition and prove that, above a certain threshold, a local algorithm (belief propagation) correctly identify most of the hidden set. Below the same threshold no local algorithm can achieve this goal. However, in this regime the subset can be identified by exhaustive search. For small hidden sets and large average degree, the phase transition for local algorithms takes an intriguingly simple form. Local algorithms succeed with high probability for deg _in - deg _out > √{deg _out/e} and fail for deg _in - deg _out < √{deg _out/e} (with deg _in, deg _out the average degrees inside and outside the community). We argue that spectral algorithms are also ineffective in the latter regime. It is an open problem whether any polynomial time algorithms might succeed for deg _in - deg _out < √{deg _out/e}.

  4. Invariant Spin in the Proton

    SciTech Connect

    Thomas, Anthony

    2008-11-01

    We discuss recent theoretical progress in understanding the distribution of spin and orbital angular momentum in the proton. Particular attention is devoted to the effect of QCD evolution and to the distinction between "chiral" and "invariant" spin. This is particularly significant with respect to the possible presence of polarized strange quarks.

  5. Invariant Spin in the Proton

    SciTech Connect

    Thomas, Anthony W.

    2008-10-13

    We discuss recent theoretical progress in understanding the distribution of spin and orbital angular momentum in the proton. Particular attention is devoted to the effect of QCD evolution and to the distinction between 'chiral' and 'invariant' spin. This is particularly significant with respect to the possible presence of polarized strange quarks.

  6. Identity from classical invariant theory

    SciTech Connect

    Stein, P.R.

    1982-01-01

    A simple derivation is given of a well-known relation involving the so-called Cayley Operator of classical invariant theory. The proof is induction-free and independent of Capelli's identity; it makes use only of a known-theorem in the theory of determinants and some elementary combinatorics.

  7. Fingerprint recognition system by use of graph matching

    NASA Astrophysics Data System (ADS)

    Shen, Wei; Shen, Jun; Zheng, Huicheng

    2001-09-01

    Fingerprint recognition is an important subject in biometrics to identify or verify persons by physiological characteristics, and has found wide applications in different domains. In the present paper, we present a finger recognition system that combines singular points and structures. The principal steps of processing in our system are: preprocessing and ridge segmentation, singular point extraction and selection, graph representation, and finger recognition by graphs matching. Our fingerprint recognition system is implemented and tested for many fingerprint images and the experimental result are satisfactory. Different techniques are used in our system, such as fast calculation of orientation field, local fuzzy dynamical thresholding, algebraic analysis of connections and fingerprints representation and matching by graphs. Wed find that for fingerprint database that is not very large, the recognition rate is very high even without using a prior coarse category classification. This system works well for both one-to-few and one-to-many problems.

  8. Browsing schematics: Query-filtered graphs with context nodes

    NASA Technical Reports Server (NTRS)

    Ciccarelli, Eugene C.; Nardi, Bonnie A.

    1988-01-01

    The early results of a research project to create tools for building interfaces to intelligent systems on the NASA Space Station are reported. One such tool is the Schematic Browser which helps users engaged in engineering problem solving find and select schematics from among a large set. Users query for schematics with certain components, and the Schematic Browser presents a graph whose nodes represent the schematics with those components. The query greatly reduces the number of choices presented to the user, filtering the graph to a manageable size. Users can reformulate and refine the query serially until they locate the schematics of interest. To help users maintain orientation as they navigate a large body of data, the graph also includes nodes that are not matches but provide global and local context for the matching nodes. Context nodes include landmarks, ancestors, siblings, children and previous matches.

  9. Synchronizability of random rectangular graphs

    SciTech Connect

    Estrada, Ernesto Chen, Guanrong

    2015-08-15

    Random rectangular graphs (RRGs) represent a generalization of the random geometric graphs in which the nodes are embedded into hyperrectangles instead of on hypercubes. The synchronizability of RRG model is studied. Both upper and lower bounds of the eigenratio of the network Laplacian matrix are determined analytically. It is proven that as the rectangular network is more elongated, the network becomes harder to synchronize. The synchronization processing behavior of a RRG network of chaotic Lorenz system nodes is numerically investigated, showing complete consistence with the theoretical results.

  10. Midlet Navigation Graphs in JML

    NASA Astrophysics Data System (ADS)

    Mostowski, Wojciech; Poll, Erik

    In the context of the EU project Mobius on Proof Carrying Code for Java programs (midlets) on mobile devices, we present a way to express midlet navigation graphs in JML. Such navigation graphs express certain security policies for a midlet. The resulting JML specifications can be automatically checked with the static checker ESC/Java2. Our work was guided by a realistically sized case study developed as demonstrator in the project. We discuss practical difficulties with creating efficient and meaningful JML specifications for automatic verification with a lightweight verification tool such as ESC/Java2, and the potential use of these specifications for PCC.

  11. Scale invariance analysis for genetic networks applying homogeneity.

    PubMed

    Bernuau, Emmanuel; Efimov, Denis; Perruquetti, Wilfrid

    2016-05-01

    Scalability is a property describing the change of the trajectory of a dynamical system under a scaling of the input stimulus and of the initial conditions. Particular cases of scalability include the scale invariance and fold change detection (when the scaling of the input does not influence the system output). In the present paper it is shown that homogeneous systems have this scalability property while locally homogeneous systems approximately possess this property. These facts are used for detecting scale invariance or approximate scalability (far from a steady state) in several biological systems. The results are illustrated by various regulatory networks. PMID:26304616

  12. Non-Abelian gauge invariance and the infrared approximation

    SciTech Connect

    Cho, H.h.; Fried, H.M.; Grandou, T.

    1988-02-15

    Two constructions are given of infrared approximations, defined by a nonlocal configuration-space restrictions, which preserve the local, non-Abelian gauge invariance of SU(N) two-dimensional QCD (QCD/sub 2/). These continuum infrared methods are used to estimate the quenched order parameter in the strong-coupling, or chiral, limit and are compared to a previous calculation where gauge invariance was not manifest. Both constructions provide results which, in the chiral limit, differ from each other and from the previous estimation by an inessential, multiplicative scaling factor.

  13. Green's function approach for quantum graphs: An overview

    NASA Astrophysics Data System (ADS)

    Andrade, Fabiano M.; Schmidt, A. G. M.; Vicentini, E.; Cheng, B. K.; da Luz, M. G. E.

    2016-08-01

    Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function (G) framework. This approach is particularly interesting because G can be written as a sum over classical-like paths, where local quantum effects are taken into account through the scattering matrix elements (basically, transmission and reflection amplitudes) defined on each one of the graph vertices. Hence, the exact G has the functional form of a generalized semiclassical formula, which through different calculation techniques (addressed in detail here) always can be cast into a closed analytic expression. It allows to solve exactly arbitrary large (although finite) graphs in a recursive and fast way. Using the Green's function method, we survey many properties of open and closed quantum graphs as scattering solutions for the former and eigenspectrum and eigenstates for the latter, also considering quasi-bound states. Concrete examples, like cube, binary trees and Sierpiński-like topologies are presented. Along the work, possible distinct applications using the Green's function methods for quantum graphs are outlined.

  14. Boosting for multi-graph classification.

    PubMed

    Wu, Jia; Pan, Shirui; Zhu, Xingquan; Cai, Zhihua

    2015-03-01

    In this paper, we formulate a novel graph-based learning problem, multi-graph classification (MGC), which aims to learn a classifier from a set of labeled bags each containing a number of graphs inside the bag. A bag is labeled positive, if at least one graph in the bag is positive, and negative otherwise. Such a multi-graph representation can be used for many real-world applications, such as webpage classification, where a webpage can be regarded as a bag with texts and images inside the webpage being represented as graphs. This problem is a generalization of multi-instance learning (MIL) but with vital differences, mainly because instances in MIL share a common feature space whereas no feature is available to represent graphs in a multi-graph bag. To solve the problem, we propose a boosting based multi-graph classification framework (bMGC). Given a set of labeled multi-graph bags, bMGC employs dynamic weight adjustment at both bag- and graph-levels to select one subgraph in each iteration as a weak classifier. In each iteration, bag and graph weights are adjusted such that an incorrectly classified bag will receive a higher weight because its predicted bag label conflicts to the genuine label, whereas an incorrectly classified graph will receive a lower weight value if the graph is in a positive bag (or a higher weight if the graph is in a negative bag). Accordingly, bMGC is able to differentiate graphs in positive and negative bags to derive effective classifiers to form a boosting model for MGC. Experiments and comparisons on real-world multi-graph learning tasks demonstrate the algorithm performance.

  15. Scale invariance of parity-invariant three-dimensional QED

    NASA Astrophysics Data System (ADS)

    Karthik, Nikhil; Narayanan, Rajamani

    2016-09-01

    We present numerical evidences using overlap fermions for a scale-invariant behavior of parity-invariant three-dimensional QED with two flavors of massless two-component fermions. Using finite-size scaling of the low-lying eigenvalues of the massless anti-Hermitian overlap Dirac operator, we rule out the presence of a bilinear condensate and estimate the mass anomalous dimension. The eigenvectors associated with these low-lying eigenvalues suggest critical behavior in the sense of a metal-insulator transition. We show that there is no mass gap in the scalar and vector correlators in the infinite-volume theory. The vector correlator does not acquire an anomalous dimension. The anomalous dimension associated with the long-distance behavior of the scalar correlator is consistent with the mass anomalous dimension.

  16. Illumination-invariant face recognition in hyperspectral images

    NASA Astrophysics Data System (ADS)

    Pan, Zhihong; Healey, Glenn E.; Prasad, Manish; Tromberg, Bruce J.

    2003-09-01

    We examine the performance of illumination-invariant face recognition in hyperspectral images on a database of 200 subjects. The images are acquired over the near-infrared spectral range of 0.7-1.0 microns. Each subject is imaged over a range of facial orientations and expressions. Faces are represented by local spectral information for several tissue types. Illumination variation is modeled by low-dimensional linear subspaces of reflected radiance spectra. One hundred outdoor illumination spectra measured at Boulder, Colorado are used to synthesize the radiance spectra for the face tissue types. Weighted invariant subspace projection over multiple tissue types is used for recognition. Illumination-invariant face recognition is tested for various face rotations as well as different facial expressions.

  17. Graphs for Early Elementary Social Studies.

    ERIC Educational Resources Information Center

    Freeland, Kent; Brewer, Samrie

    1989-01-01

    Describes a lesson plan that instructs third graders to use graphs. Explains learning objectives, motivating students, conducting a class activity that includes graph construction, and concluding and evaluating the lesson. Lists materials needed. (GG)

  18. Standard Distributions: One Graph Fits All

    ERIC Educational Resources Information Center

    Wagner, Clifford H.

    2007-01-01

    Standard distributions are ubiquitous but not unique. With suitable scaling, the graph of a standard distribution serves as the graph for every distribution in the family. The standard exponential can easily be taught in elementary statistics courses.

  19. Understanding Conic Sections Using Alternate Graph Paper

    ERIC Educational Resources Information Center

    Brown, Elizabeth M.; Jones, Elizabeth

    2006-01-01

    This article describes two alternative coordinate systems and their use in graphing conic sections. This alternative graph paper helps students explore the idea of eccentricity using the definitions of the conic sections.

  20. Graphing and Social Studies: An Interdisciplinary Activity.

    ERIC Educational Resources Information Center

    Brehm, Julia L.

    1996-01-01

    Describes a graphing activity that promotes mathematical connections with social studies lessons. Students should be familiar with graphing on the Cartesian coordinate system to play this variation of the game Battleship on maps of various regions of the world. (AIM)

  1. Comparison Graph of Sea Ice Minimum - 2010

    NASA Video Gallery

    This animated graph tracks the retreat of sea ice, measured in millions of square kilometers, averaged from the start of the satellite record in 1979 through 2000 (white). Next, the graph follows t...

  2. Mathematical Minute: Rotating a Function Graph

    ERIC Educational Resources Information Center

    Bravo, Daniel; Fera, Joseph

    2013-01-01

    Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.

  3. Dr.L: Distributed Recursive (Graph) Layout

    2007-11-19

    Dr. L provides two-dimensional visualizations of very large abstract graph structures. it can be used for data mining applications including biology, scientific literature, and social network analysis. Dr. L is a graph layout program that uses a multilevel force-directed algorithm. A graph is input and drawn using a force-directed algorithm based on simulated annealing. The resulting layout is clustered using a single link algorithm. This clustering is used to produce a coarsened graph (fewer nodes)more » which is then re-drawn. this process is repeated until a sufficiently small graph is produced. The smallest graph is drawn and then used as a basis for drawing the original graph by refining the series of coarsened graphs that were produced. The layout engine can be run in serial or in parallel.« less

  4. Microcomputer Unit: Graphing Straight Lines.

    ERIC Educational Resources Information Center

    Hastings, Ellen H.; Yates, Daniel S.

    1983-01-01

    The material is designed to help pupils investigate how the value for slope in the equation of a line affects the inclination for the graph of an equation. A program written in BASIC designed to run on an Apple microcomputer is included. Worksheet masters for duplication are provided. (MP)

  5. Situating Graphs as Workplace Knowledge

    ERIC Educational Resources Information Center

    Noss, Richard; Bakker, Arthur; Hoyles, Celia; Kent, Phillip

    2007-01-01

    We investigate the use and knowledge of graphs in the context of a large industrial factory. We are particularly interested in the question of "transparency", a question that has been extensively considered in the general literature on tool use and, more recently, by Michael Roth and his colleagues in the context of scientific work. Roth uses the…

  6. Fibonacci Identities, Matrices, and Graphs

    ERIC Educational Resources Information Center

    Huang, Danrun

    2005-01-01

    General strategies used to help discover, prove, and generalize identities for Fibonacci numbers are described along with some properties about the determinants of square matrices. A matrix proof for identity (2) that has received immense attention from many branches of mathematics, like linear algebra, dynamical systems, graph theory and others…

  7. Box graphs and singular fibers

    NASA Astrophysics Data System (ADS)

    Hayashi, Hirotaka; Lawrie, Craig; Morrison, David R.; Schafer-Nameki, Sakura

    2014-05-01

    We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional = 2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as "flopping" of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E 6, E7 and E 8.

  8. Affect and Graphing Calculator Use

    ERIC Educational Resources Information Center

    McCulloch, Allison W.

    2011-01-01

    This article reports on a qualitative study of six high school calculus students designed to build an understanding about the affect associated with graphing calculator use in independent situations. DeBellis and Goldin's (2006) framework for affect as a representational system was used as a lens through which to understand the ways in which…

  9. Ancestral Genres of Mathematical Graphs

    ERIC Educational Resources Information Center

    Gerofsky, Susan

    2011-01-01

    Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…

  10. Humidity Graphs for All Seasons.

    ERIC Educational Resources Information Center

    Esmael, F.

    1982-01-01

    In a previous article in this journal (Vol. 17, p358, 1979), a wet-bulb depression table was recommended for two simple experiments to determine relative humidity. However, the use of a graph is suggested because it gives the relative humidity directly from the wet and dry bulb readings. (JN)

  11. Graphs and Enhancing Maple Multiplication.

    ERIC Educational Resources Information Center

    Cecil, David R.; Wang, Rongdong

    2002-01-01

    Description of a technique in Maple programming language that automatically prints all paths of any desired length along with the name of each vertex, proceeding in order from the beginning vertex to the ending vertex for a given graph. (Author/MM)

  12. The solar system's invariable plane

    NASA Astrophysics Data System (ADS)

    Souami, D.; Souchay, J.

    2012-07-01

    Context. The dynamics of solar system objects, such as dwarf planets and asteroids, has become a well-established field of celestial mechanics in the past thirty years, owing to the improvements that have been made in observational techniques and numerical studies. In general, the ecliptic is taken as the reference plane in these studies, although there is no dynamical reason for doing so. In contrast, the invariable plane as originally defined by Laplace, seems to be a far more natural choice. In this context, the latest study of this plane dates back to Burkhardt. Aims: We define and determine the orientation of the invariable plane of the solar system with respect to both the ICRF and the equinox-ecliptic of J2000.0, and evaluate the accuracy of our determination. Methods: Using the long-term numerical ephemerides DE405, DE406, and INPOP10a over their entire available time span, we computed the total angular momentum of the solar system, as well as the individual contribution to it made by each of the planets, the dwarf planets Pluto and Ceres, and the two asteroids Pallas and Vesta. We then deduced the orientation of the invariable plane from these ephemerides. Results: We update the previous results on the determination of the orientation of the invariable plane with more accurate data, and a more complete analysis of the problem, taking into account the effect of the dwarf planet (1) Ceres as well as two of the biggest asteroids, (4) Vesta and (2) Pallas. We show that the inclusion of these last three bodies significantly improves the accuracy of determination of the invariable plane, whose orientation over a 100 y interval does not vary more than 0.1 mas in inclination, and 0.3 mas in longitude of the ascending node. Moreover, we determine the individual contributions of each body to the total angular momentum of the solar system, as well as the inclination and longitude of the node with respect to this latter plane. Conclusions: Owing to the high accuracy

  13. Graph-based molecular alignment (GMA).

    PubMed

    Marialke, J; Körner, R; Tietze, S; Apostolakis, Joannis

    2007-01-01

    We describe a combined 2D/3D approach for the superposition of flexible chemical structures, which is based on recent progress in the efficient identification of common subgraphs and a gradient-based torsion space optimization algorithm. The simplicity of the approach is reflected in its generality and computational efficiency: the suggested approach neither requires precalculated statistics on the conformations of the molecules nor does it make simplifying assumptions on the topology of the molecules being compared. Furthermore, graph-based molecular alignment produces alignments that are consistent with the chemistry of the molecules as well as their general structure, as it depends on both the local connectivities between atoms and the overall topology of the molecules. We validate this approach on benchmark sets taken from the literature and show that it leads to good results compared to computationally and algorithmically more involved methods. The results suggest that, for most practical purposes, graph-based molecular alignment is a viable alternative to molecular field alignment with respect to structural superposition and leads to structures of comparable quality in a fraction of the time. PMID:17381175

  14. GRAPHIE: graph based histology image explorer

    PubMed Central

    2015-01-01

    Background Histology images comprise one of the important sources of knowledge for phenotyping studies in systems biology. However, the annotation and analyses of histological data have remained a manual, subjective and relatively low-throughput process. Results We introduce Graph based Histology Image Explorer (GRAPHIE)-a visual analytics tool to explore, annotate and discover potential relationships in histology image collections within a biologically relevant context. The design of GRAPHIE is guided by domain experts' requirements and well-known InfoVis mantras. By representing each image with informative features and then subsequently visualizing the image collection with a graph, GRAPHIE allows users to effectively explore the image collection. The features were designed to capture localized morphological properties in the given tissue specimen. More importantly, users can perform feature selection in an interactive way to improve the visualization of the image collection and the overall annotation process. Finally, the annotation allows for a better prospective examination of datasets as demonstrated in the users study. Thus, our design of GRAPHIE allows for the users to navigate and explore large collections of histology image datasets. Conclusions We demonstrated the usefulness of our visual analytics approach through two case studies. Both of the cases showed efficient annotation and analysis of histology image collection. PMID:26330277

  15. A MHD invariant and the confinement regimes in a tokamak

    NASA Astrophysics Data System (ADS)

    Spineanu, F.; Vlad, M.

    2016-09-01

    Fundamental Lagrangian, frozen-in and topological invariants can be useful to explain systematic connections between plasma parameters. At high plasma temperature the dissipation is small and the robust invariances are manifested. We invoke a frozen-in invariant which is an extension of Ertel’s theorem, and connects the vorticity of the large scale motions with the profile of the safety factor and of particle density. Assuming ergodicity of the small scale turbulence we consider the approximative preservation of the invariant for changes of the vorticity in an annular region of finite radial extension (i.e. poloidal rotation). We find that the ionization-induced rotation triggered by a pellet requires a reversed-q profile. In the H-mode, the invariance requires an accumulation of the current density in the rotation layer. Then this becomes a vorticity-current sheet which may explain experimental observations related to the penetration of the resonant magnetic perturbation and the filamentation during the edge localized modes.

  16. Control by quantum dynamics on graphs

    SciTech Connect

    Godsil, Chris; Severini, Simone

    2010-05-15

    We address the study of controllability of a closed quantum system whose dynamical Lie algebra is generated by adjacency matrices of graphs. We characterize a large family of graphs that renders a system controllable. The key property is a graph-theoretic feature consisting of a particularly disordered cycle structure. Disregarding efficiency of control functions, but choosing subfamilies of sparse graphs, the results translate into continuous-time quantum walks for universal computation.

  17. Scale and Rotation Invariant Matching Using Linearly Augmented Trees.

    PubMed

    Jiang, Hao; Tian, Tai-Peng; Sclaroff, Stan

    2015-12-01

    We propose a novel linearly augmented tree method for efficient scale and rotation invariant object matching. The proposed method enforces pairwise matching consistency defined on trees, and high-order constraints on all the sites of a template. The pairwise constraints admit arbitrary metrics while the high-order constraints use L1 norms and therefore can be linearized. Such a linearly augmented tree formulation introduces hyperedges and loops into the basic tree structure. But, different from a general loopy graph, its special structure allows us to relax and decompose the optimization into a sequence of tree matching problems that are efficiently solvable by dynamic programming. The proposed method also works on continuous scale and rotation parameters; we can match with a scale up to any large value with the same efficiency. Our experiments on ground truth data and a variety of real images and videos show that the proposed method is efficient, accurate and reliable. PMID:26539858

  18. Chemical Applications of Graph Theory: Part II. Isomer Enumeration.

    ERIC Educational Resources Information Center

    Hansen, Peter J.; Jurs, Peter C.

    1988-01-01

    Discusses the use of graph theory to aid in the depiction of organic molecular structures. Gives a historical perspective of graph theory and explains graph theory terminology with organic examples. Lists applications of graph theory to current research projects. (ML)

  19. My Bar Graph Tells a Story

    ERIC Educational Resources Information Center

    McMillen, Sue; McMillen, Beth

    2010-01-01

    Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy. Even students who are able to "create" bar graphs may struggle to correctly "interpret" them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information…

  20. So Many Graphs, So Little Time

    ERIC Educational Resources Information Center

    Wall, Jennifer J.; Benson, Christine C.

    2009-01-01

    Interpreting graphs found in various content areas is an important skill for students, especially in light of high-stakes testing. In addition, reading and understanding graphs is an important part of numeracy, or numeric literacy, a skill necessary for informed citizenry. This article explores the different categories of graphs, provides…

  1. Collaborative Robotic Instruction: A Graph Teaching Experience

    ERIC Educational Resources Information Center

    Mitnik, Ruben; Recabarren, Matias; Nussbaum, Miguel; Soto, Alvaro

    2009-01-01

    Graphing is a key skill in the study of Physics. Drawing and interpreting graphs play a key role in the understanding of science, while the lack of these has proved to be a handicap and a limiting factor in the learning of scientific concepts. It has been observed that despite the amount of previous graph-working experience, students of all ages…

  2. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 47 Telecommunication 5 2010-10-01 2010-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...

  3. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 47 Telecommunication 5 2011-10-01 2011-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...

  4. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 47 Telecommunication 5 2013-10-01 2013-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...

  5. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 47 Telecommunication 5 2012-10-01 2012-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...

  6. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 47 Telecommunication 5 2014-10-01 2014-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...

  7. Emerging universe from scale invariance

    SciTech Connect

    Del Campo, Sergio; Herrera, Ramón; Guendelman, Eduardo I.; Labraña, Pedro E-mail: guendel@bgu.ac.il E-mail: plabrana@ubiobio.cl

    2010-06-01

    We consider a scale invariant model which includes a R{sup 2} term in action and show that a stable ''emerging universe'' scenario is possible. The model belongs to the general class of theories, where an integration measure independent of the metric is introduced. To implement scale invariance (S.I.), a dilaton field is introduced. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (S.S.B) of S.I. After S.S.B. of S.I. in the model with the R{sup 2} term (and first order formalism applied), it is found that a non trivial potential for the dilaton is generated. The dynamics of the scalar field becomes non linear and these non linearities are instrumental in the stability of some of the emerging universe solutions, which exists for a parameter range of the theory.

  8. Quantum mechanics from invariance principles

    NASA Astrophysics Data System (ADS)

    Moldoveanu, Florin

    2015-07-01

    Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.

  9. Anisotropic invariance in minisuperspace models

    NASA Astrophysics Data System (ADS)

    Chagoya, Javier; Sabido, Miguel

    2016-06-01

    In this paper we introduce invariance under anisotropic transformations to cosmology. This invariance is one of the key ingredients of the theory of quantum gravity at a Lifshitz point put forward by Hořava. We find that this new symmetry in the minisuperspace introduces characteristics to the model that can be relevant in the ultraviolet regime. For example, by canonical quantization we find a Schrödinger-type equation which avoids the problem of frozen time in quantum cosmology. For simple cases we obtain solutions to this quantum equation in a Kantowski–Sachs (KS) minisuperspace. At the classical level, we study KS and Friedmann–Robertson–Walker cosmologies, obtaining modifications to the solutions of general relativity that can be relevant in the early Universe.

  10. Anisotropic invariance in minisuperspace models

    NASA Astrophysics Data System (ADS)

    Chagoya, Javier; Sabido, Miguel

    2016-06-01

    In this paper we introduce invariance under anisotropic transformations to cosmology. This invariance is one of the key ingredients of the theory of quantum gravity at a Lifshitz point put forward by Hořava. We find that this new symmetry in the minisuperspace introduces characteristics to the model that can be relevant in the ultraviolet regime. For example, by canonical quantization we find a Schrödinger-type equation which avoids the problem of frozen time in quantum cosmology. For simple cases we obtain solutions to this quantum equation in a Kantowski-Sachs (KS) minisuperspace. At the classical level, we study KS and Friedmann-Robertson-Walker cosmologies, obtaining modifications to the solutions of general relativity that can be relevant in the early Universe.

  11. Geometry-invariant resonant cavities

    PubMed Central

    Liberal, I.; Mahmoud, A. M.; Engheta, N.

    2016-01-01

    Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices. PMID:27010103

  12. Holographic multiverse and conformal invariance

    SciTech Connect

    Garriga, Jaume; Vilenkin, Alexander E-mail: vilenkin@cosmos.phy.tufts.edu

    2009-11-01

    We consider a holographic description of the inflationary multiverse, according to which the wave function of the universe is interpreted as the generating functional for a lower dimensional Euclidean theory. We analyze a simple model where transitions between inflationary vacua occur through bubble nucleation, and the inflating part of spacetime consists of de Sitter regions separated by thin bubble walls. In this model, we present some evidence that the dual theory is conformally invariant in the UV.

  13. Disformal invariance of curvature perturbation

    NASA Astrophysics Data System (ADS)

    Motohashi, Hayato; White, Jonathan

    2016-02-01

    We show that under a general disformal transformation the linear comoving curvature perturbation is not identically invariant, but is invariant on superhorizon scales for any theory that is disformally related to Horndeski's theory. The difference between disformally related curvature perturbations is found to be given in terms of the comoving density perturbation associated with a single canonical scalar field. In General Relativity it is well-known that this quantity vanishes on superhorizon scales through the Poisson equation that is obtained on combining the Hamiltonian and momentum constraints, and we confirm that a similar result holds for any theory that is disformally related to Horndeski's scalar-tensor theory so long as the invertibility condition for the disformal transformation is satisfied. We also consider the curvature perturbation at full nonlinear order in the unitary gauge, and find that it is invariant under a general disformal transformation if we assume that an attractor regime has been reached. Finally, we also discuss the counting of degrees of freedom in theories disformally related to Horndeski's.

  14. Similarity, invariance, and musical variation.

    PubMed

    McAdams, S; Matzkin, D

    2001-06-01

    Perceptual similarity underlies a number of important psychological properties of musical materials, including perceptual invariance under transformation, categorization, recognition, and the sense of familiarity. Mental processes involved in the perception of musical similarity may be an integral part of the functional logic of music composition and thus underly important aspects of musical experience. How much and in what ways can musical materials be varied and still be considered as perceptually related or as belonging to the same category? The notions of musical material, musical variation, perceptual similarity and invariance, and form-bearing dimensions are considered in this light. Recent work on similarity perception has demonstrated that the transformation space for a given musical material is limited by several factors ranging from degree of match of the values of auditory attributes of the events composing the sequences to their relations of various levels of abstraction and to the degree that the transformation respects the grammar of the musical system within which the material was composed. These notions and results are considered in the light of future directions of research, particularly concerning the role of similarity and invariance in the understanding of musical form during listening.

  15. Conformal Invariance of Graphene Sheets.

    PubMed

    Giordanelli, I; Posé, N; Mendoza, M; Herrmann, H J

    2016-03-10

    Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent 0.72 ± 0.01. Here, we show that, independent of the temperature, the iso-height lines at the percolation threshold have a well-defined fractal dimension and are conformally invariant, sharing the same statistical properties as Schramm-Loewner evolution (SLEκ) curves with κ = 2.24 ± 0.07. Interestingly, iso-height lines of other rough surfaces are not necessarily conformally invariant even if they have the same Hurst exponent, e.g. random Gaussian surfaces. We have found that the distribution of the modulus of the Fourier coefficients plays an important role on this property. Our results not only introduce a new universality class and place the study of suspended graphene membranes within the theory of critical phenomena, but also provide hints on the long-standing question about the origin of conformal invariance in iso-height lines of rough surfaces.

  16. Elementary examples of adiabatic invariance

    NASA Astrophysics Data System (ADS)

    Crawford, Frank S.

    1990-04-01

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

  17. Similarity, invariance, and musical variation.

    PubMed

    McAdams, S; Matzkin, D

    2001-06-01

    Perceptual similarity underlies a number of important psychological properties of musical materials, including perceptual invariance under transformation, categorization, recognition, and the sense of familiarity. Mental processes involved in the perception of musical similarity may be an integral part of the functional logic of music composition and thus underly important aspects of musical experience. How much and in what ways can musical materials be varied and still be considered as perceptually related or as belonging to the same category? The notions of musical material, musical variation, perceptual similarity and invariance, and form-bearing dimensions are considered in this light. Recent work on similarity perception has demonstrated that the transformation space for a given musical material is limited by several factors ranging from degree of match of the values of auditory attributes of the events composing the sequences to their relations of various levels of abstraction and to the degree that the transformation respects the grammar of the musical system within which the material was composed. These notions and results are considered in the light of future directions of research, particularly concerning the role of similarity and invariance in the understanding of musical form during listening. PMID:11458867

  18. Hidden structures of knot invariants

    NASA Astrophysics Data System (ADS)

    Sleptsov, Alexey

    2014-11-01

    We discuss a connection of HOMFLY polynomials with Hurwitz covers and represent a generating function for the HOMFLY polynomial of a given knot in all representations as Hurwitz partition function, i.e. the dependence of the HOMFLY polynomials on representation R is naturally captured by symmetric group characters (cut-and-join eigenvalues). The genus expansion and the loop expansion through Vassiliev invariants explicitly demonstrate this phenomenon. We study the genus expansion and discuss its properties. We also consider the loop expansion in details. In particular, we give an algorithm to calculate Vassiliev invariants, give some examples and discuss relations among Vassiliev invariants. Then we consider superpolynomials for torus knots defined via double affine Hecke algebra. We claim that the superpolynomials are not functions of Hurwitz type: symmetric group characters do not provide an adequate linear basis for their expansions. Deformation to superpolynomials is, however, straightforward in the multiplicative basis: the Casimir operators are beta-deformed to Hamiltonians of the Calogero-Moser-Sutherland system. Applying this trick to the genus and Vassiliev expansions, we observe that the deformation is fully straightforward only for the thin knots. Beyond the family of thin knots additional algebraically independent terms appear in the Vassiliev expansions. This can suggest that the superpolynomials do in fact contain more information about knots than the colored HOMFLY and Kauffman polynomials.

  19. Conformal Invariance of Graphene Sheets

    PubMed Central

    Giordanelli, I.; Posé, N.; Mendoza, M.; Herrmann, H. J.

    2016-01-01

    Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent 0.72 ± 0.01. Here, we show that, independent of the temperature, the iso-height lines at the percolation threshold have a well-defined fractal dimension and are conformally invariant, sharing the same statistical properties as Schramm-Loewner evolution (SLEκ) curves with κ = 2.24 ± 0.07. Interestingly, iso-height lines of other rough surfaces are not necessarily conformally invariant even if they have the same Hurst exponent, e.g. random Gaussian surfaces. We have found that the distribution of the modulus of the Fourier coefficients plays an important role on this property. Our results not only introduce a new universality class and place the study of suspended graphene membranes within the theory of critical phenomena, but also provide hints on the long-standing question about the origin of conformal invariance in iso-height lines of rough surfaces. PMID:26961723

  20. Spiking Models for Level-Invariant Encoding

    PubMed Central

    Brette, Romain

    2012-01-01

    Levels of ecological sounds vary over several orders of magnitude, but the firing rate and membrane potential of a neuron are much more limited in range. In binaural neurons of the barn owl, tuning to interaural delays is independent of level differences. Yet a monaural neuron with a fixed threshold should fire earlier in response to louder sounds, which would disrupt the tuning of these neurons. How could spike timing be independent of input level? Here I derive theoretical conditions for a spiking model to be insensitive to input level. The key property is a dynamic change in spike threshold. I then show how level invariance can be physiologically implemented, with specific ionic channel properties. It appears that these ingredients are indeed present in monaural neurons of the sound localization pathway of birds and mammals. PMID:22291634

  1. Multivariate dice recognition using invariant features

    NASA Astrophysics Data System (ADS)

    Hsu, Gee-Sern; Peng, Hsiao-Chia; Yeh, Shang-Min; Lin, Chyi-Yeu

    2013-04-01

    A system is proposed for automatic reading of the number of dots on dice in general table game settings. Different from previous dice recognition systems that recognize dice of a specific color using a single top-view camera in an enclosure with controlled settings, the proposed one uses multiple cameras to recognize dice of various colors and under uncontrolled conditions. It is composed of three modules. Module-1 locates the dice using the gradient-conditioned color segmentation, proposed, to segment dice of arbitrary colors from the background. Module-2 exploits the local invariant features good for building homographies, giving a solution to segment the top faces of the dice. To identify the dots on the segmented top faces, a maximally stable extremal region detector is embedded in module-3 for its consistency in locating the dot region. Experiments show that the proposed system performs satisfactorily in various test conditions.

  2. Spiking models for level-invariant encoding.

    PubMed

    Brette, Romain

    2011-01-01

    Levels of ecological sounds vary over several orders of magnitude, but the firing rate and membrane potential of a neuron are much more limited in range. In binaural neurons of the barn owl, tuning to interaural delays is independent of level differences. Yet a monaural neuron with a fixed threshold should fire earlier in response to louder sounds, which would disrupt the tuning of these neurons. How could spike timing be independent of input level? Here I derive theoretical conditions for a spiking model to be insensitive to input level. The key property is a dynamic change in spike threshold. I then show how level invariance can be physiologically implemented, with specific ionic channel properties. It appears that these ingredients are indeed present in monaural neurons of the sound localization pathway of birds and mammals. PMID:22291634

  3. Conformally invariant fractals and potential theory

    PubMed

    Duplantier

    2000-02-14

    The multifractal (MF) distribution of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a Q-state Potts cluster, is solved in two dimensions. The dimension &fcirc;(straight theta) of the boundary set with local wedge angle straight theta is &fcirc;(straight theta) = pi / straight theta-25-c / 12 (pi-straight theta)(2) / straight theta(2pi-straight theta), with c the central charge of the model. As a corollary, the dimensions D(EP) of the external perimeter and D(H) of the hull of a Potts cluster obey the duality equation (D(EP)-1) (D(H)-1) = 1 / 4. A related covariant MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.

  4. Fast graph operations in quantum computation

    NASA Astrophysics Data System (ADS)

    Zhao, Liming; Pérez-Delgado, Carlos A.; Fitzsimons, Joseph F.

    2016-03-01

    The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in the reverse direction to yield a graph data structure, which allows for more efficient manipulation and comparison of graphs than any possible classical structure. We introduce efficient algorithms for many transformation and comparison operations on graphs represented as graph states, and prove that no classical data structure can have similar performance for the full set of operations studied.

  5. Shape invariant potentials in higher dimensions

    SciTech Connect

    Sandhya, R.; Sree Ranjani, S.; Kapoor, A.K.

    2015-08-15

    In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended to arrive at a large class of new shape invariant potentials in arbitrary dimensions. A reformulation of the shape invariance property and possible generalizations are proposed. These may lead to an important extension of the shape invariance property to Hamiltonians that are related to standard potential problems via space time transformations, which are found useful in path integral formulation of quantum mechanics.

  6. On the question of adiabatic invariants

    NASA Astrophysics Data System (ADS)

    Mitropol'Skii, Iu. A.

    Some aspects of the construction of adiabadic invariants for dynamic systems with a single degree of freedom are discussed. Adiabatic invariants are derived using classical principles and the method proposed by Djukic (1981). The discussion covers an adiabatic invariant for a dynamic system with slowly varying parameters; derivation of an expression for an adiabatic invariant by the Djukic method for a second-order equation with a variable mass; and derivation of an expression for the adiabatic invariant for a nearly integrable differential equation.

  7. Einstein gravity as a 3D conformally invariant theory

    NASA Astrophysics Data System (ADS)

    Gomes, Henrique; Gryb, Sean; Koslowski, Tim

    2011-02-01

    We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is irrelevant. The dual theory is invariant under foliation-preserving 3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume (for the spatially compact case). Locally, this symmetry is identical to that of Hořava-Lifshitz gravity in the high energy limit but our theory is equivalent to Einstein gravity. Specifically, we find that the solutions of general relativity, in a gauge where the spatial hypersurfaces have constant mean extrinsic curvature, can be mapped to solutions of a particular gauge fixing of the dual theory. Moreover, this duality is not accidental. We provide a general geometric picture for our procedure that allows us to trade foliation invariance for conformal invariance. The dual theory provides a new proposal for the theory space of quantum gravity.

  8. Constrained Graph Optimization: Interdiction and Preservation Problems

    SciTech Connect

    Schild, Aaron V

    2012-07-30

    The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.

  9. Hierarchical structure of the logical Internet graph

    NASA Astrophysics Data System (ADS)

    Ge, Zihui; Figueiredo, Daniel R.; Jaiswal, Sharad; Gao, Lixin

    2001-07-01

    The study of the Internet topology has recently received much attention from the research community. In particular, the observation that the network graph has interesting properties, such as power laws, that might be explored in a myriad of ways. Most of the work in characterizing the Internet graph is based on the physical network graph, i.e., the connectivity graph. In this paper we investigate how logical relationships between nodes of the AS graph can be used to gain insight to its structure. We characterize the logical graph using various metrics and identify the presence of power laws in the number of customers that a provider has. Using these logical relationships we define a structural model of the AS graph. The model highlights the hierarchical nature of logical relationships and the preferential connection to larger providers. We also investigate the consistency of this model over time and observe interesting properties of the hierarchical structure.

  10. Molecular graph convolutions: moving beyond fingerprints.

    PubMed

    Kearnes, Steven; McCloskey, Kevin; Berndl, Marc; Pande, Vijay; Riley, Patrick

    2016-08-01

    Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular graph convolutions, a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph-atoms, bonds, distances, etc.-which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement. PMID:27558503

  11. The Feynman Identity for Planar Graphs

    NASA Astrophysics Data System (ADS)

    da Costa, G. A. T. F.

    2016-08-01

    The Feynman identity (FI) of a planar graph relates the Euler polynomial of the graph to an infinite product over the equivalence classes of closed nonperiodic signed cycles in the graph. The main objectives of this paper are to compute the number of equivalence classes of nonperiodic cycles of given length and sign in a planar graph and to interpret the data encoded by the FI in the context of free Lie superalgebras. This solves in the case of planar graphs a problem first raised by Sherman and sets the FI as the denominator identity of a free Lie superalgebra generated from a graph. Other results are obtained. For instance, in connection with zeta functions of graphs.

  12. Fast Approximate Quadratic Programming for Graph Matching

    PubMed Central

    Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E.

    2015-01-01

    Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624

  13. Molecular graph convolutions: moving beyond fingerprints.

    PubMed

    Kearnes, Steven; McCloskey, Kevin; Berndl, Marc; Pande, Vijay; Riley, Patrick

    2016-08-01

    Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular graph convolutions, a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph-atoms, bonds, distances, etc.-which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement.

  14. On a programming language for graph algorithms

    NASA Technical Reports Server (NTRS)

    Rheinboldt, W. C.; Basili, V. R.; Mesztenyi, C. K.

    1971-01-01

    An algorithmic language, GRAAL, is presented for describing and implementing graph algorithms of the type primarily arising in applications. The language is based on a set algebraic model of graph theory which defines the graph structure in terms of morphisms between certain set algebraic structures over the node set and arc set. GRAAL is modular in the sense that the user specifies which of these mappings are available with any graph. This allows flexibility in the selection of the storage representation for different graph structures. In line with its set theoretic foundation, the language introduces sets as a basic data type and provides for the efficient execution of all set and graph operators. At present, GRAAL is defined as an extension of ALGOL 60 (revised) and its formal description is given as a supplement to the syntactic and semantic definition of ALGOL. Several typical graph algorithms are written in GRAAL to illustrate various features of the language and to show its applicability.

  15. Molecular graph convolutions: moving beyond fingerprints

    NASA Astrophysics Data System (ADS)

    Kearnes, Steven; McCloskey, Kevin; Berndl, Marc; Pande, Vijay; Riley, Patrick

    2016-08-01

    Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular "graph convolutions", a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph---atoms, bonds, distances, etc.---which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement.

  16. Line graphs as social networks

    NASA Astrophysics Data System (ADS)

    Krawczyk, M. J.; Muchnik, L.; Mańka-Krasoń, A.; Kułakowski, K.

    2011-07-01

    It was demonstrated recently that the line graphs are clustered and assortative. These topological features are known to characterize some social networks [M.E.J. Newman, Y. Park, Why social networks are different from other types of networks, Phys. Rev. E 68 (2003) 036122]; it was argued that this similarity reveals their cliquey character. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8×10 6 people.

  17. Graph distance for complex networks

    NASA Astrophysics Data System (ADS)

    Shimada, Yutaka; Hirata, Yoshito; Ikeguchi, Tohru; Aihara, Kazuyuki

    2016-10-01

    Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in the theory of complex networks. Here, we propose a graph distance between networks based on a Laplacian matrix that reflects the structural and dynamical properties of networked dynamical systems. Our results indicate that the Laplacian-based graph distance effectively quantifies the structural difference between complex networks. We further show that our approach successfully elucidates the temporal properties underlying temporal networks observed in the context of face-to-face human interactions.

  18. Graph distance for complex networks

    PubMed Central

    Shimada, Yutaka; Hirata, Yoshito; Ikeguchi, Tohru; Aihara, Kazuyuki

    2016-01-01

    Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in the theory of complex networks. Here, we propose a graph distance between networks based on a Laplacian matrix that reflects the structural and dynamical properties of networked dynamical systems. Our results indicate that the Laplacian-based graph distance effectively quantifies the structural difference between complex networks. We further show that our approach successfully elucidates the temporal properties underlying temporal networks observed in the context of face-to-face human interactions. PMID:27725690

  19. Relativity on Rotated Graph Paper

    NASA Astrophysics Data System (ADS)

    Salgado, Roberto

    2011-11-01

    We present visual calculations in special relativity using spacetime diagrams drawn on graph paper that has been rotated by 45 degrees. The rotated lines represent lightlike directions in Minkowski spacetime, and the boxes in the grid (called light-clock diamonds) represent ticks of an inertial observer's lightclock. We show that many quantitative results can be read off a spacetime diagram by counting boxes, using a minimal amount of algebra.

  20. Topological structure of dictionary graphs

    NASA Astrophysics Data System (ADS)

    Fukś, Henryk; Krzemiński, Mark

    2009-09-01

    We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers—that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 103 and 104. A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.

  1. Helping Students Make Sense of Graphs: An Experimental Trial of SmartGraphs Software

    NASA Astrophysics Data System (ADS)

    Zucker, Andrew; Kay, Rachel; Staudt, Carolyn

    2014-06-01

    Graphs are commonly used in science, mathematics, and social sciences to convey important concepts; yet students at all ages demonstrate difficulties interpreting graphs. This paper reports on an experimental study of free, Web-based software called SmartGraphs that is specifically designed to help students overcome their misconceptions regarding graphs. SmartGraphs allows students to interact with graphs and provides hints and scaffolding to help students, if they need help. SmartGraphs activities can be authored to be useful in teaching and learning a variety of topics that use graphs (such as slope, velocity, half-life, and global warming). A 2-year experimental study in physical science classrooms was conducted with dozens of teachers and thousands of students. In the first year, teachers were randomly assigned to experimental or control conditions. Data show that students of teachers who use SmartGraphs as a supplement to normal instruction make greater gains understanding graphs than control students studying the same content using the same textbooks, but without SmartGraphs. Additionally, teachers believe that the SmartGraphs activities help students meet learning goals in the physical science course, and a great majority reported they would use the activities with students again. In the second year of the study, several specific variations of SmartGraphs were researched to help determine what makes SmartGraphs effective.

  2. Quantum Weyl invariance and cosmology

    NASA Astrophysics Data System (ADS)

    Dabholkar, Atish

    2016-09-01

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

  3. Relativistic chaos is coordinate invariant.

    PubMed

    Motter, Adilson E

    2003-12-01

    The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion regarding the noninvariance of chaos in cosmology, a major claim about chaos in general relativity, necessarily involves the violation of hypotheses required for a proper definition of the Lyapunov exponents. PMID:14683170

  4. Vector spaces, invariance, and camouflage

    NASA Astrophysics Data System (ADS)

    Arsenault, Henri H.; Garcia-Martinez, Pascuala

    2004-12-01

    We present a method based on an orthonormal vector space basis representation to detect camouflaged targets in natural environments. Because the method is intensity invariant we detect camouflage targets independently of the illumination conditions. The detection technique does not require knowing the exact camouflage pattern, but only the class of patterns (foliage, netting, woods...). We used nonlinear filtering based on the calculation of several correlations. Moreover, the nonlinearity of the filtering process allows a high discrimination against false targets. Several experiments confirm the target detectability where strong camouflage might delude even human viewers.

  5. Invariant metrics for Hamiltonian systems

    SciTech Connect

    Rangarajan, G. ); Dragt, A.J. ); Neri, F. )

    1991-05-01

    In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs.

  6. Computational Genomics Using Graph Theory

    NASA Astrophysics Data System (ADS)

    Schlick, Tamar

    2005-03-01

    With exciting new discoveries concerning RNA's regulatory cellular roles in gene expression, structural and functional problems associated with DNA's venerable cousin have come to the forefront. RNA folding, for example, is analogous to the well-known protein folding problem, and seeks to link RNA's primary sequence with secondary and tertiary structures. As a single-stranded polynucleotide, RNA's secondary structures are defined by a network of hydrogen bonds, which lead to a variety of stems, loops, junctions, bulges, and other motifs. Supersecondary pseudoknot structures can also occur and, together, lead to RNA's complex tertiary interactions stabilized by salt and solvent ions in the natural cellular milieu. Besides folding, challenges in RNA research include identifying locations and functions of RNA genes, discovering RNA's structural repertoire (folding motifs), designing novel RNAs, and developing new antiviral and antibiotic compounds composed of, or targeting, RNAs. In this talk, I will describe some of these new biological findings concerning RNA and present an approach using graph theory (network theory) to represent RNA secondary structures. Because the RNA motif space using graphs is vastly smaller than RNA's sequence space, many problems related to analyzing and discovering new RNAs can be simplified and studied systematically. Some preliminary applications to designing novel RNAs will also be described.Related ReadingH. H. Gan, S. Pasquali, and T. Schlick, ``A Survey of Existing RNAs using Graph Theory with Implications to RNA Analysis and Design,'' Nuc. Acids Res. 31: 2926--2943 (2003). J. Zorn, H. H. Gan, N. Shiffeldrim, and T. Schlick, ``Structural Motifs in Ribosomal RNAs: Implications for RNA Design and Genomics,'' Biopolymers 73: 340--347 (2004). H. H. Gan, D. Fera, J. Zorn, M. Tang, N. Shiffeldrim, U. Laserson, N. Kim, and T. Schlick,``RAG: RNA-As-Graphs Database -- Concepts, Analysis, and Features,'' Bioinformatics 20: 1285--1291 (2004). U

  7. Blurred face recognition by fusing blur-invariant texture and structure features

    NASA Astrophysics Data System (ADS)

    Zhu, Mengyu; Cao, Zhiguo; Xiao, Yang; Xie, Xiaokang

    2015-10-01

    Blurred face recognition is still remaining as a challenge task, but with wide applications. Image blur can largely affect recognition performance. The local phase quantization (LPQ) was proposed to extract the blur-invariant texture information. It was used for blurred face recognition and achieved good performance. However, LPQ considers only the phase blur-invariant texture information, which is not sufficient. In addition, LPQ is extracted holistically, which cannot fully explore its discriminative power on local spatial properties. In this paper, we propose a novel method for blurred face recognition. The texture and structure blur-invariant features are extracted and fused to generate a more complete description on blurred image. For texture blur-invariant feature, LPQ is extracted in a densely sampled way and vector of locally aggregated descriptors (VLAD) is employed to enhance its performance. For structure blur-invariant feature, the histogram of oriented gradient (HOG) is used. To further enhance its blur invariance, we improve HOG by eliminating weak gradient magnitude which is more sensitive to image blur than the strong gradient. The improved HOG is then fused with the original HOG by canonical correlation analysis (CCA). At last, we fuse them together by CCA to form the final blur-invariant representation of the face image. The experiments are performed on three face datasets. The results demonstrate that our improvements and our proposition can have a good performance in blurred face recognition.

  8. Lie group invariant finite difference schemes for the neutron diffusion equation

    SciTech Connect

    Jaegers, P.J.

    1994-06-01

    Finite difference techniques are used to solve a variety of differential equations. For the neutron diffusion equation, the typical local truncation error for standard finite difference approximation is on the order of the mesh spacing squared. To improve the accuracy of the finite difference approximation of the diffusion equation, the invariance properties of the original differential equation have been incorporated into the finite difference equations. Using the concept of an invariant difference operator, the invariant difference approximations of the multi-group neutron diffusion equation were determined in one-dimensional slab and two-dimensional Cartesian coordinates, for multiple region problems. These invariant difference equations were defined to lie upon a cell edged mesh as opposed to the standard difference equations, which lie upon a cell centered mesh. Results for a variety of source approximations showed that the invariant difference equations were able to determine the eigenvalue with greater accuracy, for a given mesh spacing, than the standard difference approximation. The local truncation errors for these invariant difference schemes were found to be highly dependent upon the source approximation used, and the type of source distribution played a greater role in determining the accuracy of the invariant difference scheme than the local truncation error.

  9. Computing Information Value from RDF Graph Properties

    SciTech Connect

    al-Saffar, Sinan; Heileman, Gregory

    2010-11-08

    Information value has been implicitly utilized and mostly non-subjectively computed in information retrieval (IR) systems. We explicitly define and compute the value of an information piece as a function of two parameters, the first is the potential semantic impact the target information can subjectively have on its recipient's world-knowledge, and the second parameter is trust in the information source. We model these two parameters as properties of RDF graphs. Two graphs are constructed, a target graph representing the semantics of the target body of information and a context graph representing the context of the consumer of that information. We compute information value subjectively as a function of both potential change to the context graph (impact) and the overlap between the two graphs (trust). Graph change is computed as a graph edit distance measuring the dissimilarity between the context graph before and after the learning of the target graph. A particular application of this subjective information valuation is in the construction of a personalized ranking component in Web search engines. Based on our method, we construct a Web re-ranking system that personalizes the information experience for the information-consumer.

  10. Graph-Based Path-Planning for Titan Balloons

    NASA Technical Reports Server (NTRS)

    Blackmore, Lars James; Fathpour, Nanaz; Elfes, Alberto

    2010-01-01

    A document describes a graph-based path-planning algorithm for balloons with vertical control authority and little or no horizontal control authority. The balloons are designed to explore celestial bodies with atmospheres, such as Titan, a moon of Saturn. The algorithm discussed enables the balloon to achieve horizontal motion using the local horizontal winds. The approach is novel because it enables the balloons to use arbitrary wind field models. This is in contrast to prior approaches that used highly simplified wind field models, such as linear, or binary, winds. This new approach works by discretizing the space in which the balloon operates, and representing the possible states of the balloon as a graph whose arcs represent the time taken to move from one node to another. The approach works with arbitrary wind fields, by looking up the wind strength and direction at every node in the graph from an arbitrary wind model. Having generated the graph, search techniques such as Dijkstra s algorithm are then used to find the set of vertical actuation commands that takes the balloon from the start to the goal in minimum time. In addition, the set of reachable locations on the moon or planet can be determined.

  11. Graph theory findings in the pathophysiology of temporal lobe epilepsy

    PubMed Central

    Chiang, Sharon; Haneef, Zulfi

    2014-01-01

    Temporal lobe epilepsy (TLE) is the most common form of adult epilepsy. Accumulating evidence has shown that TLE is a disorder of abnormal epileptogenic networks, rather than focal sources. Graph theory allows for a network-based representation of TLE brain networks, and has potential to illuminate characteristics of brain topology conducive to TLE pathophysiology, including seizure initiation and spread. We review basic concepts which we believe will prove helpful in interpreting results rapidly emerging from graph theory research in TLE. In addition, we summarize the current state of graph theory findings in TLE as they pertain its pathophysiology. Several common findings have emerged from the many modalities which have been used to study TLE using graph theory, including structural MRI, diffusion tensor imaging, surface EEG, intracranial EEG, magnetoencephalography, functional MRI, cell cultures, simulated models, and mouse models, involving increased regularity of the interictal network configuration, altered local segregation and global integration of the TLE network, and network reorganization of temporal lobe and limbic structures. As different modalities provide different views of the same phenomenon, future studies integrating data from multiple modalities are needed to clarify findings and contribute to the formation of a coherent theory on the pathophysiology of TLE. PMID:24831083

  12. Graph theory findings in the pathophysiology of temporal lobe epilepsy.

    PubMed

    Chiang, Sharon; Haneef, Zulfi

    2014-07-01

    Temporal lobe epilepsy (TLE) is the most common form of adult epilepsy. Accumulating evidence has shown that TLE is a disorder of abnormal epileptogenic networks, rather than focal sources. Graph theory allows for a network-based representation of TLE brain networks, and has potential to illuminate characteristics of brain topology conducive to TLE pathophysiology, including seizure initiation and spread. We review basic concepts which we believe will prove helpful in interpreting results rapidly emerging from graph theory research in TLE. In addition, we summarize the current state of graph theory findings in TLE as they pertain its pathophysiology. Several common findings have emerged from the many modalities which have been used to study TLE using graph theory, including structural MRI, diffusion tensor imaging, surface EEG, intracranial EEG, magnetoencephalography, functional MRI, cell cultures, simulated models, and mouse models, involving increased regularity of the interictal network configuration, altered local segregation and global integration of the TLE network, and network reorganization of temporal lobe and limbic structures. As different modalities provide different views of the same phenomenon, future studies integrating data from multiple modalities are needed to clarify findings and contribute to the formation of a coherent theory on the pathophysiology of TLE.

  13. Graph analysis of dream reports is especially informative about psychosis

    NASA Astrophysics Data System (ADS)

    Mota, Natália B.; Furtado, Raimundo; Maia, Pedro P. C.; Copelli, Mauro; Ribeiro, Sidarta

    2014-01-01

    Early psychiatry investigated dreams to understand psychopathologies. Contemporary psychiatry, which neglects dreams, has been criticized for lack of objectivity. In search of quantitative insight into the structure of psychotic speech, we investigated speech graph attributes (SGA) in patients with schizophrenia, bipolar disorder type I, and non-psychotic controls as they reported waking and dream contents. Schizophrenic subjects spoke with reduced connectivity, in tight correlation with negative and cognitive symptoms measured by standard psychometric scales. Bipolar and control subjects were undistinguishable by waking reports, but in dream reports bipolar subjects showed significantly less connectivity. Dream-related SGA outperformed psychometric scores or waking-related data for group sorting. Altogether, the results indicate that online and offline processing, the two most fundamental modes of brain operation, produce nearly opposite effects on recollections: While dreaming exposes differences in the mnemonic records across individuals, waking dampens distinctions. The results also demonstrate the feasibility of the differential diagnosis of psychosis based on the analysis of dream graphs, pointing to a fast, low-cost and language-invariant tool for psychiatric diagnosis and the objective search for biomarkers. The Freudian notion that ``dreams are the royal road to the unconscious'' is clinically useful, after all.

  14. Graph analysis of dream reports is especially informative about psychosis

    PubMed Central

    Mota, Natália B.; Furtado, Raimundo; Maia, Pedro P. C.; Copelli, Mauro; Ribeiro, Sidarta

    2014-01-01

    Early psychiatry investigated dreams to understand psychopathologies. Contemporary psychiatry, which neglects dreams, has been criticized for lack of objectivity. In search of quantitative insight into the structure of psychotic speech, we investigated speech graph attributes (SGA) in patients with schizophrenia, bipolar disorder type I, and non-psychotic controls as they reported waking and dream contents. Schizophrenic subjects spoke with reduced connectivity, in tight correlation with negative and cognitive symptoms measured by standard psychometric scales. Bipolar and control subjects were undistinguishable by waking reports, but in dream reports bipolar subjects showed significantly less connectivity. Dream-related SGA outperformed psychometric scores or waking-related data for group sorting. Altogether, the results indicate that online and offline processing, the two most fundamental modes of brain operation, produce nearly opposite effects on recollections: While dreaming exposes differences in the mnemonic records across individuals, waking dampens distinctions. The results also demonstrate the feasibility of the differential diagnosis of psychosis based on the analysis of dream graphs, pointing to a fast, low-cost and language-invariant tool for psychiatric diagnosis and the objective search for biomarkers. The Freudian notion that “dreams are the royal road to the unconscious” is clinically useful, after all. PMID:24424108

  15. Graph analysis of dream reports is especially informative about psychosis.

    PubMed

    Mota, Natália B; Furtado, Raimundo; Maia, Pedro P C; Copelli, Mauro; Ribeiro, Sidarta

    2014-01-01

    Early psychiatry investigated dreams to understand psychopathologies. Contemporary psychiatry, which neglects dreams, has been criticized for lack of objectivity. In search of quantitative insight into the structure of psychotic speech, we investigated speech graph attributes (SGA) in patients with schizophrenia, bipolar disorder type I, and non-psychotic controls as they reported waking and dream contents. Schizophrenic subjects spoke with reduced connectivity, in tight correlation with negative and cognitive symptoms measured by standard psychometric scales. Bipolar and control subjects were undistinguishable by waking reports, but in dream reports bipolar subjects showed significantly less connectivity. Dream-related SGA outperformed psychometric scores or waking-related data for group sorting. Altogether, the results indicate that online and offline processing, the two most fundamental modes of brain operation, produce nearly opposite effects on recollections: While dreaming exposes differences in the mnemonic records across individuals, waking dampens distinctions. The results also demonstrate the feasibility of the differential diagnosis of psychosis based on the analysis of dream graphs, pointing to a fast, low-cost and language-invariant tool for psychiatric diagnosis and the objective search for biomarkers. The Freudian notion that "dreams are the royal road to the unconscious" is clinically useful, after all.

  16. Components in time-varying graphs

    NASA Astrophysics Data System (ADS)

    Nicosia, Vincenzo; Tang, John; Musolesi, Mirco; Russo, Giovanni; Mascolo, Cecilia; Latora, Vito

    2012-06-01

    Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, today it is possible to produce and analyze social and biological networks with detailed information on the time of occurrence and duration of each link. However, standard graph metrics introduced so far in complex network theory are mainly suited for static graphs, i.e., graphs in which the links do not change over time, or graphs built from time-varying systems by aggregating all the links as if they were concurrent in time. In this paper, we extend the notion of connectedness, and the definitions of node and graph components, to the case of time-varying graphs, which are represented as time-ordered sequences of graphs defined over a fixed set of nodes. We show that the problem of finding strongly connected components in a time-varying graph can be mapped into the problem of discovering the maximal-cliques in an opportunely constructed static graph, which we name the affine graph. It is, therefore, an NP-complete problem. As a practical example, we have performed a temporal component analysis of time-varying graphs constructed from three data sets of human interactions. The results show that taking time into account in the definition of graph components allows to capture important features of real systems. In particular, we observe a large variability in the size of node temporal in- and out-components. This is due to intrinsic fluctuations in the activity patterns of individuals, which cannot be detected by static graph analysis.

  17. Components in time-varying graphs.

    PubMed

    Nicosia, Vincenzo; Tang, John; Musolesi, Mirco; Russo, Giovanni; Mascolo, Cecilia; Latora, Vito

    2012-06-01

    Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, today it is possible to produce and analyze social and biological networks with detailed information on the time of occurrence and duration of each link. However, standard graph metrics introduced so far in complex network theory are mainly suited for static graphs, i.e., graphs in which the links do not change over time, or graphs built from time-varying systems by aggregating all the links as if they were concurrent in time. In this paper, we extend the notion of connectedness, and the definitions of node and graph components, to the case of time-varying graphs, which are represented as time-ordered sequences of graphs defined over a fixed set of nodes. We show that the problem of finding strongly connected components in a time-varying graph can be mapped into the problem of discovering the maximal-cliques in an opportunely constructed static graph, which we name the affine graph. It is, therefore, an NP-complete problem. As a practical example, we have performed a temporal component analysis of time-varying graphs constructed from three data sets of human interactions. The results show that taking time into account in the definition of graph components allows to capture important features of real systems. In particular, we observe a large variability in the size of node temporal in- and out-components. This is due to intrinsic fluctuations in the activity patterns of individuals, which cannot be detected by static graph analysis. PMID:22757508

  18. JavaGenes: Evolving Graphs with Crossover

    NASA Technical Reports Server (NTRS)

    Globus, Al; Atsatt, Sean; Lawton, John; Wipke, Todd

    2000-01-01

    Genetic algorithms usually use string or tree representations. We have developed a novel crossover operator for a directed and undirected graph representation, and used this operator to evolve molecules and circuits. Unlike strings or trees, a single point in the representation cannot divide every possible graph into two parts, because graphs may contain cycles. Thus, the crossover operator is non-trivial. A steady-state, tournament selection genetic algorithm code (JavaGenes) was written to implement and test the graph crossover operator. All runs were executed by cycle-scavagging on networked workstations using the Condor batch processing system. The JavaGenes code has evolved pharmaceutical drug molecules and simple digital circuits. Results to date suggest that JavaGenes can evolve moderate sized drug molecules and very small circuits in reasonable time. The algorithm has greater difficulty with somewhat larger circuits, suggesting that directed graphs (circuits) are more difficult to evolve than undirected graphs (molecules), although necessary differences in the crossover operator may also explain the results. In principle, JavaGenes should be able to evolve other graph-representable systems, such as transportation networks, metabolic pathways, and computer networks. However, large graphs evolve significantly slower than smaller graphs, presumably because the space-of-all-graphs explodes combinatorially with graph size. Since the representation strongly affects genetic algorithm performance, adding graphs to the evolutionary programmer's bag-of-tricks should be beneficial. Also, since graph evolution operates directly on the phenotype, the genotype-phenotype translation step, common in genetic algorithm work, is eliminated.

  19. On the spectral distribution of distance-k graph of free product graphs

    NASA Astrophysics Data System (ADS)

    Arizmendi, Octavio; Gaxiola, Tulio

    2016-08-01

    We calculate the distribution with respect to the vacuum state of the distance-k graph of a d-regular tree. From this result we show that the distance-k graph of a d-regular graphs converges to the distribution of the distance-k graph of a regular tree. Finally, we prove that, properly normalized, the asymptotic distributions of distance-k graphs of the d-fold free product graph, as d tends to infinity, is given by the distribution of Pk(s), where s is a semicirlce random variable and Pk is the kth Chebychev polynomial.

  20. A Graph Based Methodology for Temporal Signature Identification from HER.

    PubMed

    Wang, Fei; Liu, Chuanren; Wang, Yajuan; Hu, Jianying; Yu, Guoqiang

    2015-01-01

    Data driven technology is believed to be a promising technique for transforming the current status of healthcare. Electronic Health Records (EHR) is one of the main carriers for conducting the data driven healthcare research, where the goal is to derive insights from healthcare data and utilize such insights to improve the quality of care delivery. Due to the progression nature of human disease, one important aspect for analyzing healthcare data is temporality, which suggests the temporal relationships among different healthcare events and how their values evolve over time. Sequential pattern mining is a popular tool to extract time-invariant patterns from discrete sequences and has been applied in analyzing EHR before. However, due to the complexity of EHR, those approaches usually suffers from the pattern explosion problem, which means that a huge number of patterns will be detected with improper setting of the support threshold. To address this challenge, in this paper, we develop a novel representation, namely the temporal graph, for event sequences like EHR, wherein the nodes are medical events and the edges indicate the temporal relationships among those events in patient EHRs. Based on the temporal graph representation, we further develop an approach for temporal signature identification to identify the most significant and interpretable graph bases as temporal signatures, and the expressing coefficients can be treated as the embeddings of the patients in such temporal signature space. Our temporal signature identification framework is also flexible to incorporate semi-supervised/supervised information. We validate our framework on two real-world tasks. One is predicting the onset risk of heart failure. The other is predicting the risk of heart failure related hospitalization for patients with COPD pre-condition. Our results show that the prediction performance in both tasks can be improved by the proposed approaches. PMID:26958267

  1. A Graph Based Methodology for Temporal Signature Identification from HER.

    PubMed

    Wang, Fei; Liu, Chuanren; Wang, Yajuan; Hu, Jianying; Yu, Guoqiang

    2015-01-01

    Data driven technology is believed to be a promising technique for transforming the current status of healthcare. Electronic Health Records (EHR) is one of the main carriers for conducting the data driven healthcare research, where the goal is to derive insights from healthcare data and utilize such insights to improve the quality of care delivery. Due to the progression nature of human disease, one important aspect for analyzing healthcare data is temporality, which suggests the temporal relationships among different healthcare events and how their values evolve over time. Sequential pattern mining is a popular tool to extract time-invariant patterns from discrete sequences and has been applied in analyzing EHR before. However, due to the complexity of EHR, those approaches usually suffers from the pattern explosion problem, which means that a huge number of patterns will be detected with improper setting of the support threshold. To address this challenge, in this paper, we develop a novel representation, namely the temporal graph, for event sequences like EHR, wherein the nodes are medical events and the edges indicate the temporal relationships among those events in patient EHRs. Based on the temporal graph representation, we further develop an approach for temporal signature identification to identify the most significant and interpretable graph bases as temporal signatures, and the expressing coefficients can be treated as the embeddings of the patients in such temporal signature space. Our temporal signature identification framework is also flexible to incorporate semi-supervised/supervised information. We validate our framework on two real-world tasks. One is predicting the onset risk of heart failure. The other is predicting the risk of heart failure related hospitalization for patients with COPD pre-condition. Our results show that the prediction performance in both tasks can be improved by the proposed approaches.

  2. A Graph Based Methodology for Temporal Signature Identification from EHR

    PubMed Central

    Wang, Fei; Liu, Chuanren; Wang, Yajuan; Hu, Jianying; Yu, Guoqiang

    2015-01-01

    Data driven technology is believed to be a promising technique for transforming the current status of healthcare. Electronic Health Records (EHR) is one of the main carriers for conducting the data driven healthcare research, where the goal is to derive insights from healthcare data and utilize such insights to improve the quality of care delivery. Due to the progression nature of human disease, one important aspect for analyzing healthcare data is temporality, which suggests the temporal relationships among different healthcare events and how their values evolve over time. Sequential pattern mining is a popular tool to extract time-invariant patterns from discrete sequences and has been applied in analyzing EHR before. However, due to the complexity of EHR, those approaches usually suffers from the pattern explosion problem, which means that a huge number of patterns will be detected with improper setting of the support threshold. To address this challenge, in this paper, we develop a novel representation, namely the temporal graph, for event sequences like EHR, wherein the nodes are medical events and the edges indicate the temporal relationships among those events in patient EHRs. Based on the temporal graph representation, we further develop an approach for temporal signature identification to identify the most significant and interpretable graph bases as temporal signatures, and the expressing coefficients can be treated as the embeddings of the patients in such temporal signature space. Our temporal signature identification framework is also flexible to incorporate semi-supervised/supervised information. We validate our framework on two real-world tasks. One is predicting the onset risk of heart failure. The other is predicting the risk of heart failure related hospitalization for patients with COPD pre-condition. Our results show that the prediction performance in both tasks can be improved by the proposed approaches. PMID:26958267

  3. Limit cycles and conformal invariance

    NASA Astrophysics Data System (ADS)

    Fortin, Jean-François; Grinstein, Benjamín; Stergiou, Andreas

    2013-01-01

    There is a widely held belief that conformal field theories (CFTs) require zero beta functions. Nevertheless, the work of Jack and Osborn implies that the beta functions are not actually the quantites that decide conformality, but until recently no such behavior had been exhibited. Our recent work has led to the discovery of CFTs with nonzero beta functions, more precisely CFTs that live on recurrent trajectories, e.g., limit cycles, of the beta-function vector field. To demonstrate this we study the S function of Jack and Osborn. We use Weyl consistency conditions to show that it vanishes at fixed points and agrees with the generator Q of limit cycles on them. Moreover, we compute S to third order in perturbation theory, and explicitly verify that it agrees with our previous determinations of Q. A byproduct of our analysis is that, in perturbation theory, unitarity and scale invariance imply conformal invariance in four-dimensional quantum field theories. Finally, we study some properties of these new, "cyclic" CFTs, and point out that the a-theorem still governs the asymptotic behavior of renormalization-group flows.

  4. Invariant imbedding in two dimensions

    SciTech Connect

    Faber, V.; Seth, D.L.; Wing, G.M.

    1988-01-01

    J. Corones has noted that the doubling and addition formulas of invariant imbedding can be extended conceptually to very general situations. All that is needed is a black box ''process'' with n ''ports.'' The /ital i/th port has vector input I/sub i/ and vector output J/sub i/. Addition formulas result when two or more of these processes are joined together to form a new process in some regular way. For example, four congruent squares can be juxtaposed to form a larger square. At each join, the output of one process becomes the input of the other and vice versa. (We always suppose the join to occur at one or more ports.) Addition formulas result from the combination of these shared quantities. Corones has thus pointed out that invariant imbedding is not, as is sometimes asserted, an inherently one-dimensional (1-D) method, but works conceptually in any number of dimensions; some previous work that is conceptually along these lines, with references to other such works, can be found in Refs. 2-4. The details can, of course, become very complicated. We shall show that the method is computationally feasible for certain two-dimensional (2-D) problems. To conform to the thrust of these proceedings, we shall usually phrase our discussions in terms of transport theory rather than speaking of more abstract processes. 7 refs., 13 figs.

  5. Yang-Mills theory on a momentum lattice: Gauge invariance, chiral invariance, and no fermion doubling

    SciTech Connect

    Berube, D.; Kroeger, H.; Lafrance, R.; Marleau, L. )

    1991-02-15

    We discuss properties of a noncompact formulation of gauge theories with fermions on a momentum ({ital k}) lattice. (a) This formulation is suitable to build in Fourier acceleration in a direct way. (b) The numerical effort to compute the action (by fast Fourier transform) goes essentially like log{ital V} with the lattice volume {ital V}. (c) For the Yang-Mills theory we find that the action conserves gauge symmetry and chiral symmetry in a weak sense: On a finite lattice the action is invariant under infinitesimal transformations with compact support. Under finite transformations these symmetries are approximately conserved and they are restored on an infinite lattice and in the continuum limit. Moreover, these symmetries also hold on a finite lattice under finite transformations, if the classical fields, instead of being {ital c}-number valued, take values from a finite Galois field. (d) There is no fermion doubling. (e) For the {phi}{sup 4} model we investigate the transition towards the continuum limit in lattice perturbation theory up to second order. We compute the two- and four-point functions and find local and Lorentz-invariant results. (f) In QED we compute a one-loop vacuum polarization and find in the continuum limit the standard result. (g) As a numerical application, we compute the propagator {l angle}{phi}({ital k}){phi}({ital k}{prime}){r angle} in the {phi}{sup 4} model, investigate Euclidean invariance, and extract {ital m}{sub {ital R}} as well as {ital Z}{sub {ital R}}. Moreover we compute {l angle}{ital F}{sub {mu}{nu}}({ital k}){ital F}{sub {mu}{nu}}({ital k}{prime}){r angle} in the SU(2) model.

  6. Quadratic invariants for discrete clusters of weakly interacting waves

    NASA Astrophysics Data System (ADS)

    Harper, Katie L.; Bustamante, Miguel D.; Nazarenko, Sergey V.

    2013-06-01

    We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix {A} with entries 1, -1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N - M* ⩾ N - M, where M* is the number of linearly independent rows in {A}. Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney-Hasegawa-Mima wave model, and by showing a classification of small (up to three-triad) clusters.

  7. Protein Surface Characterization Using an Invariant Descriptor

    PubMed Central

    Abu Deeb, Zainab; Adjeroh, Donald A.; Jiang, Bing-Hua

    2011-01-01

    Aim. To develop a new invariant descriptor for the characterization of protein surfaces, suitable for various analysis tasks, such as protein functional classification, and search and retrieval of protein surfaces over a large database. Methods. We start with a local descriptor of selected circular patches on the protein surface. The descriptor records the distance distribution between the central residue and the residues within the patch, keeping track of the number of particular pairwise residue cooccurrences in the patch. A global descriptor for the entire protein surface is then constructed by combining information from the local descriptors. Our method is novel in its focus on residue-specific distance distributions, and the use of residue-distance co-occurrences as the basis for the proposed protein surface descriptors. Results. Results are presented for protein classification and for retrieval for three protein families. For the three families, we obtained an area under the curve for precision and recall ranging from 0.6494 (without residue co-occurrences) to 0.6683 (with residue co-occurrences). Large-scale screening using two other protein families placed related family members at the top of the rank, with a number of uncharacterized proteins also retrieved. Comparative results with other proposed methods are included. PMID:22144981

  8. Area law for random graph states

    NASA Astrophysics Data System (ADS)

    Collins, Benoît; Nechita, Ion; Życzkowski, Karol

    2013-08-01

    Random pure states of multi-partite quantum systems, associated with arbitrary graphs, are investigated. Each vertex of the graph represents a generic interaction between subsystems, described by a random unitary matrix distributed according to the Haar measure, while each edge of the graph represents a bipartite, maximally entangled state. For any splitting of the graph into two parts we consider the corresponding partition of the quantum system and compute the average entropy of entanglement. First, in the special case where the partition does not cross any vertex of the graph, we show that the area law is satisfied exactly. In the general case, we show that the entropy of entanglement obeys an area law on average, this time with a correction term that depends on the topologies of the graph and of the partition. The results obtained are applied to the problem of distribution of quantum entanglement in a quantum network with prescribed topology.

  9. Replica methods for loopy sparse random graphs

    NASA Astrophysics Data System (ADS)

    Coolen, ACC

    2016-03-01

    I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement. This paper is dedicated to the memory of our colleague and friend Jun-Ichi Inoue, with whom the author has had the great pleasure and privilege of collaborating.

  10. Graph Frequency Analysis of Brain Signals

    NASA Astrophysics Data System (ADS)

    Huang, Weiyu; Goldsberry, Leah; Wymbs, Nicholas F.; Grafton, Scott T.; Bassett, Danielle S.; Ribeiro, Alejandro

    2016-10-01

    This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters traditionally defined for signals supported on regular domains such as discrete time and image grids has been recently generalized to irregular graph domains, and defines brain graph frequencies associated with different levels of spatial smoothness across the brain regions. Brain network frequency also enables the decomposition of brain signals into pieces corresponding to smooth or rapid variations. We relate graph frequency with principal component analysis when the networks of interest denote functional connectivity. The methods are utilized to analyze brain networks and signals as subjects master a simple motor skill. We observe that brain signals corresponding to different graph frequencies exhibit different levels of adaptability throughout learning. Further, we notice a strong association between graph spectral properties of brain networks and the level of exposure to tasks performed, and recognize the most contributing and important frequency signatures at different task familiarity.

  11. Fast generation of sparse random kernel graphs

    SciTech Connect

    Hagberg, Aric; Lemons, Nathan; Du, Wen -Bo

    2015-09-10

    The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in time at most ο(n(logn)²). As an example, we show how to generate samples of power-law degree distribution graphs with tunable assortativity.

  12. Fast generation of sparse random kernel graphs

    DOE PAGESBeta

    Hagberg, Aric; Lemons, Nathan; Du, Wen -Bo

    2015-09-10

    The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in timemore » at most ο(n(logn)²). As an example, we show how to generate samples of power-law degree distribution graphs with tunable assortativity.« less

  13. Image clustering using fuzzy graph theory

    NASA Astrophysics Data System (ADS)

    Jafarkhani, Hamid; Tarokh, Vahid

    1999-12-01

    We propose an image clustering algorithm which uses fuzzy graph theory. First, we define a fuzzy graph and the concept of connectivity for a fuzzy graph. Then, based on our definition of connectivity we propose an algorithm which finds connected subgraphs of the original fuzzy graph. Each connected subgraph can be considered as a cluster. As an application of our algorithm, we consider a database of images. We calculate a similarity measure between any paris of images in the database and generate the corresponding fuzzy graph. The, we find the subgraphs of the resulting fuzzy graph using our algorithm. Each subgraph corresponds to a cluster. We apply our image clustering algorithm to the key frames of news programs to find the anchorperson clusters. Simulation results show that our algorithm is successful to find most of anchorperson frames from the database.

  14. Spectral correlations of individual quantum graphs.

    PubMed

    Gnutzmann, Sven; Altland, Alexander

    2005-11-01

    We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the energy-average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric nonlinear -model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner-Dyson random matrix theory. We explore the stability of the universal random matrix behavior with regard to perturbations, and discuss the crossover between different types of symmetries.

  15. Spectral correlations of individual quantum graphs

    SciTech Connect

    Gnutzmann, Sven; Altland, Alexander

    2005-11-01

    We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the energy-average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric nonlinear {sigma}-model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner-Dyson random matrix theory. We explore the stability of the universal random matrix behavior with regard to perturbations, and discuss the crossover between different types of symmetries.

  16. Separability of Generalized Graph Product States

    NASA Astrophysics Data System (ADS)

    Zhao, Hui; Fan, Jiao

    2013-09-01

    We construct two classes of generalized graph product states and study the entanglement of these states. It is first presented that the density matrices of complex edge-weighted digraphs associated with the generalized graph product in mn systems are positive partial transformation and separable states. Then we prove that the density matrices of the vertex-weighted digraphs associated with another generalized graph product are entangled states.

  17. Multiple-invariance esprit for DOA estimation

    NASA Astrophysics Data System (ADS)

    Linczuk, Maciej

    2004-07-01

    We consider the problem of estimating the direction of arrival (DOA) of multiple sources in the presence of noise. First, we introduce a narrowband signal model disturbed by white, Gaussian noise. This signal is detected by Uniform Linear Antenna Array -- ULA. Next, we discuss some properties of this signal model and its cross correlation matrix. Using this properties we introduce SINGLE SHIFT INVARIANCE algorithm for DOA estimation: ESPRIT. Next, we describe an idea of MULTIPLE INVARIANCE algorithm based on MULTIPLE INVARIANCE ESPRIT. In the last section we examine some statistical properties of both algorithms: ESPRIT and MULTIPLE INVARIANCE ESPRIT.

  18. Breddin's graph for tectonic regimes

    NASA Astrophysics Data System (ADS)

    Célérier, Bernard; Séranne, Michel

    2001-05-01

    A simple graphical method is proposed to infer the tectonic regime from a fault and slip data set. An abacus is overlaid on a plot of the rake versus strike of the data. This yields the horizontal principal stress directions and a constraint on the stress tensor aspect ratio, in a manner similar to Breddin's graph for two-dimensional strain analysis. The main requirement is that one of the principal stress directions is close to the vertical. This method is illustrated on monophase synthetic and natural data, but is also expected to help sort out multiphase data sets.

  19. Naming on a Directed Graph

    NASA Astrophysics Data System (ADS)

    Gosti, Giorgio; Batchelder, William H.

    We address how the structure of a social communication system affects language coordination. The naming game is an abstraction of lexical acquisition dynamics, in which N agents try to find an agreement on the names to give to objects. Most results on naming games are specific to certain communication network topologies. We present two important results that are general to any graph topology: the first proves that under certain topologies the system always converges to a name-object agreement; the second proves that if these conditions are not met the system may end up in a state in which sub-networks with different competing object-name associations coexist.

  20. The alignment-distribution graph

    NASA Technical Reports Server (NTRS)

    Chatterjee, Siddhartha; Gilbert, John R.; Schreiber, Robert

    1993-01-01

    Implementing a data-parallel language such as Fortran 90 on a distributed-memory parallel computer requires distributing aggregate data objects (such as arrays) among the memory modules attached to the processors. The mapping of objects to the machine determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. We present a program representation called the alignment-distribution graph that makes these communication requirements explicit. We describe the details of the representation, show how to model communication cost in this framework, and outline several algorithms for determining object mappings that approximately minimize residual communication.

  1. The alignment-distribution graph

    NASA Technical Reports Server (NTRS)

    Chatterjee, Siddhartha; Gilbert, John R.; Schreiber, Robert

    1993-01-01

    Implementing a data-parallel language such as Fortran 90 on a distributed-memory parallel computer requires distributing aggregate data objects (such as arrays) among the memory modules attached to the processors. The mapping of objects to the machine determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. We present a program representation called the alignment distribution graph that makes these communication requirements explicit. We describe the details of the representation, show how to model communication cost in this framework, and outline several algorithms for determining object mappings that approximately minimize residual communication.

  2. Givental Graphs and Inversion Symmetry

    NASA Astrophysics Data System (ADS)

    Dunin-Barkowski, Petr; Shadrin, Sergey; Spitz, Loek

    2013-05-01

    Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy.

  3. Graph algorithms in the titan toolkit.

    SciTech Connect

    McLendon, William Clarence, III; Wylie, Brian Neil

    2009-10-01

    Graph algorithms are a key component in a wide variety of intelligence analysis activities. The Graph-Based Informatics for Non-Proliferation and Counter-Terrorism project addresses the critical need of making these graph algorithms accessible to Sandia analysts in a manner that is both intuitive and effective. Specifically we describe the design and implementation of an open source toolkit for doing graph analysis, informatics, and visualization that provides Sandia with novel analysis capability for non-proliferation and counter-terrorism.

  4. Evolutionary Games of Multiplayer Cooperation on Graphs.

    PubMed

    Peña, Jorge; Wu, Bin; Arranz, Jordi; Traulsen, Arne

    2016-08-01

    There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering. PMID:27513946

  5. Simple scale interpolator facilitates reading of graphs

    NASA Technical Reports Server (NTRS)

    Fetterman, D. E., Jr.

    1965-01-01

    Simple transparent overlay with interpolation scale facilitates accurate, rapid reading of graph coordinate points. This device can be used for enlarging drawings and locating points on perspective drawings.

  6. Evolutionary Games of Multiplayer Cooperation on Graphs.

    PubMed

    Peña, Jorge; Wu, Bin; Arranz, Jordi; Traulsen, Arne

    2016-08-01

    There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering.

  7. Generation of graph-state streams

    SciTech Connect

    Ballester, Daniel; Cho, Jaeyoon; Kim, M. S.

    2011-01-15

    We propose a protocol to generate a stream of mobile qubits in a graph state through a single stationary parent qubit and discuss two types of its physical implementation, namely, the generation of photonic graph states through an atomlike qubit and the generation of flying atoms through a cavity-mode photonic qubit. The generated graph states fall into an important class that can hugely reduce the resource requirement of fault-tolerant linear optics quantum computation, which was previously known to be far from realistic. In regard to the flying atoms, we also propose a heralded generation scheme, which allows for high-fidelity graph states even under the photon loss.

  8. Evolutionary Games of Multiplayer Cooperation on Graphs

    PubMed Central

    Arranz, Jordi; Traulsen, Arne

    2016-01-01

    There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering. PMID:27513946

  9. Asymptotic invariants of homotopy groups

    NASA Astrophysics Data System (ADS)

    Manin, Fedor

    We study the homotopy groups of a finite CW complex X via constraints on the geometry of representatives of their elements. For example, one can measure the "size" of alpha ∈ pi n (X) by the optimal Lipschitz constant or volume of a representative. By comparing the geometrical structure thus obtained with the algebraic structure of the group, one can define functions such as growth and distortion in pin(X), analogously to the way that such functions are studied in asymptotic geometric group theory. We provide a number of examples and techniques for studying these invariants, with a special focus on spaces with few rational homotopy groups. Our main theorem characterizes those X in which all non-torsion homotopy classes are undistorted, that is, their volume distortion functions, and hence also their Lipschitz distortion functions, are linear.

  10. Geometrically robust image watermarking using scale-invariant feature transform and Zernike moments

    NASA Astrophysics Data System (ADS)

    Li, Leida; Guo, Baolong; Shao, Kai

    2007-06-01

    In order to resist geometric attacks, a robust image watermarking algorithm is proposed using scale-invariant feature transform (SIFT) and Zernike moments. As SIFT features are invariant to rotation and scaling, we employ SIFT to extract feature points. Then circular patches are generated using the most robust points. An invariant watermark is generated from each circular patch based on Zernike moments. The watermark is embedded into multiple patches for resisting locally cropping attacks. Experimental results show that the proposed scheme is robust to both geometric attacks and signal processing attacks.

  11. Construction of invariants of the coadjoint representation of Lie groups using linear algebra methods

    NASA Astrophysics Data System (ADS)

    Kurnyavko, O. L.; Shirokov, I. V.

    2016-07-01

    We offer a method for constructing invariants of the coadjoint representation of Lie groups that reduces this problem to known problems of linear algebra. This method is based on passing to symplectic coordinates on the coadjoint representation orbits, which play the role of local coordinates on those orbits. The corresponding transition functions are their parametric equations. Eliminating the symplectic coordinates from the transition functions, we can obtain the complete set of invariants. The proposed method allows solving the problem of constructing invariants of the coadjoint representation for Lie groups with an arbitrary dimension and structure.

  12. Aspects of Performance on Line Graph Description Tasks: Influenced by Graph Familiarity and Different Task Features

    ERIC Educational Resources Information Center

    Xi, Xiaoming

    2010-01-01

    Motivated by cognitive theories of graph comprehension, this study systematically manipulated characteristics of a line graph description task in a speaking test in ways to mitigate the influence of graph familiarity, a potential source of construct-irrelevant variance. It extends Xi (2005), which found that the differences in holistic scores on…

  13. GPD: a graph pattern diffusion kernel for accurate graph classification with applications in cheminformatics.

    PubMed

    Smalter, Aaron; Huan, Jun Luke; Jia, Yi; Lushington, Gerald

    2010-01-01

    Graph data mining is an active research area. Graphs are general modeling tools to organize information from heterogeneous sources and have been applied in many scientific, engineering, and business fields. With the fast accumulation of graph data, building highly accurate predictive models for graph data emerges as a new challenge that has not been fully explored in the data mining community. In this paper, we demonstrate a novel technique called graph pattern diffusion (GPD) kernel. Our idea is to leverage existing frequent pattern discovery methods and to explore the application of kernel classifier (e.g., support vector machine) in building highly accurate graph classification. In our method, we first identify all frequent patterns from a graph database. We then map subgraphs to graphs in the graph database and use a process we call "pattern diffusion" to label nodes in the graphs. Finally, we designed a graph alignment algorithm to compute the inner product of two graphs. We have tested our algorithm using a number of chemical structure data. The experimental results demonstrate that our method is significantly better than competing methods such as those kernel functions based on paths, cycles, and subgraphs.

  14. Helping Students Make Sense of Graphs: An Experimental Trial of SmartGraphs Software

    ERIC Educational Resources Information Center

    Zucker, Andrew; Kay, Rachel; Staudt, Carolyn

    2014-01-01

    Graphs are commonly used in science, mathematics, and social sciences to convey important concepts; yet students at all ages demonstrate difficulties interpreting graphs. This paper reports on an experimental study of free, Web-based software called SmartGraphs that is specifically designed to help students overcome their misconceptions regarding…

  15. Clique percolation in random graphs

    NASA Astrophysics Data System (ADS)

    Li, Ming; Deng, Youjin; Wang, Bing-Hong

    2015-10-01

    As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two k cliques means that they share at least l graphs, which gives not only the exact solutions of the critical point, but also the corresponding order parameter. Based on this, we prove theoretically that the fraction ψ of cliques in the giant clique cluster always makes a continuous phase transition as the classical percolation. However, the fraction ϕ of vertices in the giant clique cluster for l >1 makes a step-function-like discontinuous phase transition in the thermodynamic limit and a continuous phase transition for l =1 . More interesting, our analysis shows that at the critical point, the order parameter ϕc for l >1 is neither 0 nor 1, but a constant depending on k and l . All these theoretical findings are in agreement with the simulation results, which give theoretical support and clarification for previous simulation studies of clique percolation.

  16. Hybrid graphs as a framework for the small-world effect

    NASA Astrophysics Data System (ADS)

    Lehmann, Katharina A.; Post, Hendrik D.; Kaufmann, Michael

    2006-05-01

    In this paper we formalize the small-world effect which describes the surprising fact that a hybrid graph composed of a local graph component and a very sparse random graph has a diameter of O(lnn) whereby the diameter of both components alone is much higher. We show that a large family of these hybrid graphs shows this effect and that this generalized family also includes classic small-world models proposed by various authors although not all of them are captured by the small-world definition given by Watts and Strogatz. Furthermore, we give a detailed upper bound of the hybrid’s graph diameter for different choices of the expected number of random edges by applying a new kind of proof pattern that is applicable to a large number of hybrid graphs. The focus in this paper is on presenting a flexible family of hybrid graphs showing the small-world effect that can be tuned closely to real-world systems.

  17. Support vector machine classification of major depressive disorder using diffusion-weighted neuroimaging and graph theory.

    PubMed

    Sacchet, Matthew D; Prasad, Gautam; Foland-Ross, Lara C; Thompson, Paul M; Gotlib, Ian H

    2015-01-01

    Recently, there has been considerable interest in understanding brain networks in major depressive disorder (MDD). Neural pathways can be tracked in the living brain using diffusion-weighted imaging (DWI); graph theory can then be used to study properties of the resulting fiber networks. To date, global abnormalities have not been reported in tractography-based graph metrics in MDD, so we used a machine learning approach based on "support vector machines" to differentiate depressed from healthy individuals based on multiple brain network properties. We also assessed how important specific graph metrics were for this differentiation. Finally, we conducted a local graph analysis to identify abnormal connectivity at specific nodes of the network. We were able to classify depression using whole-brain graph metrics. Small-worldness was the most useful graph metric for classification. The right pars orbitalis, right inferior parietal cortex, and left rostral anterior cingulate all showed abnormal network connectivity in MDD. This is the first use of structural global graph metrics to classify depressed individuals. These findings highlight the importance of future research to understand network properties in depression across imaging modalities, improve classification results, and relate network alterations to psychiatric symptoms, medication, and comorbidities.

  18. Constructing a Nonnegative Low-Rank and Sparse Graph With Data-Adaptive Features.

    PubMed

    Zhuang, Liansheng; Gao, Shenghua; Tang, Jinhui; Wang, Jingjing; Lin, Zhouchen; Ma, Yi; Yu, Nenghai

    2015-11-01

    This paper aims at constructing a good graph to discover the intrinsic data structures under a semisupervised learning setting. First, we propose to build a nonnegative low-rank and sparse (referred to as NNLRS) graph for the given data representation. In particular, the weights of edges in the graph are obtained by seeking a nonnegative low-rank and sparse reconstruction coefficients matrix that represents each data sample as a linear combination of others. The so-obtained NNLRS-graph captures both the global mixture of subspaces structure (by the low-rankness) and the locally linear structure (by the sparseness) of the data, hence it is both generative and discriminative. Second, as good features are extremely important for constructing a good graph, we propose to learn the data embedding matrix and construct the graph simultaneously within one framework, which is termed as NNLRS with embedded features (referred to as NNLRS-EF). Extensive NNLRS experiments on three publicly available data sets demonstrate that the proposed method outperforms the state-of-the-art graph construction method by a large margin for both semisupervised classification and discriminative analysis, which verifies the effectiveness of our proposed method.

  19. Proximity graphs based multi-scale image segmentation

    SciTech Connect

    Skurikhin, Alexei N

    2008-01-01

    We present a novel multi-scale image segmentation approach based on irregular triangular and polygonal tessellations produced by proximity graphs. Our approach consists of two separate stages: polygonal seeds generation followed by an iterative bottom-up polygon agglomeration into larger chunks. We employ constrained Delaunay triangulation combined with the principles known from the visual perception to extract an initial ,irregular polygonal tessellation of the image. These initial polygons are built upon a triangular mesh composed of irregular sized triangles and their shapes are ad'apted to the image content. We then represent the image as a graph with vertices corresponding to the polygons and edges reflecting polygon relations. The segmentation problem is then formulated as Minimum Spanning Tree extraction. We build a successive fine-to-coarse hierarchy of irregular polygonal grids by an iterative graph contraction constructing Minimum Spanning Tree. The contraction uses local information and merges the polygons bottom-up based on local region-and edge-based characteristics.

  20. Enabling Graph Appliance for Genome Assembly

    SciTech Connect

    Singh, Rina; Graves, Jeffrey A; Lee, Sangkeun; Sukumar, Sreenivas R; Shankar, Mallikarjun

    2015-01-01

    In recent years, there has been a huge growth in the amount of genomic data available as reads generated from various genome sequencers. The number of reads generated can be huge, ranging from hundreds to billions of nucleotide, each varying in size. Assembling such large amounts of data is one of the challenging computational problems for both biomedical and data scientists. Most of the genome assemblers developed have used de Bruijn graph techniques. A de Bruijn graph represents a collection of read sequences by billions of vertices and edges, which require large amounts of memory and computational power to store and process. This is the major drawback to de Bruijn graph assembly. Massively parallel, multi-threaded, shared memory systems can be leveraged to overcome some of these issues. The objective of our research is to investigate the feasibility and scalability issues of de Bruijn graph assembly on Cray s Urika-GD system; Urika-GD is a high performance graph appliance with a large shared memory and massively multithreaded custom processor designed for executing SPARQL queries over large-scale RDF data sets. However, to the best of our knowledge, there is no research on representing a de Bruijn graph as an RDF graph or finding Eulerian paths in RDF graphs using SPARQL for potential genome discovery. In this paper, we address the issues involved in representing a de Bruin graphs as RDF graphs and propose an iterative querying approach for finding Eulerian paths in large RDF graphs. We evaluate the performance of our implementation on real world ebola genome datasets and illustrate how genome assembly can be accomplished with Urika-GD using iterative SPARQL queries.

  1. Cross-National Invariance of Children's Temperament

    ERIC Educational Resources Information Center

    Benson, Nicholas; Oakland, Thomas; Shermis, Mark

    2009-01-01

    Measurement of temperament is an important endeavor with international appeal; however, cross-national invariance (i.e., equivalence of test scores across countries as established by empirical comparisons) of temperament tests has not been established in published research. This study examines the cross-national invariance of school-aged…

  2. Invariance or Noninvariance, that Is the Question

    ERIC Educational Resources Information Center

    Widaman, Keith F.; Grimm, Kevin J.

    2009-01-01

    Nesselroade, Gerstorf, Hardy, and Ram developed a new and interesting way to enforce invariance at the second-order level in P-technique models, while allowing first-order structure to stray from invariance. We discuss our concerns with this approach under the headings of falsifiability, the nature of manifest variables included in models, and…

  3. Factorial invariance in multilevel confirmatory factor analysis.

    PubMed

    Ryu, Ehri

    2014-02-01

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

  4. Geometric invariance of compressible turbulent boundary layers

    NASA Astrophysics Data System (ADS)

    Bi, Wei-Tao; Wu, Bin; She, Zhen-Su; Hussain, Fazle

    2015-11-01

    A symmetry based approach is applied to analyze the mean velocity and temperature fields of compressible, flat plate turbulent boundary layers (CTBL). A Reynolds stress length scale and a turbulent heat flux length scale are identified to possess the same defect scaling law in the CTBL bulk, which is solely owing to the constraint of the wall to the geometry of the wall-attached eddies, but invariant to compressibility and wall heat transfer. This invariance is called the geometric invariance of CTBL eddies and is likely the origin of the Mach number invariance of Morkovin's hypothesis, as well as the similarity of energy and momentum transports. A closure for the turbulent transport by using the invariant lengths is attainted to predict the mean velocity and temperature profiles in the CTBL bulk- superior to the van Driest transformation and the Reynolds analogy based relations for its sound physics and higher accuracy. Additionally, our approach offers a new understanding of turbulent Prandtl number.

  5. Teaching Discrete Mathematics with Graphing Calculators.

    ERIC Educational Resources Information Center

    Masat, Francis E.

    Graphing calculator use is often thought of in terms of pre-calculus or continuous topics in mathematics. This paper contains examples and activities that demonstrate useful, interesting, and easy ways to use a graphing calculator with discrete topics. Examples are given for each of the following topics: functions, mathematical induction and…

  6. Student Reasoning about Graphs in Different Contexts

    ERIC Educational Resources Information Center

    Ivanjek, Lana; Susac, Ana; Planinic, Maja; Andrasevic, Aneta; Milin-Sipus, Zeljka

    2016-01-01

    This study investigates university students' graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the…

  7. Universal spectral statistics in quantum graphs.

    PubMed

    Gnutzmann, Sven; Altland, Alexander

    2004-11-01

    We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random-matrix theory. The stability of these correlations with regard to nonuniversal corrections is analyzed in terms of the linear operator governing the classical dynamics on the graph.

  8. Graphs and Statistics: A Resource Handbook.

    ERIC Educational Resources Information Center

    New York State Education Dept., Albany. Bureau of General Education Curriculum Development.

    Graphical representation of statistical data is the focus of this resource handbook. Only graphs which present numerical information are discussed. Activities involving the making, interpreting, and use of various types of graphs and tables are included. Sections are also included which discuss statistical terms, normal distribution and…

  9. Using a Microcomputer for Graphing Practice.

    ERIC Educational Resources Information Center

    Beichner, Robert J.

    1986-01-01

    Describes a laboratory exercise that introduces physics students to graphing. Presents the program format and sample output of a computer simulation of an experiment which tests the effects of sound intensity on the crawling speed of a snail. Provides students with practice in making exponential or logarithmic graphs. (ML)

  10. Graphing Calculators: The Newest Revolution in Mathematics.

    ERIC Educational Resources Information Center

    Clutter, Martha

    1999-01-01

    Asserts that there are numerous advantages to using graphing calculators, including the teaching of higher-level thinking skills and allowing students to draw conclusions about what they are learning. However, mathematics educators face such challenges as teaching students when it is appropriate to use graphing calculators, course-content…

  11. Cognitive Aids for Guiding Graph Comprehension

    ERIC Educational Resources Information Center

    Mautone, Patricia D.; Mayer, Richard E.

    2007-01-01

    This study sought to improve students' comprehension of scientific graphs by adapting scaffolding techniques used to aid text comprehension. In 3 experiments involving 121 female and 88 male college students, some students were shown cognitive aids prior to viewing 4 geography graphs whereas others were not; all students were then asked to write a…

  12. Pattern Perception and the Comprehension of Graphs.

    ERIC Educational Resources Information Center

    Pinker, Steven

    Three experiments tested the hypothesis that graphs convey information effectively because they can display global trends as geometric patterns that visual systems encode easily. A novel type of graph was invented in which angles/lengths of line segments joined end-to-end represented variables of rainfall and temperature of a set of months. It was…

  13. Developing Data Graph Comprehension. Third Edition

    ERIC Educational Resources Information Center

    Curcio, Frances

    2010-01-01

    Since the dawn of civilization, pictorial representations and symbols have been used to communicate simple statistics. Efficient and effective, they are still used today in the form of pictures and graphs to record and present data. Who can tie their shoes? How many calories are in your favorite food? Make data and graphs relevant and interesting…

  14. A Ring Construction Using Finite Directed Graphs

    ERIC Educational Resources Information Center

    Bardzell, Michael

    2012-01-01

    In this paper we discuss an interesting class of noncommutative rings which can be constructed using finite directed graphs. This construction also creates a vector space. These structures provide undergraduate students connections between ring theory and graph theory and, among other things, allow them to see a ring unity element that looks quite…

  15. TI-83 Graphing Calculator Keystroke Guide.

    ERIC Educational Resources Information Center

    Panik, Cathy

    This document presents keystrokes for the Texas Instrument (TI-83) graphing calculator. After presenting some basic TI-83 keystrokes, activities for student practice are listed. This is followed by keystrokes for TI-83 advanced functions such as evaluating function values, finding the zero of a function, finding the intersection of two graphs,…

  16. Supplantation of Mental Operations on Graphs

    ERIC Educational Resources Information Center

    Vogel, Markus; Girwidz, Raimund; Engel, Joachim

    2007-01-01

    Research findings show the difficulties younger students have in working with graphs. Higher mental operations are necessary for a skilled interpretation of abstract representations. We suggest connecting a concrete representation of the modeled problem with the related graph. The idea is to illustrate essential mental operations externally. This…

  17. Invariance property of wave scattering through disordered media.

    PubMed

    Pierrat, Romain; Ambichl, Philipp; Gigan, Sylvain; Haber, Alexander; Carminati, Rémi; Rotter, Stefan

    2014-12-16

    A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the system's boundary geometry and is thus unaffected by the value of the mean free path. Here we show that this result is rooted on a much deeper level than that of a random walk, which allows us to extend the reach of this universal invariance property beyond the diffusion approximation. Specifically, we demonstrate that an equivalent invariance relation also holds for the scattering of waves in resonant structures as well as in ballistic, chaotic or in Anderson localized systems. Our work unifies a number of specific observations made in quite diverse fields of science ranging from the movement of ants to nuclear scattering theory. Potential experimental realizations using light fields in disordered media are discussed.

  18. Invariance property of wave scattering through disordered media

    PubMed Central

    Pierrat, Romain; Ambichl, Philipp; Gigan, Sylvain; Haber, Alexander; Carminati, Rémi; Rotter, Stefan

    2014-01-01

    A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the system's boundary geometry and is thus unaffected by the value of the mean free path. Here we show that this result is rooted on a much deeper level than that of a random walk, which allows us to extend the reach of this universal invariance property beyond the diffusion approximation. Specifically, we demonstrate that an equivalent invariance relation also holds for the scattering of waves in resonant structures as well as in ballistic, chaotic or in Anderson localized systems. Our work unifies a number of specific observations made in quite diverse fields of science ranging from the movement of ants to nuclear scattering theory. Potential experimental realizations using light fields in disordered media are discussed. PMID:25425671

  19. Invariance property of wave scattering through disordered media.

    PubMed

    Pierrat, Romain; Ambichl, Philipp; Gigan, Sylvain; Haber, Alexander; Carminati, Rémi; Rotter, Stefan

    2014-12-16

    A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the system's boundary geometry and is thus unaffected by the value of the mean free path. Here we show that this result is rooted on a much deeper level than that of a random walk, which allows us to extend the reach of this universal invariance property beyond the diffusion approximation. Specifically, we demonstrate that an equivalent invariance relation also holds for the scattering of waves in resonant structures as well as in ballistic, chaotic or in Anderson localized systems. Our work unifies a number of specific observations made in quite diverse fields of science ranging from the movement of ants to nuclear scattering theory. Potential experimental realizations using light fields in disordered media are discussed. PMID:25425671

  20. Generalized Random Sequential Adsorption on Erdős-Rényi Random Graphs

    NASA Astrophysics Data System (ADS)

    Dhara, Souvik; van Leeuwaarden, Johan S. H.; Mukherjee, Debankur

    2016-09-01

    We investigate random sequential adsorption (RSA) on a random graph via the following greedy algorithm: Order the n vertices at random, and sequentially declare each vertex either active or frozen, depending on some local rule in terms of the state of the neighboring vertices. The classical RSA rule declares a vertex active if none of its neighbors is, in which case the set of active nodes forms an independent set of the graph. We generalize this nearest-neighbor blocking rule in three ways and apply it to the Erdős-Rényi random graph. We consider these generalizations in the large-graph limit n→ ∞ and characterize the jamming constant, the limiting proportion of active vertices in the maximal greedy set.

  1. Graph states of prime-power dimension from generalized CNOT quantum circuit.

    PubMed

    Chen, Lin; Zhou, D L

    2016-01-01

    We construct multipartite graph states whose dimension is the power of a prime number. This is realized by the finite field, as well as the generalized controlled-NOT quantum circuit acting on two qudits. We propose the standard form of graph states up to local unitary transformations and particle permutations. The form greatly simplifies the classification of graph states as we illustrate up to five qudits. We also show that some graph states are multipartite maximally entangled states in the sense that any bipartition of the system produces a bipartite maximally entangled state. We further prove that 4-partite maximally entangled states exist when the dimension is an odd number at least three or a multiple of four. PMID:27272401

  2. Graph states of prime-power dimension from generalized CNOT quantum circuit

    PubMed Central

    Chen, Lin; Zhou, D. L.

    2016-01-01

    We construct multipartite graph states whose dimension is the power of a prime number. This is realized by the finite field, as well as the generalized controlled-NOT quantum circuit acting on two qudits. We propose the standard form of graph states up to local unitary transformations and particle permutations. The form greatly simplifies the classification of graph states as we illustrate up to five qudits. We also show that some graph states are multipartite maximally entangled states in the sense that any bipartition of the system produces a bipartite maximally entangled state. We further prove that 4-partite maximally entangled states exist when the dimension is an odd number at least three or a multiple of four. PMID:27272401

  3. Graph states of prime-power dimension from generalized CNOT quantum circuit.

    PubMed

    Chen, Lin; Zhou, D L

    2016-06-07

    We construct multipartite graph states whose dimension is the power of a prime number. This is realized by the finite field, as well as the generalized controlled-NOT quantum circuit acting on two qudits. We propose the standard form of graph states up to local unitary transformations and particle permutations. The form greatly simplifies the classification of graph states as we illustrate up to five qudits. We also show that some graph states are multipartite maximally entangled states in the sense that any bipartition of the system produces a bipartite maximally entangled state. We further prove that 4-partite maximally entangled states exist when the dimension is an odd number at least three or a multiple of four.

  4. Sparsified-dynamics modeling of discrete point vortices with graph theory

    NASA Astrophysics Data System (ADS)

    Taira, Kunihiko; Nair, Aditya

    2014-11-01

    We utilize graph theory to derive a sparsified interaction-based model that captures unsteady point vortex dynamics. The present model builds upon the Biot-Savart law and keeps the number of vortices (graph nodes) intact and reduces the number of inter-vortex interactions (graph edges). We achieve this reduction in vortex interactions by spectral sparsification of graphs. This approach drastically reduces the computational cost to predict the dynamical behavior, sharing characteristics of reduced-order models. Sparse vortex dynamics are illustrated through an example of point vortex clusters interacting amongst themselves. We track the centroids of the individual vortex clusters to evaluate the error in bulk motion of the point vortices in the sparsified setup. To further improve the accuracy in predicting the nonlinear behavior of the vortices, resparsification strategies are employed for the sparsified interaction-based models. The model retains the nonlinearity of the interaction and also conserves the invariants of discrete vortex dynamics; namely the Hamiltonian, linear impulse, and angular impulse as well as circulation. Work supported by US Army Research Office (W911NF-14-1-0386) and US Air Force Office of Scientific Research (YIP: FA9550-13-1-0183).

  5. Scale Space Graph Representation and Kernel Matching for Non Rigid and Textured 3D Shape Retrieval.

    PubMed

    Garro, Valeria; Giachetti, Andrea

    2016-06-01

    In this paper we introduce a novel framework for 3D object retrieval that relies on tree-based shape representations (TreeSha) derived from the analysis of the scale-space of the Auto Diffusion Function (ADF) and on specialized graph kernels designed for their comparison. By coupling maxima of the Auto Diffusion Function with the related basins of attraction, we can link the information at different scales encoding spatial relationships in a graph description that is isometry invariant and can easily incorporate texture and additional geometrical information as node and edge features. Using custom graph kernels it is then possible to estimate shape dissimilarities adapted to different specific tasks and on different categories of models, making the procedure a powerful and flexible tool for shape recognition and retrieval. Experimental results demonstrate that the method can provide retrieval scores similar or better than state-of-the-art on textured and non textured shape retrieval benchmarks and give interesting insights on effectiveness of different shape descriptors and graph kernels.

  6. Leader-following control of multiple nonholonomic systems over directed communication graphs

    NASA Astrophysics Data System (ADS)

    Dong, Wenjie; Djapic, Vladimir

    2016-06-01

    This paper considers the leader-following control problem of multiple nonlinear systems with directed communication topology and a leader. If the state of each system is measurable, distributed state feedback controllers are proposed using neighbours' state information with the aid of Lyapunov techniques and properties of Laplacian matrix for time-invariant communication graph and time-varying communication graph. It is shown that the state of each system exponentially converges to the state of a leader. If the state of each system is not measurable, distributed observer-based output feedback control laws are proposed. As an application of the proposed results, formation control of wheeled mobile robots is studied. The simulation results show the effectiveness of the proposed results.

  7. Graph Mining Meets the Semantic Web

    SciTech Connect

    Lee, Sangkeun; Sukumar, Sreenivas R; Lim, Seung-Hwan

    2015-01-01

    The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today, data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. We address that need through implementation of three popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, and PageRank). We implement these algorithms as SPARQL queries, wrapped within Python scripts. We evaluate the performance of our implementation on 6 real world data sets and show graph mining algorithms (that have a linear-algebra formulation) can indeed be unleashed on data represented as RDF graphs using the SPARQL query interface.

  8. Vortices and superfields on a graph

    SciTech Connect

    Kan, Nahomi; Kobayashi, Koichiro; Shiraishi, Kiyoshi

    2009-08-15

    We extend the dimensional deconstruction by utilizing the knowledge of graph theory. In the dimensional deconstruction, one uses the moose diagram to exhibit the structure of the 'theory space'. We generalize the moose diagram to a general graph with oriented edges. In the present paper, we consider only the U(1) gauge symmetry. We also introduce supersymmetry into our model by use of superfields. We suppose that vector superfields reside at the vertices and chiral superfields at the edges of a given graph. Then we can consider multivector, multi-Higgs models. In our model, [U(1)]{sup p} (where p is the number of vertices) is broken to a single U(1). Therefore, for specific graphs, we get vortexlike classical solutions in our model. We show some examples of the graphs admitting the vortex solutions of simple structure as the Bogomolnyi solution.

  9. Vortices and superfields on a graph

    NASA Astrophysics Data System (ADS)

    Kan, Nahomi; Kobayashi, Koichiro; Shiraishi, Kiyoshi

    2009-08-01

    We extend the dimensional deconstruction by utilizing the knowledge of graph theory. In the dimensional deconstruction, one uses the moose diagram to exhibit the structure of the “theory space.” We generalize the moose diagram to a general graph with oriented edges. In the present paper, we consider only the U(1) gauge symmetry. We also introduce supersymmetry into our model by use of superfields. We suppose that vector superfields reside at the vertices and chiral superfields at the edges of a given graph. Then we can consider multivector, multi-Higgs models. In our model, [U(1)]p (where p is the number of vertices) is broken to a single U(1). Therefore, for specific graphs, we get vortexlike classical solutions in our model. We show some examples of the graphs admitting the vortex solutions of simple structure as the Bogomolnyi solution.

  10. On linear area embedding of planar graphs

    NASA Astrophysics Data System (ADS)

    Dolev, D.; Trickey, H.

    1981-09-01

    Planar embedding with minimal area of graphs on an integer grid is one of the major issues in VLSI. Valiant (V) gave an algorithm to construct a planar embedding for trees in linear area; he also proved that there are planar graphs that require quadratic area. An algorithm to embed outerplanar graphs in linear area is given. This algorithm is extended to work for every planar graph that has the following property: for every vertex there exists a path of length less than K to the exterior face, where K is a constant. Finally, finding a minimal embedding area is shown to be NP-complete for forests, and hence more general types of graphs.

  11. Structure and strategy in encoding simplified graphs

    NASA Technical Reports Server (NTRS)

    Schiano, Diane J.; Tversky, Barbara

    1992-01-01

    Tversky and Schiano (1989) found a systematic bias toward the 45-deg line in memory for the slopes of identical lines when embedded in graphs, but not in maps, suggesting the use of a cognitive reference frame specifically for encoding meaningful graphs. The present experiments explore this issue further using the linear configurations alone as stimuli. Experiments 1 and 2 demonstrate that perception and immediate memory for the slope of a test line within orthogonal 'axes' are predictable from purely structural considerations. In Experiments 3 and 4, subjects were instructed to use a diagonal-reference strategy in viewing the stimuli, which were described as 'graphs' only in Experiment 3. Results for both studies showed the diagonal bias previously found only for graphs. This pattern provides converging evidence for the diagonal as a cognitive reference frame in encoding linear graphs, and demonstrates that even in highly simplified displays, strategic factors can produce encoding biases not predictable solely from stimulus structure alone.

  12. Hierarchical, 4-connected Small-World Graph

    NASA Astrophysics Data System (ADS)

    Goncalves, Bruno; Boettcher, Stefan

    2008-03-01

    A new sequences of graphs are introduced that mimic small-world properties. The graphs are recursively constructed but retain a fixed, regular degree. They consist of a one-dimensional lattice backbone overlayed by a hierarchical sequence of long-distance links in a pattern reminiscent of the tower-of-hanoi sequence. These 4-regular graphs are non-planar, have a diameter growing as 2^√2N^2 (or as [2N]^α with α˜√2N^2/22N^2), and a nontrivial phase transition Tc>0, for the Ising ferromagnet. These results suggest that these graphs are similar to small-world graphs with mean-field-like properties.

  13. Quantum graphs and random-matrix theory

    NASA Astrophysics Data System (ADS)

    Pluhař, Z.; Weidenmüller, H. A.

    2015-07-01

    For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas-Giannoni-Schmit (BGS) conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that the generating function for every (P,Q) correlation function for both closed and open graphs coincides with the corresponding expression of random-matrix theory. We show that the classical Perron-Frobenius operator is bistochastic and possesses a single eigenvalue +1. In the quantum case that implies the existence of a zero (or massless) mode of the effective action. That mode causes universal fluctuation properties. Avoiding the saddle-point approximation we show that for graphs that are classically mixing (i.e. for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap) and that do not carry a special class of bound states, the zero mode dominates in the limit of infinite graph size.

  14. GraphReduce: Large-Scale Graph Analytics on Accelerator-Based HPC Systems

    SciTech Connect

    Sengupta, Dipanjan; Agarwal, Kapil; Song, Shuaiwen; Schwan, Karsten

    2015-09-30

    Recent work on real-world graph analytics has sought to leverage the massive amount of parallelism offered by GPU devices, but challenges remain due to the inherent irregularity of graph algorithms and limitations in GPU-resident memory for storing large graphs. We present GraphReduce, a highly efficient and scalable GPU-based framework that operates on graphs that exceed the device’s internal memory capacity. GraphReduce adopts a combination of both edge- and vertex-centric implementations of the Gather-Apply-Scatter programming model and operates on multiple asynchronous GPU streams to fully exploit the high degrees of parallelism in GPUs with efficient graph data movement between the host and the device.

  15. GraphReduce: Processing Large-Scale Graphs on Accelerator-Based Systems

    SciTech Connect

    Sengupta, Dipanjan; Song, Shuaiwen; Agarwal, Kapil; Schwan, Karsten

    2015-11-15

    Recent work on real-world graph analytics has sought to leverage the massive amount of parallelism offered by GPU devices, but challenges remain due to the inherent irregularity of graph algorithms and limitations in GPU-resident memory for storing large graphs. We present GraphReduce, a highly efficient and scalable GPU-based framework that operates on graphs that exceed the device’s internal memory capacity. GraphReduce adopts a combination of edge- and vertex-centric implementations of the Gather-Apply-Scatter programming model and operates on multiple asynchronous GPU streams to fully exploit the high degrees of parallelism in GPUs with efficient graph data movement between the host and device.

  16. Balanced Paths in Colored Graphs

    NASA Astrophysics Data System (ADS)

    Bianco, Alessandro; Faella, Marco; Mogavero, Fabio; Murano, Aniello

    We consider finite graphs whose edges are labeled with elements, called colors, taken from a fixed finite alphabet. We study the problem of determining whether there is an infinite path where either (i) all colors occur with the same asymptotic frequency, or (ii) there is a constant which bounds the difference between the occurrences of any two colors for all prefixes of the path. These two notions can be viewed as refinements of the classical notion of fair path, whose simplest form checks whether all colors occur infinitely often. Our notions provide stronger criteria, particularly suitable for scheduling applications based on a coarse-grained model of the jobs involved. We show that both problems are solvable in polynomial time, by reducing them to the feasibility of a linear program.

  17. Relativity on rotated graph paper

    NASA Astrophysics Data System (ADS)

    Salgado, Roberto B.

    2016-05-01

    We demonstrate a method for constructing spacetime diagrams for special relativity on graph paper that has been rotated by 45°. The diagonal grid lines represent light-flash worldlines in Minkowski spacetime, and the boxes in the grid (called "clock diamonds") represent units of measurement corresponding to the ticks of an inertial observer's light clock. We show that many quantitative results can be read off a spacetime diagram simply by counting boxes, with very little algebra. In particular, we show that the squared interval between two events is equal to the signed area of the parallelogram on the grid (called the "causal diamond") with opposite vertices corresponding to those events. We use the Doppler effect—without explicit use of the Doppler formula—to motivate the method.

  18. Stereo Correspondence Using Moment Invariants

    NASA Astrophysics Data System (ADS)

    Premaratne, Prashan; Safaei, Farzad

    Autonomous navigation is seen as a vital tool in harnessing the enormous potential of Unmanned Aerial Vehicles (UAV) and small robotic vehicles for both military and civilian use. Even though, laser based scanning solutions for Simultaneous Location And Mapping (SLAM) is considered as the most reliable for depth estimation, they are not feasible for use in UAV and land-based small vehicles due to their physical size and weight. Stereovision is considered as the best approach for any autonomous navigation solution as stereo rigs are considered to be lightweight and inexpensive. However, stereoscopy which estimates the depth information through pairs of stereo images can still be computationally expensive and unreliable. This is mainly due to some of the algorithms used in successful stereovision solutions require high computational requirements that cannot be met by small robotic vehicles. In our research, we implement a feature-based stereovision solution using moment invariants as a metric to find corresponding regions in image pairs that will reduce the computational complexity and improve the accuracy of the disparity measures that will be significant for the use in UAVs and in small robotic vehicles.

  19. Adjusting for Network Size and Composition Effects in Exponential-Family Random Graph Models.

    PubMed

    Krivitsky, Pavel N; Handcock, Mark S; Morris, Martina

    2011-07-01

    Exponential-family random graph models (ERGMs) provide a principled way to model and simulate features common in human social networks, such as propensities for homophily and friend-of-a-friend triad closure. We show that, without adjustment, ERGMs preserve density as network size increases. Density invariance is often not appropriate for social networks. We suggest a simple modification based on an offset which instead preserves the mean degree and accommodates changes in network composition asymptotically. We demonstrate that this approach allows ERGMs to be applied to the important situation of egocentrically sampled data. We analyze data from the National Health and Social Life Survey (NHSLS). PMID:21691424

  20. Adjusting for Network Size and Composition Effects in Exponential-Family Random Graph Models

    PubMed Central

    Krivitsky, Pavel N.; Handcock, Mark S.; Morris, Martina

    2011-01-01

    Exponential-family random graph models (ERGMs) provide a principled way to model and simulate features common in human social networks, such as propensities for homophily and friend-of-a-friend triad closure. We show that, without adjustment, ERGMs preserve density as network size increases. Density invariance is often not appropriate for social networks. We suggest a simple modification based on an offset which instead preserves the mean degree and accommodates changes in network composition asymptotically. We demonstrate that this approach allows ERGMs to be applied to the important situation of egocentrically sampled data. We analyze data from the National Health and Social Life Survey (NHSLS). PMID:21691424