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Sample records for random graph model

  1. Random graph models of social networks

    PubMed Central

    Newman, M. E. J.; Watts, D. J.; Strogatz, S. H.

    2002-01-01

    We describe some new exactly solvable models of the structure of social networks, based on random graphs with arbitrary degree distributions. We give models both for simple unipartite networks, such as acquaintance networks, and bipartite networks, such as affiliation networks. We compare the predictions of our models to data for a number of real-world social networks and find that in some cases, the models are in remarkable agreement with the data, whereas in others the agreement is poorer, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph. PMID:11875211

  2. Threshold Graph Limits and Random Threshold Graphs

    PubMed Central

    Diaconis, Persi; Holmes, Susan; Janson, Svante

    2010-01-01

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

  3. Bayesian Models of Graphs, Arrays and Other Exchangeable Random Structures.

    PubMed

    Orbanz, Peter; Roy, Daniel M

    2015-02-01

    The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and many other parametric and nonparametric Bayesian models fall within the remit of this framework; many problems arising in modern data analysis do not. This article provides an introduction to Bayesian models of graphs, matrices, and other data that can be modeled by random structures. We describe results in probability theory that generalize de Finetti's theorem to such data and discuss their relevance to nonparametric Bayesian modeling. With the basic ideas in place, we survey example models available in the literature; applications of such models include collaborative filtering, link prediction, and graph and network analysis. We also highlight connections to recent developments in graph theory and probability, and sketch the more general mathematical foundation of Bayesian methods for other types of data beyond sequences and arrays.

  4. Asymptotic Structure of Constrained Exponential Random Graph Models

    NASA Astrophysics Data System (ADS)

    Zhu, Lingjiong

    2017-03-01

    In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that there exists non-trivial regions in the phase plane where the asymptotic structure is uniform and there also exists non-trivial regions in the phase plane where the asymptotic structure is non-uniform. We will get more refined results for the star model and in particular the two-star model for which a sharp transition from uniform to non-uniform structure, a stationary point and phase transitions will be obtained.

  5. Exponential-family random graph models for valued networks

    PubMed Central

    Krivitsky, Pavel N.

    2013-01-01

    Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through choice of model terms (sufficient statistics). However, those ERGMs modeling the more complex features have, to date, been limited to binary data: presence or absence of ties. Thus, analysis of valued networks, such as those where counts, measurements, or ranks are observed, has necessitated dichotomizing them, losing information and introducing biases. In this work, we generalize ERGMs to valued networks. Focusing on modeling counts, we formulate an ERGM for networks whose ties are counts and discuss issues that arise when moving beyond the binary case. We introduce model terms that generalize and model common social network features for such data and apply these methods to a network dataset whose values are counts of interactions. PMID:24678374

  6. Application of statistical physics to random graph models of networks

    NASA Astrophysics Data System (ADS)

    Sreenivasan, Sameet

    This thesis deals with the application of concepts from statistical physics to the understanding of static and dynamical properties of random networks. The classical paradigm for random networks is the Erdos-Renyi (ER) random graph model denoted as G(N, p), in which a network of N nodes is created by placing a link between each of the N(N--1)/2 pairs of nodes with a probability p. The probability distribution of the number of links per node, or the degree distribution, is a Poissonian distribution in the limit of asymptotic network sizes. Recent investigations of the structure of networks such as the internet have revealed a power law in the degree distribution of the network. The question then arises as how the presence of this power law affects the behavior of static and dynamic properties of a network and how this behavior is different from that seen in ER random graphs. In general, irrespective of other details of their structure, networks having a power law degree distribution are known as "scale-free" (SF) networks. In this thesis, we focus on the simplest model of SF networks, known as the configuration model. In the first chapter, we introduce ER and SF networks, and define central concepts that will be used throughout this thesis. In the second chapter we address the problem of optimal paths on weighted networks, formulated as follows. On a network with weighted links where link weights represent transit times along the link, we define the optimal path as the path between two nodes with the least total transit time. We study the scaling of optimal path length ℓopt as a function of the network size N, and as a function of the parameters in the weight distribution. We show that when link weights are highly disordered, only paths on the "minimal spanning tree"---the tree with the lowest total link weight---are used, and this leads to a crossover between two regimes of scaling behavior for ℓopt. For a simple distribution of link weights, we derive for ER

  7. Auxiliary Parameter MCMC for Exponential Random Graph Models

    NASA Astrophysics Data System (ADS)

    Byshkin, Maksym; Stivala, Alex; Mira, Antonietta; Krause, Rolf; Robins, Garry; Lomi, Alessandro

    2016-11-01

    Exponential random graph models (ERGMs) are a well-established family of statistical models for analyzing social networks. Computational complexity has so far limited the appeal of ERGMs for the analysis of large social networks. Efficient computational methods are highly desirable in order to extend the empirical scope of ERGMs. In this paper we report results of a research project on the development of snowball sampling methods for ERGMs. We propose an auxiliary parameter Markov chain Monte Carlo (MCMC) algorithm for sampling from the relevant probability distributions. The method is designed to decrease the number of allowed network states without worsening the mixing of the Markov chains, and suggests a new approach for the developments of MCMC samplers for ERGMs. We demonstrate the method on both simulated and actual (empirical) network data and show that it reduces CPU time for parameter estimation by an order of magnitude compared to current MCMC methods.

  8. CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.

    PubMed

    Shalizi, Cosma Rohilla; Rinaldo, Alessandro

    2013-04-01

    The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling, or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM's expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses.

  9. On Edge Exchangeable Random Graphs

    NASA Astrophysics Data System (ADS)

    Janson, Svante

    2017-06-01

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

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

    PubMed

    Schweinberger, Michael; Handcock, Mark S

    2015-06-01

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

  11. 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

  12. Tailored Random Graph Ensembles

    NASA Astrophysics Data System (ADS)

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

    2013-02-01

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

  13. 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.

  14. Random broadcast on random geometric graphs

    SciTech Connect

    Bradonjic, Milan; Elsasser, Robert; Friedrich, Tobias

    2009-01-01

    In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.

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

    NASA Astrophysics Data System (ADS)

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

    2017-08-01

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

  16. Graphs, random sums, and sojourn time distributions, with application to ion-channel modeling.

    PubMed

    Edeson, R O; Yeo, G F; Milne, R K; Madsen, B W

    1990-11-01

    This paper considers the distribution of a sojourn time in a class of states of a stochastic process having finite discrete state space where sojourn times in any individual state are independent and identically distributed, and transitions between states follow a Markov chain. The state space and possible transitions of the process are represented by a graph. Class sojourn time distributions are derived by modifying this graph using 'composition' of states, defining a new Markov chain on the modified graph, and expressing the sojourn time in a composition state as a random sum. Appropriate compositions are chosen according to the possible "cores" of sojourns in the particular class, where a core describes the structure of a sojourn in terms of a single state or a chain in the original graph. Graph methods provide an algorithmic basis for the derivation, which can be simplified by using symmetry results. Models of ion-channel kinetics are used throughout for illustration; class sojourn time distributions are important in such models because individual states are often indistinguishable experimentally. Markov processes are the special case where sojourn times in individual states are exponentially distributed. In this case kinetic parameter estimation based on the observed class sojourn time distribution is briefly discussed; explicit estimating equations applicable to sequential models of nicotinic receptor kinetics are given.

  17. 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.

  18. Fast generation of sparse random kernel graphs

    DOE PAGES

    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

  19. Effect of disorder on condensation in the lattice gas model on a random graph

    NASA Astrophysics Data System (ADS)

    Handford, Thomas P.; Dear, Alexander; Pérez-Reche, Francisco J.; Taraskin, Sergei N.

    2014-07-01

    The lattice gas model of condensation in a heterogeneous pore system, represented by a random graph of cells, is studied using an exact analytical solution. A binary mixture of pore cells with different coordination numbers is shown to exhibit two phase transitions as a function of chemical potential in a certain temperature range. Heterogeneity in interaction strengths is demonstrated to reduce the critical temperature and, for large-enough degreeS of disorder, divides the cells into ones which are either on average occupied or unoccupied. Despite treating the pore space loops in a simplified manner, the random-graph model provides a good description of condensation in porous structures containing loops. This is illustrated by considering capillary condensation in a structural model of mesoporous silica SBA-15.

  20. Spectral statistics of random geometric graphs

    NASA Astrophysics Data System (ADS)

    Dettmann, C. P.; Georgiou, O.; Knight, G.

    2017-04-01

    We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short-range correlations in the level spacings of the spectrum via the nearest-neighbour and next-nearest-neighbour spacing distribution and long-range correlations via the spectral rigidity Δ3 statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find a parameter-dependent transition between Poisson and Gaussian orthogonal ensemble statistics. That is the spectral statistics of spatial random geometric graphs fits the universality of random matrix theory found in other models such as Erdős-Rényi, Barabási-Albert and Watts-Strogatz random graphs.

  1. A Reexamination of Connectivity Trends via Exponential Random Graph Modeling in Two IDU Risk Networks

    PubMed Central

    Dombrowski, Kirk; Khan, Bilal; McLean, Katherine; Curtis, Ric; Wendel, Travis; Misshula, Evan; Friedman, Samuel

    2014-01-01

    Patterns of risk in injecting drug user (IDU) networks have been a key focus of network approaches to HIV transmission histories. New network modeling techniques allow for a reexamination of these patterns with greater statistical accuracy and the comparative weighting of model elements. This paper describes the results of a reexamination of network data from the SFHR and P90 data sets using Exponential Random Graph Modeling. The results show that “transitive closure” is an important feature of IDU network topologies, and provides relative importance measures for race/ethnicity, age, gender, and number of risk partners in predicting risk relationships. PMID:23819740

  2. Approximating the XY model on a random graph with a q -state clock model

    NASA Astrophysics Data System (ADS)

    Lupo, Cosimo; Ricci-Tersenghi, Federico

    2017-02-01

    Numerical simulations of spin glass models with continuous variables set the problem of a reliable but efficient discretization of such variables. In particular, the main question is how fast physical observables computed in the discretized model converge toward the ones of the continuous model when the number of states of the discretized model increases. We answer this question for the XY model and its discretization, the q -state clock model, in the mean-field setting provided by random graphs. It is found that the convergence of physical observables is exponentially fast in the number q of states of the clock model, so allowing a very reliable approximation of the XY model by using a rather small number of states. Furthermore, such an exponential convergence is found to be independent from the disorder distribution used. Only at T =0 , the convergence is slightly slower (stretched exponential). Thanks to the analytical solution to the q -state clock model, we compute accurate phase diagrams in the temperature versus disorder strength plane. We find that, at zero temperature, spontaneous replica symmetry breaking takes place for any amount of disorder, even an infinitesimal one. We also study the one step of replica symmetry breaking (1RSB) solution in the low-temperature spin glass phase.

  3. Ising Critical Behavior of Inhomogeneous Curie-Weiss Models and Annealed Random Graphs

    NASA Astrophysics Data System (ADS)

    Dommers, Sander; Giardinà, Cristian; Giberti, Claudio; van der Hofstad, Remco; Prioriello, Maria Luisa

    2016-11-01

    We study the critical behavior for inhomogeneous versions of the Curie-Weiss model, where the coupling constant {J_{ij}(β)} for the edge {ij} on the complete graph is given by {J_{ij}(β)=β w_iw_j/( {sum_{kin[N]}w_k})}. We call the product form of these couplings the rank-1 inhomogeneous Curie-Weiss model. This model also arises [with inverse temperature {β} replaced by {sinh(β)} ] from the annealed Ising model on the generalized random graph. We assume that the vertex weights {(w_i)_{iin[N]}} are regular, in the sense that their empirical distribution converges and the second moment converges as well. We identify the critical temperatures and exponents for these models, as well as a non-classical limit theorem for the total spin at the critical point. These depend sensitively on the number of finite moments of the weight distribution. When the fourth moment of the weight distribution converges, then the critical behavior is the same as on the (homogeneous) Curie-Weiss model, so that the inhomogeneity is weak. When the fourth moment of the weights converges to infinity, and the weights satisfy an asymptotic power law with exponent {τ} with {τin(3,5)}, then the critical exponents depend sensitively on {τ}. In addition, at criticality, the total spin {S_N} satisfies that {S_N/N^{(τ-2)/(τ-1)}} converges in law to some limiting random variable whose distribution we explicitly characterize.

  4. Antiferromagnetic Potts Model on the Erdős-Rényi Random Graph

    NASA Astrophysics Data System (ADS)

    Contucci, Pierluigi; Dommers, Sander; Giardinà, Cristian; Starr, Shannon

    2013-10-01

    We study the antiferromagnetic Potts model on the Poissonian Erdős-Rényi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis we prove the existence of a phase transition at a positive critical temperature. Upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution (recovered in the framework of Derrida-Ruelle probability cascades) and from an entropy positivity argument.

  5. Random Graphs Associated to Some Discrete and Continuous Time Preferential Attachment Models

    NASA Astrophysics Data System (ADS)

    Pachon, Angelica; Polito, Federico; Sacerdote, Laura

    2016-03-01

    We give a common description of Simon, Barabási-Albert, II-PA and Price growth models, by introducing suitable random graph processes with preferential attachment mechanisms. Through the II-PA model, we prove the conditions for which the asymptotic degree distribution of the Barabási-Albert model coincides with the asymptotic in-degree distribution of the Simon model. Furthermore, we show that when the number of vertices in the Simon model (with parameter α ) goes to infinity, a portion of them behave as a Yule model with parameters (λ ,β ) = (1-α ,1), and through this relation we explain why asymptotic properties of a random vertex in Simon model, coincide with the asymptotic properties of a random genus in Yule model. As a by-product of our analysis, we prove the explicit expression of the in-degree distribution for the II-PA model, given without proof in Newman (Contemp Phys 46:323-351, 2005). References to traditional and recent applications of the these models are also discussed.

  6. Role Analysis in Networks using Mixtures of Exponential Random Graph Models

    PubMed Central

    Salter-Townshend, Michael; Murphy, Thomas Brendan

    2014-01-01

    A novel and flexible framework for investigating the roles of actors within a network is introduced. Particular interest is in roles as defined by local network connectivity patterns, identified using the ego-networks extracted from the network. A mixture of Exponential-family Random Graph Models is developed for these ego-networks in order to cluster the nodes into roles. We refer to this model as the ego-ERGM. An Expectation-Maximization algorithm is developed to infer the unobserved cluster assignments and to estimate the mixture model parameters using a maximum pseudo-likelihood approximation. The flexibility and utility of the method are demonstrated on examples of simulated and real networks. PMID:26101465

  7. Social influencing and associated random walk models: Asymptotic consensus times on the complete graph

    NASA Astrophysics Data System (ADS)

    Zhang, W.; Lim, C.; Sreenivasan, S.; Xie, J.; Szymanski, B. K.; Korniss, G.

    2011-06-01

    We investigate consensus formation and the asymptotic consensus times in stylized individual- or agent-based models, in which global agreement is achieved through pairwise negotiations with or without a bias. Considering a class of individual-based models on finite complete graphs, we introduce a coarse-graining approach (lumping microscopic variables into macrostates) to analyze the ordering dynamics in an associated random-walk framework. Within this framework, yielding a linear system, we derive general equations for the expected consensus time and the expected time spent in each macro-state. Further, we present the asymptotic solutions of the 2-word naming game and separately discuss its behavior under the influence of an external field and with the introduction of committed agents.

  8. Chromatic polynomials of random graphs

    NASA Astrophysics Data System (ADS)

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

    2010-04-01

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

  9. Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase

    NASA Astrophysics Data System (ADS)

    Metz, Fernando L.; Castillo, Isaac Pérez

    2017-08-01

    We calculate the level compressibility χ (W ,L ) of the energy levels inside [-L /2 ,L /2 ] for the Anderson model on infinitely large random regular graphs with on-site potentials distributed uniformly in [-W /2 ,W /2 ] . We show that χ (W ,L ) approaches the limit limL→0+χ (W ,L ) =0 for a broad interval of the disorder strength W within the extended phase, including the region of W close to the critical point for the Anderson transition. These results strongly suggest that the energy levels follow the Wigner-Dyson statistics in the extended phase, consistent with earlier analytical predictions for the Anderson model on an Erdös-Rényi random graph. Our results are obtained from the accurate numerical solution of an exact set of equations valid for infinitely large regular random graphs.

  10. Agreement dynamics on directed random graphs

    NASA Astrophysics Data System (ADS)

    Lipowski, Adam; Lipowska, Dorota; Ferreira, António Luis

    2017-06-01

    We examine some agreement-dynamics models that are placed on directed random graphs. In such systems, a fraction of sites \\exp(-z) , where z is the average degree, become permanently fixed or flickering. In the voter model, which has no surface tension, such zealots or flickers freely spread their opinions and that makes the system disordered. For models with a surface tension, like the Ising model or the Naming Game model, their role is limited, and such systems are ordered at large z. However, when z decreases, the density of zealots or flickers increases, and below a certain threshold (z∼ 1.9-2.0 ) the system becomes disordered. On undirected random graphs, agreement dynamics is very different and ordering appears as soon the graph is above the percolation threshold at z  =  1.

  11. Advances in Exponential Random Graph (p*) Models Applied to a Large Social Network.

    PubMed

    Goodreau, Steven M

    2007-05-01

    Recent advances in statistical network analysis based on the family of exponential random graph (ERG) models have greatly improved our ability to conduct inference on dependence in large social networks (Snijders 2002, Pattison and Robins 2002, Handcock 2002, Handcock 2003, Snijders et al. 2006, Hunter et al. 2005, Goodreau et al. 2005, previous papers this issue). This paper applies advances in both model parameterizations and computational algorithms to an examination of the structure observed in an adolescent friendship network of 1,681 actors from the National Longitudinal Study of Adolescent Health (AddHealth). ERG models of social network structure are fit using the R package statnet, and their adequacy assessed through comparison of model predictions with the observed data for higher-order network statistics.For this friendship network, the commonly used model of Markov dependence leads to the problems of degeneracy discussed by Handcock (2002, 2003). On the other hand, model parameterizations introduced by Snijders et al (2006) and Hunter and Handcock (2006) avoid degeneracy and provide reasonable fit to the data. Degree-only models did a poor job of capturing observed network structure; those that did best included terms both for heterogeneous mixing on exogenous attributes (grade and self-reported race) as well as endogenous clustering. Networks simulated from this model were largely consistent with the observed network on multiple higher-order network statistics, including the number of triangles, the size of the largest component, the overall reachability, the distribution of geodesic distances, the degree distribution, and the shared partner distribution. The ability to fit such models to large datasets and to make inference about the underling processes generating the network represents a major advance in the field of statistical network analysis.

  12. Limitations of individual causal models, causal graphs, and ignorability assumptions, as illustrated by random confounding and design unfaithfulness.

    PubMed

    Greenland, Sander; Mansournia, Mohammad Ali

    2015-10-01

    We describe how ordinary interpretations of causal models and causal graphs fail to capture important distinctions among ignorable allocation mechanisms for subject selection or allocation. We illustrate these limitations in the case of random confounding and designs that prevent such confounding. In many experimental designs individual treatment allocations are dependent, and explicit population models are needed to show this dependency. In particular, certain designs impose unfaithful covariate-treatment distributions to prevent random confounding, yet ordinary causal graphs cannot discriminate between these unconfounded designs and confounded studies. Causal models for populations are better suited for displaying these phenomena than are individual-level models, because they allow representation of allocation dependencies as well as outcome dependencies across individuals. Nonetheless, even with this extension, ordinary graphical models still fail to capture distinctions between hypothetical superpopulations (sampling distributions) and observed populations (actual distributions), although potential-outcome models can be adapted to show these distinctions and their consequences.

  13. Range-dependent random graphs and their application to modeling large small-world Proteome datasets

    NASA Astrophysics Data System (ADS)

    Grindrod, Peter

    2002-12-01

    In this paper we consider the problem of characterizing and modeling large-scale networks using classes of range-dependent graphs which possess appropriate small-world properties. The application we have in mind is to bioinformatics, where methods of rapid protein identification mean that such proteome datasets, listing various observed protein-protein associations, will become more and more prevalent. We introduce a class of range-dependent graphs, governed by a power law relating intervertex range to edge probability, which are amenable to analysis, and for which macroscopic graph parameters are given by explicit forms. We show how these may be employed in representing a given network using a maximum likelihood approach. This in turn annotates every given edge with its range, representing the tendency for such an association to be transitive. We apply this technique to published proteome data, and demonstrate that known protein associations are thus identified.

  14. Random walk and graph cut based active contour model for three-dimension interactive pituitary adenoma segmentation from MR images

    NASA Astrophysics Data System (ADS)

    Sun, Min; Chen, Xinjian; Zhang, Zhiqiang; Ma, Chiyuan

    2017-02-01

    Accurate volume measurements of pituitary adenoma are important to the diagnosis and treatment for this kind of sellar tumor. The pituitary adenomas have different pathological representations and various shapes. Particularly, in the case of infiltrating to surrounding soft tissues, they present similar intensities and indistinct boundary in T1-weighted (T1W) magnetic resonance (MR) images. Then the extraction of pituitary adenoma from MR images is still a challenging task. In this paper, we propose an interactive method to segment the pituitary adenoma from brain MR data, by combining graph cuts based active contour model (GCACM) and random walk algorithm. By using the GCACM method, the segmentation task is formulated as an energy minimization problem by a hybrid active contour model (ACM), and then the problem is solved by the graph cuts method. The region-based term in the hybrid ACM considers the local image intensities as described by Gaussian distributions with different means and variances, expressed as maximum a posteriori probability (MAP). Random walk is utilized as an initialization tool to provide initialized surface for GCACM. The proposed method is evaluated on the three-dimensional (3-D) T1W MR data of 23 patients and compared with the standard graph cuts method, the random walk method, the hybrid ACM method, a GCACM method which considers global mean intensity in region forces, and a competitive region-growing based GrowCut method planted in 3D Slicer. Based on the experimental results, the proposed method is superior to those methods.

  15. Prediction of Pig Trade Movements in Different European Production Systems Using Exponential Random Graph Models

    PubMed Central

    Relun, Anne; Grosbois, Vladimir; Alexandrov, Tsviatko; Sánchez-Vizcaíno, Jose M.; Waret-Szkuta, Agnes; Molia, Sophie; Etter, Eric Marcel Charles; Martínez-López, Beatriz

    2017-01-01

    In most European countries, data regarding movements of live animals are routinely collected and can greatly aid predictive epidemic modeling. However, the use of complete movements’ dataset to conduct policy-relevant predictions has been so far limited by the massive amount of data that have to be processed (e.g., in intensive commercial systems) or the restricted availability of timely and updated records on animal movements (e.g., in areas where small-scale or extensive production is predominant). The aim of this study was to use exponential random graph models (ERGMs) to reproduce, understand, and predict pig trade networks in different European production systems. Three trade networks were built by aggregating movements of pig batches among premises (farms and trade operators) over 2011 in Bulgaria, Extremadura (Spain), and Côtes-d’Armor (France), where small-scale, extensive, and intensive pig production are predominant, respectively. Three ERGMs were fitted to each network with various demographic and geographic attributes of the nodes as well as six internal network configurations. Several statistical and graphical diagnostic methods were applied to assess the goodness of fit of the models. For all systems, both exogenous (attribute-based) and endogenous (network-based) processes appeared to govern the structure of pig trade network, and neither alone were capable of capturing all aspects of the network structure. Geographic mixing patterns strongly structured pig trade organization in the small-scale production system, whereas belonging to the same company or keeping pigs in the same housing system appeared to be key drivers of pig trade, in intensive and extensive production systems, respectively. Heterogeneous mixing between types of production also explained a part of network structure, whichever production system considered. Limited information is thus needed to capture most of the global structure of pig trade networks. Such findings will be

  16. Prediction of Pig Trade Movements in Different European Production Systems Using Exponential Random Graph Models.

    PubMed

    Relun, Anne; Grosbois, Vladimir; Alexandrov, Tsviatko; Sánchez-Vizcaíno, Jose M; Waret-Szkuta, Agnes; Molia, Sophie; Etter, Eric Marcel Charles; Martínez-López, Beatriz

    2017-01-01

    In most European countries, data regarding movements of live animals are routinely collected and can greatly aid predictive epidemic modeling. However, the use of complete movements' dataset to conduct policy-relevant predictions has been so far limited by the massive amount of data that have to be processed (e.g., in intensive commercial systems) or the restricted availability of timely and updated records on animal movements (e.g., in areas where small-scale or extensive production is predominant). The aim of this study was to use exponential random graph models (ERGMs) to reproduce, understand, and predict pig trade networks in different European production systems. Three trade networks were built by aggregating movements of pig batches among premises (farms and trade operators) over 2011 in Bulgaria, Extremadura (Spain), and Côtes-d'Armor (France), where small-scale, extensive, and intensive pig production are predominant, respectively. Three ERGMs were fitted to each network with various demographic and geographic attributes of the nodes as well as six internal network configurations. Several statistical and graphical diagnostic methods were applied to assess the goodness of fit of the models. For all systems, both exogenous (attribute-based) and endogenous (network-based) processes appeared to govern the structure of pig trade network, and neither alone were capable of capturing all aspects of the network structure. Geographic mixing patterns strongly structured pig trade organization in the small-scale production system, whereas belonging to the same company or keeping pigs in the same housing system appeared to be key drivers of pig trade, in intensive and extensive production systems, respectively. Heterogeneous mixing between types of production also explained a part of network structure, whichever production system considered. Limited information is thus needed to capture most of the global structure of pig trade networks. Such findings will be useful

  17. 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.

  18. Kinetic Ising models with various single-spin-flip dynamics on quenched and annealed random regular graphs

    NASA Astrophysics Data System (ADS)

    Jedrzejewski, Arkadiusz; Chmiel, Anna; Sznajd-Weron, Katarzyna

    2017-07-01

    We investigate a kinetic Ising model with several single-spin-flip dynamics (including Metropolis and heat bath) on quenched and annealed random regular graphs. As expected, on the quenched structures all proposed algorithms reproduce the same results since the conditions for the detailed balance and the Boltzmann distribution in an equilibrium are satisfied. However, on the annealed graphs the situation is far less clear—the network annealing disturbs the equilibrium moving the system away from it. Consequently, distinct dynamics lead to different steady states. We show that some algorithms are more resistant to the annealed disorder, which causes only small quantitative changes in the model behavior. On the other hand, there are dynamics for which the influence of annealing on the system is significant, and qualitative changes arise like switching the type of phase transition from a continuous to a discontinuous one. We try to identify features of the proposed dynamics which are responsible for the above phenomenon.

  19. A Simulation Study Comparing Epidemic Dynamics on Exponential Random Graph and Edge-Triangle Configuration Type Contact Network Models.

    PubMed

    Rolls, David A; Wang, Peng; McBryde, Emma; Pattison, Philippa; Robins, Garry

    2015-01-01

    We compare two broad types of empirically grounded random network models in terms of their abilities to capture both network features and simulated Susceptible-Infected-Recovered (SIR) epidemic dynamics. The types of network models are exponential random graph models (ERGMs) and extensions of the configuration model. We use three kinds of empirical contact networks, chosen to provide both variety and realistic patterns of human contact: a highly clustered network, a bipartite network and a snowball sampled network of a "hidden population". In the case of the snowball sampled network we present a novel method for fitting an edge-triangle model. In our results, ERGMs consistently capture clustering as well or better than configuration-type models, but the latter models better capture the node degree distribution. Despite the additional computational requirements to fit ERGMs to empirical networks, the use of ERGMs provides only a slight improvement in the ability of the models to recreate epidemic features of the empirical network in simulated SIR epidemics. Generally, SIR epidemic results from using configuration-type models fall between those from a random network model (i.e., an Erdős-Rényi model) and an ERGM. The addition of subgraphs of size four to edge-triangle type models does improve agreement with the empirical network for smaller densities in clustered networks. Additional subgraphs do not make a noticeable difference in our example, although we would expect the ability to model cliques to be helpful for contact networks exhibiting household structure.

  20. 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.

  1. Component evolution in general random intersection graphs

    SciTech Connect

    Bradonjic, Milan; Hagberg, Aric; Hengartner, Nick; Percus, Allon G

    2010-01-01

    We analyze component evolution in general random intersection graphs (RIGs) and give conditions on existence and uniqueness of the giant component. Our techniques generalize the existing methods for analysis on component evolution in RIGs. That is, we analyze survival and extinction properties of a dependent, inhomogeneous Galton-Watson branching process on general RIGs. Our analysis relies on bounding the branching processes and inherits the fundamental concepts from the study on component evolution in Erdos-Renyi graphs. The main challenge becomes from the underlying structure of RIGs, when the number of offsprings follows a binomial distribution with a different number of nodes and different rate at each step during the evolution. RIGs can be interpreted as a model for large randomly formed non-metric data sets. Besides the mathematical analysis on component evolution, which we provide in this work, we perceive RIGs as an important random structure which has already found applications in social networks, epidemic networks, blog readership, or wireless sensor networks.

  2. Network Statistical Models for Language Learning Contexts: Exponential Random Graph Models and Willingness to Communicate

    ERIC Educational Resources Information Center

    Gallagher, H. Colin; Robins, Garry

    2015-01-01

    As part of the shift within second language acquisition (SLA) research toward complex systems thinking, researchers have called for investigations of social network structure. One strand of social network analysis yet to receive attention in SLA is network statistical models, whereby networks are explained in terms of smaller substructures of…

  3. Network Statistical Models for Language Learning Contexts: Exponential Random Graph Models and Willingness to Communicate

    ERIC Educational Resources Information Center

    Gallagher, H. Colin; Robins, Garry

    2015-01-01

    As part of the shift within second language acquisition (SLA) research toward complex systems thinking, researchers have called for investigations of social network structure. One strand of social network analysis yet to receive attention in SLA is network statistical models, whereby networks are explained in terms of smaller substructures of…

  4. A Simulation Study Comparing Epidemic Dynamics on Exponential Random Graph and Edge-Triangle Configuration Type Contact Network Models

    PubMed Central

    Rolls, David A.; Wang, Peng; McBryde, Emma; Pattison, Philippa; Robins, Garry

    2015-01-01

    We compare two broad types of empirically grounded random network models in terms of their abilities to capture both network features and simulated Susceptible-Infected-Recovered (SIR) epidemic dynamics. The types of network models are exponential random graph models (ERGMs) and extensions of the configuration model. We use three kinds of empirical contact networks, chosen to provide both variety and realistic patterns of human contact: a highly clustered network, a bipartite network and a snowball sampled network of a “hidden population”. In the case of the snowball sampled network we present a novel method for fitting an edge-triangle model. In our results, ERGMs consistently capture clustering as well or better than configuration-type models, but the latter models better capture the node degree distribution. Despite the additional computational requirements to fit ERGMs to empirical networks, the use of ERGMs provides only a slight improvement in the ability of the models to recreate epidemic features of the empirical network in simulated SIR epidemics. Generally, SIR epidemic results from using configuration-type models fall between those from a random network model (i.e., an Erdős-Rényi model) and an ERGM. The addition of subgraphs of size four to edge-triangle type models does improve agreement with the empirical network for smaller densities in clustered networks. Additional subgraphs do not make a noticeable difference in our example, although we would expect the ability to model cliques to be helpful for contact networks exhibiting household structure. PMID:26555701

  5. 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.

  6. Clique percolation in random graphs.

    PubMed

    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 lgraphs, 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 ϕ(c) 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.

  7. 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.

  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. Network robustness and fragility: percolation on random graphs.

    PubMed

    Callaway, D S; Newman, M E; Strogatz, S H; Watts, D J

    2000-12-18

    Recent work on the Internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes or links. Such deletions include, for example, the failure of Internet routers or power transmission lines. Percolation models on random graphs provide a simple representation of this process but have typically been limited to graphs with Poisson degree distribution at their vertices. Such graphs are quite unlike real-world networks, which often possess power-law or other highly skewed degree distributions. In this paper we study percolation on graphs with completely general degree distribution, giving exact solutions for a variety of cases, including site percolation, bond percolation, and models in which occupation probabilities depend on vertex degree. We discuss the application of our theory to the understanding of network resilience.

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

    PubMed

    Parida, Laxmi

    2010-10-01

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

  11. Absence of first order transition in the random crystal field Blume-Capel model on a fully connected graph

    NASA Astrophysics Data System (ADS)

    Sumedha; Jana, Nabin Kumar

    2017-01-01

    In this paper we solve the Blume-Capel model on a complete graph in the presence of random crystal field with a distribution, P≤ft({{ Δ }i}\\right)=pδ ≤ft({{ Δ }i}- Δ \\right)+(1-p)δ ≤ft({{ Δ }i}+ Δ \\right) , using large deviation techniques. We find that the first order transition of the pure system is destroyed for 0.046  <  p  <  0.954 for all values of the crystal field, Δ . The system has a line of continuous transition for this range of p from -∞ < Δ <∞ . For values of p outside this interval, the phase diagram of the system is similar to the pure model, with a tricritical point separating the line of first order and continuous transitions. We find that in this regime, the order vanishes for large Δ for p  <  0.046(and for large - Δ for p  >  0.954) even at zero temperature.

  12. Random walk on lattices: Graph-theoretic approach to simulating long-range diffusion-attachment growth models

    NASA Astrophysics Data System (ADS)

    Limkumnerd, Surachate

    2014-03-01

    Interest in thin-film fabrication for industrial applications have driven both theoretical and computational aspects of modeling its growth. One of the earliest attempts toward understanding the morphological structure of a film's surface is through a class of solid-on-solid limited-mobility growth models such as the Family, Wolf-Villain, or Das Sarma-Tamborenea models, which have produced fascinating surface roughening behaviors. These models, however, restrict the motion of an incidence atom to be within the neighborhood of its landing site, which renders them inept for simulating long-distance surface diffusion such as that observed in thin-film growth using a molecular-beam epitaxy technique. Naive extension of these models by repeatedly applying the local diffusion rules for each hop to simulate large diffusion length can be computationally very costly when certain statistical aspects are demanded. We present a graph-theoretic approach to simulating a long-range diffusion-attachment growth model. Using the Markovian assumption and given a local diffusion bias, we derive the transition probabilities for a random walker to traverse from one lattice site to the others after a large, possibly infinite, number of steps. Only computation with linear-time complexity is required for the surface morphology calculation without other probabilistic measures. The formalism is applied, as illustrations, to simulate surface growth on a two-dimensional flat substrate and around a screw dislocation under the modified Wolf-Villain diffusion rule. A rectangular spiral ridge is observed in the latter case with a smooth front feature similar to that obtained from simulations using the well-known multiple registration technique. An algorithm for computing the inverse of a class of substochastic matrices is derived as a corollary.

  13. Random walk on lattices: graph-theoretic approach to simulating long-range diffusion-attachment growth models.

    PubMed

    Limkumnerd, Surachate

    2014-03-01

    Interest in thin-film fabrication for industrial applications have driven both theoretical and computational aspects of modeling its growth. One of the earliest attempts toward understanding the morphological structure of a film's surface is through a class of solid-on-solid limited-mobility growth models such as the Family, Wolf-Villain, or Das Sarma-Tamborenea models, which have produced fascinating surface roughening behaviors. These models, however, restrict the motion of an incidence atom to be within the neighborhood of its landing site, which renders them inept for simulating long-distance surface diffusion such as that observed in thin-film growth using a molecular-beam epitaxy technique. Naive extension of these models by repeatedly applying the local diffusion rules for each hop to simulate large diffusion length can be computationally very costly when certain statistical aspects are demanded. We present a graph-theoretic approach to simulating a long-range diffusion-attachment growth model. Using the Markovian assumption and given a local diffusion bias, we derive the transition probabilities for a random walker to traverse from one lattice site to the others after a large, possibly infinite, number of steps. Only computation with linear-time complexity is required for the surface morphology calculation without other probabilistic measures. The formalism is applied, as illustrations, to simulate surface growth on a two-dimensional flat substrate and around a screw dislocation under the modified Wolf-Villain diffusion rule. A rectangular spiral ridge is observed in the latter case with a smooth front feature similar to that obtained from simulations using the well-known multiple registration technique. An algorithm for computing the inverse of a class of substochastic matrices is derived as a corollary.

  14. Potts model and graph theory

    NASA Astrophysics Data System (ADS)

    Wu, F. Y.

    1988-07-01

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

  15. Exact and approximate graph matching using random walks.

    PubMed

    Gori, Marco; Maggini, Marco; Sarti, Lorenzo

    2005-07-01

    In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection.

  16. The Condensation Phase Transition in Random Graph Coloring

    NASA Astrophysics Data System (ADS)

    Bapst, Victor; Coja-Oghlan, Amin; Hetterich, Samuel; Raßmann, Felicia; Vilenchik, Dan

    2016-01-01

    Based on a non-rigorous formalism called the "cavity method", physicists have put forward intriguing predictions on phase transitions in diluted mean-field models, in which the geometry of interactions is induced by a sparse random graph or hypergraph. One example of such a model is the graph coloring problem on the Erdős-Renyi random graph G( n, d/ n), which can be viewed as the zero temperature case of the Potts antiferromagnet. The cavity method predicts that in addition to the k-colorability phase transition studied intensively in combinatorics, there exists a second phase transition called the condensation phase transition (Krzakala et al. in Proc Natl Acad Sci 104:10318-10323, 2007). In fact, there is a conjecture as to the precise location of this phase transition in terms of a certain distributional fixed point problem. In this paper we prove this conjecture for k exceeding a certain constant k 0.

  17. Regular graphs maximize the variability of random neural networks.

    PubMed

    Wainrib, Gilles; Galtier, Mathieu

    2015-09-01

    In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on a combination of a classical mean-field theory originally developed in the context of dynamical spin-glass models, and the heterogeneous mean-field theory developed to study epidemic propagation on graphs. Our main result is that, surprisingly, increasing the variance of the in-degree distribution does not result in a more variable dynamical behavior, but on the contrary that the most variable behaviors are obtained in the regular graph setting. We further study how the dynamical complexity of the attractors is influenced by the statistical properties of the in-degree distribution.

  18. Clifford Algebras, Random Graphs, and Quantum Random Variables

    NASA Astrophysics Data System (ADS)

    Schott, René; Staples, G. Stacey

    2008-08-01

    For fixed n > 0, the space of finite graphs on n vertices is canonically associated with an abelian, nilpotent-generated subalgebra of the Clifford algebra {C}l2n,2n which is canonically isomorphic to the 2n-particle fermion algebra. Using the generators of the subalgebra, an algebraic probability space of "Clifford adjacency matrices" associated with finite graphs is defined. Each Clifford adjacency matrix is a quantum random variable whose mth moment corresponds to the number of m-cycles in the graph G. Each matrix admits a canonical "quantum decomposition" into a sum of three algebraic random variables: a = aΔ + aΥ + aΛ, where aΔ is classical while aΥ and aΛ are quantum. Moreover, within the Clifford algebra context the NP problem of cycle enumeration is reduced to matrix multiplication, requiring no more than n4 Clifford (geo-metric) multiplications within the algebra.

  19. General and exact approach to percolation on random graphs

    NASA Astrophysics Data System (ADS)

    Allard, Antoine; Hébert-Dufresne, Laurent; Young, Jean-Gabriel; Dubé, Louis J.

    2015-12-01

    We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative equations that solve the exact distribution of the size and composition of components in finite-size quenched or random multitype graphs. (ii) We define a very general random graph ensemble that encompasses most of the models published to this day and also makes it possible to model structural properties not yet included in a theoretical framework. Site and bond percolation on this ensemble is solved exactly in the infinite-size limit using probability generating functions [i.e., the percolation threshold, the size, and the composition of the giant (extensive) and small components]. Several examples and applications are also provided. (iii) Our approach can be adapted to model interdependent graphs—whose most striking feature is the emergence of an extensive component via a discontinuous phase transition—in an equally general fashion. We show how a graph can successively undergo a continuous then a discontinuous phase transition, and preliminary results suggest that clustering increases the amplitude of the discontinuity at the transition.

  20. Efficient broadcast on random geometric graphs

    SciTech Connect

    Bradonjic, Milan; Elsasser, Robert; Friedrich, Tobias; Sauerwald, Thomas

    2009-01-01

    A Randon Geometric Graph (RGG) is constructed by distributing n nodes uniformly at random in the unit square and connecting two nodes if their Euclidean distance is at most r, for some prescribed r. They analyze the following randomized broadcast algorithm on RGGs. At the beginning, there is only one informed node. Then in each round, each informed node chooses a neighbor uniformly at random and informs it. They prove that this algorithm informs every node in the largest component of a RGG in {Omicron}({radical}n/r) rounds with high probability. This holds for any value of r larger than the critical value for the emergence of a giant component. In particular, the result implies that the diameter of the giant component is {Theta}({radical}n/r).

  1. Protein localization prediction using random walks on graphs

    PubMed Central

    2013-01-01

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

  2. Cross over of recurrence networks to random graphs and random geometric graphs

    NASA Astrophysics Data System (ADS)

    Jacob, Rinku; Harikrishnan, K. P.; Misra, R.; Ambika, G.

    2017-02-01

    Recurrence networks are complex networks constructed from the time series of chaotic dynamical systems where the connection between two nodes is limited by the recurrence threshold. This condition makes the topology of every recurrence network unique with the degree distribution determined by the probability density variations of the representative attractor from which it is constructed. Here we numerically investigate the properties of recurrence networks from standard low-dimensional chaotic attractors using some basic network measures and show how the recurrence networks are different from random and scale-free networks. In particular, we show that all recurrence networks can cross over to random geometric graphs by adding sufficient amount of noise to the time series and into the classical random graphs by increasing the range of interaction to the system size. We also highlight the effectiveness of a combined plot of characteristic path length and clustering coefficient in capturing the small changes in the network characteristics.

  3. Graph modeling systems and methods

    SciTech Connect

    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.

  4. Topics in networks: Community detection, random graphs, and network epidemiology

    NASA Astrophysics Data System (ADS)

    Karrer, Brian C.

    In this dissertation, we present research on several topics in networks including community detection, random graphs, and network epidemiology. Traditional stochastic blockmodels may produce inaccurate fits to complex networks with heterogeneous degree distributions and we devise a degree-corrected block-model that alleviates this problematic behavior. The resulting objective function for community detection using the degree-corrected version outperforms the traditional model at finding communities on a variety of real-world and synthetic tests. Then we study a different generative model that associates communities to the edges of the network and naturally includes overlapping vertex communities. We create a fast and accurate algorithm to fit this model to empirical networks and show that it can be used to quickly find non-overlapping communities as well. We also develop random graph models for directed acyclic graphs, a class of networks including family trees and citation networks. We argue that the lack of cycles comes from an ordering constraint and then generalize the configuration model to incorporate this constraint. We calculate many properties of these models and demonstrate that sonic of the model predictions agree quite well with real-world networks, emphasizing the importance of vertex ordering to generating directed acyclic networks with realistic properties. Finally, we examine the spread of disease over networks, starting with a simple model of two diseases spreading with cross-immunity, where infection by one disease makes an individual immune to the other disease and vice versa. Utilizing a timescale separation argument, we map the system to consecutive bond percolation, one disease spreading after the other. The resulting phase diagram includes discontinuous and continuous phase transitions and a coexistence region where both diseases can spread to a substantial fraction of the population. Then we analyze a flexible susceptible

  5. Using Exponential Random Graph Models to Analyze the Character of Peer Relationship Networks and Their Effects on the Subjective Well-being of Adolescents

    PubMed Central

    Jiao, Can; Wang, Ting; Liu, Jianxin; Wu, Huanjie; Cui, Fang; Peng, Xiaozhe

    2017-01-01

    The influences of peer relationships on adolescent subjective well-being were investigated within the framework of social network analysis, using exponential random graph models as a methodological tool. The participants in the study were 1,279 students (678 boys and 601 girls) from nine junior middle schools in Shenzhen, China. The initial stage of the research used a peer nomination questionnaire and a subjective well-being scale (used in previous studies) to collect data on the peer relationship networks and the subjective well-being of the students. Exponential random graph models were then used to explore the relationships between students with the aim of clarifying the character of the peer relationship networks and the influence of peer relationships on subjective well being. The results showed that all the adolescent peer relationship networks in our investigation had positive reciprocal effects, positive transitivity effects and negative expansiveness effects. However, none of the relationship networks had obvious receiver effects or leaders. The adolescents in partial peer relationship networks presented similar levels of subjective well-being on three dimensions (satisfaction with life, positive affects and negative affects) though not all network friends presented these similarities. The study shows that peer networks can affect an individual’s subjective well-being. However, whether similarities among adolescents are the result of social influences or social choices needs further exploration, including longitudinal studies that investigate the potential processes of subjective well-being similarities among adolescents. PMID:28450845

  6. Using Exponential Random Graph Models to Analyze the Character of Peer Relationship Networks and Their Effects on the Subjective Well-being of Adolescents.

    PubMed

    Jiao, Can; Wang, Ting; Liu, Jianxin; Wu, Huanjie; Cui, Fang; Peng, Xiaozhe

    2017-01-01

    The influences of peer relationships on adolescent subjective well-being were investigated within the framework of social network analysis, using exponential random graph models as a methodological tool. The participants in the study were 1,279 students (678 boys and 601 girls) from nine junior middle schools in Shenzhen, China. The initial stage of the research used a peer nomination questionnaire and a subjective well-being scale (used in previous studies) to collect data on the peer relationship networks and the subjective well-being of the students. Exponential random graph models were then used to explore the relationships between students with the aim of clarifying the character of the peer relationship networks and the influence of peer relationships on subjective well being. The results showed that all the adolescent peer relationship networks in our investigation had positive reciprocal effects, positive transitivity effects and negative expansiveness effects. However, none of the relationship networks had obvious receiver effects or leaders. The adolescents in partial peer relationship networks presented similar levels of subjective well-being on three dimensions (satisfaction with life, positive affects and negative affects) though not all network friends presented these similarities. The study shows that peer networks can affect an individual's subjective well-being. However, whether similarities among adolescents are the result of social influences or social choices needs further exploration, including longitudinal studies that investigate the potential processes of subjective well-being similarities among adolescents.

  7. Random graphs with arbitrary degree distributions and their applications

    NASA Astrophysics Data System (ADS)

    Newman, M. E. J.; Strogatz, S. H.; Watts, D. J.

    2001-08-01

    Recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in the past. In this paper we develop in detail the theory of random graphs with arbitrary degree distributions. In addition to simple undirected, unipartite graphs, we examine the properties of directed and bipartite graphs. Among other results, we derive exact expressions for the position of the phase transition at which a giant component first forms, the mean component size, the size of the giant component if there is one, the mean number of vertices a certain distance away from a randomly chosen vertex, and the average vertex-vertex distance within a graph. We apply our theory to some real-world graphs, including the world-wide web and collaboration graphs of scientists and Fortune 1000 company directors. We demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.

  8. An internet graph model based on trade-off optimization

    NASA Astrophysics Data System (ADS)

    Alvarez-Hamelin, J. I.; Schabanel, N.

    2004-03-01

    This paper presents a new model for the Internet graph (AS graph) based on the concept of heuristic trade-off optimization, introduced by Fabrikant, Koutsoupias and Papadimitriou in[CITE] to grow a random tree with a heavily tailed degree distribution. We propose here a generalization of this approach to generate a general graph, as a candidate for modeling the Internet. We present the results of our simulations and an analysis of the standard parameters measured in our model, compared with measurements from the physical Internet graph.

  9. Brain graphs: graphical models of the human brain connectome.

    PubMed

    Bullmore, Edward T; Bassett, Danielle S

    2011-01-01

    Brain graphs provide a relatively simple and increasingly popular way of modeling the human brain connectome, using graph theory to abstractly define a nervous system as a set of nodes (denoting anatomical regions or recording electrodes) and interconnecting edges (denoting structural or functional connections). Topological and geometrical properties of these graphs can be measured and compared to random graphs and to graphs derived from other neuroscience data or other (nonneural) complex systems. Both structural and functional human brain graphs have consistently demonstrated key topological properties such as small-worldness, modularity, and heterogeneous degree distributions. Brain graphs are also physically embedded so as to nearly minimize wiring cost, a key geometric property. Here we offer a conceptual review and methodological guide to graphical analysis of human neuroimaging data, with an emphasis on some of the key assumptions, issues, and trade-offs facing the investigator.

  10. The Lexical Restructuring Hypothesis and Graph Theoretic Analyses of Networks Based on Random Lexicons

    ERIC Educational Resources Information Center

    Gruenenfelder, Thomas M.; Pisoni, David B.

    2009-01-01

    Purpose: The mental lexicon of words used for spoken word recognition has been modeled as a complex network or graph. Do the characteristics of that graph reflect processes involved in its growth (M. S. Vitevitch, 2008) or simply the phonetic overlap between similar-sounding words? Method: Three pseudolexicons were generated by randomly selecting…

  11. Probabilistic graphs using coupled random variables

    NASA Astrophysics Data System (ADS)

    Nelson, Kenric P.; Barbu, Madalina; Scannell, Brian J.

    2014-05-01

    Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic reasoning, but the restrictions reduce the expressive capability of each node making network designs complex. The ability to model coupled random variables using the calculus of nonextensive statistical mechanics provides a neural node design incorporating nonlinear coupling between input states while maintaining the rigor of probabilistic reasoning. A generalization of Bayes rule using the coupled product enables a single node to model correlation between hundreds of random variables. A coupled Markov random field is designed for the inferencing and classification of UCI's MLR `Multiple Features Data Set' such that thousands of linear correlation parameters can be replaced with a single coupling parameter with just a (3%, 4%) reduction in (classification, inference) performance.

  12. Motifs in triadic random graphs based on Steiner triple systems

    NASA Astrophysics Data System (ADS)

    Winkler, Marco; Reichardt, Jörg

    2013-08-01

    Conventionally, pairwise relationships between nodes are considered to be the fundamental building blocks of complex networks. However, over the last decade, the overabundance of certain subnetwork patterns, i.e., the so-called motifs, has attracted much attention. It has been hypothesized that these motifs, instead of links, serve as the building blocks of network structures. Although the relation between a network's topology and the general properties of the system, such as its function, its robustness against perturbations, or its efficiency in spreading information, is the central theme of network science, there is still a lack of sound generative models needed for testing the functional role of subgraph motifs. Our work aims to overcome this limitation. We employ the framework of exponential random graph models (ERGMs) to define models based on triadic substructures. The fact that only a small portion of triads can actually be set independently poses a challenge for the formulation of such models. To overcome this obstacle, we use Steiner triple systems (STSs). These are partitions of sets of nodes into pair-disjoint triads, which thus can be specified independently. Combining the concepts of ERGMs and STSs, we suggest generative models capable of generating ensembles of networks with nontrivial triadic Z-score profiles. Further, we discover inevitable correlations between the abundance of triad patterns, which occur solely for statistical reasons and need to be taken into account when discussing the functional implications of motif statistics. Moreover, we calculate the degree distributions of our triadic random graphs analytically.

  13. Parameter Tuning Patterns for Random Graph Coloring with Quantum Annealing

    PubMed Central

    Titiloye, Olawale; Crispin, Alan

    2012-01-01

    Quantum annealing is a combinatorial optimization technique inspired by quantum mechanics. Here we show that a spin model for the k-coloring of large dense random graphs can be field tuned so that its acceptance ratio diverges during Monte Carlo quantum annealing, until a ground state is reached. We also find that simulations exhibiting such a diverging acceptance ratio are generally more effective than those tuned to the more conventional pattern of a declining and/or stagnating acceptance ratio. This observation facilitates the discovery of solutions to several well-known benchmark k-coloring instances, some of which have been open for almost two decades. PMID:23166818

  14. Parameter tuning patterns for random graph coloring with quantum annealing.

    PubMed

    Titiloye, Olawale; Crispin, Alan

    2012-01-01

    Quantum annealing is a combinatorial optimization technique inspired by quantum mechanics. Here we show that a spin model for the k-coloring of large dense random graphs can be field tuned so that its acceptance ratio diverges during Monte Carlo quantum annealing, until a ground state is reached. We also find that simulations exhibiting such a diverging acceptance ratio are generally more effective than those tuned to the more conventional pattern of a declining and/or stagnating acceptance ratio. This observation facilitates the discovery of solutions to several well-known benchmark k-coloring instances, some of which have been open for almost two decades.

  15. Constrained Markovian Dynamics of Random Graphs

    NASA Astrophysics Data System (ADS)

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

    2009-09-01

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

  16. Joint large deviation result for empirical measures of the coloured random geometric graphs.

    PubMed

    Doku-Amponsah, Kwabena

    2016-01-01

    We prove joint large deviation principle for the empirical pair measure and empirical locality measure of the near intermediate coloured random geometric graph models on n points picked uniformly in a d-dimensional torus of a unit circumference. From this result we obtain large deviation principles for the number of edges per vertex, the degree distribution and the proportion of isolated vertices for the near intermediate random geometric graph models.

  17. Exploring community structure in biological networks with random graphs

    PubMed Central

    2014-01-01

    Background Community structure is ubiquitous in biological networks. There has been an increased interest in unraveling the community structure of biological systems as it may provide important insights into a system’s functional components and the impact of local structures on dynamics at a global scale. Choosing an appropriate community detection algorithm to identify the community structure in an empirical network can be difficult, however, as the many algorithms available are based on a variety of cost functions and are difficult to validate. Even when community structure is identified in an empirical system, disentangling the effect of community structure from other network properties such as clustering coefficient and assortativity can be a challenge. Results Here, we develop a generative model to produce undirected, simple, connected graphs with a specified degrees and pattern of communities, while maintaining a graph structure that is as random as possible. Additionally, we demonstrate two important applications of our model: (a) to generate networks that can be used to benchmark existing and new algorithms for detecting communities in biological networks; and (b) to generate null models to serve as random controls when investigating the impact of complex network features beyond the byproduct of degree and modularity in empirical biological networks. Conclusion Our model allows for the systematic study of the presence of community structure and its impact on network function and dynamics. This process is a crucial step in unraveling the functional consequences of the structural properties of biological systems and uncovering the mechanisms that drive these systems. PMID:24965130

  18. Ising Critical Exponents on Random Trees and Graphs

    NASA Astrophysics Data System (ADS)

    Dommers, Sander; Giardinà, Cristian; van der Hofstad, Remco

    2014-05-01

    We study the critical behavior of the ferromagnetic Ising model on random trees as well as so-called locally tree-like random graphs. We pay special attention to trees and graphs with a power-law offspring or degree distribution whose tail behavior is characterized by its power-law exponent τ > 2. We show that the critical inverse temperature of the Ising model equals the hyperbolic arctangent of the reciprocal of the mean offspring or mean forward degree distribution. In particular, the critical inverse temperature equals zero when where this mean equals infinity. We further study the critical exponents δ, β and γ, describing how the (root) magnetization behaves close to criticality. We rigorously identify these critical exponents and show that they take the values as predicted by Dorogovstev et al. (Phys Rev E 66:016104, 2002) and Leone et al. (Eur Phys J B 28:191-197, 2002). These values depend on the power-law exponent τ, taking the same values as the mean-field Curie-Weiss model (Exactly solved models in statistical mechanics, Academic Press, London, 1982) for τ > 5, but different values for.

  19. Discontinuous percolation transitions in epidemic processes, surface depinning in random media, and Hamiltonian random graphs

    NASA Astrophysics Data System (ADS)

    Bizhani, Golnoosh; Paczuski, Maya; Grassberger, Peter

    2012-07-01

    Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and nonequilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first-order behaviors in two different classes of models: The first are generalized epidemic processes that describe in their spatially embedded version—either on or off a regular lattice—compact or fractal cluster growth in random media at zero temperature. A random graph version of these processes is mapped onto a model previously proposed for complex social contagion. We compute detailed phase diagrams and compare our numerical results at the tricritical point in d=3 with field theory predictions of Janssen [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.70.026114 70, 026114 (2004)]. The second class consists of exponential (“Hamiltonian,” i.e., formally equilibrium) random graph models and includes the Strauss and the two-star model, where “chemical potentials” control the densities of links, triangles, or two-stars. When the chemical potentials in either graph model are O(logN), the percolation transition can coincide with a first-order phase transition in the density of links, making the former also discontinuous. Hysteresis loops can then be of mixed order, with second-order behavior for decreasing link fugacity, and a jump (first order) when it increases.

  20. Discontinuous percolation transitions in epidemic processes, surface depinning in random media, and Hamiltonian random graphs.

    PubMed

    Bizhani, Golnoosh; Paczuski, Maya; Grassberger, Peter

    2012-07-01

    Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and nonequilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first-order behaviors in two different classes of models: The first are generalized epidemic processes that describe in their spatially embedded version--either on or off a regular lattice--compact or fractal cluster growth in random media at zero temperature. A random graph version of these processes is mapped onto a model previously proposed for complex social contagion. We compute detailed phase diagrams and compare our numerical results at the tricritical point in d = 3 with field theory predictions of Janssen et al. [Phys. Rev. E 70, 026114 (2004)]. The second class consists of exponential ("Hamiltonian," i.e., formally equilibrium) random graph models and includes the Strauss and the two-star model, where "chemical potentials" control the densities of links, triangles, or two-stars. When the chemical potentials in either graph model are O(logN), the percolation transition can coincide with a first-order phase transition in the density of links, making the former also discontinuous. Hysteresis loops can then be of mixed order, with second-order behavior for decreasing link fugacity, and a jump (first order) when it increases.

  1. The average distances in random graphs with given expected degrees

    NASA Astrophysics Data System (ADS)

    Chung, Fan; Lu, Linyuan

    2002-12-01

    Random graph theory is used to examine the "small-world phenomenon"; any two strangers are connected through a short chain of mutual acquaintances. We will show that for certain families of random graphs with given expected degrees the average distance is almost surely of order log n/log , where is the weighted average of the sum of squares of the expected degrees. Of particular interest are power law random graphs in which the number of vertices of degree k is proportional to 1/k for some fixed exponent . For the case of > 3, we prove that the average distance of the power law graphs is almost surely of order log n/log β < 3 for which the power law random graphs have average distance almost surely of order log log n, but have diameter of order log n (provided having some mild constraints for the average distance and maximum degree). In particular, these graphs contain a dense subgraph, which we call the core, having nc/log log n vertices. Almost all vertices are within distance log log n of the core although there are vertices at distance log n from the core.


  2. Limits on relief through constrained exchange on random graphs

    NASA Astrophysics Data System (ADS)

    LaViolette, Randall A.; Ellebracht, Lory A.; Gieseler, Charles J.

    2007-09-01

    Agents are represented by nodes on a random graph (e.g., “small world”). Each agent is endowed with a zero-mean random value that may be either positive or negative. All agents attempt to find relief, i.e., to reduce the magnitude of that initial value, to zero if possible, through exchanges. The exchange occurs only between the agents that are linked, a constraint that turns out to dominate the results. The exchange process continues until Pareto equilibrium is achieved. Only 40-90% of the agents achieved relief on small-world graphs with mean degree between 2 and 40. Even fewer agents achieved relief on scale-free-like graphs with a truncated power-law degree distribution. The rate at which relief grew with increasing degree was slow, only at most logarithmic for all of the graphs considered; viewed in reverse, the fraction of nodes that achieve relief is resilient to the removal of links.

  3. Measuring edge importance: a quantitative analysis of the stochastic shielding approximation for random processes on graphs.

    PubMed

    Schmidt, Deena R; Thomas, Peter J

    2014-04-17

    Mathematical models of cellular physiological mechanisms often involve random walks on graphs representing transitions within networks of functional states. Schmandt and Galán recently introduced a novel stochastic shielding approximation as a fast, accurate method for generating approximate sample paths from a finite state Markov process in which only a subset of states are observable. For example, in ion-channel models, such as the Hodgkin-Huxley or other conductance-based neural models, a nerve cell has a population of ion channels whose states comprise the nodes of a graph, only some of which allow a transmembrane current to pass. The stochastic shielding approximation consists of neglecting fluctuations in the dynamics associated with edges in the graph not directly affecting the observable states. We consider the problem of finding the optimal complexity reducing mapping from a stochastic process on a graph to an approximate process on a smaller sample space, as determined by the choice of a particular linear measurement functional on the graph. The partitioning of ion-channel states into conducting versus nonconducting states provides a case in point. In addition to establishing that Schmandt and Galán's approximation is in fact optimal in a specific sense, we use recent results from random matrix theory to provide heuristic error estimates for the accuracy of the stochastic shielding approximation for an ensemble of random graphs. Moreover, we provide a novel quantitative measure of the contribution of individual transitions within the reaction graph to the accuracy of the approximate process.

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

    PubMed

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

    2012-01-01

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

  5. Graph Theoretical Model of a Sensorimotor Connectome in Zebrafish

    PubMed Central

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

    2012-01-01

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

  6. Some features of the spread of epidemics and information on a random graph

    PubMed Central

    Durrett, Rick

    2010-01-01

    Random graphs are useful models of social and technological networks. To date, most of the research in this area has concerned geometric properties of the graphs. Here we focus on processes taking place on the network. In particular we are interested in how their behavior on networks differs from that in homogeneously mixing populations or on regular lattices of the type commonly used in ecological models. PMID:20167800

  7. The peculiar phase structure of random graph bisection

    SciTech Connect

    Percus, Allon G; Istrate, Gabriel; Goncalves, Bruno T; Sumi, Robert Z

    2008-01-01

    The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of 'cut' edges with an endpoint in each subset. When considered over sparse random graphs, the phase structure of the graph bisection problem displays certain familiar properties, but also some surprises. It is known that when the mean degree is below the critical value of 2 log 2, the cutsize is zero with high probability. We study how the minimum cutsize increases with mean degree above this critical threshold, finding a new analytical upper bound that improves considerably upon previous bounds. Combined with recent results on expander graphs, our bound suggests the unusual scenario that random graph bisection is replica symmetric up to and beyond the critical threshold, with a replica symmetry breaking transition possibly taking place above the threshold. An intriguing algorithmic consequence is that although the problem is NP-hard, we can find near-optimal cutsizes (whose ratio to the optimal value approaches 1 asymptotically) in polynomial time for typical instances near the phase transition.

  8. Graph-Driven Diffusion and Random Walk Schemes for Image Segmentation.

    PubMed

    Bampis, Christos G; Maragos, Petros; Bovik, Alan C

    2016-10-26

    We propose graph-driven approaches to image segmentation by developing diffusion processes defined on arbitrary graphs. We formulate a solution to the image segmentation problem modeled as the result of infectious wavefronts propagating on an image-driven graph where pixels correspond to nodes of an arbitrary graph. By relating the popular Susceptible - Infected - Recovered epidemic propagation model to the Random Walker algorithm, we develop the Normalized Random Walker and a lazy random walker variant. The underlying iterative solutions of these methods are derived as the result of infections transmitted on this arbitrary graph. The main idea is to incorporate a degree-aware term into the original Random Walker algorithm in order to account for the node centrality of every neighboring node and to weigh the contribution of every neighbor to the underlying diffusion process. Our lazy random walk variant models the tendency of patients or nodes to resist changes in their infection status. We also show how previous work can be naturally extended to take advantage of this degreeaware term which enables the design of other novel methods. Through an extensive experimental analysis, we demonstrate the reliability of our approach, its small computational burden and the dimensionality reduction capabilities of graph-driven approaches. Without applying any regular grid constraint, the proposed graph clustering scheme allows us to consider pixellevel, node-level approaches and multidimensional input data by naturally integrating the importance of each node to the final clustering or segmentation solution. A software release containing implementations of this work and supplementary material can be found at: http://cvsp.cs.ntua.gr/research/GraphClustering/.

  9. Muller's ratchet in random graphs and scale-free networks

    NASA Astrophysics Data System (ADS)

    Campos, Paulo R. A.; Combadão, Jaime; Dionisio, Francisco; Gordo, Isabel

    2006-10-01

    Muller’s ratchet is an evolutionary process that has been implicated in the extinction of asexual species, the evolution of mitochondria, the degeneration of the Y chromosome, the evolution of sex and recombination and the evolution of microbes. Here we study the speed of Muller’s ratchet in a population subdivided into many small subpopulations connected by migration, and distributed on a network. We compare the speed of the ratchet in two distinct types of topologies: scale free networks and random graphs. The difference between the topologies is noticeable when the average connectivity of the network and the migration rate is large. In this situation we observe that the ratchet clicks faster in scale free networks than in random graphs. So contrary to intuition, scale free networks are more prone to loss of genetic information than random graphs. On the other hand, we show that scale free networks are more robust to the random extinction than random graphs. Since these complex networks have been shown to describe well real-life systems, our results open a framework for studying the evolution of microbes and disease epidemics.

  10. Critical behaviour of spanning forests on random planar graphs

    NASA Astrophysics Data System (ADS)

    Bondesan, Roberto; Caracciolo, Sergio; Sportiello, Andrea

    2017-02-01

    As a follow-up of previous work of the authors, we analyse the statistical mechanics model of random spanning forests on random planar graphs. Special emphasis is given to the analysis of the critical behaviour. Exploiting an exact relation with a model of \\text{O}(-2) -loops and dimers, previously solved by Kostov and Staudacher, we identify critical and multicritical loci, and find them consistent with recent results of Bousquet-Mélou and Courtiel. This is also consistent with the KPZ relation, and the Berker-Kadanoff phase in the anti-ferromagnetic regime of the Potts Model on periodic lattices, predicted by Saleur. To our knowledge, this is the first known example of KPZ appearing explicitly to work within a Berker-Kadanoff phase. We set up equations for the generating function, at the value t  =  -1 of the fugacity, which is of combinatorial interest, and we investigate the resulting numerical series, a favourite problem of Tony Guttmann’s. Dedicated to Tony Guttmann on the occasion of his 70th birthday.

  11. Graph Coloring Used to Model Traffic Lights.

    ERIC Educational Resources Information Center

    Williams, John

    1992-01-01

    Two scheduling problems, one involving setting up an examination schedule and the other describing traffic light problems, are modeled as colorings of graphs consisting of a set of vertices and edges. The chromatic number, the least number of colors necessary for coloring a graph, is employed in the solutions. (MDH)

  12. Nonergodic Phases in Strongly Disordered Random Regular Graphs.

    PubMed

    Altshuler, B L; Cuevas, E; Ioffe, L B; Kravtsov, V E

    2016-10-07

    We combine numerical diagonalization with semianalytical calculations to prove the existence of the intermediate nonergodic but delocalized phase in the Anderson model on disordered hierarchical lattices. We suggest a new generalized population dynamics that is able to detect the violation of ergodicity of the delocalized states within the Abou-Chakra, Anderson, and Thouless recursive scheme. This result is supplemented by statistics of random wave functions extracted from exact diagonalization of the Anderson model on ensemble of disordered random regular graphs (RRG) of N sites with the connectivity K=2. By extrapolation of the results of both approaches to N→∞ we obtain the fractal dimensions D_{1}(W) and D_{2}(W) as well as the population dynamics exponent D(W) with the accuracy sufficient to claim that they are nontrivial in the broad interval of disorder strength W_{E}10^{5} reveals a singularity in D_{1,2}(W) dependencies which provides clear evidence for the first order transition between the two delocalized phases on RRG at W_{E}≈10.0. We discuss the implications of these results for quantum and classical nonintegrable and many-body systems.

  13. Nonergodic Phases in Strongly Disordered Random Regular Graphs

    NASA Astrophysics Data System (ADS)

    Altshuler, B. L.; Cuevas, E.; Ioffe, L. B.; Kravtsov, V. E.

    2016-10-01

    We combine numerical diagonalization with semianalytical calculations to prove the existence of the intermediate nonergodic but delocalized phase in the Anderson model on disordered hierarchical lattices. We suggest a new generalized population dynamics that is able to detect the violation of ergodicity of the delocalized states within the Abou-Chakra, Anderson, and Thouless recursive scheme. This result is supplemented by statistics of random wave functions extracted from exact diagonalization of the Anderson model on ensemble of disordered random regular graphs (RRG) of N sites with the connectivity K =2 . By extrapolation of the results of both approaches to N →∞ we obtain the fractal dimensions D1(W ) and D2(W ) as well as the population dynamics exponent D (W ) with the accuracy sufficient to claim that they are nontrivial in the broad interval of disorder strength WE1 05 reveals a singularity in D1 ,2(W ) dependencies which provides clear evidence for the first order transition between the two delocalized phases on RRG at WE≈10.0 . We discuss the implications of these results for quantum and classical nonintegrable and many-body systems.

  14. Computational Graph Theoretical Model of the Zebrafish Sensorimotor Pathway

    NASA Astrophysics Data System (ADS)

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

    2011-11-01

    Mapping the detailed connectivity patterns of neural circuits is a central goal of neuroscience and has been the focus of extensive current research [4, 3]. The best quantitative approach to analyze the acquired data is still unclear but graph theory has been used with success [3, 1]. We present a graph theoretical model with vertices and edges representing neurons and synaptic connections, respectively. Our system is the zebrafish posterior lateral line sensorimotor pathway. The goal of our analysis is to elucidate mechanisms of information processing in this neural pathway by comparing the mathematical properties of its graph to those of other, previously described graphs. We create a zebrafish model based on currently known anatomical data. The degree distributions and small-world measures of this model is compared to small-world, random and 3-compartment random graphs of the same size (with over 2500 nodes and 160,000 connections). We find that the zebrafish graph shows small-worldness similar to other neural networks and does not have a scale-free distribution of connections.

  15. A model of language inflection graphs

    NASA Astrophysics Data System (ADS)

    Fukś, Henryk; Farzad, Babak; Cao, Yi

    2014-01-01

    Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to the abundance of inflectional forms. We construct the simplest form of inflection graphs, namely a bipartite graph in which one group of vertices corresponds to dictionary headwords and the other group to inflected forms encountered in a given text. We, then, study projection of this graph on the set of headwords. The projection decomposes into a large number of connected components, to be called word groups. Distribution of sizes of word group exhibits some remarkable properties, resembling cluster distribution in a lattice percolation near the critical point. We propose a simple model which produces graphs of this type, reproducing the desired component distribution and other topological features.

  16. 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.

  17. Anderson localization and ergodicity on random regular graphs

    NASA Astrophysics Data System (ADS)

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

    2016-12-01

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

  18. Random geometric graph description of connectedness percolation in rod systems.

    PubMed

    Chatterjee, Avik P; Grimaldi, Claudio

    2015-09-01

    The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The probability that an edge (or link) connects any randomly selected pair of nodes depends upon the rod volume fraction as well as the distribution over their sizes and shapes, and also upon quantities that characterize their state of dispersion (such as the orientational distribution function). We employ the observation that contributions from closed loops of connected rods are negligible in the limit of large aspect ratios to obtain percolation thresholds that are fully equivalent to those calculated within the second-virial approximation of the connectedness Ornstein-Zernike equation. Our formulation can account for effects due to interactions between the rods, and many-body features can be partially addressed by suitable choices for the edge probabilities.

  19. Random geometric graph description of connectedness percolation in rod systems

    NASA Astrophysics Data System (ADS)

    Chatterjee, Avik P.; Grimaldi, Claudio

    2015-09-01

    The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The probability that an edge (or link) connects any randomly selected pair of nodes depends upon the rod volume fraction as well as the distribution over their sizes and shapes, and also upon quantities that characterize their state of dispersion (such as the orientational distribution function). We employ the observation that contributions from closed loops of connected rods are negligible in the limit of large aspect ratios to obtain percolation thresholds that are fully equivalent to those calculated within the second-virial approximation of the connectedness Ornstein-Zernike equation. Our formulation can account for effects due to interactions between the rods, and many-body features can be partially addressed by suitable choices for the edge probabilities.

  20. Measuring Edge Importance: A Quantitative Analysis of the Stochastic Shielding Approximation for Random Processes on Graphs

    PubMed Central

    2014-01-01

    Mathematical models of cellular physiological mechanisms often involve random walks on graphs representing transitions within networks of functional states. Schmandt and Galán recently introduced a novel stochastic shielding approximation as a fast, accurate method for generating approximate sample paths from a finite state Markov process in which only a subset of states are observable. For example, in ion-channel models, such as the Hodgkin–Huxley or other conductance-based neural models, a nerve cell has a population of ion channels whose states comprise the nodes of a graph, only some of which allow a transmembrane current to pass. The stochastic shielding approximation consists of neglecting fluctuations in the dynamics associated with edges in the graph not directly affecting the observable states. We consider the problem of finding the optimal complexity reducing mapping from a stochastic process on a graph to an approximate process on a smaller sample space, as determined by the choice of a particular linear measurement functional on the graph. The partitioning of ion-channel states into conducting versus nonconducting states provides a case in point. In addition to establishing that Schmandt and Galán’s approximation is in fact optimal in a specific sense, we use recent results from random matrix theory to provide heuristic error estimates for the accuracy of the stochastic shielding approximation for an ensemble of random graphs. Moreover, we provide a novel quantitative measure of the contribution of individual transitions within the reaction graph to the accuracy of the approximate process. PMID:24742077

  1. Horizontal visibility graphs: exact results for random time series.

    PubMed

    Luque, B; Lacasa, L; Ballesteros, F; Luque, J

    2009-10-01

    The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows us to apply methods of complex network theory for characterizing time series. In this work we present the horizontal visibility algorithm, a geometrically simpler and analytically solvable version of our former algorithm, focusing on the mapping of random series (series of independent identically distributed random variables). After presenting some properties of the algorithm, we present exact results on the topological properties of graphs associated with random series, namely, the degree distribution, the clustering coefficient, and the mean path length. We show that the horizontal visibility algorithm stands as a simple method to discriminate randomness in time series since any random series maps to a graph with an exponential degree distribution of the shape P(k)=(1/3)(2/3)(k-2), independent of the probability distribution from which the series was generated. Accordingly, visibility graphs with other P(k) are related to nonrandom series. Numerical simulations confirm the accuracy of the theorems for finite series. In a second part, we show that the method is able to distinguish chaotic series from independent and identically distributed (i.i.d.) theory, studying the following situations: (i) noise-free low-dimensional chaotic series, (ii) low-dimensional noisy chaotic series, even in the presence of large amounts of noise, and (iii) high-dimensional chaotic series (coupled map lattice), without needs for additional techniques such as surrogate data or noise reduction methods. Finally, heuristic arguments are given to explain the topological properties of chaotic series, and several sequences that are conjectured to be random are analyzed.

  2. Bond percolation on a class of correlated and clustered random graphs

    NASA Astrophysics Data System (ADS)

    Allard, A.; Hébert-Dufresne, L.; Noël, P.-A.; Marceau, V.; Dubé, L. J.

    2012-10-01

    We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the configuration model where nodes of different types are connected via different types of hyperedges, edges that can link more than two nodes. We argue that the multitype approach coupled with the use of clustered hyperedges can reproduce a wide spectrum of complex patterns, and thus enhances our capability to model real complex networks. As an illustration of this claim, we use our formalism to highlight unusual behaviours of the size and composition of the components (small and giant) in a synthetic, albeit realistic, social network.

  3. Visibility graphs of random scalar fields and spatial data

    NASA Astrophysics Data System (ADS)

    Lacasa, Lucas; Iacovacci, Jacopo

    2017-07-01

    We extend the family of visibility algorithms to map scalar fields of arbitrary dimension into graphs, enabling the analysis of spatially extended data structures as networks. We introduce several possible extensions and provide analytical results on the topological properties of the graphs associated to different types of real-valued matrices, which can be understood as the high and low disorder limits of real-valued scalar fields. In particular, we find a closed expression for the degree distribution of these graphs associated to uncorrelated random fields of generic dimension. This result holds independently of the field's marginal distribution and it directly yields a statistical randomness test, applicable in any dimension. We showcase its usefulness by discriminating spatial snapshots of two-dimensional white noise from snapshots of a two-dimensional lattice of diffusively coupled chaotic maps, a system that generates high dimensional spatiotemporal chaos. The range of potential applications of this combinatorial framework includes image processing in engineering, the description of surface growth in material science, soft matter or medicine, and the characterization of potential energy surfaces in chemistry, disordered systems, and high energy physics. An illustration on the applicability of this method for the classification of the different stages involved in carcinogenesis is briefly discussed.

  4. Using Combinatorica/Mathematica for Student Projects in Random Graph Theory

    ERIC Educational Resources Information Center

    Pfaff, Thomas J.; Zaret, Michele

    2006-01-01

    We give an example of a student project that experimentally explores a topic in random graph theory. We use the "Combinatorica" package in "Mathematica" to estimate the minimum number of edges needed in a random graph to have a 50 percent chance that the graph is connected. We provide the "Mathematica" code and compare it to the known theoretical…

  5. Using Combinatorica/Mathematica for Student Projects in Random Graph Theory

    ERIC Educational Resources Information Center

    Pfaff, Thomas J.; Zaret, Michele

    2006-01-01

    We give an example of a student project that experimentally explores a topic in random graph theory. We use the "Combinatorica" package in "Mathematica" to estimate the minimum number of edges needed in a random graph to have a 50 percent chance that the graph is connected. We provide the "Mathematica" code and compare it to the known theoretical…

  6. Graph-Based Transform for 2D Piecewise Smooth Signals With Random Discontinuity Locations.

    PubMed

    Zhang, Dong; Liang, Jie

    2017-04-01

    The graph-based block transform recently emerged as an effective tool for compressing some special signals such as depth images in 3D videos. However, in existing methods, overheads are required to describe the graph of the block, from which the decoder has to calculate the transform via time-consuming eigendecomposition. To address these problems, in this paper, we aim to develop a single graph-based transform for a class of 2D piecewise smooth signals with similar discontinuity patterns. We first consider the deterministic case with a known discontinuity location in each row. We propose a 2D first-order autoregression (2D AR1) model and a 2D graph for this type of signals. We show that the closed-form expression of the inverse of a biased Laplacian matrix of the proposed 2D graph is exactly the covariance matrix of the proposed 2D AR1 model. Therefore, the optimal transform for the signal are the eigenvectors of the proposed graph Laplacian. Next, we show that similar results hold in the random case, where the locations of the discontinuities in different rows are randomly distributed within a confined region, and we derive the closed-form expression of the corresponding optimal 2D graph Laplacian. The theory developed in this paper can be used to design both pre-computed transforms and signal-dependent transforms with low complexities. Finally, depth image coding experiments demonstrate that our methods can achieve similar performance to the state-of-the-art method, but our complexity is much lower.

  7. Modeling Transmission Line Networks Using Quantum Graphs

    NASA Astrophysics Data System (ADS)

    Koch, Trystan; Antonsen, Thomas

    Quantum graphs--one dimensional edges, connecting nodes, that support propagating Schrödinger wavefunctions--have been studied extensively as tractable models of wave chaotic behavior (Smilansky and Gnutzmann 2006, Berkolaiko and Kuchment 2013). Here we consider the electrical analog, in which the graph represents an electrical network where the edges are transmission lines (Hul et. al. 2004) and the nodes contain either discrete circuit elements or intricate circuit elements best represented by arbitrary scattering matrices. Including these extra degrees of freedom at the nodes leads to phenomena that do not arise in simpler graph models. We investigate the properties of eigenfrequencies and eigenfunctions on these graphs, and relate these to the statistical description of voltages on the transmission lines when driving the network externally. The study of electromagnetic compatibility, the effect of external radiation on complicated systems with numerous interconnected cables, motivates our research into this extension of the graph model. Work supported by the Office of Naval Research (N0014130474) and the Air Force Office of Scientific Research.

  8. Tapping Spin Glasses and Ferromagnets on Random Graphs

    SciTech Connect

    Dean, David S.; Lef {grave e}vre, Alexandre

    2001-06-18

    We consider a tapping dynamics, analogous to that in experiments on granular media, on spin glasses and ferromagnets on random thin graphs. Between taps, zero temperature single spin flip dynamics takes the system to a metastable state. Tapping corresponds to flipping simultaneously any spin with probability p . This dynamics leads to a stationary regime with a steady state energy E(p) . We analytically solve this dynamics for the one-dimensional ferromagnet and {+-}J spin glass. Numerical simulations for spin glasses and ferromagnets of higher connectivity are carried out; in particular, we find a novel first order transition for the ferromagnetic systems.

  9. Kinetic theory of random graphs: from paths to cycles.

    PubMed

    Ben-Naim, E; Krapivsky, P L

    2005-02-01

    The structural properties of evolving random graphs are investigated. Treating linking as a dynamic aggregation process, rate equations for the distribution of node to node distances (paths) and of cycles are formulated and solved analytically. At the gelation point, the typical length of paths and cycles, l , scales with the component size k as l approximately k(1/2) . Dynamic and finite-size scaling laws for the behavior at and near the gelation point are obtained. Finite-size scaling laws are verified using numerical simulations.

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

    NASA Astrophysics Data System (ADS)

    Hamma, Alioscia; Santra, Siddhartha; Zanardi, Paolo

    2012-11-01

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

  11. 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.

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

    PubMed

    Metz, Fernando L; Pérez Castillo, Isaac

    2016-09-02

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

  13. A conjecture on the maximum cut and bisection width in random regular graphs

    NASA Astrophysics Data System (ADS)

    Zdeborová, Lenka; Boettcher, Stefan

    2010-02-01

    The asymptotic properties of random regular graphs are objects of extensive study in mathematics and physics. In this paper we argue, using the theory of spin glasses in physics, that in random regular graphs the maximum cut size asymptotically equals the number of edges in the graph minus the minimum bisection size. Maximum cut and minimal bisection are two famous NP-complete problems with no known general relation between them; hence our conjecture is a surprising property for random regular graphs. We further support the conjecture with numerical simulations. A rigorous proof of this relation is an obvious challenge.

  14. Evolution of tag-based cooperation on Erdős-Rényi random graphs

    NASA Astrophysics Data System (ADS)

    Lima, F. W. S.; Hadzibeganovic, Tarik; Stauffer, Dietrich

    2014-12-01

    Here, we study an agent-based model of the evolution of tag-mediated cooperation on Erdős-Rényi random graphs. In our model, agents with heritable phenotypic traits play pairwise Prisoner's Dilemma-like games and follow one of the four possible strategies: Ethnocentric, altruistic, egoistic and cosmopolitan. Ethnocentric and cosmopolitan strategies are conditional, i.e. their selection depends upon the shared phenotypic similarity among interacting agents. The remaining two strategies are always unconditional, meaning that egoists always defect while altruists always cooperate. Our simulations revealed that ethnocentrism can win in both early and later evolutionary stages on directed random graphs when reproduction of artificial agents was asexual; however, under the sexual mode of reproduction on a directed random graph, we found that altruists dominate initially for a rather short period of time, whereas ethnocentrics and egoists suppress other strategists and compete for dominance in the intermediate and later evolutionary stages. Among our results, we also find surprisingly regular oscillations which are not damped in the course of time even after half a million Monte Carlo steps. Unlike most previous studies, our findings highlight conditions under which ethnocentrism is less stable or suppressed by other competing strategies.

  15. Neural Population Dynamics Modeled by Mean-Field Graphs

    NASA Astrophysics Data System (ADS)

    Kozma, Robert; Puljic, Marko

    2011-09-01

    In this work we apply random graph theory approach to describe neural population dynamics. There are important advantages of using random graph theory approach in addition to ordinary and partial differential equations. The mathematical theory of large-scale random graphs provides an efficient tool to describe transitions between high- and low-dimensional spaces. Recent advances in studying neural correlates of higher cognition indicate the significance of sudden changes in space-time neurodynamics, which can be efficiently described as phase transitions in the neuropil medium. Phase transitions are rigorously defined mathematically on random graph sequences and they can be naturally generalized to a class of percolation processes called neuropercolation. In this work we employ mean-field graphs with given vertex degree distribution and edge strength distribution. We demonstrate the emergence of collective oscillations in the style of brains.

  16. Navigability of Random Geometric Graphs in the Universe and Other Spacetimes.

    PubMed

    Cunningham, William; Zuev, Konstantin; Krioukov, Dmitri

    2017-08-18

    Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asymptotically de Sitter spacetimes, such as the Lorentzian spacetime of our accelerating universe, are more attractive as their predictions are more consistent with observations in real networks. Yet another important property of hyperbolic graphs is their navigability, and it remains unclear if de Sitter graphs are as navigable as hyperbolic ones. Here we study the navigability of random geometric graphs in three Lorentzian manifolds corresponding to universes filled only with dark energy (de Sitter spacetime), only with matter, and with a mixture of dark energy and matter. We find these graphs are navigable only in the manifolds with dark energy. This result implies that, in terms of navigability, random geometric graphs in asymptotically de Sitter spacetimes are as good as random hyperbolic graphs. It also establishes a connection between the presence of dark energy and navigability of the discretized causal structure of spacetime, which provides a basis for a different approach to the dark energy problem in cosmology.

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

    NASA Astrophysics Data System (ADS)

    Slanina, František

    2017-05-01

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

  18. Bonabeau model on a fully connected graph

    NASA Astrophysics Data System (ADS)

    Malarz, K.; Stauffer, D.; Kułakowski, K.

    2006-03-01

    Numerical simulations are reported on the Bonabeau model on a fully connected graph, where spatial degrees of freedom are absent. The control parameter is the memory factor f. The phase transition is observed at the dispersion of the agents power hi. The critical value fC shows a hysteretic behavior with respect to the initial distribution of hi. fC decreases with the system size; this decrease can be compensated by a greater number of fights between a global reduction of the distribution width of hi. The latter step is equivalent to a partial forgetting.

  19. A weak zero-one law for sequences of random distance graphs

    SciTech Connect

    Zhukovskii, Maksim E

    2012-07-31

    We study zero-one laws for properties of random distance graphs. Properties written in a first-order language are considered. For p(N) such that pN{sup {alpha}}{yields}{infinity} as N{yields}{infinity}, and (1-p)N{sup {alpha}} {yields} {infinity} as N {yields} {infinity} for any {alpha}>0, we succeed in refuting the law. In this connection, we consider a weak zero-one j-law. For this law, we obtain results for random distance graphs which are similar to the assertions concerning the classical zero-one law for random graphs. Bibliography: 18 titles.

  20. The XXZ Heisenberg model on random surfaces

    NASA Astrophysics Data System (ADS)

    Ambjørn, J.; Sedrakyan, A.

    2013-09-01

    We consider integrable models, or in general any model defined by an R-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. They can also be associated with the random graphs of multiparticle scattering nodes. As an example we formulate a random matrix model where the partition function reproduces the annealed average of the XXZ Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.

  1. Graph Partitioning Models for Parallel Computing

    SciTech Connect

    Hendrickson, B.; Kolda, T.G.

    1999-03-02

    Calculations can naturally be described as graphs in which vertices represent computation and edges reflect data dependencies. By partitioning the vertices of a graph, the calculation can be divided among processors of a parallel computer. However, the standard methodology for graph partitioning minimizes the wrong metric and lacks expressibility. We survey several recently proposed alternatives and discuss their relative merits.

  2. Hyperbolic graph generator

    NASA Astrophysics Data System (ADS)

    Aldecoa, Rodrigo; Orsini, Chiara; Krioukov, Dmitri

    2015-11-01

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

  3. Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks

    DOE PAGES

    Rudinger, Kenneth; Gamble, John King; Bach, Eric; ...

    2013-07-01

    Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erencesmore » in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.« less

  4. Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks

    SciTech Connect

    Rudinger, Kenneth; Gamble, John King; Bach, Eric; Friesen, Mark; Joynt, Robert; Coppersmith, S. N.

    2013-07-01

    Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erences in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.

  5. Simple graph models of information spread in finite populations

    PubMed Central

    Voorhees, Burton; Ryder, Bergerud

    2015-01-01

    We consider several classes of simple graphs as potential models for information diffusion in a structured population. These include biases cycles, dual circular flows, partial bipartite graphs and what we call ‘single-link’ graphs. In addition to fixation probabilities, we study structure parameters for these graphs, including eigenvalues of the Laplacian, conductances, communicability and expected hitting times. In several cases, values of these parameters are related, most strongly so for partial bipartite graphs. A measure of directional bias in cycles and circular flows arises from the non-zero eigenvalues of the antisymmetric part of the Laplacian and another measure is found for cycles as the value of the transition probability for which hitting times going in either direction of the cycle are equal. A generalization of circular flow graphs is used to illustrate the possibility of tuning edge weights to match pre-specified values for graph parameters; in particular, we show that generalizations of circular flows can be tuned to have fixation probabilities equal to the Moran probability for a complete graph by tuning vertex temperature profiles. Finally, single-link graphs are introduced as an example of a graph involving a bottleneck in the connection between two components and these are compared to the partial bipartite graphs. PMID:26064661

  6. Complete graph model for community detection

    NASA Astrophysics Data System (ADS)

    Sun, Peng Gang; Sun, Xiya

    2017-04-01

    Community detection brings plenty of considerable problems, which has attracted more attention for many years. This paper develops a new framework, which tries to measure the interior and the exterior of a community based on a same metric, complete graph model. In particular, the exterior is modeled as a complete bipartite. We partition a network into subnetworks by maximizing the difference between the interior and the exterior of the subnetworks. In addition, we compare our approach with some state of the art methods on computer-generated networks based on the LFR benchmark as well as real-world networks. The experimental results indicate that our approach obtains better results for community detection, is capable of splitting irregular networks and achieves perfect results on the karate network and the dolphin network.

  7. Hierarchical graphs for rule-based modeling of biochemical systems

    PubMed Central

    2011-01-01

    Background In rule-based modeling, graphs are used to represent molecules: a colored vertex represents a component of a molecule, a vertex attribute represents the internal state of a component, and an edge represents a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions. A rule that specifies addition (removal) of an edge represents a class of association (dissociation) reactions, and a rule that specifies a change of a vertex attribute represents a class of reactions that affect the internal state of a molecular component. A set of rules comprises an executable model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system. Results For purposes of model annotation, we propose the use of hierarchical graphs to represent structural relationships among components and subcomponents of molecules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR) complex. We also show that computational methods developed for regular graphs can be applied to hierarchical graphs. In particular, we describe a generalization of Nauty, a graph isomorphism and canonical labeling algorithm. The generalized version of the Nauty procedure, which we call HNauty, can be used to assign canonical labels to hierarchical graphs or more generally to graphs with multiple edge types. The difference between the Nauty and HNauty procedures is minor, but for completeness, we provide an explanation of the entire HNauty algorithm. Conclusions Hierarchical graphs provide more intuitive formal representations of proteins and other structured molecules with multiple functional components than do the regular graphs of current languages for specifying rule-based models

  8. A formal definition of data flow graph models

    NASA Technical Reports Server (NTRS)

    Kavi, Krishna M.; Buckles, Bill P.; Bhat, U. Narayan

    1986-01-01

    In this paper, a new model for parallel computations and parallel computer systems that is based on data flow principles is presented. Uninterpreted data flow graphs can be used to model computer systems including data driven and parallel processors. A data flow graph is defined to be a bipartite graph with actors and links as the two vertex classes. Actors can be considered similar to transitions in Petri nets, and links similar to places. The nondeterministic nature of uninterpreted data flow graphs necessitates the derivation of liveness conditions.

  9. A concatenational graph evolution aging model.

    PubMed

    Suo, Jinli; Chen, Xilin; Shan, Shiguang; Gao, Wen; Dai, Qionghai

    2012-11-01

    Modeling the long-term face aging process is of great importance for face recognition and animation, but there is a lack of sufficient long-term face aging sequences for model learning. To address this problem, we propose a CONcatenational GRaph Evolution (CONGRE) aging model, which adopts decomposition strategy in both spatial and temporal aspects to learn long-term aging patterns from partially dense aging databases. In spatial aspect, we build a graphical face representation, in which a human face is decomposed into mutually interrelated subregions under anatomical guidance. In temporal aspect, the long-term evolution of the above graphical representation is then modeled by connecting sequential short-term patterns following the Markov property of aging process under smoothness constraints between neighboring short-term patterns and consistency constraints among subregions. The proposed model also considers the diversity of face aging by proposing probabilistic concatenation strategy between short-term patterns and applying scholastic sampling in aging prediction. In experiments, the aging prediction results generated by the learned aging models are evaluated both subjectively and objectively to validate the proposed model.

  10. Ghana randomized air pollution and health study (GRAPHS): study protocol for a randomized controlled trial.

    PubMed

    Jack, Darby W; Asante, Kwaku Poku; Wylie, Blair J; Chillrud, Steve N; Whyatt, Robin M; Ae-Ngibise, Kenneth A; Quinn, Ashlinn K; Yawson, Abena Konadu; Boamah, Ellen Abrafi; Agyei, Oscar; Mujtaba, Mohammed; Kaali, Seyram; Kinney, Patrick; Owusu-Agyei, Seth

    2015-09-22

    Household air pollution exposure is a major health risk, but validated interventions remain elusive. The Ghana Randomized Air Pollution and Health Study (GRAPHS) is a cluster-randomized trial that evaluates the efficacy of clean fuels (liquefied petroleum gas, or LPG) and efficient biomass cookstoves in the Brong-Ahafo region of central Ghana. We recruit pregnant women into LPG, efficient cookstove, and control arms and track birth weight and physician-assessed severe pneumonia incidence in the first year of life. A woman is eligible to participate if she is in the first or second trimester of pregnancy and carrying a live singleton fetus, if she is the primary cook, and if she does not smoke. We hypothesize that babies born to intervention mothers will weigh more and will have fewer cases of physician-assessed severe pneumonia in the first year of life. Additionally, an extensive personal air pollution exposure monitoring effort opens the way for exposure-response analyses, which we will present alongside intention-to-treat analyses. Major funding was provided by the National Institute of Environmental Health Sciences, The Thrasher Research Fund, and the Global Alliance for Clean Cookstoves. Household air pollution exposure is a major health risk that requires well-tested interventions. GRAPHS will provide important new evidence on the efficacy of both efficient biomass cookstoves and LPG, and will thus help inform health and energy policies in developing countries. The trial was registered with clinicaltrials.gov on 13 April 2011 with the identifier NCT01335490 .

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

    PubMed

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

    2013-04-05

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

  12. Modularity-based graph partitioning using conditional expected models

    PubMed Central

    Chang, Yu-Teng; Leahy, Richard M.; Pantazis, Dimitrios

    2013-01-01

    Modularity-based partitioning methods divide networks into modules by comparing their structure against random networks conditioned to have the same number of nodes, edges, and degree distribution. We propose a novel way to measure modularity and divide graphs, based on conditional probabilities of the edge strength of random networks. We provide closed-form solutions for the expected strength of an edge when it is conditioned on the degrees of the two neighboring nodes, or alternatively on the degrees of all nodes comprising the network. We analytically compute the expected network under the assumptions of Gaussian and Bernoulli distributions. When the Gaussian distribution assumption is violated, we prove that our expression is the best linear unbiased estimator. Finally, we investigate the performance of our conditional expected model in partitioning simulated and real-world networks. PMID:22400627

  13. Reducing Redundancies in Reconfigurable Antenna Structures Using Graph Models

    SciTech Connect

    Costantine, Joseph; al-Saffar, Sinan; Christodoulou, Christos G.; Abdallah, Chaouki T.

    2010-04-23

    Many reconfigurable antennas have redundant components in their structures. In this paper we present an approach for reducing redundancies in reconfigurable antenna structures using graph models. We study reconfigurable antennas, which are grouped, categorized and modeled according to a set of proposed graph rules. Several examples are presented and discussed to demonstrate the validity of this new technique.

  14. Robust Spectral Clustering Using Statistical Sub-Graph Affinity Model

    PubMed Central

    Eichel, Justin A.; Wong, Alexander; Fieguth, Paul; Clausi, David A.

    2013-01-01

    Spectral clustering methods have been shown to be effective for image segmentation. Unfortunately, the presence of image noise as well as textural characteristics can have a significant negative effect on the segmentation performance. To accommodate for image noise and textural characteristics, this study introduces the concept of sub-graph affinity, where each node in the primary graph is modeled as a sub-graph characterizing the neighborhood surrounding the node. The statistical sub-graph affinity matrix is then constructed based on the statistical relationships between sub-graphs of connected nodes in the primary graph, thus counteracting the uncertainty associated with the image noise and textural characteristics by utilizing more information than traditional spectral clustering methods. Experiments using both synthetic and natural images under various levels of noise contamination demonstrate that the proposed approach can achieve improved segmentation performance when compared to existing spectral clustering methods. PMID:24386111

  15. Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

    NASA Astrophysics Data System (ADS)

    Ni, Xiao-Hui; Jiang, Zhi-Qiang; Zhou, Wei-Xing

    2009-10-01

    The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.

  16. Fragmentation properties of two-dimensional proximity graphs considering random failures and targeted attacks

    NASA Astrophysics Data System (ADS)

    Norrenbrock, C.; Melchert, O.; Hartmann, A. K.

    2016-12-01

    The pivotal quality of proximity graphs is connectivity, i.e., all nodes in the graph are connected to one another either directly or via intermediate nodes. These types of graphs are often robust, i.e., they are able to function well even if they are subject to limited removal of elementary building blocks, as may occur for random failures or targeted attacks. Here, we study how the structure of these graphs is affected when nodes get removed successively until an extensive fraction is removed such that the graphs fragment. We study different types of proximity graphs for various node-removal strategies. We use different types of observables to monitor the fragmentation process, simple ones like the number and sizes of connected components and more complex ones like the hop diameter and the backup capacity, which is needed to make a network N -1 resilient. The actual fragmentation turns out to be described by a second-order phase transition. Using finite-size scaling analyses we numerically assess the threshold fraction of removed nodes, which is characteristic for the particular graph type and node deletion scheme; this suffices to decompose the underlying graphs.

  17. Using graph approach for managing connectivity in integrative landscape modelling

    NASA Astrophysics Data System (ADS)

    Rabotin, Michael; Fabre, Jean-Christophe; Libres, Aline; Lagacherie, Philippe; Crevoisier, David; Moussa, Roger

    2013-04-01

    In cultivated landscapes, a lot of landscape elements such as field boundaries, ditches or banks strongly impact water flows, mass and energy fluxes. At the watershed scale, these impacts are strongly conditionned by the connectivity of these landscape elements. An accurate representation of these elements and of their complex spatial arrangements is therefore of great importance for modelling and predicting these impacts.We developped in the framework of the OpenFLUID platform (Software Environment for Modelling Fluxes in Landscapes) a digital landscape representation that takes into account the spatial variabilities and connectivities of diverse landscape elements through the application of the graph theory concepts. The proposed landscape representation consider spatial units connected together to represent the flux exchanges or any other information exchanges. Each spatial unit of the landscape is represented as a node of a graph and relations between units as graph connections. The connections are of two types - parent-child connection and up/downstream connection - which allows OpenFLUID to handle hierarchical graphs. Connections can also carry informations and graph evolution during simulation is possible (connections or elements modifications). This graph approach allows a better genericity on landscape representation, a management of complex connections and facilitate development of new landscape representation algorithms. Graph management is fully operational in OpenFLUID for developers or modelers ; and several graph tools are available such as graph traversal algorithms or graph displays. Graph representation can be managed i) manually by the user (for example in simple catchments) through XML-based files in easily editable and readable format or ii) by using methods of the OpenFLUID-landr library which is an OpenFLUID library relying on common open-source spatial libraries (ogr vector, geos topologic vector and gdal raster libraries). Open

  18. Random Forest classification based on star graph topological indices for antioxidant proteins.

    PubMed

    Fernández-Blanco, Enrique; Aguiar-Pulido, Vanessa; Munteanu, Cristian Robert; Dorado, Julian

    2013-01-21

    Aging and life quality is an important research topic nowadays in areas such as life sciences, chemistry, pharmacology, etc. People live longer, and, thus, they want to spend that extra time with a better quality of life. At this regard, there exists a tiny subset of molecules in nature, named antioxidant proteins that may influence the aging process. However, testing every single protein in order to identify its properties is quite expensive and inefficient. For this reason, this work proposes a model, in which the primary structure of the protein is represented using complex network graphs that can be used to reduce the number of proteins to be tested for antioxidant biological activity. The graph obtained as a representation will help us describe the complex system by using topological indices. More specifically, in this work, Randić's Star Networks have been used as well as the associated indices, calculated with the S2SNet tool. In order to simulate the existing proportion of antioxidant proteins in nature, a dataset containing 1999 proteins, of which 324 are antioxidant proteins, was created. Using this data as input, Star Graph Topological Indices were calculated with the S2SNet tool. These indices were then used as input to several classification techniques. Among the techniques utilised, the Random Forest has shown the best performance, achieving a score of 94% correctly classified instances. Although the target class (antioxidant proteins) represents a tiny subset inside the dataset, the proposed model is able to achieve a percentage of 81.8% correctly classified instances for this class, with a precision of 81.3%.

  19. 3D Mesh Segmentation Based on Markov Random Fields and Graph Cuts

    NASA Astrophysics Data System (ADS)

    Shi, Zhenfeng; Le, Dan; Yu, Liyang; Niu, Xiamu

    3D Mesh segmentation has become an important research field in computer graphics during the past few decades. Many geometry based and semantic oriented approaches for 3D mesh segmentation has been presented. However, only a few algorithms based on Markov Random Field (MRF) has been presented for 3D object segmentation. In this letter, we present a definition of mesh segmentation according to the labeling problem. Inspired by the capability of MRF combining the geometric information and the topology information of a 3D mesh, we propose a novel 3D mesh segmentation model based on MRF and Graph Cuts. Experimental results show that our MRF-based schema achieves an effective segmentation.

  20. Voter model on the two-clique graph

    NASA Astrophysics Data System (ADS)

    Masuda, Naoki

    2014-07-01

    I examine the mean consensus time (i.e., exit time) of the voter model in the so-called two-clique graph. The two-clique graph is composed of two cliques interconnected by some links and considered as a toy model of networks with community structure or multilayer networks. I analytically show that, as the number of interclique links per node is varied, the mean consensus time experiences a crossover between a fast consensus regime [i.e., O (N)] and a slow consensus regime [i.e., O (N2)], where N is the number of nodes. The fast regime is consistent with the result for homogeneous well-mixed graphs such as the complete graph. The slow regime appears only when the entire network has O (1) interclique links. The present results suggest that the effect of community structure on the consensus time of the voter model is fairly limited.

  1. Voter model on the two-clique graph.

    PubMed

    Masuda, Naoki

    2014-07-01

    I examine the mean consensus time (i.e., exit time) of the voter model in the so-called two-clique graph. The two-clique graph is composed of two cliques interconnected by some links and considered as a toy model of networks with community structure or multilayer networks. I analytically show that, as the number of interclique links per node is varied, the mean consensus time experiences a crossover between a fast consensus regime [i.e., O(N)] and a slow consensus regime [i.e., O(N(2))], where N is the number of nodes. The fast regime is consistent with the result for homogeneous well-mixed graphs such as the complete graph. The slow regime appears only when the entire network has O(1) interclique links. The present results suggest that the effect of community structure on the consensus time of the voter model is fairly limited.

  2. The Replica Symmetric Solution for Potts Models on d-Regular Graphs

    NASA Astrophysics Data System (ADS)

    Dembo, Amir; Montanari, Andrea; Sly, Allan; Sun, Nike

    2014-04-01

    We establish an explicit formula for the limiting free energy density (log-partition function divided by the number of vertices) for ferromagnetic Potts models on uniformly sparse graph sequences converging locally to the d-regular tree for d even, covering all temperature regimes. This formula coincides with the Bethe free energy functional evaluated at a suitable fixed point of the belief propagation recursion on the d-regular tree, the so-called replica symmetric solution. For uniformly random d-regular graphs we further show that the replica symmetric Bethe formula is an upper bound for the asymptotic free energy for any model with permissive interactions.

  3. Phase Transitions for the Cavity Approach to the Clique Problem on Random Graphs

    NASA Astrophysics Data System (ADS)

    Gaudillière, Alexandre; Scoppola, Benedetto; Scoppola, Elisabetta; Viale, Massimiliano

    2011-12-01

    We give a rigorous proof of two phase transitions for a disordered statistical mechanics system used to define an algorithm to find large cliques inside Erdös random graphs. Such a system is a conservative probabilistic cellular automaton inspired by the cavity method originally introduced in spin glass theory.

  4. Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs

    SciTech Connect

    Aizenman, Michael; Warzel, Simone

    2012-09-15

    We discuss the dynamical implications of the recent proof that for a quantum particle in a random potential on a regular tree graph absolutely continuous (ac) spectrum occurs non-perturbatively through rare fluctuation-enabled resonances. The main result is spelled in the title.

  5. Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs

    NASA Astrophysics Data System (ADS)

    Aizenman, Michael; Warzel, Simone

    2012-09-01

    We discuss the dynamical implications of the recent proof that for a quantum particle in a random potential on a regular tree graph absolutely continuous (ac) spectrum occurs non-perturbatively through rare fluctuation-enabled resonances. The main result is spelled in the title.

  6. A graph-theoretic approach to modeling metabolic pathways

    NASA Astrophysics Data System (ADS)

    Gifford, Eric; Johnson, Mark; Tsai, Chun-che

    1991-08-01

    The metabolic pathways of medazepam, oxazepam, and diazepam were modeled using graph-theoretic transforms which are incorporable into computer-assisted metabolic analysis programs. The information, represented in the form of a graph-theoretic transform kit, which was obtained from these pathways was then used to predict the metabolites of other benzodiazepine compounds. The transform kits gave statistically significant predictions with respect to a statistical method for evaluating the performance of the transform kits.

  7. Termination of Multipartite Graph Series Arising from Complex Network Modelling

    NASA Astrophysics Data System (ADS)

    Latapy, Matthieu; Phan, Thi Ha Duong; Crespelle, Christophe; Nguyen, Thanh Qui

    An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs. However, this approach has, until now, severe limitations resulting from its incapacity to reproduce a key property of this object: the overlapping nature of cliques in complex networks. In order to get rid of these limitations we propose to encode the structure of clique overlaps in a network thanks to a process consisting in iteratively factorising the maximal bicliques between the upper level and the other levels of a multipartite graph. We show that the most natural definition of this factorising process leads to infinite series for some instances. Our main result is to design a restriction of this process that terminates for any arbitrary graph. Moreover, we show that the resulting multipartite graph has remarkable combinatorial properties and is closely related to another fundamental combinatorial object. Finally, we show that, in practice, this multipartite graph is computationally tractable and has a size that makes it suitable for complex network modelling.

  8. Spectra of random graphs with community structure and arbitrary degrees.

    PubMed

    Zhang, Xiao; Nadakuditi, Raj Rao; Newman, M E J

    2014-04-01

    Using methods from random matrix theory researchers have recently calculated the full spectra of random networks with arbitrary degrees and with community structure. Both reveal interesting spectral features, including deviations from the Wigner semicircle distribution and phase transitions in the spectra of community structured networks. In this paper we generalize both calculations, giving a prescription for calculating the spectrum of a network with both community structure and an arbitrary degree distribution. In general the spectrum has two parts, a continuous spectral band, which can depart strongly from the classic semicircle form, and a set of outlying eigenvalues that indicate the presence of communities.

  9. Bounding the Edge Cover Time of Random Walks on Graphs

    DTIC Science & Technology

    2011-07-21

    34. The Annals of Probability, Vol 16, No. 1, pp. 189-199, 1988. [21] Niels Erik N6rlund. Vorlesungen Uber Diffcrcnzenrechnung. New York, Chelsea, 1954...16, No. 1, pp. 189-199, 1988. [21] Niels Erik N6rlund. Voriesungen Uber Differenzenrcchnung. New York, Chelsea, 1954. [22] Prasad Tetali. "Random

  10. Intelligent diagnosis of jaundice with dynamic uncertain causality graph model.

    PubMed

    Hao, Shao-Rui; Geng, Shi-Chao; Fan, Lin-Xiao; Chen, Jia-Jia; Zhang, Qin; Li, Lan-Juan

    2017-05-01

    Jaundice is a common and complex clinical symptom potentially occurring in hepatology, general surgery, pediatrics, infectious diseases, gynecology, and obstetrics, and it is fairly difficult to distinguish the cause of jaundice in clinical practice, especially for general practitioners in less developed regions. With collaboration between physicians and artificial intelligence engineers, a comprehensive knowledge base relevant to jaundice was created based on demographic information, symptoms, physical signs, laboratory tests, imaging diagnosis, medical histories, and risk factors. Then a diagnostic modeling and reasoning system using the dynamic uncertain causality graph was proposed. A modularized modeling scheme was presented to reduce the complexity of model construction, providing multiple perspectives and arbitrary granularity for disease causality representations. A "chaining" inference algorithm and weighted logic operation mechanism were employed to guarantee the exactness and efficiency of diagnostic reasoning under situations of incomplete and uncertain information. Moreover, the causal interactions among diseases and symptoms intuitively demonstrated the reasoning process in a graphical manner. Verification was performed using 203 randomly pooled clinical cases, and the accuracy was 99.01% and 84.73%, respectively, with or without laboratory tests in the model. The solutions were more explicable and convincing than common methods such as Bayesian Networks, further increasing the objectivity of clinical decision-making. The promising results indicated that our model could be potentially used in intelligent diagnosis and help decrease public health expenditure.

  11. Intelligent diagnosis of jaundice with dynamic uncertain causality graph model*

    PubMed Central

    Hao, Shao-rui; Geng, Shi-chao; Fan, Lin-xiao; Chen, Jia-jia; Zhang, Qin; Li, Lan-juan

    2017-01-01

    Jaundice is a common and complex clinical symptom potentially occurring in hepatology, general surgery, pediatrics, infectious diseases, gynecology, and obstetrics, and it is fairly difficult to distinguish the cause of jaundice in clinical practice, especially for general practitioners in less developed regions. With collaboration between physicians and artificial intelligence engineers, a comprehensive knowledge base relevant to jaundice was created based on demographic information, symptoms, physical signs, laboratory tests, imaging diagnosis, medical histories, and risk factors. Then a diagnostic modeling and reasoning system using the dynamic uncertain causality graph was proposed. A modularized modeling scheme was presented to reduce the complexity of model construction, providing multiple perspectives and arbitrary granularity for disease causality representations. A “chaining” inference algorithm and weighted logic operation mechanism were employed to guarantee the exactness and efficiency of diagnostic reasoning under situations of incomplete and uncertain information. Moreover, the causal interactions among diseases and symptoms intuitively demonstrated the reasoning process in a graphical manner. Verification was performed using 203 randomly pooled clinical cases, and the accuracy was 99.01% and 84.73%, respectively, with or without laboratory tests in the model. The solutions were more explicable and convincing than common methods such as Bayesian Networks, further increasing the objectivity of clinical decision-making. The promising results indicated that our model could be potentially used in intelligent diagnosis and help decrease public health expenditure. PMID:28471111

  12. Exact epidemic models on graphs using graph-automorphism driven lumping.

    PubMed

    Simon, Péter L; Taylor, Michael; Kiss, Istvan Z

    2011-04-01

    The dynamics of disease transmission strongly depends on the properties of the population contact network. Pair-approximation models and individual-based network simulation have been used extensively to model contact networks with non-trivial properties. In this paper, using a continuous time Markov chain, we start from the exact formulation of a simple epidemic model on an arbitrary contact network and rigorously derive and prove some known results that were previously mainly justified based on some biological hypotheses. The main result of the paper is the illustration of the link between graph automorphisms and the process of lumping whereby the number of equations in a system of linear differential equations can be significantly reduced. The main advantage of lumping is that the simplified lumped system is not an approximation of the original system but rather an exact version of this. For a special class of graphs, we show how the lumped system can be obtained by using graph automorphisms. Finally, we discuss the advantages and possible applications of exact epidemic models and lumping.

  13. Statistical mechanics of random geometric graphs: Geometry-induced first-order phase transition.

    PubMed

    Ostilli, Massimo; Bianconi, Ginestra

    2015-04-01

    Random geometric graphs (RGGs) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables model and apply the resulting equations to RGGs. For any RGG, defined through a rigid or a soft geometric rule, the method reduces to a nontrivial satisfaction problem: Given N nodes, a domain D, and a desired average connectivity 〈k〉, find, if any, the distribution of nodes having support in D and average connectivity 〈k〉. We find out that, in the thermodynamic limit, nodes are either uniformly distributed or highly condensed in a small region, the two regimes being separated by a first-order phase transition characterized by a O(N) jump of 〈k〉. Other intermediate values of 〈k〉 correspond to very rare graph realizations. The phase transition is observed as a function of a parameter a∈[0,1] that tunes the underlying geometry. In particular, a=1 indicates a rigid geometry where only close nodes are connected, while a=0 indicates a rigid antigeometry where only distant nodes are connected. Consistently, when a=1/2 there is no geometry and no phase transition. After discussing the numerical analysis, we provide a combinatorial argument to fully explain the mechanism inducing this phase transition and recognize it as an easy-hard-easy transition. Our result shows that, in general, ad hoc optimized networks can hardly be designed, unless to rely to specific heterogeneous constructions, not necessarily scale free.

  14. Emergence of the giant weak component in directed random graphs with arbitrary degree distributions

    NASA Astrophysics Data System (ADS)

    Kryven, Ivan

    2016-07-01

    The weak component generalizes the idea of connected components to directed graphs. In this paper, an exact criterion for the existence of the giant weak component is derived for directed graphs with arbitrary bivariate degree distributions. In addition, we consider a random process for evolving directed graphs with bounded degrees. The bounds are not the same for different vertices but satisfy a predefined distribution. The analytic expression obtained for the evolving degree distribution is then combined with the weak-component criterion to obtain the exact time of the phase transition. The phase-transition time is obtained as a function of the distribution that bounds the degrees. Remarkably, when viewed from the step-polymerization formalism, the new results yield Flory-Stockmayer gelation theory and generalize it to a broader scope.

  15. Emergence of the giant weak component in directed random graphs with arbitrary degree distributions.

    PubMed

    Kryven, Ivan

    2016-07-01

    The weak component generalizes the idea of connected components to directed graphs. In this paper, an exact criterion for the existence of the giant weak component is derived for directed graphs with arbitrary bivariate degree distributions. In addition, we consider a random process for evolving directed graphs with bounded degrees. The bounds are not the same for different vertices but satisfy a predefined distribution. The analytic expression obtained for the evolving degree distribution is then combined with the weak-component criterion to obtain the exact time of the phase transition. The phase-transition time is obtained as a function of the distribution that bounds the degrees. Remarkably, when viewed from the step-polymerization formalism, the new results yield Flory-Stockmayer gelation theory and generalize it to a broader scope.

  16. Dynamic modeling of electrochemical systems using linear graph theory

    NASA Astrophysics Data System (ADS)

    Dao, Thanh-Son; McPhee, John

    An electrochemical cell is a multidisciplinary system which involves complex chemical, electrical, and thermodynamical processes. The primary objective of this paper is to develop a linear graph-theoretical modeling for the dynamic description of electrochemical systems through the representation of the system topologies. After a brief introduction to the topic and a review of linear graphs, an approach to develop linear graphs for electrochemical systems using a circuitry representation is discussed, followed in turn by the use of the branch and chord transformation techniques to generate final dynamic equations governing the system. As an example, the application of linear graph theory to modeling a nickel metal hydride (NiMH) battery will be presented. Results show that not only the number of equations are reduced significantly, but also the linear graph model simulates faster compared to the original lumped parameter model. The approach presented in this paper can be extended to modeling complex systems such as an electric or hybrid electric vehicle where a battery pack is interconnected with other components in many different domains.

  17. A maxent-stress model for graph layout.

    PubMed

    Gansner, Emden R; Hu, Yifan; North, Stephen

    2013-06-01

    In some applications of graph visualization, input edges have associated target lengths. Dealing with these lengths is a challenge, especially for large graphs. Stress models are often employed in this situation. However, the traditional full stress model is not scalable due to its reliance on an initial all-pairs shortest path calculation. A number of fast approximation algorithms have been proposed. While they work well for some graphs, the results are less satisfactory on graphs of intrinsically high dimension, because some nodes may be placed too close together, or even share the same position. We propose a solution, called the maxent-stress model, which applies the principle of maximum entropy to cope with the extra degrees of freedom. We describe a force-augmented stress majorization algorithm that solves the maxent-stress model. Numerical results show that the algorithm scales well, and provides acceptable layouts for large, nonrigid graphs. This also has potential applications to scalable algorithms for statistical multidimensional scaling (MDS) with variable distances.

  18. Stationary Random Metrics on Hierarchical Graphs Via {(min,+)}-type Recursive Distributional Equations

    NASA Astrophysics Data System (ADS)

    Khristoforov, Mikhail; Kleptsyn, Victor; Triestino, Michele

    2016-07-01

    This paper is inspired by the problem of understanding in a mathematical sense the Liouville quantum gravity on surfaces. Here we show how to define a stationary random metric on self-similar spaces which are the limit of nice finite graphs: these are the so-called hierarchical graphs. They possess a well-defined level structure and any level is built using a simple recursion. Stopping the construction at any finite level, we have a discrete random metric space when we set the edges to have random length (using a multiplicative cascade with fixed law {m}). We introduce a tool, the cut-off process, by means of which one finds that renormalizing the sequence of metrics by an exponential factor, they converge in law to a non-trivial metric on the limit space. Such limit law is stationary, in the sense that glueing together a certain number of copies of the random limit space, according to the combinatorics of the brick graph, the obtained random metric has the same law when rescaled by a random factor of law {m} . In other words, the stationary random metric is the solution of a distributional equation. When the measure m has continuous positive density on {mathbf{R}+}, the stationary law is unique up to rescaling and any other distribution tends to a rescaled stationary law under the iterations of the hierarchical transformation. We also investigate topological and geometric properties of the random space when m is log-normal, detecting a phase transition influenced by the branching random walk associated to the multiplicative cascade.

  19. Strong Scalability Study of Distributed Memory Parallel Markov Random Fields Using Graph Partitioning

    NASA Astrophysics Data System (ADS)

    Heinemann, Colleen

    Research in material science is increasingly reliant on image-based data from experiments, demanding construction of new analysis tools that help scientists discover information from digital images. Because there is such a wide variety of materials and image modalities, detecting different compounds from imaged materials continues to be a challenging task. A vast collection of algorithms for filtering, image segmentation, and texture description have facilitated and improved accuracy for sample measurements (see Chapter 1 Introduction and Literature Review). Despite this, the community still lacks scalable, general purpose, easily configurable image analysis frameworks that allow pattern detection on different imaging modalities across multiple scales. The need for such a framework was the motivation behind the development of a distributed-memory parallel Markov Random Field based framework. Markov Random Field (MRF) algorithms provide the ability to explore contextual information about a given dataset. Given the complexity of such algorithms, however, they are limited by performance when running serial. Thus, running in some sort of parallel fashion is necessary. The effects are twofold. Not only does running the MRF algorithm in parallel provide the ability to run current datasets faster and more efficiently, it also provides the ability for datasets to continue to grow in size and still be able to be run with such frameworks. The variation of the Markov Random Field algorithm utilized in this study first oversegments the given input image and constructs a graph model based on photometric and geometric distances. Next, the resulting graph model is refactored specifically into the MRF model to target image segmentation. Finally, a distributed approach is used for the optimization process to obtain the best labeling for the graph, which is essentially the goal of using a MRF algorithm. Given the concept of using a distributed memory parallel framework, specifically

  20. Monadic structures over an ordered universal random graph and finite automata

    NASA Astrophysics Data System (ADS)

    Dudakov, Sergey M.

    2011-10-01

    We continue the investigation of the expressive power of the language of predicate logic for finite algebraic systems embedded in infinite systems. This investigation stems from papers of M. A. Taitslin, M. Benedikt and L. Libkin, among others. We study the properties of a finite monadic system which can be expressed by formulae if such a system is embedded in a random graph that is totally ordered in an arbitrary way. The Büchi representation is used to connect monadic structures and formal languages. It is shown that, if one restricts attention to formulae that are -invariant in totally ordered random graphs, then these formulae correspond to finite automata. We show that =-invariant formulae expressing the properties of the embedded system itself can express only Boolean combinations of properties of the form `the cardinality of an intersection of one-place predicates belongs to one of finitely many fixed finite or infinite arithmetic progressions'.

  1. Random Walk Graph Laplacian-Based Smoothness Prior for Soft Decoding of JPEG Images.

    PubMed

    Liu, Xianming; Cheung, Gene; Wu, Xiaolin; Zhao, Debin

    2017-02-01

    Given the prevalence of joint photographic experts group (JPEG) compressed images, optimizing image reconstruction from the compressed format remains an important problem. Instead of simply reconstructing a pixel block from the centers of indexed discrete cosine transform (DCT) coefficient quantization bins (hard decoding), soft decoding reconstructs a block by selecting appropriate coefficient values within the indexed bins with the help of signal priors. The challenge thus lies in how to define suitable priors and apply them effectively. In this paper, we combine three image priors-Laplacian prior for DCT coefficients, sparsity prior, and graph-signal smoothness prior for image patches-to construct an efficient JPEG soft decoding algorithm. Specifically, we first use the Laplacian prior to compute a minimum mean square error initial solution for each code block. Next, we show that while the sparsity prior can reduce block artifacts, limiting the size of the overcomplete dictionary (to lower computation) would lead to poor recovery of high DCT frequencies. To alleviate this problem, we design a new graph-signal smoothness prior (desired signal has mainly low graph frequencies) based on the left eigenvectors of the random walk graph Laplacian matrix (LERaG). Compared with the previous graph-signal smoothness priors, LERaG has desirable image filtering properties with low computation overhead. We demonstrate how LERaG can facilitate recovery of high DCT frequencies of a piecewise smooth signal via an interpretation of low graph frequency components as relaxed solutions to normalized cut in spectral clustering. Finally, we construct a soft decoding algorithm using the three signal priors with appropriate prior weights. Experimental results show that our proposal outperforms the state-of-the-art soft decoding algorithms in both objective and subjective evaluations noticeably.

  2. Random Walk Graph Laplacian-Based Smoothness Prior for Soft Decoding of JPEG Images

    NASA Astrophysics Data System (ADS)

    Liu, Xianming; Cheung, Gene; Wu, Xiaolin; Zhao, Debin

    2017-02-01

    Given the prevalence of JPEG compressed images, optimizing image reconstruction from the compressed format remains an important problem. Instead of simply reconstructing a pixel block from the centers of indexed DCT coefficient quantization bins (hard decoding), soft decoding reconstructs a block by selecting appropriate coefficient values within the indexed bins with the help of signal priors. The challenge thus lies in how to define suitable priors and apply them effectively. In this paper, we combine three image priors---Laplacian prior for DCT coefficients, sparsity prior and graph-signal smoothness prior for image patches---to construct an efficient JPEG soft decoding algorithm. Specifically, we first use the Laplacian prior to compute a minimum mean square error (MMSE) initial solution for each code block. Next, we show that while the sparsity prior can reduce block artifacts, limiting the size of the over-complete dictionary (to lower computation) would lead to poor recovery of high DCT frequencies. To alleviate this problem, we design a new graph-signal smoothness prior (desired signal has mainly low graph frequencies) based on the left eigenvectors of the random walk graph Laplacian matrix (LERaG). Compared to previous graph-signal smoothness priors, LERaG has desirable image filtering properties with low computation overhead. We demonstrate how LERaG can facilitate recovery of high DCT frequencies of a piecewise smooth (PWS) signal via an interpretation of low graph frequency components as relaxed solutions to normalized cut in spectral clustering. Finally, we construct a soft decoding algorithm using the three signal priors with appropriate prior weights. Experimental results show that our proposal outperforms state-of-the-art soft decoding algorithms in both objective and subjective evaluations noticeably.

  3. The Edge-Disjoint Path Problem on Random Graphs by Message-Passing

    PubMed Central

    2015-01-01

    We present a message-passing algorithm to solve a series of edge-disjoint path problems on graphs based on the zero-temperature cavity equations. Edge-disjoint paths problems are important in the general context of routing, that can be defined by incorporating under a unique framework both traffic optimization and total path length minimization. The computation of the cavity equations can be performed efficiently by exploiting a mapping of a generalized edge-disjoint path problem on a star graph onto a weighted maximum matching problem. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behavior of both the number of paths to be accommodated and their minimum total length. PMID:26710102

  4. A Graph Theory Practice on Transformed Image: A Random Image Steganography

    PubMed Central

    Thanikaiselvan, V.; Arulmozhivarman, P.; Subashanthini, S.; Amirtharajan, Rengarajan

    2013-01-01

    Modern day information age is enriched with the advanced network communication expertise but unfortunately at the same time encounters infinite security issues when dealing with secret and/or private information. The storage and transmission of the secret information become highly essential and have led to a deluge of research in this field. In this paper, an optimistic effort has been taken to combine graceful graph along with integer wavelet transform (IWT) to implement random image steganography for secure communication. The implementation part begins with the conversion of cover image into wavelet coefficients through IWT and is followed by embedding secret image in the randomly selected coefficients through graph theory. Finally stegoimage is obtained by applying inverse IWT. This method provides a maximum of 44 dB peak signal to noise ratio (PSNR) for 266646 bits. Thus, the proposed method gives high imperceptibility through high PSNR value and high embedding capacity in the cover image due to adaptive embedding scheme and high robustness against blind attack through graph theoretic random selection of coefficients. PMID:24453857

  5. A graph theory practice on transformed image: a random image steganography.

    PubMed

    Thanikaiselvan, V; Arulmozhivarman, P; Subashanthini, S; Amirtharajan, Rengarajan

    2013-01-01

    Modern day information age is enriched with the advanced network communication expertise but unfortunately at the same time encounters infinite security issues when dealing with secret and/or private information. The storage and transmission of the secret information become highly essential and have led to a deluge of research in this field. In this paper, an optimistic effort has been taken to combine graceful graph along with integer wavelet transform (IWT) to implement random image steganography for secure communication. The implementation part begins with the conversion of cover image into wavelet coefficients through IWT and is followed by embedding secret image in the randomly selected coefficients through graph theory. Finally stegoimage is obtained by applying inverse IWT. This method provides a maximum of 44 dB peak signal to noise ratio (PSNR) for 266646 bits. Thus, the proposed method gives high imperceptibility through high PSNR value and high embedding capacity in the cover image due to adaptive embedding scheme and high robustness against blind attack through graph theoretic random selection of coefficients.

  6. Vulnerability of networks: Fractional percolation on random graphs

    NASA Astrophysics Data System (ADS)

    Shang, Yilun

    2014-01-01

    We present a theoretical framework for understanding nonbinary, nonindependent percolation on networks with general degree distributions. The model incorporates a partially functional (PF) state of nodes so that both intensity and extensity of error are characterized. Two connected nodes in a PF state cannot sustain the load and therefore break their link. We give exact solutions for the percolation threshold, the fraction of giant cluster, and the mean size of small clusters. The robustness-fragility transition point for scale-free networks with a degree distribution pk∝k-α is identified to be α =3. The analysis reveals that scale-free networks are vulnerable to targeted attack at hubs: a more complete picture of their Achilles' heel turns out to be not only the hubs themselves but also the edges linking them together.

  7. NewGOA: predicting new GO annotations of proteins by bi-random walks on a hybrid graph.

    PubMed

    Yu, Guoxian; Fu, Guangyuan; Wang, Jun; Zhao, Yingwen

    2017-06-15

    A remaining key challenge of modern biology is annotating the functional roles of proteins. Various computational models have been proposed for this challenge. Most of them assume the annotations of annotated proteins are complete. But in fact, many of them are incomplete. We proposed a method called NewGOA to predict new Gene Ontology (GO) annotations for incompletely annotated proteins and for completely un-annotated ones. NewGOA employs a hybrid graph, composed of two types of nodes (proteins and GO terms), to encode interactions between proteins, hierarchical relationships between terms and available annotations of proteins. To account for structural difference between the terms subgraph and the proteins subgraph, NewGOA applies a bi-random walks algorithm, which executes asynchronous random walks on the hybrid graph, to predict new GO annotations of proteins. Experimental study on archived GO annotations of two model species (H. Sapiens and S. cerevisiae) shows that NewGOA can more accurately and efficiently predict new annotations of proteins than other related methods. Experimental results also indicate the bi-random walks can explore and further exploit the structural difference between terms subgraph and proteins subgraph. The supplementary files and codes of NewGOA are available at: http://mlda.swu.edu.cn/codes.php?name=NewGO.

  8. An approach to multiscale modelling with graph grammars

    PubMed Central

    Ong, Yongzhi; Streit, Katarína; Henke, Michael; Kurth, Winfried

    2014-01-01

    Background and Aims Functional–structural plant models (FSPMs) simulate biological processes at different spatial scales. Methods exist for multiscale data representation and modification, but the advantages of using multiple scales in the dynamic aspects of FSPMs remain unclear. Results from multiscale models in various other areas of science that share fundamental modelling issues with FSPMs suggest that potential advantages do exist, and this study therefore aims to introduce an approach to multiscale modelling in FSPMs. Methods A three-part graph data structure and grammar is revisited, and presented with a conceptual framework for multiscale modelling. The framework is used for identifying roles, categorizing and describing scale-to-scale interactions, thus allowing alternative approaches to model development as opposed to correlation-based modelling at a single scale. Reverse information flow (from macro- to micro-scale) is catered for in the framework. The methods are implemented within the programming language XL. Key Results Three example models are implemented using the proposed multiscale graph model and framework. The first illustrates the fundamental usage of the graph data structure and grammar, the second uses probabilistic modelling for organs at the fine scale in order to derive crown growth, and the third combines multiscale plant topology with ozone trends and metabolic network simulations in order to model juvenile beech stands under exposure to a toxic trace gas. Conclusions The graph data structure supports data representation and grammar operations at multiple scales. The results demonstrate that multiscale modelling is a viable method in FSPM and an alternative to correlation-based modelling. Advantages and disadvantages of multiscale modelling are illustrated by comparisons with single-scale implementations, leading to motivations for further research in sensitivity analysis and run-time efficiency for these models. PMID:25134929

  9. An approach to multiscale modelling with graph grammars.

    PubMed

    Ong, Yongzhi; Streit, Katarína; Henke, Michael; Kurth, Winfried

    2014-09-01

    Functional-structural plant models (FSPMs) simulate biological processes at different spatial scales. Methods exist for multiscale data representation and modification, but the advantages of using multiple scales in the dynamic aspects of FSPMs remain unclear. Results from multiscale models in various other areas of science that share fundamental modelling issues with FSPMs suggest that potential advantages do exist, and this study therefore aims to introduce an approach to multiscale modelling in FSPMs. A three-part graph data structure and grammar is revisited, and presented with a conceptual framework for multiscale modelling. The framework is used for identifying roles, categorizing and describing scale-to-scale interactions, thus allowing alternative approaches to model development as opposed to correlation-based modelling at a single scale. Reverse information flow (from macro- to micro-scale) is catered for in the framework. The methods are implemented within the programming language XL. Three example models are implemented using the proposed multiscale graph model and framework. The first illustrates the fundamental usage of the graph data structure and grammar, the second uses probabilistic modelling for organs at the fine scale in order to derive crown growth, and the third combines multiscale plant topology with ozone trends and metabolic network simulations in order to model juvenile beech stands under exposure to a toxic trace gas. The graph data structure supports data representation and grammar operations at multiple scales. The results demonstrate that multiscale modelling is a viable method in FSPM and an alternative to correlation-based modelling. Advantages and disadvantages of multiscale modelling are illustrated by comparisons with single-scale implementations, leading to motivations for further research in sensitivity analysis and run-time efficiency for these models.

  10. GraphCrunch 2: Software tool for network modeling, alignment and clustering

    PubMed Central

    2011-01-01

    Background Recent advancements in experimental biotechnology have produced large amounts of protein-protein interaction (PPI) data. The topology of PPI networks is believed to have a strong link to their function. Hence, the abundance of PPI data for many organisms stimulates the development of computational techniques for the modeling, comparison, alignment, and clustering of networks. In addition, finding representative models for PPI networks will improve our understanding of the cell just as a model of gravity has helped us understand planetary motion. To decide if a model is representative, we need quantitative comparisons of model networks to real ones. However, exact network comparison is computationally intractable and therefore several heuristics have been used instead. Some of these heuristics are easily computable "network properties," such as the degree distribution, or the clustering coefficient. An important special case of network comparison is the network alignment problem. Analogous to sequence alignment, this problem asks to find the "best" mapping between regions in two networks. It is expected that network alignment might have as strong an impact on our understanding of biology as sequence alignment has had. Topology-based clustering of nodes in PPI networks is another example of an important network analysis problem that can uncover relationships between interaction patterns and phenotype. Results We introduce the GraphCrunch 2 software tool, which addresses these problems. It is a significant extension of GraphCrunch which implements the most popular random network models and compares them with the data networks with respect to many network properties. Also, GraphCrunch 2 implements the GRAph ALigner algorithm ("GRAAL") for purely topological network alignment. GRAAL can align any pair of networks and exposes large, dense, contiguous regions of topological and functional similarities far larger than any other existing tool. Finally, Graph

  11. Pointwise approach for change detection between synthetic aperture radar images using bilaterally weighted graph and irregular Markov random field

    NASA Astrophysics Data System (ADS)

    Wang, Jun; Yang, Xuezhi; Jia, Lu; Zhou, Fang; Ai, Jiaqiu

    2017-04-01

    The problem of change detection in bitemporal synthetic aperture radar (SAR) images is studied. Motivated by utilizing nondense neighborhoods around pixels to detect the change level, a pointwise change detection approach is developed by employing a bilaterally weighted graph model and an irregular Markov random field (I-MRF). First, keypoints with local maximum intensity are extracted from one of the bitemporal images to describe the textural information of the images. Then, two bilaterally weighted graphs with the same topology are constructed for the bitemporal images using the keypoints, respectively. They utilize both the spatial structural and intensity information to provide good performance for feature-based change detection. Next, a change measure function is designed to evaluate the similarity between the graphs, and then the nondense difference image (NDI) is generated. Finally, an I-MRF with a generalized neighborhood system is proposed to classify the discrete keypoints on the NDI. Experiments on real SAR images show that the proposed NDI improves separability between changed and unchanged areas, and I-MRF provides high accuracy and strong noise immunity for change detection tasks with noise-contaminated SAR images. On the whole, the proposed approach is a good candidate for SAR image change detection.

  12. Independence numbers and chromatic numbers of the random subgraphs of some distance graphs

    NASA Astrophysics Data System (ADS)

    Bogolubsky, L. I.; Gusev, A. S.; Pyaderkin, M. M.; Raigorodskii, A. M.

    2015-10-01

    This work is concerned with the Nelson-Hadwiger classical problem of finding the chromatic numbers of distance graphs in ℝn. Most consideration is given to the class of graphs G(n, r, s)= (V(n, r), E(n, r, s)) defined as follows: \\displaystyle V(n, r)=\\bigl\\{\\mathbf{x}=(x_1,\\dots,x_n) : x_i\\in\\{0, 1\\}, x_1+\\dots+x_n=r\\bigr\\},//\\displaystyle E(n, r, s)=\\bigl\\{\\{\\mathbf{x}, \\mathbf{y}: (\\mathbf{x}, \\mathbf{y})=s\\}\\bigr\\}, where (x, y) is the Euclidean inner product. In particular, the chromatic number of G(n, 3, 1) was recently found by Balogh, Kostochka and Raigorodskii. The objects of the study are the random subgraphs 𝒢(G(n, r, s), p) whose edges are independently taken from the set E(n, r, s), each with probability p. The independence number and the chromatic number of such graphs are estimated both from below and from above. In the case when r - s is a prime power and r <= 2s + 1, the order of growth of α(𝒢(G(n, r, s), p)) and χ(𝒢(G(n, r, s), p)) is established. Bibliography: 51 titles.

  13. Modeling Traffic on the Web Graph

    NASA Astrophysics Data System (ADS)

    Meiss, Mark R.; Gonçalves, Bruno; Ramasco, José J.; Flammini, Alessandro; Menczer, Filippo

    Analysis of aggregate and individual Web requests shows that PageRank is a poor predictor of traffic. We use empirical data to characterize properties of Web traffic not reproduced by Markovian models, including both aggregate statistics such as page and link traffic, and individual statistics such as entropy and session size. As no current model reconciles all of these observations, we present an agent-based model that explains them through realistic browsing behaviors: (1) revisiting bookmarked pages; (2) backtracking; and (3) seeking out novel pages of topical interest. The resulting model can reproduce the behaviors we observe in empirical data, especially heterogeneous session lengths, reconciling the narrowly focused browsing patterns of individual users with the extreme variance in aggregate traffic measurements. We can thereby identify a few salient features that are necessary and sufficient to interpret Web traffic data. Beyond the descriptive and explanatory power of our model, these results may lead to improvements in Web applications such as search and crawling.

  14. Model validation of simple-graph representations of metabolism

    PubMed Central

    Holme, Petter

    2009-01-01

    The large-scale properties of chemical reaction systems, such as metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information, lists of chemical reactions, available in databases. Even for the simplest type of graph representation, this reduction can be done in several ways. We investigate different simple network representations by testing how well they encode information about one biologically important network structure—network modularity (the propensity for edges to be clustered into dense groups that are sparsely connected between each other). To achieve this goal, we design a model of reaction systems where network modularity can be controlled and measure how well the reduction to simple graphs captures the modular structure of the model reaction system. We find that the network types that best capture the modular structure of the reaction system are substrate–product networks (where substrates are linked to products of a reaction) and substance networks (with edges between all substances participating in a reaction). Furthermore, we argue that the proposed model for reaction systems with tunable clustering is a general framework for studies of how reaction systems are affected by modularity. To this end, we investigate statistical properties of the model and find, among other things, that it recreates correlations between degree and mass of the molecules. PMID:19158012

  15. Multidimensional Dataflow Graph Modeling and Mapping for Efficient GPU Implementation

    DTIC Science & Technology

    2012-10-01

    design space exploration. Index Terms— Dataflow graph, multidimensional syn- chronous dataflow, graphics processing unit, integral his- togram. 1 ...with audio and video data stream pro- cessing, digital communications, and image processing (e.g., see [ 1 ]). Dataflow provides a formal mechanism for de...well as support for efficient scheduling and buffer size optimization [ 1 ]. However, the SDF model is well suited only for one-dimensional DSP

  16. Graph's Topology and Free Energy of a Spin Model on the Graph

    NASA Astrophysics Data System (ADS)

    Choi, Jeong-Mo; Gilson, Amy I.; Shakhnovich, Eugene I.

    2017-02-01

    In this Letter we investigate a direct relationship between a graph's topology and the free energy of a spin system on the graph. We develop a method of separating topological and energetic contributions to the free energy, and find that considering the topology is sufficient to qualitatively compare the free energies of different graph systems at high temperature, even when the energetics are not fully known. This method was applied to the metal lattice system with defects, and we found that it partially explains why point defects are more stable than high-dimensional defects. Given the energetics, we can even quantitatively compare free energies of different graph structures via a closed form of linear graph contributions. The closed form is applied to predict the sequence-space free energy of lattice proteins, which is a key factor determining the designability of a protein structure.

  17. Centrifuge Rotor Models: A Comparison of the Euler-Lagrange and the Bond Graph Modeling Approach

    NASA Technical Reports Server (NTRS)

    Granda, Jose J.; Ramakrishnan, Jayant; Nguyen, Louis H.

    2006-01-01

    A viewgraph presentation on centrifuge rotor models with a comparison using Euler-Lagrange and bond graph methods is shown. The topics include: 1) Objectives; 2) MOdeling Approach Comparisons; 3) Model Structures; and 4) Application.

  18. Heuristic-driven graph wavelet modeling of complex terrain

    NASA Astrophysics Data System (ADS)

    Cioacǎ, Teodor; Dumitrescu, Bogdan; Stupariu, Mihai-Sorin; Pǎtru-Stupariu, Ileana; Nǎpǎrus, Magdalena; Stoicescu, Ioana; Peringer, Alexander; Buttler, Alexandre; Golay, François

    2015-03-01

    We present a novel method for building a multi-resolution representation of large digital surface models. The surface points coincide with the nodes of a planar graph which can be processed using a critically sampled, invertible lifting scheme. To drive the lazy wavelet node partitioning, we employ an attribute aware cost function based on the generalized quadric error metric. The resulting algorithm can be applied to multivariate data by storing additional attributes at the graph's nodes. We discuss how the cost computation mechanism can be coupled with the lifting scheme and examine the results by evaluating the root mean square error. The algorithm is experimentally tested using two multivariate LiDAR sets representing terrain surface and vegetation structure with different sampling densities.

  19. A study of physician collaborations through social network and exponential random graph

    PubMed Central

    2013-01-01

    Background Physician collaboration, which evolves among physicians during the course of providing healthcare services to hospitalised patients, has been seen crucial to effective patient outcomes in healthcare organisations and hospitals. This study aims to explore physician collaborations using measures of social network analysis (SNA) and exponential random graph (ERG) model. Methods Based on the underlying assumption that collaborations evolve among physicians when they visit a common hospitalised patient, this study first proposes an approach to map collaboration network among physicians from the details of their visits to patients. This paper terms this network as physician collaboration network (PCN). Second, SNA measures of degree centralisation, betweenness centralisation and density are used to examine the impact of SNA measures on hospitalisation cost and readmission rate. As a control variable, the impact of patient age on the relation between network measures (i.e. degree centralisation, betweenness centralisation and density) and hospital outcome variables (i.e. hospitalisation cost and readmission rate) are also explored. Finally, ERG models are developed to identify micro-level structural properties of (i) high-cost versus low-cost PCN; and (ii) high-readmission rate versus low-readmission rate PCN. An electronic health insurance claim dataset of a very large Australian health insurance organisation is utilised to construct and explore PCN in this study. Results It is revealed that the density of PCN is positively correlated with hospitalisation cost and readmission rate. In contrast, betweenness centralisation is found negatively correlated with hospitalisation cost and readmission rate. Degree centralisation shows a negative correlation with readmission rate, but does not show any correlation with hospitalisation cost. Patient age does not have any impact for the relation of SNA measures with hospitalisation cost and hospital readmission rate. The

  20. A novel 3D graph cut based co-segmentation of lung tumor on PET-CT images with Gaussian mixture models

    NASA Astrophysics Data System (ADS)

    Yu, Kai; Chen, Xinjian; Shi, Fei; Zhu, Weifang; Zhang, Bin; Xiang, Dehui

    2016-03-01

    Positron Emission Tomography (PET) and Computed Tomography (CT) have been widely used in clinical practice for radiation therapy. Most existing methods only used one image modality, either PET or CT, which suffers from the low spatial resolution in PET or low contrast in CT. In this paper, a novel 3D graph cut method is proposed, which integrated Gaussian Mixture Models (GMMs) into the graph cut method. We also employed the random walk method as an initialization step to provide object seeds for the improvement of the graph cut based segmentation on PET and CT images. The constructed graph consists of two sub-graphs and a special link between the sub-graphs which penalize the difference segmentation between the two modalities. Finally, the segmentation problem is solved by the max-flow/min-cut method. The proposed method was tested on 20 patients' PET-CT images, and the experimental results demonstrated the accuracy and efficiency of the proposed algorithm.

  1. Gaussian covariance graph models accounting for correlated marker effects in genome-wide prediction.

    PubMed

    Martínez, C A; Khare, K; Rahman, S; Elzo, M A

    2017-10-01

    Several statistical models used in genome-wide prediction assume uncorrelated marker allele substitution effects, but it is known that these effects may be correlated. In statistics, graphical models have been identified as a useful tool for covariance estimation in high-dimensional problems and it is an area that has recently experienced a great expansion. In Gaussian covariance graph models (GCovGM), the joint distribution of a set of random variables is assumed to be Gaussian and the pattern of zeros of the covariance matrix is encoded in terms of an undirected graph G. In this study, methods adapting the theory of GCovGM to genome-wide prediction were developed (Bayes GCov, Bayes GCov-KR and Bayes GCov-H). In simulated data sets, improvements in correlation between phenotypes and predicted breeding values and accuracies of predicted breeding values were found. Our models account for correlation of marker effects and permit to accommodate general structures as opposed to models proposed in previous studies, which consider spatial correlation only. In addition, they allow incorporation of biological information in the prediction process through its use when constructing graph G, and their extension to the multi-allelic loci case is straightforward. © 2017 Blackwell Verlag GmbH.

  2. Graph theoretic modeling of large-scale semantic networks.

    PubMed

    Bales, Michael E; Johnson, Stephen B

    2006-08-01

    During the past several years, social network analysis methods have been used to model many complex real-world phenomena, including social networks, transportation networks, and the Internet. Graph theoretic methods, based on an elegant representation of entities and relationships, have been used in computational biology to study biological networks; however they have not yet been adopted widely by the greater informatics community. The graphs produced are generally large, sparse, and complex, and share common global topological properties. In this review of research (1998-2005) on large-scale semantic networks, we used a tailored search strategy to identify articles involving both a graph theoretic perspective and semantic information. Thirty-one relevant articles were retrieved. The majority (28, 90.3%) involved an investigation of a real-world network. These included corpora, thesauri, dictionaries, large computer programs, biological neuronal networks, word association networks, and files on the Internet. Twenty-two of the 28 (78.6%) involved a graph comprised of words or phrases. Fifteen of the 28 (53.6%) mentioned evidence of small-world characteristics in the network investigated. Eleven (39.3%) reported a scale-free topology, which tends to have a similar appearance when examined at varying scales. The results of this review indicate that networks generated from natural language have topological properties common to other natural phenomena. It has not yet been determined whether artificial human-curated terminology systems in biomedicine share these properties. Large network analysis methods have potential application in a variety of areas of informatics, such as in development of controlled vocabularies and for characterizing a given domain.

  3. Enhanced Contact Graph Routing (ECGR) MACHETE Simulation Model

    NASA Technical Reports Server (NTRS)

    Segui, John S.; Jennings, Esther H.; Clare, Loren P.

    2013-01-01

    Contact Graph Routing (CGR) for Delay/Disruption Tolerant Networking (DTN) space-based networks makes use of the predictable nature of node contacts to make real-time routing decisions given unpredictable traffic patterns. The contact graph will have been disseminated to all nodes before the start of route computation. CGR was designed for space-based networking environments where future contact plans are known or are independently computable (e.g., using known orbital dynamics). For each data item (known as a bundle in DTN), a node independently performs route selection by examining possible paths to the destination. Route computation could conceivably run thousands of times a second, so computational load is important. This work refers to the simulation software model of Enhanced Contact Graph Routing (ECGR) for DTN Bundle Protocol in JPL's MACHETE simulation tool. The simulation model was used for performance analysis of CGR and led to several performance enhancements. The simulation model was used to demonstrate the improvements of ECGR over CGR as well as other routing methods in space network scenarios. ECGR moved to using earliest arrival time because it is a global monotonically increasing metric that guarantees the safety properties needed for the solution's correctness since route re-computation occurs at each node to accommodate unpredicted changes (e.g., traffic pattern, link quality). Furthermore, using earliest arrival time enabled the use of the standard Dijkstra algorithm for path selection. The Dijkstra algorithm for path selection has a well-known inexpensive computational cost. These enhancements have been integrated into the open source CGR implementation. The ECGR model is also useful for route metric experimentation and comparisons with other DTN routing protocols particularly when combined with MACHETE's space networking models and Delay Tolerant Link State Routing (DTLSR) model.

  4. Exact Potts model partition functions on ladder graphs

    NASA Astrophysics Data System (ADS)

    Shrock, Robert

    2000-08-01

    We present exact calculations of the partition function Z of the q-state Potts model and its generalization to real q, for arbitrary temperature on n-vertex ladder graphs, i.e., strips of the square lattice with width Ly=2 and arbitrary length Lx, with free, cyclic, and Möbius longitudinal boundary conditions. These partition functions are equivalent to Tutte/Whitney polynomials for these graphs. The free energy is calculated exactly for the infinite-length limit of these ladder graphs and the thermodynamics is discussed. By comparison with strip graphs of other widths, we analyze how the singularities at the zero-temperature critical point of the ferromagnet on infinite-length, finite-width strips depend on the width. We point out and study the following noncommutativity at certain special values q s: lim n→∞ limq→q s Z 1/n≠ limq→q s limn→∞ Z 1/n. It is shown that the Potts antiferromagnet on both the infinite-length line and ladder graphs with cyclic or Möbius boundary conditions exhibits a phase transition at finite temperature if 0< q<2, but with unphysical properties, including negative specific heat and non-existence, in the low-temperature phase, of an n→∞ limit for thermodynamic functions that is independent of boundary conditions. Considering the full generalization to arbitrary complex q and temperature, we determine the singular locus B in the corresponding C2 space, arising as the accumulation set of partition function zeros as n→∞. In particular, we study the connection with the T=0 limit of the Potts antiferromagnet where B reduces to the accumulation set of chromatic zeros. Certain properties of the complex-temperature phase diagrams are shown to exhibit close connections with those of the model on the square lattice, showing that exact solutions on infinite-length strips provide a way of gaining insight into these complex-temperature phase diagrams.

  5. Some generalisations of linear-graph modelling for dynamic systems

    NASA Astrophysics Data System (ADS)

    de Silva, Clarence W.; Pourazadi, Shahram

    2013-11-01

    Proper modelling of a dynamic system can benefit analysis, simulation, design, evaluation and control of the system. The linear-graph (LG) approach is suitable for modelling lumped-parameter dynamic systems. By using the concepts of graph trees, it provides a graphical representation of the system, with a direct correspondence to the physical component topology. This paper systematically extends the application of LGs to multi-domain (mixed-domain or multi-physics) dynamic systems by presenting a unified way to represent different domains - mechanical, electrical, thermal and fluid. Preservation of the structural correspondence across domains is a particular advantage of LGs when modelling mixed-domain systems. The generalisation of Thevenin and Norton equivalent circuits to mixed-domain systems, using LGs, is presented. The structure of an LG model may follow a specific pattern. Vector LGs are introduced to take advantage of such patterns, giving a general LG representation for them. Through these vector LGs, the model representation becomes simpler and rather compact, both topologically and parametrically. A new single LG element is defined to facilitate the modelling of distributed-parameter (DP) systems. Examples are presented using multi-domain systems (a motion-control system and a flow-controlled pump), a multi-body mechanical system (robot manipulator) and DP systems (structural rods) to illustrate the application and advantages of the methodologies developed in the paper.

  6. O( N) Random Tensor Models

    NASA Astrophysics Data System (ADS)

    Carrozza, Sylvain; Tanasa, Adrian

    2016-11-01

    We define in this paper a class of three-index tensor models, endowed with {O(N)^{⊗ 3}} invariance ( N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the U( N) invariant models. We first exhibit the existence of a large N expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.

  7. Random Walk and Graph Cut for Co-Segmentation of Lung Tumor on PET-CT Images.

    PubMed

    Ju, Wei; Xiang, Dehui; Xiang, Deihui; Zhang, Bin; Wang, Lirong; Kopriva, Ivica; Chen, Xinjian

    2015-12-01

    Accurate lung tumor delineation plays an important role in radiotherapy treatment planning. Since the lung tumor has poor boundary in positron emission tomography (PET) images and low contrast in computed tomography (CT) images, segmentation of tumor in the PET and CT images is a challenging task. In this paper, we effectively integrate the two modalities by making fully use of the superior contrast of PET images and superior spatial resolution of CT images. Random walk and graph cut method is integrated to solve the segmentation problem, in which random walk is utilized as an initialization tool to provide object seeds for graph cut segmentation on the PET and CT images. The co-segmentation problem is formulated as an energy minimization problem which is solved by max-flow/min-cut method. A graph, including two sub-graphs and a special link, is constructed, in which one sub-graph is for the PET and another is for CT, and the special link encodes a context term which penalizes the difference of the tumor segmentation on the two modalities. To fully utilize the characteristics of PET and CT images, a novel energy representation is devised. For the PET, a downhill cost and a 3D derivative cost are proposed. For the CT, a shape penalty cost is integrated into the energy function which helps to constrain the tumor region during the segmentation. We validate our algorithm on a data set which consists of 18 PET-CT images. The experimental results indicate that the proposed method is superior to the graph cut method solely using the PET or CT is more accurate compared with the random walk method, random walk co-segmentation method, and non-improved graph cut method.

  8. Identifying the minor set cover of dense connected bipartite graphs via random matching edge sets

    NASA Astrophysics Data System (ADS)

    Hamilton, Kathleen E.; Humble, Travis S.

    2017-04-01

    Using quantum annealing to solve an optimization problem requires minor embedding a logic graph into a known hardware graph. In an effort to reduce the complexity of the minor embedding problem, we introduce the minor set cover (MSC) of a known graph G: a subset of graph minors which contain any remaining minor of the graph as a subgraph. Any graph that can be embedded into G will be embeddable into a member of the MSC. Focusing on embedding into the hardware graph of commercially available quantum annealers, we establish the MSC for a particular known virtual hardware, which is a complete bipartite graph. We show that the complete bipartite graph K_{N,N} has a MSC of N minors, from which K_{N+1} is identified as the largest clique minor of K_{N,N}. The case of determining the largest clique minor of hardware with faults is briefly discussed but remains an open question.

  9. Identifying the minor set cover of dense connected bipartite graphs via random matching edge sets

    DOE PAGES

    Hamilton, Kathleen E.; Humble, Travis S.

    2017-02-23

    Using quantum annealing to solve an optimization problem requires minor embedding a logic graph into a known hardware graph. We introduce the minor set cover (MSC) of a known graph GG : a subset of graph minors which contain any remaining minor of the graph as a subgraph, in an effort to reduce the complexity of the minor embedding problem. Any graph that can be embedded into GG will be embeddable into a member of the MSC. Focusing on embedding into the hardware graph of commercially available quantum annealers, we establish the MSC for a particular known virtual hardware, whichmore » is a complete bipartite graph. Furthermore, we show that the complete bipartite graph KN,N has a MSC of N minors, from which KN+1 is identified as the largest clique minor of KN,N. In the case of determining the largest clique minor of hardware with faults we briefly discussed this open question.« less

  10. Safety models incorporating graph theory based transit indicators.

    PubMed

    Quintero, Liliana; Sayed, Tarek; Wahba, Mohamed M

    2013-01-01

    There is a considerable need for tools to enable the evaluation of the safety of transit networks at the planning stage. One interesting approach for the planning of public transportation systems is the study of networks. Network techniques involve the analysis of systems by viewing them as a graph composed of a set of vertices (nodes) and edges (links). Once the transport system is visualized as a graph, various network properties can be evaluated based on the relationships between the network elements. Several indicators can be calculated including connectivity, coverage, directness and complexity, among others. The main objective of this study is to investigate the relationship between network-based transit indicators and safety. The study develops macro-level collision prediction models that explicitly incorporate transit physical and operational elements and transit network indicators as explanatory variables. Several macro-level (zonal) collision prediction models were developed using a generalized linear regression technique, assuming a negative binomial error structure. The models were grouped into four main themes: transit infrastructure, transit network topology, transit route design, and transit performance and operations. The safety models showed that collisions were significantly associated with transit network properties such as: connectivity, coverage, overlapping degree and the Local Index of Transit Availability. As well, the models showed a significant relationship between collisions and some transit physical and operational attributes such as the number of routes, frequency of routes, bus density, length of bus and 3+ priority lanes. Copyright © 2012 Elsevier Ltd. All rights reserved.

  11. Model predictive control of P-time event graphs

    NASA Astrophysics Data System (ADS)

    Hamri, H.; Kara, R.; Amari, S.

    2016-12-01

    This paper deals with model predictive control of discrete event systems modelled by P-time event graphs. First, the model is obtained by using the dater evolution model written in the standard algebra. Then, for the control law, we used the finite-horizon model predictive control. For the closed-loop control, we used the infinite-horizon model predictive control (IH-MPC). The latter is an approach that calculates static feedback gains which allows the stability of the closed-loop system while respecting the constraints on the control vector. The problem of IH-MPC is formulated as a linear convex programming subject to a linear matrix inequality problem. Finally, the proposed methodology is applied to a transportation system.

  12. Nonlinear complexity of random visibility graph and Lempel-Ziv on multitype range-intensity interacting financial dynamics

    NASA Astrophysics Data System (ADS)

    Zhang, Yali; Wang, Jun

    2017-09-01

    In an attempt to investigate the nonlinear complex evolution of financial dynamics, a new financial price model - the multitype range-intensity contact (MRIC) financial model, is developed based on the multitype range-intensity interacting contact system, in which the interaction and transmission of different types of investment attitudes in a stock market are simulated by viruses spreading. Two new random visibility graph (VG) based analyses and Lempel-Ziv complexity (LZC) are applied to study the complex behaviors of return time series and the corresponding random sorted series. The VG method is the complex network theory, and the LZC is a non-parametric measure of complexity reflecting the rate of new pattern generation of a series. In this work, the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model. Further, the numerical empirical study shows the similar complexity behaviors between the model and the real markets, the research confirms that the financial model is reasonable to some extent.

  13. Scientist-Centered Graph-Based Models of Scientific Knowledge

    SciTech Connect

    Chin, George; Stephan, Eric G.; Gracio, Deborah K.; Kuchar, Olga A.; Whitney, Paul D.; Schuchardt, Karen L.

    2005-07-01

    At the Pacific Northwest National Laboratory, we are researching and developing visual models and paradigms that will allow scientists to capture and represent conceptual models in a computational form that may linked to and integrated with scientific data sets and applications. Captured conceptual models may be logical in conveying how individual concepts tie together to form a higher theory, analytical in conveying intermediate or final analysis results, or temporal in describing the experimental process in which concepts are physically and computationally explored. In this paper, we describe and contrast three different research and development systems that allow scientists to capture and interact with computational graph-based models of scientific knowledge. Through these examples, we explore and examine ways in which researchers may graphically encode and apply scientific theory and practice on computer systems.

  14. A new graph model and algorithms for consistent superstring problems†

    PubMed Central

    Na, Joong Chae; Cho, Sukhyeun; Choi, Siwon; Kim, Jin Wook; Park, Kunsoo; Sim, Jeong Seop

    2014-01-01

    Problems related to string inclusion and non-inclusion have been vigorously studied in diverse fields such as data compression, molecular biology and computer security. Given a finite set of positive strings and a finite set of negative strings , a string α is a consistent superstring if every positive string is a substring of α and no negative string is a substring of α. The shortest (resp. longest) consistent superstring problem is to find a string α that is the shortest (resp. longest) among all the consistent superstrings for the given sets of strings. In this paper, we first propose a new graph model for consistent superstrings for given and . In our graph model, the set of strings represented by paths satisfying some conditions is the same as the set of consistent superstrings for and . We also present algorithms for the shortest and the longest consistent superstring problems. Our algorithms solve the consistent superstring problems for all cases, including cases that are not considered in previous work. Moreover, our algorithms solve in polynomial time the consistent superstring problems for more cases than the previous algorithms. For the polynomially solvable cases, our algorithms are more efficient than the previous ones. PMID:24751868

  15. A new graph model and algorithms for consistent superstring problems.

    PubMed

    Na, Joong Chae; Cho, Sukhyeun; Choi, Siwon; Kim, Jin Wook; Park, Kunsoo; Sim, Jeong Seop

    2014-05-28

    Problems related to string inclusion and non-inclusion have been vigorously studied in diverse fields such as data compression, molecular biology and computer security. Given a finite set of positive strings P and a finite set of negative strings N, a string α is a consistent superstring if every positive string is a substring of α and no negative string is a substring of α. The shortest (resp. longest) consistent superstring problem is to find a string α that is the shortest (resp. longest) among all the consistent superstrings for the given sets of strings. In this paper, we first propose a new graph model for consistent superstrings for given P and N. In our graph model, the set of strings represented by paths satisfying some conditions is the same as the set of consistent superstrings for P and N. We also present algorithms for the shortest and the longest consistent superstring problems. Our algorithms solve the consistent superstring problems for all cases, including cases that are not considered in previous work. Moreover, our algorithms solve in polynomial time the consistent superstring problems for more cases than the previous algorithms. For the polynomially solvable cases, our algorithms are more efficient than the previous ones.

  16. Adjusting protein graphs based on graph entropy.

    PubMed

    Peng, Sheng-Lung; Tsay, Yu-Wei

    2014-01-01

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

  17. Dynamic graph of an oxy-fuel combustion system using autocatalytic set model

    NASA Astrophysics Data System (ADS)

    Harish, Noor Ainy; Bakar, Sumarni Abu

    2017-08-01

    Evaporation process is one of the main processes besides combustion process in an oxy-combustion boiler system. An Autocatalytic Set (ASC) Model has successfully applied in developing graphical representation of the chemical reactions that occurs in the evaporation process in the system. Seventeen variables identified in the process are represented as nodes and the catalytic relationships are represented as edges in the graph. In addition, in this paper graph dynamics of ACS is further investigated. By using Dynamic Autocatalytic Set Graph Algorithm (DAGA), the adjacency matrix for each of the graphs and its relations to Perron-Frobenius Theorem is investigated. The dynamic graph obtained is further investigated where the connection of the graph to fuzzy graph Type 1 is established.

  18. 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.

  19. Sequence design in lattice models by graph theoretical methods

    NASA Astrophysics Data System (ADS)

    Sanjeev, B. S.; Patra, S. M.; Vishveshwara, S.

    2001-01-01

    A general strategy has been developed based on graph theoretical methods, for finding amino acid sequences that take up a desired conformation as the native state. This problem of inverse design has been addressed by assigning topological indices for the monomer sites (vertices) of the polymer on a 3×3×3 cubic lattice. This is a simple design strategy, which takes into account only the topology of the target protein and identifies the best sequence for a given composition. The procedure allows the design of a good sequence for a target native state by assigning weights for the vertices on a lattice site in a given conformation. It is seen across a variety of conformations that the predicted sequences perform well both in sequence and in conformation space, in identifying the target conformation as native state for a fixed composition of amino acids. Although the method is tested in the framework of the HP model [K. F. Lau and K. A. Dill, Macromolecules 22, 3986 (1989)] it can be used in any context if proper potential functions are available, since the procedure derives unique weights for all the sites (vertices, nodes) of the polymer chain of a chosen conformation (graph).

  20. Departure of some parameter-dependent spectral statistics of irregular quantum graphs from random matrix theory predictions.

    PubMed

    Hul, Oleh; Seba, Petr; Sirko, Leszek

    2009-06-01

    Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities c(x) and c[over ](omega,x) as well as the distributions of level curvatures and avoided crossing gaps are calculated. The numerical results are compared with the predictions of random matrix theory for Gaussian orthogonal ensemble (GOE) and for coupled GOE matrices. The application of coupled GOE matrices was justified by studying localization phenomena in graphs' wave functions Psi(x) using the inverse participation ratio and the amplitude distribution P(Psi(x)) .

  1. Non-parametric iterative model constraint graph min-cut for automatic kidney segmentation.

    PubMed

    Freiman, M; Kronman, A; Esses, S J; Joskowicz, L; Sosna, J

    2010-01-01

    We present a new non-parametric model constraint graph min-cut algorithm for automatic kidney segmentation in CT images. The segmentation is formulated as a maximum a-posteriori estimation of a model-driven Markov random field. A non-parametric hybrid shape and intensity model is treated as a latent variable in the energy functional. The latent model and labeling map that minimize the energy functional are then simultaneously computed with an expectation maximization approach. The main advantages of our method are that it does not assume a fixed parametric prior model, which is subjective to inter-patient variability and registration errors, and that it combines both the model and the image information into a unified graph min-cut based segmentation framework. We evaluated our method on 20 kidneys from 10 CT datasets with and without contrast agent for which ground-truth segmentations were generated by averaging three manual segmentations. Our method yields an average volumetric overlap error of 10.95%, and average symmetric surface distance of 0.79 mm. These results indicate that our method is accurate and robust for kidney segmentation.

  2. A Graph Decomposition Technique Based on a High-Density Clustering Model on Graphs.

    DTIC Science & Technology

    1980-07-01

    ADAO90 3A8 ALFRED P SLOAN SCHOOL OF MANAGEMNT CAMBRIDGE MA CEN-ETC FIG 12 GRAPH DECOMPOSITION TECHNIQUE BASEO ON A HIGH-DENSITY CLUSTER-ETC(U) JUL 0...ELEMENT.’ PROJECT, TASK Center for Information Systems Research AREAO G ORK UNIT NUMBERS Sloan School of Management, M.I.T. V Cambridge,_MA__02139...See Kernighan and Lin (1970), Lukes (1974, 1975), anc Christofides and Brooker (1976) for methods that operate under some size constraints on the

  3. Spectral partitioning in equitable graphs

    NASA Astrophysics Data System (ADS)

    Barucca, Paolo

    2017-06-01

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

  4. 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

  5. Random sequential renormalization and agglomerative percolation in networks: application to Erdös-Rényi and scale-free graphs.

    PubMed

    Bizhani, Golnoosh; Grassberger, Peter; Paczuski, Maya

    2011-12-01

    We study the statistical behavior under random sequential renormalization (RSR) of several network models including Erdös-Rényi (ER) graphs, scale-free networks, and an annealed model related to ER graphs. In RSR the network is locally coarse grained by choosing at each renormalization step a node at random and joining it to all its neighbors. Compared to previous (quasi-)parallel renormalization methods [Song et al., Nature (London) 433, 392 (2005)], RSR allows a more fine-grained analysis of the renormalization group (RG) flow and unravels new features that were not discussed in the previous analyses. In particular, we find that all networks exhibit a second-order transition in their RG flow. This phase transition is associated with the emergence of a giant hub and can be viewed as a new variant of percolation, called agglomerative percolation. We claim that this transition exists also in previous graph renormalization schemes and explains some of the scaling behavior seen there. For critical trees it happens as N/N(0) → 0 in the limit of large systems (where N(0) is the initial size of the graph and N its size at a given RSR step). In contrast, it happens at finite N/N(0) in sparse ER graphs and in the annealed model, while it happens for N/N(0) → 1 on scale-free networks. Critical exponents seem to depend on the type of the graph but not on the average degree and obey usual scaling relations for percolation phenomena. For the annealed model they agree with the exponents obtained from a mean-field theory. At late times, the networks exhibit a starlike structure in agreement with the results of Radicchi et al. [Phys. Rev. Lett. 101, 148701 (2008)]. While degree distributions are of main interest when regarding the scheme as network renormalization, mass distributions (which are more relevant when considering "supernodes" as clusters) are much easier to study using the fast Newman-Ziff algorithm for percolation, allowing us to obtain very high statistics.

  6. Bipartite graphs as models of population structures in evolutionary multiplayer games.

    PubMed

    Peña, Jorge; Rochat, Yannick

    2012-01-01

    By combining evolutionary game theory and graph theory, "games on graphs" study the evolutionary dynamics of frequency-dependent selection in population structures modeled as geographical or social networks. Networks are usually represented by means of unipartite graphs, and social interactions by two-person games such as the famous prisoner's dilemma. Unipartite graphs have also been used for modeling interactions going beyond pairwise interactions. In this paper, we argue that bipartite graphs are a better alternative to unipartite graphs for describing population structures in evolutionary multiplayer games. To illustrate this point, we make use of bipartite graphs to investigate, by means of computer simulations, the evolution of cooperation under the conventional and the distributed N-person prisoner's dilemma. We show that several implicit assumptions arising from the standard approach based on unipartite graphs (such as the definition of replacement neighborhoods, the intertwining of individual and group diversity, and the large overlap of interaction neighborhoods) can have a large impact on the resulting evolutionary dynamics. Our work provides a clear example of the importance of construction procedures in games on graphs, of the suitability of bigraphs and hypergraphs for computational modeling, and of the importance of concepts from social network analysis such as centrality, centralization and bipartite clustering for the understanding of dynamical processes occurring on networked population structures.

  7. Very Large Graphs for Information Extraction (VLG). Summary of First-Year Proof-of-Concept Study

    DTIC Science & Technology

    2013-08-20

    vertex . This technique fuses multiple random graph models and provides a exible approach to model graphs of various types with additional side information...strong as a star graph ( vertex with extremely high degree ) with twice as many vertices. The coauthor graph , on the bottom in the gure, contains two...smallest gap between consecutive eigenvalues . For most random graph models, however, the residuals matrix is dense. Thus, for computational tractability, it

  8. A comparative study of theoretical graph models for characterizing structural networks of human brain.

    PubMed

    Li, Xiaojin; Hu, Xintao; Jin, Changfeng; Han, Junwei; Liu, Tianming; Guo, Lei; Hao, Wei; Li, Lingjiang

    2013-01-01

    Previous studies have investigated both structural and functional brain networks via graph-theoretical methods. However, there is an important issue that has not been adequately discussed before: what is the optimal theoretical graph model for describing the structural networks of human brain? In this paper, we perform a comparative study to address this problem. Firstly, large-scale cortical regions of interest (ROIs) are localized by recently developed and validated brain reference system named Dense Individualized Common Connectivity-based Cortical Landmarks (DICCCOL) to address the limitations in the identification of the brain network ROIs in previous studies. Then, we construct structural brain networks based on diffusion tensor imaging (DTI) data. Afterwards, the global and local graph properties of the constructed structural brain networks are measured using the state-of-the-art graph analysis algorithms and tools and are further compared with seven popular theoretical graph models. In addition, we compare the topological properties between two graph models, namely, stickiness-index-based model (STICKY) and scale-free gene duplication model (SF-GD), that have higher similarity with the real structural brain networks in terms of global and local graph properties. Our experimental results suggest that among the seven theoretical graph models compared in this study, STICKY and SF-GD models have better performances in characterizing the structural human brain network.

  9. Graph Modeling for Quadratic Assignment Problems Associated with the Hypercube

    NASA Astrophysics Data System (ADS)

    Mittelmann, Hans; Peng, Jiming; Wu, Xiaolin

    2009-07-01

    In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least n different optimal solutions to the underlying QAPs. Moreover, the inherent symmetries in the associated hypercube allow us to obtain partial information regarding the optimal solutions and thus shrink the search space and improve all the existing QAP solvers for the underlying QAPs. Secondly, we use graph modeling technique to derive a new integer linear program (ILP) models for the underlying QAPs. The new ILP model has n(n-1) binary variables and O(n3 log(n)) linear constraints. This yields the smallest known number of binary variables for the ILP reformulation of QAPs. Various relaxations of the new ILP model are obtained based on the graphical characterization of the hypercube, and the lower bounds provided by the LP relaxations of the new model are analyzed and compared with what provided by several classical LP relaxations of QAPs in the literature.

  10. Exact two-point resistance, and the simple random walk on the complete graph minus N edges

    SciTech Connect

    Chair, Noureddine

    2012-12-15

    An analytical approach is developed to obtain the exact expressions for the two-point resistance and the total effective resistance of the complete graph minus N edges of the opposite vertices. These expressions are written in terms of certain numbers that we introduce, which we call the Bejaia and the Pisa numbers; these numbers are the natural generalizations of the bisected Fibonacci and Lucas numbers. The correspondence between random walks and the resistor networks is then used to obtain the exact expressions for the first passage and mean first passage times on this graph. - Highlights: Black-Right-Pointing-Pointer We obtain exact formulas for the two-point resistance of the complete graph minus N edges. Black-Right-Pointing-Pointer We obtain also the total effective resistance of this graph. Black-Right-Pointing-Pointer We modified Schwatt's formula on trigonometrical power sum to suit our computations. Black-Right-Pointing-Pointer We introduced the generalized bisected Fibonacci and Lucas numbers: the Bejaia and the Pisa numbers. Black-Right-Pointing-Pointer The first passage and mean first passage times of the random walks have exact expressions.

  11. Quantum Ergodicity on Regular Graphs

    NASA Astrophysics Data System (ADS)

    Anantharaman, Nalini

    2017-07-01

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

  12. Cell-graph mining for breast tissue modeling and classification.

    PubMed

    Bilgin, Cagatay; Demir, Cigdem; Nagi, Chandandeep; Yener, Bulent

    2007-01-01

    We consider the problem of automated cancer diagnosis in the context of breast tissues. We present graph theoretical techniques that identify and compute quantitative metrics for tissue characterization and classification. We segment digital images of histopatological tissue samples using k-means algorithm. For each segmented image we generate different cell-graphs using positional coordinates of cells and surrounding matrix components. These cell-graphs have 500-2000 cells(nodes) with 1000-10000 links depending on the tissue and the type of cell-graph being used. We calculate a set of global metrics from cell-graphs and use them as the feature set for learning. We compare our technique, hierarchical cell graphs, with other techniques based on intensity values of images, Delaunay triangulation of the cells, the previous technique we proposed for brain tissue images and with the hybrid approach that we introduce in this paper. Among the compared techniques, hierarchical-graph approach gives 81.8% accuracy whereas we obtain 61.0%, 54.1% and 75.9% accuracy with intensity-based features, Delaunay triangulation and our previous technique, respectively.

  13. Estimating Causal Effects with Ancestral Graph Markov Models

    PubMed Central

    Malinsky, Daniel; Spirtes, Peter

    2017-01-01

    We present an algorithm for estimating bounds on causal effects from observational data which combines graphical model search with simple linear regression. We assume that the underlying system can be represented by a linear structural equation model with no feedback, and we allow for the possibility of latent variables. Under assumptions standard in the causal search literature, we use conditional independence constraints to search for an equivalence class of ancestral graphs. Then, for each model in the equivalence class, we perform the appropriate regression (using causal structure information to determine which covariates to include in the regression) to estimate a set of possible causal effects. Our approach is based on the “IDA” procedure of Maathuis et al. (2009), which assumes that all relevant variables have been measured (i.e., no unmeasured confounders). We generalize their work by relaxing this assumption, which is often violated in applied contexts. We validate the performance of our algorithm on simulated data and demonstrate improved precision over IDA when latent variables are present. PMID:28217244

  14. Free energy disconnectivity graphs: Application to peptide models

    NASA Astrophysics Data System (ADS)

    Krivov, Sergei V.; Karplus, Martin

    2002-12-01

    Disconnectivity graphs are widely used for understanding the multidimensional potential energy surfaces (PES) of complex systems. Since entropic contributions to the free energy can be important, particularly for polypeptide chains and other polymers, conclusions concerning the equilibrium properties and kinetics of the system based on potential energy disconnectivity graphs (PE DG) can be misleading. We present an approach for constructing free energy surfaces (FES) and free energy disconnectivity graphs (FE DG) and give examples of their applications to peptides. They show that the FES and FE DG can differ significantly from the PES and PE DG.

  15. Graph Unification and Tangram Hypothesis Explanation Representation (GATHER) and System and Component Modeling Framework (SCMF)

    DTIC Science & Technology

    2008-08-01

    AFRL-RI-RS-TR-2008-228 Final Technical Report August 2008 GRAPH UNIFICATION AND TANGRAM HYPOTHESIS EXPLANATION REPRESENTATION...AND SUBTITLE GRAPH UNIFICATION AND TANGRAM HYPOTHESIS EXPLANATION REPRESENTATION (GATHER) AND SYSTEM AND COMPONENT MODELING FRAMEWORK (SCMF) 5a...31  ii LIST OF FIGURES Figure 1: Tangram High Level Architecture

  16. Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games

    PubMed Central

    Peña, Jorge; Rochat, Yannick

    2012-01-01

    By combining evolutionary game theory and graph theory, “games on graphs” study the evolutionary dynamics of frequency-dependent selection in population structures modeled as geographical or social networks. Networks are usually represented by means of unipartite graphs, and social interactions by two-person games such as the famous prisoner’s dilemma. Unipartite graphs have also been used for modeling interactions going beyond pairwise interactions. In this paper, we argue that bipartite graphs are a better alternative to unipartite graphs for describing population structures in evolutionary multiplayer games. To illustrate this point, we make use of bipartite graphs to investigate, by means of computer simulations, the evolution of cooperation under the conventional and the distributed N-person prisoner’s dilemma. We show that several implicit assumptions arising from the standard approach based on unipartite graphs (such as the definition of replacement neighborhoods, the intertwining of individual and group diversity, and the large overlap of interaction neighborhoods) can have a large impact on the resulting evolutionary dynamics. Our work provides a clear example of the importance of construction procedures in games on graphs, of the suitability of bigraphs and hypergraphs for computational modeling, and of the importance of concepts from social network analysis such as centrality, centralization and bipartite clustering for the understanding of dynamical processes occurring on networked population structures. PMID:22970237

  17. Graph-Switching Based Modeling of Mode Transition Constraints for Model Predictive Control of Hybrid Systems

    NASA Astrophysics Data System (ADS)

    Kobayashi, Koichi; Hiraishi, Kunihiko

    The model predictive/optimal control problem for hybrid systems is reduced to a mixed integer quadratic programming (MIQP) problem. However, the MIQP problem has one serious weakness, i.e., the computation time to solve the MIQP problem is too long for practical plants. For overcoming this technical issue, there are several approaches. In this paper, a modeling of mode transition constraints, which are expressed by a directed graph, is focused, and a new method to represent a directed graph is proposed. The effectiveness of the proposed method is shown by numerical examples on linear switched systems and piecewise linear systems.

  18. Stochastic dynamics of model proteins on a directed graph

    NASA Astrophysics Data System (ADS)

    Bongini, Lorenzo; Casetti, Lapo; Livi, Roberto; Politi, Antonio; Torcini, Alessandro

    2009-06-01

    A method for reconstructing the potential energy landscape of simple polypeptidic chains is described. We show how to obtain a faithful representation of the energy landscape in terms of a suitable directed graph. Topological and dynamical indicators of the graph are shown to yield an effective estimate of the time scales associated with both folding and equilibration processes. This conclusion is drawn by comparing molecular dynamics simulations at constant temperature with the dynamics on the graph, defined as a temperature-dependent Markov process. The main advantage of the graph representation is that its dynamics can be naturally renormalized by collecting nodes into “hubs” while redefining their connectivity. We show that the dynamical properties at large time scales are preserved by the renormalization procedure. Moreover, we obtain clear indications that the heteropolymers exhibit common topological properties, at variance with the homopolymer, whose peculiar graph structure stems from its spatial homogeneity. In order to distinguish between “fast” and “slow” folders, one has to look at the kinetic properties of the corresponding directed graphs. In particular, we find that the average time needed to the fast folder for reaching its native configuration is two orders of magnitude smaller than its equilibration time while for the bad folder these time scales are comparable.

  19. Stochastic dynamics of model proteins on a directed graph.

    PubMed

    Bongini, Lorenzo; Casetti, Lapo; Livi, Roberto; Politi, Antonio; Torcini, Alessandro

    2009-06-01

    A method for reconstructing the potential energy landscape of simple polypeptidic chains is described. We show how to obtain a faithful representation of the energy landscape in terms of a suitable directed graph. Topological and dynamical indicators of the graph are shown to yield an effective estimate of the time scales associated with both folding and equilibration processes. This conclusion is drawn by comparing molecular dynamics simulations at constant temperature with the dynamics on the graph, defined as a temperature-dependent Markov process. The main advantage of the graph representation is that its dynamics can be naturally renormalized by collecting nodes into "hubs" while redefining their connectivity. We show that the dynamical properties at large time scales are preserved by the renormalization procedure. Moreover, we obtain clear indications that the heteropolymers exhibit common topological properties, at variance with the homopolymer, whose peculiar graph structure stems from its spatial homogeneity. In order to distinguish between "fast" and "slow" folders, one has to look at the kinetic properties of the corresponding directed graphs. In particular, we find that the average time needed to the fast folder for reaching its native configuration is two orders of magnitude smaller than its equilibration time while for the bad folder these time scales are comparable.

  20. Visualizing Dataflow Graphs of Deep Learning Models in TensorFlow.

    PubMed

    Wongsuphasawat, Kanit; Smilkov, Daniel; Wexler, James; Wilson, Jimbo; Mane, Dandelion; Fritz, Doug; Krishnan, Dilip; Viegas, Fernanda B; Wattenberg, Martin

    2017-08-29

    We present a design study of the TensorFlow Graph Visualizer, part of the TensorFlow machine intelligence platform. This tool helps users understand complex machine learning architectures by visualizing their underlying dataflow graphs. The tool works by applying a series of graph transformations that enable standard layout techniques to produce a legible interactive diagram. To declutter the graph, we decouple non-critical nodes from the layout. To provide an overview, we build a clustered graph using the hierarchical structure annotated in the source code. To support exploration of nested structure on demand, we perform edge bundling to enable stable and responsive cluster expansion. Finally, we detect and highlight repeated structures to emphasize a model's modular composition. To demonstrate the utility of the visualizer, we describe example usage scenarios and report user feedback. Overall, users find the visualizer useful for understanding, debugging, and sharing the structures of their models.

  1. A componential model of human interaction with graphs: 1. Linear regression modeling

    NASA Technical Reports Server (NTRS)

    Gillan, Douglas J.; Lewis, Robert

    1994-01-01

    Task analyses served as the basis for developing the Mixed Arithmetic-Perceptual (MA-P) model, which proposes (1) that people interacting with common graphs to answer common questions apply a set of component processes-searching for indicators, encoding the value of indicators, performing arithmetic operations on the values, making spatial comparisons among indicators, and repsonding; and (2) that the type of graph and user's task determine the combination and order of the components applied (i.e., the processing steps). Two experiments investigated the prediction that response time will be linearly related to the number of processing steps according to the MA-P model. Subjects used line graphs, scatter plots, and stacked bar graphs to answer comparison questions and questions requiring arithmetic calculations. A one-parameter version of the model (with equal weights for all components) and a two-parameter version (with different weights for arithmetic and nonarithmetic processes) accounted for 76%-85% of individual subjects' variance in response time and 61%-68% of the variance taken across all subjects. The discussion addresses possible modifications in the MA-P model, alternative models, and design implications from the MA-P model.

  2. A componential model of human interaction with graphs: 1. Linear regression modeling

    NASA Technical Reports Server (NTRS)

    Gillan, Douglas J.; Lewis, Robert

    1994-01-01

    Task analyses served as the basis for developing the Mixed Arithmetic-Perceptual (MA-P) model, which proposes (1) that people interacting with common graphs to answer common questions apply a set of component processes-searching for indicators, encoding the value of indicators, performing arithmetic operations on the values, making spatial comparisons among indicators, and repsonding; and (2) that the type of graph and user's task determine the combination and order of the components applied (i.e., the processing steps). Two experiments investigated the prediction that response time will be linearly related to the number of processing steps according to the MA-P model. Subjects used line graphs, scatter plots, and stacked bar graphs to answer comparison questions and questions requiring arithmetic calculations. A one-parameter version of the model (with equal weights for all components) and a two-parameter version (with different weights for arithmetic and nonarithmetic processes) accounted for 76%-85% of individual subjects' variance in response time and 61%-68% of the variance taken across all subjects. The discussion addresses possible modifications in the MA-P model, alternative models, and design implications from the MA-P model.

  3. Non-perturbative corrections to mean-field critical behavior: the spherical model on a spider-web graph

    NASA Astrophysics Data System (ADS)

    Balram, Ajit C.; Dhar, Deepak

    2012-03-01

    We consider the spherical model on a spider-web graph. This graph is effectively infinite dimensional, similar to the Bethe lattice, but has loops. We show that these lead to non-trivial corrections to the simple mean-field behavior. We first determine all normal modes of the coupled springs problem on this graph, using its large symmetry group. In the thermodynamic limit, the spectrum is a set of δ-functions, and all the modes are localized. The fractional number of modes with frequency less than ω varies as exp ( - C/ω) for ω tending to zero, where C is a constant. For an unbiased random walk on the vertices of this graph, this implies that the probability of return to the origin at time t varies as exp ( - C‧t1/3), for large t, where C‧ is a constant. For the spherical model, we show that while the critical exponents take the values expected from the mean-field theory, the free energy per site at temperature T, near and above the critical temperature Tc, also has an essential singularity of the type exp [ - K(T - Tc)-1/2].

  4. Modeling spatial relation in skin lesion images by the graph walk kernel.

    PubMed

    Situ, Ning; Wadhawan, Tarun; Yuan, Xiaojing; Zouridakis, George

    2010-01-01

    Early skin cancer detection with the help of dermoscopic images is becoming more and more important. Previous methods generally ignored the spatial relation of the pixels or regions inside the lesion. We propose to employ a graph representation of the skin lesion to model the spatial relation. We then use the graph walk kernel, a similarity measure between two graphs, to build a classifier based on support vector machines for melanoma detection. In experiments, we compare the sensitivities and specificities of models with and without spatial information. Experimental results show that the model with spatial information performs the best in both sensitivity and specificity. Statistical test indicates that the improvement is significant.

  5. 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.

  6. Topological determinants of self-sustained activity in a simple model of excitable dynamics on graphs

    PubMed Central

    Fretter, Christoph; Lesne, Annick; Hilgetag, Claus C.; Hütt, Marc-Thorsten

    2017-01-01

    Simple models of excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This topic is of practical relevance to diverse fields, ranging from neuroscience to engineering. Here we analyze how a single excitation propagates through a random network as a function of the excitation threshold, that is, the relative amount of activity in the neighborhood required for the excitation of a node. We observe that two sharp transitions delineate a region of sustained activity. Using analytical considerations and numerical simulation, we show that these transitions originate from the presence of barriers to propagation and the excitation of topological cycles, respectively, and can be predicted from the network topology. Our findings are interpreted in the context of network reverberations and self-sustained activity in neural systems, which is a question of long-standing interest in computational neuroscience. PMID:28186182

  7. Topological determinants of self-sustained activity in a simple model of excitable dynamics on graphs

    NASA Astrophysics Data System (ADS)

    Fretter, Christoph; Lesne, Annick; Hilgetag, Claus C.; Hütt, Marc-Thorsten

    2017-02-01

    Simple models of excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This topic is of practical relevance to diverse fields, ranging from neuroscience to engineering. Here we analyze how a single excitation propagates through a random network as a function of the excitation threshold, that is, the relative amount of activity in the neighborhood required for the excitation of a node. We observe that two sharp transitions delineate a region of sustained activity. Using analytical considerations and numerical simulation, we show that these transitions originate from the presence of barriers to propagation and the excitation of topological cycles, respectively, and can be predicted from the network topology. Our findings are interpreted in the context of network reverberations and self-sustained activity in neural systems, which is a question of long-standing interest in computational neuroscience.

  8. Graph theory as a proxy for spatially explicit population models in conservation planning.

    PubMed

    Minor, Emily S; Urban, Dean L

    2007-09-01

    Spatially explicit population models (SEPMs) are often considered the best way to predict and manage species distributions in spatially heterogeneous landscapes. However, they are computationally intensive and require extensive knowledge of species' biology and behavior, limiting their application in many cases. An alternative to SEPMs is graph theory, which has minimal data requirements and efficient algorithms. Although only recently introduced to landscape ecology, graph theory is well suited to ecological applications concerned with connectivity or movement. This paper compares the performance of graph theory to a SEPM in selecting important habitat patches for Wood Thrush (Hylocichla mustelina) conservation. We use both models to identify habitat patches that act as population sources and persistent patches and also use graph theory to identify patches that act as stepping stones for dispersal. Correlations of patch rankings were very high between the two models. In addition, graph theory offers the ability to identify patches that are very important to habitat connectivity and thus long-term population persistence across the landscape. We show that graph theory makes very similar predictions in most cases and in other cases offers insight not available from the SEPM, and we conclude that graph theory is a suitable and possibly preferable alternative to SEPMs for species conservation in heterogeneous landscapes.

  9. Probabilistic image modeling with an extended chain graph for human activity recognition and image segmentation.

    PubMed

    Zhang, Lei; Zeng, Zhi; Ji, Qiang

    2011-09-01

    Chain graph (CG) is a hybrid probabilistic graphical model (PGM) capable of modeling heterogeneous relationships among random variables. So far, however, its application in image and video analysis is very limited due to lack of principled learning and inference methods for a CG of general topology. To overcome this limitation, we introduce methods to extend the conventional chain-like CG model to CG model with more general topology and the associated methods for learning and inference in such a general CG model. Specifically, we propose techniques to systematically construct a generally structured CG, to parameterize this model, to derive its joint probability distribution, to perform joint parameter learning, and to perform probabilistic inference in this model. To demonstrate the utility of such an extended CG, we apply it to two challenging image and video analysis problems: human activity recognition and image segmentation. The experimental results show improved performance of the extended CG model over the conventional directed or undirected PGMs. This study demonstrates the promise of the extended CG for effective modeling and inference of complex real-world problems.

  10. Automated Modeling and Simulation Using the Bond Graph Method for the Aerospace Industry

    NASA Technical Reports Server (NTRS)

    Granda, Jose J.; Montgomery, Raymond C.

    2003-01-01

    Bond graph modeling was originally developed in the late 1950s by the late Prof. Henry M. Paynter of M.I.T. Prof. Paynter acted well before his time as the main advantage of his creation, other than the modeling insight that it provides and the ability of effectively dealing with Mechatronics, came into fruition only with the recent advent of modern computer technology and the tools derived as a result of it, including symbolic manipulation, MATLAB, and SIMULINK and the Computer Aided Modeling Program (CAMPG). Thus, only recently have these tools been available allowing one to fully utilize the advantages that the bond graph method has to offer. The purpose of this paper is to help fill the knowledge void concerning its use of bond graphs in the aerospace industry. The paper first presents simple examples to serve as a tutorial on bond graphs for those not familiar with the technique. The reader is given the basic understanding needed to appreciate the applications that follow. After that, several aerospace applications are developed such as modeling of an arresting system for aircraft carrier landings, suspension models used for landing gears and multibody dynamics. The paper presents also an update on NASA's progress in modeling the International Space Station (ISS) using bond graph techniques, and an advanced actuation system utilizing shape memory alloys. The later covers the Mechatronics advantages of the bond graph method, applications that simultaneously involves mechanical, hydraulic, thermal, and electrical subsystem modeling.

  11. A Comparison of Video Modeling, Text-Based Instruction, and No Instruction for Creating Multiple Baseline Graphs in Microsoft Excel

    ERIC Educational Resources Information Center

    Tyner, Bryan C.; Fienup, Daniel M.

    2015-01-01

    Graphing is socially significant for behavior analysts; however, graphing can be difficult to learn. Video modeling (VM) may be a useful instructional method but lacks evidence for effective teaching of computer skills. A between-groups design compared the effects of VM, text-based instruction, and no instruction on graphing performance.…

  12. A Comparison of Video Modeling, Text-Based Instruction, and No Instruction for Creating Multiple Baseline Graphs in Microsoft Excel

    ERIC Educational Resources Information Center

    Tyner, Bryan C.; Fienup, Daniel M.

    2015-01-01

    Graphing is socially significant for behavior analysts; however, graphing can be difficult to learn. Video modeling (VM) may be a useful instructional method but lacks evidence for effective teaching of computer skills. A between-groups design compared the effects of VM, text-based instruction, and no instruction on graphing performance.…

  13. Interval Graph Limits

    PubMed Central

    Diaconis, Persi; Holmes, Susan; Janson, Svante

    2015-01-01

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

  14. graph-GPA: A graphical model for prioritizing GWAS results and investigating pleiotropic architecture.

    PubMed

    Chung, Dongjun; Kim, Hang J; Zhao, Hongyu

    2017-02-01

    Genome-wide association studies (GWAS) have identified tens of thousands of genetic variants associated with hundreds of phenotypes and diseases, which have provided clinical and medical benefits to patients with novel biomarkers and therapeutic targets. However, identification of risk variants associated with complex diseases remains challenging as they are often affected by many genetic variants with small or moderate effects. There has been accumulating evidence suggesting that different complex traits share common risk basis, namely pleiotropy. Recently, several statistical methods have been developed to improve statistical power to identify risk variants for complex traits through a joint analysis of multiple GWAS datasets by leveraging pleiotropy. While these methods were shown to improve statistical power for association mapping compared to separate analyses, they are still limited in the number of phenotypes that can be integrated. In order to address this challenge, in this paper, we propose a novel statistical framework, graph-GPA, to integrate a large number of GWAS datasets for multiple phenotypes using a hidden Markov random field approach. Application of graph-GPA to a joint analysis of GWAS datasets for 12 phenotypes shows that graph-GPA improves statistical power to identify risk variants compared to statistical methods based on smaller number of GWAS datasets. In addition, graph-GPA also promotes better understanding of genetic mechanisms shared among phenotypes, which can potentially be useful for the development of improved diagnosis and therapeutics. The R implementation of graph-GPA is currently available at https://dongjunchung.github.io/GGPA/.

  15. graph-GPA: A graphical model for prioritizing GWAS results and investigating pleiotropic architecture

    PubMed Central

    Zhao, Hongyu

    2017-01-01

    Genome-wide association studies (GWAS) have identified tens of thousands of genetic variants associated with hundreds of phenotypes and diseases, which have provided clinical and medical benefits to patients with novel biomarkers and therapeutic targets. However, identification of risk variants associated with complex diseases remains challenging as they are often affected by many genetic variants with small or moderate effects. There has been accumulating evidence suggesting that different complex traits share common risk basis, namely pleiotropy. Recently, several statistical methods have been developed to improve statistical power to identify risk variants for complex traits through a joint analysis of multiple GWAS datasets by leveraging pleiotropy. While these methods were shown to improve statistical power for association mapping compared to separate analyses, they are still limited in the number of phenotypes that can be integrated. In order to address this challenge, in this paper, we propose a novel statistical framework, graph-GPA, to integrate a large number of GWAS datasets for multiple phenotypes using a hidden Markov random field approach. Application of graph-GPA to a joint analysis of GWAS datasets for 12 phenotypes shows that graph-GPA improves statistical power to identify risk variants compared to statistical methods based on smaller number of GWAS datasets. In addition, graph-GPA also promotes better understanding of genetic mechanisms shared among phenotypes, which can potentially be useful for the development of improved diagnosis and therapeutics. The R implementation of graph-GPA is currently available at https://dongjunchung.github.io/GGPA/. PMID:28212402

  16. A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

    NASA Astrophysics Data System (ADS)

    DeSantis, Emilio; Marinelli, Carlo

    2007-09-01

    We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove 'fixation', i.e. players will adopt a constant strategy after a finite time. The resulting dynamics is related to zero-temperature Glauber dynamics on random graphs of possibly infinite volume.

  17. A New Model of Graph and Visualization Usage

    DTIC Science & Technology

    2001-01-01

    comprehension is Bertin’s (1983) task analysis that suggests three main processes in graph and visual- ization comprehension: 1. Encode visual elements of the...2. Translate the elements into patterns: For example, notice that one bar is taller than another or the slope of a line. This stage is affected by...PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval

  18. Bond graph modeling, simulation, and reflex control of the Mars planetary automatic vehicle

    NASA Astrophysics Data System (ADS)

    Amara, Maher; Friconneau, Jean Pierre; Micaelli, Alain

    1993-01-01

    The bond graph modeling, simulation, and reflex control study of the Planetary Automatic Vehicle are considered. A simulator derived from a complete bond graph model of the vehicle is presented. This model includes both knowledge and representation models of the mechanical structure, the floor contact, and the Mars site. The MACSYMEN (French acronym for aided design method of multi-energetic systems) is used and applied to study the input-output power transfers. The reflex control is then considered. Controller architecture and locomotion specificity are described. A numerical stage highlights some interesting results of the robot and the controller capabilities.

  19. Exact solution of the isotropic majority-vote model on complete graphs

    NASA Astrophysics Data System (ADS)

    Fronczak, Agata; Fronczak, Piotr

    2017-07-01

    The isotropic majority-vote (MV) model, which, apart from the one-dimensional case, is thought to be nonequilibrium and violating the detailed balance condition. We show that this is not true when the model is defined on a complete graph. In the stationary regime, the MV model on a fully connected graph fulfills the detailed balance and is equivalent to the modified Ehrenfest urn model. Using the master equation approach, we derive the exact expression for the probability distribution of finding the system in a given spin configuration. We show that it only depends on the absolute value of magnetization. Our theoretical predictions are validated by numerical simulations.

  20. a Graph Based Model for the Detection of Tidal Channels Using Marked Point Processes

    NASA Astrophysics Data System (ADS)

    Schmidt, A.; Rottensteiner, F.; Soergel, U.; Heipke, C.

    2015-08-01

    In this paper we propose a new method for the automatic extraction of tidal channels in digital terrain models (DTM) using a sampling approach based on marked point processes. In our model, the tidal channel system is represented by an undirected, acyclic graph. The graph is iteratively generated and fitted to the data using stochastic optimization based on a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler and simulated annealing. The nodes of the graph represent junction points of the channel system and the edges straight line segments with a certain width in between. In each sampling step, the current configuration of nodes and edges is modified. The changes are accepted or rejected depending on the probability density function for the configuration which evaluates the conformity of the current status with a pre-defined model for tidal channels. In this model we favour high DTM gradient magnitudes at the edge borders and penalize a graph configuration consisting of non-connected components, overlapping segments and edges with atypical intersection angles. We present the method of our graph based model and show results for lidar data, which serve of a proof of concept of our approach.

  1. 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

  2. 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.

  3. Adjusting protein graphs based on graph entropy

    PubMed Central

    2014-01-01

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

  4. An Interactive Teaching System for Bond Graph Modeling and Simulation in Bioengineering

    ERIC Educational Resources Information Center

    Roman, Monica; Popescu, Dorin; Selisteanu, Dan

    2013-01-01

    The objective of the present work was to implement a teaching system useful in modeling and simulation of biotechnological processes. The interactive system is based on applications developed using 20-sim modeling and simulation software environment. A procedure for the simulation of bioprocesses modeled by bond graphs is proposed and simulators…

  5. An Interactive Teaching System for Bond Graph Modeling and Simulation in Bioengineering

    ERIC Educational Resources Information Center

    Roman, Monica; Popescu, Dorin; Selisteanu, Dan

    2013-01-01

    The objective of the present work was to implement a teaching system useful in modeling and simulation of biotechnological processes. The interactive system is based on applications developed using 20-sim modeling and simulation software environment. A procedure for the simulation of bioprocesses modeled by bond graphs is proposed and simulators…

  6. Bond Graph Modeling and Validation of an Energy Regenerative System for Emulsion Pump Tests

    PubMed Central

    Li, Yilei; Zhu, Zhencai; Chen, Guoan

    2014-01-01

    The test system for emulsion pump is facing serious challenges due to its huge energy consumption and waste nowadays. To settle this energy issue, a novel energy regenerative system (ERS) for emulsion pump tests is briefly introduced at first. Modeling such an ERS of multienergy domains needs a unified and systematic approach. Bond graph modeling is well suited for this task. The bond graph model of this ERS is developed by first considering the separate components before assembling them together and so is the state-space equation. Both numerical simulation and experiments are carried out to validate the bond graph model of this ERS. Moreover the simulation and experiments results show that this ERS not only satisfies the test requirements, but also could save at least 25% of energy consumption as compared to the original test system, demonstrating that it is a promising method of energy regeneration for emulsion pump tests. PMID:24967428

  7. Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs

    NASA Astrophysics Data System (ADS)

    Vasudevan, K.; Cavers, M.; Ware, A.

    2015-09-01

    Earthquake sequencing studies allow us to investigate empirical relationships among spatio-temporal parameters describing the complexity of earthquake properties. We have recently studied the relevance of Markov chain models to draw information from global earthquake catalogues. In these studies, we considered directed graphs as graph theoretic representations of the Markov chain model and analyzed their properties. Here, we look at earthquake sequencing itself as a directed graph. In general, earthquakes are occurrences resulting from significant stress interactions among faults. As a result, stress-field fluctuations evolve continuously. We propose that they are akin to the dynamics of the collective behavior of weakly coupled non-linear oscillators. Since mapping of global stress-field fluctuations in real time at all scales is an impossible task, we consider an earthquake zone as a proxy for a collection of weakly coupled oscillators, the dynamics of which would be appropriate for the ubiquitous Kuramoto model. In the present work, we apply the Kuramoto model with phase lag to the non-linear dynamics on a directed graph of a sequence of earthquakes. For directed graphs with certain properties, the Kuramoto model yields synchronization, and inclusion of non-local effects evokes the occurrence of chimera states or the co-existence of synchronous and asynchronous behavior of oscillators. In this paper, we show how we build the directed graphs derived from global seismicity data. Then, we present conditions under which chimera states could occur and, subsequently, point out the role of the Kuramoto model in understanding the evolution of synchronous and asynchronous regions. We surmise that one implication of the emergence of chimera states will lead to investigation of the present and other mathematical models in detail to generate global chimera-state maps similar to global seismicity maps for earthquake forecasting studies.

  8. Hierarchical graphs for better annotations of rule-based models of biochemical systems

    SciTech Connect

    Hu, Bin; Hlavacek, William

    2009-01-01

    In the graph-based formalism of the BioNetGen language (BNGL), graphs are used to represent molecules, with a colored vertex representing a component of a molecule, a vertex label representing the internal state of a component, and an edge representing a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions, with a rule that specifies addition (removal) of an edge representing a class of association (dissociation) reactions and with a rule that specifies a change of vertex label representing a class of reactions that affect the internal state of a molecular component. A set of rules comprises a mathematical/computational model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system. Here, for purposes of model annotation, we propose an extension of BNGL that involves the use of hierarchical graphs to represent (1) relationships among components and subcomponents of molecules and (2) relationships among classes of reactions defined by rules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR)/CD3 complex. Likewise, we illustrate how hierarchical graphs can be used to document the similarity of two related rules for kinase-catalyzed phosphorylation of a protein substrate. We also demonstrate how a hierarchical graph representing a protein can be encoded in an XML-based format.

  9. Connections between the Sznajd model with general confidence rules and graph theory.

    PubMed

    Timpanaro, André M; Prado, Carmen P C

    2012-10-01

    The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabási-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q>2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

  10. Connections between the Sznajd model with general confidence rules and graph theory

    NASA Astrophysics Data System (ADS)

    Timpanaro, André M.; Prado, Carmen P. C.

    2012-10-01

    The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabási-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q>2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

  11. QSPR modeling mineral crystal lattice energy by optimal descriptors of the graph of atomic orbitals

    NASA Astrophysics Data System (ADS)

    Toropova, A. P.; Toropov, A. A.; Maksudov, S. Kh.

    2006-09-01

    Models of the crystal lattice of minerals of general formula of A mC n: m, n = 1,2: A = Li, K, Na, Mg, Ca, Mn, Cu, Zn, Sr, Cd, Ba, Hg, Pb, Cs, and Rb ; C = Be, O, F, S, Cl, Br, and I; as a mathematical function of their structure have been constructed. Two elucidations of molecular structure have been used: molecular graph (vertexes are atoms, i.e., Li, Na, K, etc.) and graph of atomic orbitals, GAO (vertexes are atomic orbitals, i.e., 1s 2, 2p 5, 3d 10, etc). Statistical characteristics of the GAO-based models are better.

  12. A Poisson model for random multigraphs

    PubMed Central

    Ranola, John M. O.; Ahn, Sangtae; Sehl, Mary; Smith, Desmond J.; Lange, Kenneth

    2010-01-01

    Motivation: Biological networks are often modeled by random graphs. A better modeling vehicle is a multigraph where each pair of nodes is connected by a Poisson number of edges. In the current model, the mean number of edges equals the product of two propensities, one for each node. In this context it is possible to construct a simple and effective algorithm for rapid maximum likelihood estimation of all propensities. Given estimated propensities, it is then possible to test statistically for functionally connected nodes that show an excess of observed edges over expected edges. The model extends readily to directed multigraphs. Here, propensities are replaced by outgoing and incoming propensities. Results: The theory is applied to real data on neuronal connections, interacting genes in radiation hybrids, interacting proteins in a literature curated database, and letter and word pairs in seven Shaskespearean plays. Availability: All data used are fully available online from their respective sites. Source code and software is available from http://code.google.com/p/poisson-multigraph/ Contact: klange@ucla.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:20554690

  13. Fixation Probability in a Two-Locus Model by the Ancestral Recombination–Selection Graph

    PubMed Central

    Lessard, Sabin; Kermany, Amir R.

    2012-01-01

    We use the ancestral influence graph (AIG) for a two-locus, two-allele selection model in the limit of a large population size to obtain an analytic approximation for the probability of ultimate fixation of a single mutant allele A. We assume that this new mutant is introduced at a given locus into a finite population in which a previous mutant allele B is already segregating with a wild type at another linked locus. We deduce that the fixation probability increases as the recombination rate increases if allele A is either in positive epistatic interaction with B and allele B is beneficial or in no epistatic interaction with B and then allele A itself is beneficial. This holds at least as long as the recombination fraction and the selection intensity are small enough and the population size is large enough. In particular this confirms the Hill–Robertson effect, which predicts that recombination renders more likely the ultimate fixation of beneficial mutants at different loci in a population in the presence of random genetic drift even in the absence of epistasis. More importantly, we show that this is true from weak negative epistasis to positive epistasis, at least under weak selection. In the case of deleterious mutants, the fixation probability decreases as the recombination rate increases. This supports Muller’s ratchet mechanism to explain the accumulation of deleterious mutants in a population lacking recombination. PMID:22095080

  14. Graph pyramids as models of human problem solving

    NASA Astrophysics Data System (ADS)

    Pizlo, Zygmunt; Li, Zheng

    2004-05-01

    Prior theories have assumed that human problem solving involves estimating distances among states and performing search through the problem space. The role of mental representation in those theories was minimal. Results of our recent experiments suggest that humans are able to solve some difficult problems quickly and accurately. Specifically, in solving these problems humans do not seem to rely on distances or on search. It is quite clear that producing good solutions without performing search requires a very effective mental representation. In this paper we concentrate on studying the nature of this representation. Our theory takes the form of a graph pyramid. To verify the psychological plausibility of this theory we tested subjects in a Euclidean Traveling Salesman Problem in the presence of obstacles. The role of the number and size of obstacles was tested for problems with 6-50 cities. We analyzed the effect of experimental conditions on solution time per city and on solution error. The main result is that time per city is systematically affected only by the size of obstacles, but not by their number, or by the number of cities.

  15. 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).

  16. Bim-Gis Integrated Geospatial Information Model Using Semantic Web and Rdf Graphs

    NASA Astrophysics Data System (ADS)

    Hor, A.-H.; Jadidi, A.; Sohn, G.

    2016-06-01

    In recent years, 3D virtual indoor/outdoor urban modelling becomes a key spatial information framework for many civil and engineering applications such as evacuation planning, emergency and facility management. For accomplishing such sophisticate decision tasks, there is a large demands for building multi-scale and multi-sourced 3D urban models. Currently, Building Information Model (BIM) and Geographical Information Systems (GIS) are broadly used as the modelling sources. However, data sharing and exchanging information between two modelling domains is still a huge challenge; while the syntactic or semantic approaches do not fully provide exchanging of rich semantic and geometric information of BIM into GIS or vice-versa. This paper proposes a novel approach for integrating BIM and GIS using semantic web technologies and Resources Description Framework (RDF) graphs. The novelty of the proposed solution comes from the benefits of integrating BIM and GIS technologies into one unified model, so-called Integrated Geospatial Information Model (IGIM). The proposed approach consists of three main modules: BIM-RDF and GIS-RDF graphs construction, integrating of two RDF graphs, and query of information through IGIM-RDF graph using SPARQL. The IGIM generates queries from both the BIM and GIS RDF graphs resulting a semantically integrated model with entities representing both BIM classes and GIS feature objects with respect to the target-client application. The linkage between BIM-RDF and GIS-RDF is achieved through SPARQL endpoints and defined by a query using set of datasets and entity classes with complementary properties, relationships and geometries. To validate the proposed approach and its performance, a case study was also tested using IGIM system design.

  17. 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.

  18. A Model of Knowledge Based Information Retrieval with Hierarchical Concept Graph.

    ERIC Educational Resources Information Center

    Kim, Young Whan; Kim, Jin H.

    1990-01-01

    Proposes a model of knowledge-based information retrieval (KBIR) that is based on a hierarchical concept graph (HCG) which shows relationships between index terms and constitutes a hierarchical thesaurus as a knowledge base. Conceptual distance between a query and an object is discussed and the use of Boolean operators is described. (25…

  19. New Graph Models and Algorithms for Detecting Salient Structures from Cluttered Images

    DTIC Science & Technology

    2010-02-24

    Development of graph models and algorithms to detect boundaries that show certain levels of symmetry, an important geometric property of many...Bookstein. Morphometric tools for landmark data. Cambridge University Press, 1991. [8] F. L. Bookstein. Principal warps: Thin-plate splines and the

  20. Physics Students' Performance Using Computational Modelling Activities to Improve Kinematics Graphs Interpretation

    ERIC Educational Resources Information Center

    Araujo, Ives Solano; Veit, Eliane Angela; Moreira, Marco Antonio

    2008-01-01

    The purpose of this study was to investigate undergraduate students' performance while exposed to complementary computational modelling activities to improve physics learning, using the software "Modellus." Interpretation of kinematics graphs was the physics topic chosen for investigation. The theoretical framework adopted was based on Halloun's…

  1. 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.

  2. Physics Students' Performance Using Computational Modelling Activities to Improve Kinematics Graphs Interpretation

    ERIC Educational Resources Information Center

    Araujo, Ives Solano; Veit, Eliane Angela; Moreira, Marco Antonio

    2008-01-01

    The purpose of this study was to investigate undergraduate students' performance while exposed to complementary computational modelling activities to improve physics learning, using the software "Modellus." Interpretation of kinematics graphs was the physics topic chosen for investigation. The theoretical framework adopted was based on Halloun's…

  3. Protein and gene model inference based on statistical modeling in k-partite graphs.

    PubMed

    Gerster, Sarah; Qeli, Ermir; Ahrens, Christian H; Bühlmann, Peter

    2010-07-06

    One of the major goals of proteomics is the comprehensive and accurate description of a proteome. Shotgun proteomics, the method of choice for the analysis of complex protein mixtures, requires that experimentally observed peptides are mapped back to the proteins they were derived from. This process is also known as protein inference. We present Markovian Inference of Proteins and Gene Models (MIPGEM), a statistical model based on clearly stated assumptions to address the problem of protein and gene model inference for shotgun proteomics data. In particular, we are dealing with dependencies among peptides and proteins using a Markovian assumption on k-partite graphs. We are also addressing the problems of shared peptides and ambiguous proteins by scoring the encoding gene models. Empirical results on two control datasets with synthetic mixtures of proteins and on complex protein samples of Saccharomyces cerevisiae, Drosophila melanogaster, and Arabidopsis thaliana suggest that the results with MIPGEM are competitive with existing tools for protein inference.

  4. 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…

  5. 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…

  6. A comparison of video modeling, text-based instruction, and no instruction for creating multiple baseline graphs in Microsoft Excel.

    PubMed

    Tyner, Bryan C; Fienup, Daniel M

    2015-09-01

    Graphing is socially significant for behavior analysts; however, graphing can be difficult to learn. Video modeling (VM) may be a useful instructional method but lacks evidence for effective teaching of computer skills. A between-groups design compared the effects of VM, text-based instruction, and no instruction on graphing performance. Participants who used VM constructed graphs significantly faster and with fewer errors than those who used text-based instruction or no instruction. Implications for instruction are discussed. © Society for the Experimental Analysis of Behavior.

  7. Assessing statistical significance in causal graphs

    PubMed Central

    2012-01-01

    Background Causal graphs are an increasingly popular tool for the analysis of biological datasets. In particular, signed causal graphs--directed graphs whose edges additionally have a sign denoting upregulation or downregulation--can be used to model regulatory networks within a cell. Such models allow prediction of downstream effects of regulation of biological entities; conversely, they also enable inference of causative agents behind observed expression changes. However, due to their complex nature, signed causal graph models present special challenges with respect to assessing statistical significance. In this paper we frame and solve two fundamental computational problems that arise in practice when computing appropriate null distributions for hypothesis testing. Results First, we show how to compute a p-value for agreement between observed and model-predicted classifications of gene transcripts as upregulated, downregulated, or neither. Specifically, how likely are the classifications to agree to the same extent under the null distribution of the observed classification being randomized? This problem, which we call "Ternary Dot Product Distribution" owing to its mathematical form, can be viewed as a generalization of Fisher's exact test to ternary variables. We present two computationally efficient algorithms for computing the Ternary Dot Product Distribution and investigate its combinatorial structure analytically and numerically to establish computational complexity bounds. Second, we develop an algorithm for efficiently performing random sampling of causal graphs. This enables p-value computation under a different, equally important null distribution obtained by randomizing the graph topology but keeping fixed its basic structure: connectedness and the positive and negative in- and out-degrees of each vertex. We provide an algorithm for sampling a graph from this distribution uniformly at random. We also highlight theoretical challenges unique to signed

  8. Cycle graph analysis for 3D roof structure modelling: Concepts and performance

    NASA Astrophysics Data System (ADS)

    Perera, Gamage Sanka Nirodha; Maas, Hans-Gerd

    2014-07-01

    The paper presents a cycle graph analysis approach to the automatic reconstruction of 3D roof models from airborne laser scanner data. The nature of convergences of topological relations of plane adjacencies, allowing for the reconstruction of roof corner geometries with preserved topology, can be derived from cycles in roof topology graphs. The topology between roof adjacencies is defined in terms of ridge-lines and step-edges. In the proposed method, the input point cloud is first segmented and roof topology is derived while extracting roof planes from identified non-terrain segments. Orientation and placement regularities are applied on weakly defined edges using a piecewise regularization approach prior to the reconstruction, which assists in preserving symmetries in building geometry. Roof corners are geometrically modelled using the shortest closed cycles and the outermost cycle derived from roof topology graph in which external target graphs are no longer required. Based on test results, we show that the proposed approach can handle complexities with nearly 90% of the detected roof faces reconstructed correctly. The approach allows complex height jumps and various types of building roofs to be firmly reconstructed without prior knowledge of primitive building types.

  9. A Spectral Graph Regression Model for Learning Brain Connectivity of Alzheimer’s Disease

    PubMed Central

    Hu, Chenhui; Cheng, Lin; Sepulcre, Jorge; Johnson, Keith A.; Fakhri, Georges E.; Lu, Yue M.; Li, Quanzheng

    2015-01-01

    Understanding network features of brain pathology is essential to reveal underpinnings of neurodegenerative diseases. In this paper, we introduce a novel graph regression model (GRM) for learning structural brain connectivity of Alzheimer's disease (AD) measured by amyloid-β deposits. The proposed GRM regards 11C-labeled Pittsburgh Compound-B (PiB) positron emission tomography (PET) imaging data as smooth signals defined on an unknown graph. This graph is then estimated through an optimization framework, which fits the graph to the data with an adjustable level of uniformity of the connection weights. Under the assumed data model, results based on simulated data illustrate that our approach can accurately reconstruct the underlying network, often with better reconstruction than those obtained by both sample correlation and ℓ1-regularized partial correlation estimation. Evaluations performed upon PiB-PET imaging data of 30 AD and 40 elderly normal control (NC) subjects demonstrate that the connectivity patterns revealed by the GRM are easy to interpret and consistent with known pathology. Moreover, the hubs of the reconstructed networks match the cortical hubs given by functional MRI. The discriminative network features including both global connectivity measurements and degree statistics of specific nodes discovered from the AD and NC amyloid-beta networks provide new potential biomarkers for preclinical and clinical AD. PMID:26024224

  10. Convergence of the Graph Allen-Cahn Scheme

    NASA Astrophysics Data System (ADS)

    Luo, Xiyang; Bertozzi, Andrea L.

    2017-05-01

    The graph Laplacian and the graph cut problem are closely related to Markov random fields, and have many applications in clustering and image segmentation. The diffuse interface model is widely used for modeling in material science, and can also be used as a proxy to total variation minimization. In Bertozzi and Flenner (Multiscale Model Simul 10(3):1090-1118, 2012), an algorithm was developed to generalize the diffuse interface model to graphs to solve the graph cut problem. This work analyzes the conditions for the graph diffuse interface algorithm to converge. Using techniques from numerical PDE and convex optimization, monotonicity in function value and convergence under an a posteriori condition are shown for a class of schemes under a graph-independent stepsize condition. We also generalize our results to incorporate spectral truncation, a common technique used to save computation cost, and also to the case of multiclass classification. Various numerical experiments are done to compare theoretical results with practical performance.

  11. Most Undirected Random Graphs Are Amplifiers of Selection for Birth-Death Dynamics, but Suppressors of Selection for Death-Birth Dynamics.

    PubMed

    Hindersin, Laura; Traulsen, Arne

    2015-11-01

    We analyze evolutionary dynamics on graphs, where the nodes represent individuals of a population. The links of a node describe which other individuals can be displaced by the offspring of the individual on that node. Amplifiers of selection are graphs for which the fixation probability is increased for advantageous mutants and decreased for disadvantageous mutants. A few examples of such amplifiers have been developed, but so far it is unclear how many such structures exist and how to construct them. Here, we show that almost any undirected random graph is an amplifier of selection for Birth-death updating, where an individual is selected to reproduce with probability proportional to its fitness and one of its neighbors is replaced by that offspring at random. If we instead focus on death-Birth updating, in which a random individual is removed and its neighbors compete for the empty spot, then the same ensemble of graphs consists of almost only suppressors of selection for which the fixation probability is decreased for advantageous mutants and increased for disadvantageous mutants. Thus, the impact of population structure on evolutionary dynamics is a subtle issue that will depend on seemingly minor details of the underlying evolutionary process.

  12. The role of reliability graph models in assuring dependable operation of complex hardware/software systems

    NASA Technical Reports Server (NTRS)

    Patterson-Hine, F. A.; Davis, Gloria J.; Pedar, A.

    1991-01-01

    The complexity of computer systems currently being designed for critical applications in the scientific, commercial, and military arenas requires the development of new techniques for utilizing models of system behavior in order to assure 'ultra-dependability'. The complexity of these systems, such as Space Station Freedom and the Air Traffic Control System, stems from their highly integrated designs containing both hardware and software as critical components. Reliability graph models, such as fault trees and digraphs, are used frequently to model hardware systems. Their applicability for software systems has also been demonstrated for software safety analysis and the analysis of software fault tolerance. This paper discusses further uses of graph models in the design and implementation of fault management systems for safety critical applications.

  13. Using a high-dimensional graph of semantic space to model relationships among words

    PubMed Central

    Jackson, Alice F.; Bolger, Donald J.

    2014-01-01

    The GOLD model (Graph Of Language Distribution) is a network model constructed based on co-occurrence in a large corpus of natural language that may be used to explore what information may be present in a graph-structured model of language, and what information may be extracted through theoretically-driven algorithms as well as standard graph analysis methods. The present study will employ GOLD to examine two types of relationship between words: semantic similarity and associative relatedness. Semantic similarity refers to the degree of overlap in meaning between words, while associative relatedness refers to the degree to which two words occur in the same schematic context. It is expected that a graph structured model of language constructed based on co-occurrence should easily capture associative relatedness, because this type of relationship is thought to be present directly in lexical co-occurrence. However, it is hypothesized that semantic similarity may be extracted from the intersection of the set of first-order connections, because two words that are semantically similar may occupy similar thematic or syntactic roles across contexts and thus would co-occur lexically with the same set of nodes. Two versions the GOLD model that differed in terms of the co-occurence window, bigGOLD at the paragraph level and smallGOLD at the adjacent word level, were directly compared to the performance of a well-established distributional model, Latent Semantic Analysis (LSA). The superior performance of the GOLD models (big and small) suggest that a single acquisition and storage mechanism, namely co-occurrence, can account for associative and conceptual relationships between words and is more psychologically plausible than models using singular value decomposition (SVD). PMID:24860525

  14. A graph model for preventing railway accidents based on the maximal information coefficient

    NASA Astrophysics Data System (ADS)

    Shao, Fubo; Li, Keping

    2017-01-01

    A number of factors influences railway safety. It is an important work to identify important influencing factors and to build the relationship between railway accident and its influencing factors. The maximal information coefficient (MIC) is a good measure of dependence for two-variable relationships which can capture a wide range of associations. Employing MIC, a graph model is proposed for preventing railway accidents which avoids complex mathematical computation. In the graph, nodes denote influencing factors of railway accidents and edges represent dependence of the two linked factors. With the increasing of dependence level, the graph changes from a globally coupled graph to isolated points. Moreover, the important influencing factors are identified from many factors which are the monitor key. Then the relationship between railway accident and important influencing factors is obtained by employing the artificial neural networks. With the relationship, a warning mechanism is built by giving the dangerous zone. If the related factors fall into the dangerous zone in railway operations, the warning level should be raised. The built warning mechanism can prevent railway accidents and can promote railway safety.

  15. Graphing Matters.

    ERIC Educational Resources Information Center

    Paine, Carolyn

    1983-01-01

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

  16. Stability and optimization in structured population models on graphs.

    PubMed

    Colombo, Rinaldo M; Garavello, Mauro

    2015-04-01

    We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular choice of the boundary condition allows to comprehend models with very different structures. In particular, we consider a juvenile-adult model, the problem of the optimal mating ratio and a model for the optimal management of biological resources. The stability result obtained allows to tackle various optimal management/control problems, providing sufficient conditions for the existence of optimal choices/controls.

  17. International Space Station Centrifuge Rotor Models A Comparison of the Euler-Lagrange and the Bond Graph Modeling Approach

    NASA Technical Reports Server (NTRS)

    Nguyen, Louis H.; Ramakrishnan, Jayant; Granda, Jose J.

    2006-01-01

    The assembly and operation of the International Space Station (ISS) require extensive testing and engineering analysis to verify that the Space Station system of systems would work together without any adverse interactions. Since the dynamic behavior of an entire Space Station cannot be tested on earth, math models of the Space Station structures and mechanical systems have to be built and integrated in computer simulations and analysis tools to analyze and predict what will happen in space. The ISS Centrifuge Rotor (CR) is one of many mechanical systems that need to be modeled and analyzed to verify the ISS integrated system performance on-orbit. This study investigates using Bond Graph modeling techniques as quick and simplified ways to generate models of the ISS Centrifuge Rotor. This paper outlines the steps used to generate simple and more complex models of the CR using Bond Graph Computer Aided Modeling Program with Graphical Input (CAMP-G). Comparisons of the Bond Graph CR models with those derived from Euler-Lagrange equations in MATLAB and those developed using multibody dynamic simulation at the National Aeronautics and Space Administration (NASA) Johnson Space Center (JSC) are presented to demonstrate the usefulness of the Bond Graph modeling approach for aeronautics and space applications.

  18. Human connectome module pattern detection using a new multi-graph MinMax cut model.

    PubMed

    De, Wang; Wang, Yang; Nie, Feiping; Yan, Jingwen; Cai, Weidong; Saykin, Andrew J; Shen, Li; Huang, Heng

    2014-01-01

    Many recent scientific efforts have been devoted to constructing the human connectome using Diffusion Tensor Imaging (DTI) data for understanding the large-scale brain networks that underlie higher-level cognition in human. However, suitable computational network analysis tools are still lacking in human connectome research. To address this problem, we propose a novel multi-graph min-max cut model to detect the consistent network modules from the brain connectivity networks of all studied subjects. A new multi-graph MinMax cut model is introduced to solve this challenging computational neuroscience problem and the efficient optimization algorithm is derived. In the identified connectome module patterns, each network module shows similar connectivity patterns in all subjects, which potentially associate to specific brain functions shared by all subjects. We validate our method by analyzing the weighted fiber connectivity networks. The promising empirical results demonstrate the effectiveness of our method.

  19. Linear finite-difference bond graph model of an ionic polymer actuator

    NASA Astrophysics Data System (ADS)

    Bentefrit, M.; Grondel, S.; Soyer, C.; Fannir, A.; Cattan, E.; Madden, J. D.; Nguyen, T. M. G.; Plesse, C.; Vidal, F.

    2017-09-01

    With the recent growing interest for soft actuation, many new types of ionic polymers working in air have been developed. Due to the interrelated mechanical, electrical, and chemical properties which greatly influence the characteristics of such actuators, their behavior is complex and difficult to understand, predict and optimize. In light of this challenge, an original linear multiphysics finite difference bond graph model was derived to characterize this ionic actuation. This finite difference scheme was divided into two coupled subparts, each related to a specific physical, electrochemical or mechanical domain, and then converted into a bond graph model as this language is particularly suited for systems from multiple energy domains. Simulations were then conducted and a good agreement with the experimental results was obtained. Furthermore, an analysis of the power efficiency of such actuators as a function of space and time was proposed and allowed to evaluate their performance.

  20. Intrinsic graph structure estimation using graph Laplacian.

    PubMed

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

    2014-07-01

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

  1. Formal modeling of Gene Ontology annotation predictions based on factor graphs

    NASA Astrophysics Data System (ADS)

    Spetale, Flavio; Murillo, Javier; Tapia, Elizabeth; Arce, Débora; Ponce, Sergio; Bulacio, Pilar

    2016-04-01

    Gene Ontology (GO) is a hierarchical vocabulary for gene product annotation. Its synergy with machine learning classification methods has been widely used for the prediction of protein functions. Current classification methods rely on heuristic solutions to check the consistency with some aspects of the underlying GO structure. In this work we formalize the GO is-a relationship through predicate logic. Moreover, an ontology model based on Forney Factor Graph (FFG) is shown on a general fragment of Cellular Component GO.

  2. Graph theoretical analysis of the energy landscape of model polymers.

    PubMed

    Baiesi, Marco; Bongini, Lorenzo; Casetti, Lapo; Tattini, Lorenzo

    2009-07-01

    In systems characterized by a rough potential-energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and splitting of metastable states, have nontrivial effects on such networks and must be taken into account. We do this by means of a recently proposed renormalization procedure. This method is applied to analyze the topology of the network of metastable states for different polypeptidic sequences in a minimalistic polymer model. A smaller spectral dimension emerges as a hallmark of stability of the global energy minimum and highlights a nonobvious link between dynamic and thermodynamic properties.

  3. Ranking Medical Subject Headings using a factor graph model.

    PubMed

    Wei, Wei; Demner-Fushman, Dina; Wang, Shuang; Jiang, Xiaoqian; Ohno-Machado, Lucila

    2015-01-01

    Automatically assigning MeSH (Medical Subject Headings) to articles is an active research topic. Recent work demonstrated the feasibility of improving the existing automated Medical Text Indexer (MTI) system, developed at the National Library of Medicine (NLM). Encouraged by this work, we propose a novel data-driven approach that uses semantic distances in the MeSH ontology for automated MeSH assignment. Specifically, we developed a graphical model to propagate belief through a citation network to provide robust MeSH main heading (MH) recommendation. Our preliminary results indicate that this approach can reach high Mean Average Precision (MAP) in some scenarios.

  4. Augmenting Parametric Optimal Ascent Trajectory Modeling with Graph Theory

    NASA Technical Reports Server (NTRS)

    Dees, Patrick D.; Zwack, Matthew R.; Edwards, Stephen; Steffens, Michael

    2016-01-01

    into Conceptual and Pre-Conceptual design, knowledge of the effects originating from changes to the vehicle must be calculated. In order to do this, a model capable of quantitatively describing any vehicle within the entire design space under consideration must be constructed. This model must be based upon analysis of acceptable fidelity, which in this work comes from POST. Design space interrogation can be achieved with surrogate modeling, a parametric, polynomial equation representing a tool. A surrogate model must be informed by data from the tool with enough points to represent the solution space for the chosen number of variables with an acceptable level of error. Therefore, Design Of Experiments (DOE) is used to select points within the design space to maximize information gained on the design space while minimizing number of data points required. To represent a design space with a non-trivial number of variable parameters the number of points required still represent an amount of work which would take an inordinate amount of time via the current paradigm of manual analysis, and so an automated method was developed. The best practices of expert trajectory analysts working within NASA Marshall's Advanced Concepts Office (ACO) were implemented within a tool called multiPOST. These practices include how to use the output data from a previous run of POST to inform the next, determining whether a trajectory solution is feasible from a real-world perspective, and how to handle program execution errors. The tool was then augmented with multiprocessing capability to enable analysis on multiple trajectories simultaneously, allowing throughput to scale with available computational resources. In this update to the previous work the authors discuss issues with the method and solutions.

  5. Analysis of Business Connections Utilizing Theory of Topology of Random Graphs

    NASA Astrophysics Data System (ADS)

    Trelewicz, Jennifer Q.; Volovich, Igor V.

    2006-03-01

    A business ecosystem is a system that describes interactions between organizations. In this paper, we build a theoretical framework that defines a model which can be used to analyze the business ecosystem. The basic concepts within the framework are organizations, business connections, and market, that are all defined in the paper. Many researchers analyze the performance and structure of business using the workflow of the business. Our work in business connections answers a different set of questions, concerning the monetary value in the business ecosystem, rather than the task-interaction view that is provided by workflow analysis. We apply methods for analysis of the topology of complex networks, characterized by the concepts of small path length, clustering, and scale-free degree distributions. To model the dynamics of the business ecosystem we analyze the notion of the state of an organization at a given instant of time. We point out that the notion of state in this case is fundamentally different from the concept of state of the system which is used in classical or quantum physics. To describe the state of the organization at a given time one has to know the probability of payments to contracts which in fact depend on the future behavior of the agents on the market. Therefore methods of p-adic analysis are appropriate to explore such a behavior. Microeconomic and macroeconomic factors are indivisible and moreover the actual state of the organization depends on the future. In this framework some simple models are analyzed in detail. Company strategy can be influenced by analysis of models, which can provide a probabilistic understanding of the market, giving degrees of predictability.

  6. Multi-Modal Clique-Graph Matching for View-Based 3D Model Retrieval.

    PubMed

    Liu, An-An; Nie, Wei-Zhi; Gao, Yue; Su, Yu-Ting

    2016-05-01

    Multi-view matching is an important but a challenging task in view-based 3D model retrieval. To address this challenge, we propose an original multi-modal clique graph (MCG) matching method in this paper. We systematically present a method for MCG generation that is composed of cliques, which consist of neighbor nodes in multi-modal feature space and hyper-edges that link pairwise cliques. Moreover, we propose an image set-based clique/edgewise similarity measure to address the issue of the set-to-set distance measure, which is the core problem in MCG matching. The proposed MCG provides the following benefits: 1) preserves the local and global attributes of a graph with the designed structure; 2) eliminates redundant and noisy information by strengthening inliers while suppressing outliers; and 3) avoids the difficulty of defining high-order attributes and solving hyper-graph matching. We validate the MCG-based 3D model retrieval using three popular single-modal data sets and one novel multi-modal data set. Extensive experiments show the superiority of the proposed method through comparisons. Moreover, we contribute a novel real-world 3D object data set, the multi-view RGB-D object data set. To the best of our knowledge, it is the largest real-world 3D object data set containing multi-modal and multi-view information.

  7. Graph Library

    SciTech Connect

    Schulz, Martin; Arnold, Dorian

    2007-06-12

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

  8. A geometric graph model for citation networks of exponentially growing scientific papers

    NASA Astrophysics Data System (ADS)

    Xie, Zheng; Ouyang, Zhenzheng; Liu, Qi; Li, Jianping

    2016-08-01

    In citation networks, the content relativity of papers is a precondition of engendering citations, which is hard to model by a topological graph. A geometric graph is proposed to predict some features of the citation networks with exponentially growing papers, which addresses the precondition by using coordinates of nodes to model the research contents of papers, and geometric distances between nodes to diversities of research contents between papers. Citations between modeled papers are drawn according to a geometric rule, which addresses the precondition as well as some other factors engendering citations, namely academic influences of papers, aging of those influences, and incomplete copying of references. Instead of cumulative advantage of degree, the model illustrates that the scale-free property of modeled networks arises from the inhomogeneous academic influences of modeled papers. The model can also reproduce some other statistical features of citation networks, e.g. in- and out-assortativities, which show the model provides a suitable tool to understand some aspects of citation networks by geometry.

  9. 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.

  10. Modeling spatial decisions with graph theory: logging roads and forest fragmentation in the Brazilian Amazon.

    PubMed

    Walker, Robert; Arima, Eugenio; Messina, Joe; Soares-Filho, Britaldo; Perz, Stephen; Vergara, Dante; Sales, Marcio; Pereira, Ritaumaria; Castro, Williams

    2013-01-01

    This article addresses the spatial decision-making of loggers and implications for forest fragmentation in the Amazon basin. It provides a behavioral explanation for fragmentation by modeling how loggers build road networks, typically abandoned upon removal of hardwoods. Logging road networks provide access to land, and the settlers who take advantage of them clear fields and pastures that accentuate their spatial signatures. In shaping agricultural activities, these networks organize emergent patterns of forest fragmentation, even though the loggers move elsewhere. The goal of the article is to explicate how loggers shape their road networks, in order to theoretically explain an important type of forest fragmentation found in the Amazon basin, particularly in Brazil. This is accomplished by adapting graph theory to represent the spatial decision-making of loggers, and by implementing computational algorithms that build graphs interpretable as logging road networks. The economic behavior of loggers is conceptualized as a profit maximization problem, and translated into spatial decision-making by establishing a formal correspondence between mathematical graphs and road networks. New computational approaches, adapted from operations research, are used to construct graphs and simulate spatial decision-making as a function of discount rates, land tenure, and topographic constraints. The algorithms employed bracket a range of behavioral settings appropriate for areas of terras de volutas, public lands that have not been set aside for environmental protection, indigenous peoples, or colonization. The simulation target sites are located in or near so-called Terra do Meio, once a major logging frontier in the lower Amazon Basin. Simulation networks are compared to empirical ones identified by remote sensing and then used to draw inferences about factors influencing the spatial behavior of loggers. Results overall suggest that Amazonia's logging road networks induce more

  11. Guidelines for a graph-theoretic implementation of structural equation modeling

    USGS Publications Warehouse

    Grace, James B.; Schoolmaster, Donald R.; Guntenspergen, Glenn R.; Little, Amanda M.; Mitchell, Brian R.; Miller, Kathryn M.; Schweiger, E. William

    2012-01-01

    Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of data. New ideas and methods emerging from the study of causality, influences from the field of graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of SEM. Guidelines for implementing the expanded capabilities of SEM are currently lacking. In this paper we describe new developments in SEM that we believe constitute a third-generation of the methodology. Most characteristic of this new approach is the generalization of the structural equation model as a causal graph. In this generalization, analyses are based on graph theoretic principles rather than analyses of matrices. Also, new devices such as metamodels and causal diagrams, as well as an increased emphasis on queries and probabilistic reasoning, are now included. Estimation under a graph theory framework permits the use of Bayesian or likelihood methods. The guidelines presented start from a declaration of the goals of the analysis. We then discuss how theory frames the modeling process, requirements for causal interpretation, model specification choices, selection of estimation method, model evaluation options, and use of queries, both to summarize retrospective results and for prospective analyses. The illustrative example presented involves monitoring data from wetlands on Mount Desert Island, home of Acadia National Park. Our presentation walks through the decision process involved in developing and evaluating models, as well as drawing inferences from the resulting prediction equations. In addition to evaluating hypotheses about the connections between human activities and biotic responses, we illustrate how the structural equation (SE) model can be queried to understand how interventions might take advantage of an environmental threshold to limit Typha invasions. The guidelines presented provide for

  12. A Mixed Effects Randomized Item Response Model

    ERIC Educational Resources Information Center

    Fox, J.-P.; Wyrick, Cheryl

    2008-01-01

    The randomized response technique ensures that individual item responses, denoted as true item responses, are randomized before observing them and so-called randomized item responses are observed. A relationship is specified between randomized item response data and true item response data. True item response data are modeled with a (non)linear…

  13. The many faces of graph dynamics

    NASA Astrophysics Data System (ADS)

    Pignolet, Yvonne Anne; Roy, Matthieu; Schmid, Stefan; Tredan, Gilles

    2017-06-01

    The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a ‘one fits it all’ model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.

  14. Graphing trillions of triangles

    PubMed Central

    Burkhardt, Paul

    2016-01-01

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

  15. Structural modeling and analysis of an effluent treatment process for electroplating--a graph theoretic approach.

    PubMed

    Kumar, Abhishek; Clement, Shibu; Agrawal, V P

    2010-07-15

    An attempt is made to address a few ecological and environment issues by developing different structural models for effluent treatment system for electroplating. The effluent treatment system is defined with the help of different subsystems contributing to waste minimization. Hierarchical tree and block diagram showing all possible interactions among subsystems are proposed. These non-mathematical diagrams are converted into mathematical models for design improvement, analysis, comparison, storage retrieval and commercially off-the-shelf purchases of different subsystems. This is achieved by developing graph theoretic model, matrix models and variable permanent function model. Analysis is carried out by permanent function, hierarchical tree and block diagram methods. Storage and retrieval is done using matrix models. The methodology is illustrated with the help of an example. Benefits to the electroplaters/end user are identified. 2010 Elsevier B.V. All rights reserved.

  16. Evolutionary stability on graphs.

    PubMed

    Ohtsuki, Hisashi; Nowak, Martin A

    2008-04-21

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

  17. Evolutionary stability on graphs

    PubMed Central

    Ohtsuki, Hisashi; Nowak, Martin A.

    2008-01-01

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

  18. Mathematic Modeling of Complex Hydraulic Machinery Systems When Evaluating Reliability Using Graph Theory

    NASA Astrophysics Data System (ADS)

    Zemenkova, M. Yu; Shipovalov, A. N.; Zemenkov, Yu D.

    2016-04-01

    The main technological equipment of pipeline transport of hydrocarbons are hydraulic machines. During transportation of oil mainly used of centrifugal pumps, designed to work in the “pumping station-pipeline” system. Composition of a standard pumping station consists of several pumps, complex hydraulic piping. The authors have developed a set of models and algorithms for calculating system reliability of pumps. It is based on the theory of reliability. As an example, considered one of the estimation methods with the application of graph theory.

  19. Non-Hermitian random matrix models: Free random variable approach

    SciTech Connect

    Janik, R.A.,; Nowak, M.A., ||; Papp, G.,; Wambach, J.,; Zahed, I., |

    1997-04-01

    Using the standard concepts of free random variables, we show that for a large class of non-Hermitian random matrix models, the support of the eigenvalue distribution follows from their Hermitian analogs using a conformal transformation. We also extend the concepts of free random variables to the class of non-Hermitian matrices, and apply them to the models discussed by Ginibre-Girko (elliptic ensemble) [J. Ginibre, J. Math. Phys. {bold 6}, 1440 (1965); V. L. Girko, {ital Spectral Theory of Random Matrices} (in Russian) (Nauka, Moscow, 1988)] and Mahaux-Weidenm{umlt u}ller (chaotic resonance scattering) [C. Mahaux and H. A. Weidenm{umlt u}ller, {ital Shell-model Approach to Nuclear Reactions} (North-Holland, Amsterdam, 1969)]. {copyright} {ital 1997} {ital The American Physical Society}

  20. Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids

    PubMed Central

    José, Marco V.; Morgado, Eberto R.; Guimarães, Romeu Cardoso; Zamudio, Gabriel S.; de Farías, Sávio Torres; Bobadilla, Juan R.; Sosa, Daniela

    2014-01-01

    Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state. PMID:25370377

  1. An efficient and scalable graph modeling approach for capturing information at different levels in next generation sequencing reads

    PubMed Central

    2013-01-01

    Background Next generation sequencing technologies have greatly advanced many research areas of the biomedical sciences through their capability to generate massive amounts of genetic information at unprecedented rates. The advent of next generation sequencing has led to the development of numerous computational tools to analyze and assemble the millions to billions of short sequencing reads produced by these technologies. While these tools filled an important gap, current approaches for storing, processing, and analyzing short read datasets generally have remained simple and lack the complexity needed to efficiently model the produced reads and assemble them correctly. Results Previously, we presented an overlap graph coarsening scheme for modeling read overlap relationships on multiple levels. Most current read assembly and analysis approaches use a single graph or set of clusters to represent the relationships among a read dataset. Instead, we use a series of graphs to represent the reads and their overlap relationships across a spectrum of information granularity. At each information level our algorithm is capable of generating clusters of reads from the reduced graph, forming an integrated graph modeling and clustering approach for read analysis and assembly. Previously we applied our algorithm to simulated and real 454 datasets to assess its ability to efficiently model and cluster next generation sequencing data. In this paper we extend our algorithm to large simulated and real Illumina datasets to demonstrate that our algorithm is practical for both sequencing technologies. Conclusions Our overlap graph theoretic algorithm is able to model next generation sequencing reads at various levels of granularity through the process of graph coarsening. Additionally, our model allows for efficient representation of the read overlap relationships, is scalable for large datasets, and is practical for both Illumina and 454 sequencing technologies. PMID:24564333

  2. The aggregate path coupling method for the Potts model on bipartite graph

    NASA Astrophysics Data System (ADS)

    Hernández, José C.; Kovchegov, Yevgeniy; Otto, Peter T.

    2017-02-01

    In this paper, we derive the large deviation principle for the Potts model on the complete bipartite graph Kn,n as n increases to infinity. Next, for the Potts model on Kn,n, we provide an extension of the method of aggregate path coupling that was originally developed in the work of Kovchegov, Otto, and Titus [J. Stat. Phys. 144(5), 1009-1027 (2011)] for the mean-field Blume-Capel model and in Kovchegov and Otto [J. Stat. Phys. 161(3), 553-576 (2015)] for a general mean-field setting that included the generalized Curie-Weiss-Potts model analyzed in the work of Jahnel et al. [Markov Process. Relat. Fields 20, 601-632 (2014)]. We use the aggregate path coupling method to identify and determine the threshold value βs separating the rapid and slow mixing regimes for the Glauber dynamics of the Potts model on Kn,n.

  3. 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.

  4. 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.

  5. Modeling and Density Estimation of an Urban Freeway Network Based on Dynamic Graph Hybrid Automata

    PubMed Central

    Chen, Yangzhou; Guo, Yuqi; Wang, Ying

    2017-01-01

    In this paper, in order to describe complex network systems, we firstly propose a general modeling framework by combining a dynamic graph with hybrid automata and thus name it Dynamic Graph Hybrid Automata (DGHA). Then we apply this framework to model traffic flow over an urban freeway network by embedding the Cell Transmission Model (CTM) into the DGHA. With a modeling procedure, we adopt a dual digraph of road network structure to describe the road topology, use linear hybrid automata to describe multi-modes of dynamic densities in road segments and transform the nonlinear expressions of the transmitted traffic flow between two road segments into piecewise linear functions in terms of multi-mode switchings. This modeling procedure is modularized and rule-based, and thus is easily-extensible with the help of a combination algorithm for the dynamics of traffic flow. It can describe the dynamics of traffic flow over an urban freeway network with arbitrary topology structures and sizes. Next we analyze mode types and number in the model of the whole freeway network, and deduce a Piecewise Affine Linear System (PWALS) model. Furthermore, based on the PWALS model, a multi-mode switched state observer is designed to estimate the traffic densities of the freeway network, where a set of observer gain matrices are computed by using the Lyapunov function approach. As an example, we utilize the PWALS model and the corresponding switched state observer to traffic flow over Beijing third ring road. In order to clearly interpret the principle of the proposed method and avoid computational complexity, we adopt a simplified version of Beijing third ring road. Practical application for a large-scale road network will be implemented by decentralized modeling approach and distributed observer designing in the future research. PMID:28353664

  6. Modeling and Density Estimation of an Urban Freeway Network Based on Dynamic Graph Hybrid Automata.

    PubMed

    Chen, Yangzhou; Guo, Yuqi; Wang, Ying

    2017-03-29

    In this paper, in order to describe complex network systems, we firstly propose a general modeling framework by combining a dynamic graph with hybrid automata and thus name it Dynamic Graph Hybrid Automata (DGHA). Then we apply this framework to model traffic flow over an urban freeway network by embedding the Cell Transmission Model (CTM) into the DGHA. With a modeling procedure, we adopt a dual digraph of road network structure to describe the road topology, use linear hybrid automata to describe multi-modes of dynamic densities in road segments and transform the nonlinear expressions of the transmitted traffic flow between two road segments into piecewise linear functions in terms of multi-mode switchings. This modeling procedure is modularized and rule-based, and thus is easily-extensible with the help of a combination algorithm for the dynamics of traffic flow. It can describe the dynamics of traffic flow over an urban freeway network with arbitrary topology structures and sizes. Next we analyze mode types and number in the model of the whole freeway network, and deduce a Piecewise Affine Linear System (PWALS) model. Furthermore, based on the PWALS model, a multi-mode switched state observer is designed to estimate the traffic densities of the freeway network, where a set of observer gain matrices are computed by using the Lyapunov function approach. As an example, we utilize the PWALS model and the corresponding switched state observer to traffic flow over Beijing third ring road. In order to clearly interpret the principle of the proposed method and avoid computational complexity, we adopt a simplified version of Beijing third ring road. Practical application for a large-scale road network will be implemented by decentralized modeling approach and distributed observer designing in the future research.

  7. The effects of node exclusion on the centrality measures in graph models of interacting economic agents

    NASA Astrophysics Data System (ADS)

    Caetano, Marco Antonio Leonel; Yoneyama, Takashi

    2015-07-01

    This work concerns the study of the effects felt by a network as a whole when a specific node is perturbed. Many real world systems can be described by network models in which the interactions of the various agents can be represented as an edge of a graph. With a graph model in hand, it is possible to evaluate the effect of deleting some of its edges on the architecture and values of nodes of the network. Eventually a node may end up isolated from the rest of the network and an interesting problem is to have a quantitative measure of the impact of such an event. For instance, in the field of finance, the network models are very popular and the proposed methodology allows to carry out "what if" tests in terms of weakening the links between the economic agents, represented as nodes. The two main concepts employed in the proposed methodology are (i) the vibrational IC-Information Centrality, which can provide a measure of the relative importance of a particular node in a network and (ii) autocatalytic networks that can indicate the evolutionary trends of the network. Although these concepts were originally proposed in the context of other fields of knowledge, they were also found to be useful in analyzing financial networks. In order to illustrate the applicability of the proposed methodology, a case of study using the actual data comprising stock market indices of 12 countries is presented.

  8. Reaction spreading on graphs.

    PubMed

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

    2012-11-01

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

  9. 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.

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

    NASA Astrophysics Data System (ADS)

    Kotzagiannidis, Madeleine S.; Dragotti, Pier Luigi

    2015-08-01

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

  11. Robust model-based object recognition using a dual-hierarchy graph

    NASA Astrophysics Data System (ADS)

    Weiss, Isaac

    2012-05-01

    We present a general purpose, inherently robust system for object representation and recognition. The system is model-based and knowledge-based, with knowledge derived from analysis of objects and images, unlike many of the current methods which rely on generic statistical inference. This knowledge is intrinsic to the objects themselves, based on geometric and semantic relations among objects. Therefor the system is insensitive to external interferences such as viewpoint changes (scale, pose etc.), illumination changes, occlusion, shadows, sensor noise etc. It also handles variability in the object itself, e.g. articulation or camouflage. We represent all available models in a graph containing two independent but interlocking hierarchies. One of these intrinsic hierarchies is based on parts, e.g. a truck has a cabin, a trunk, wheels etc. The other hierarchy we call the "Level of Abstraction (LOA), e.g. a vehicle is more abstract than a truck, a rectangle is more abstract than a door. This enables us to represent and recognize generic objects just as easily as specific ones. A new algorithm for traversing our graph, combining the advantages of both top-down and bottom-up strategies, has been implemented.

  12. Interactive vessel-tracking with a hybrid model-based and graph-based approach

    NASA Astrophysics Data System (ADS)

    Fritz, Dominik; Beck, Thomas; Scheuering, Michael

    2009-02-01

    For assessment of coronary artery disease (CAD) and peripheral artery disease (PAD) the automatic extraction of vessel centerlines is a crucial technology. In the most common approach two seed points have to be manually placed in the vessel and the centerline is automatically computed between these points. This methodology is appropriate for the quantitative analysis of single vessel segments. However, for an interactive and fast reading of complete datasets a more interactive approach would be beneficial. In this work we introduce an interactive vessel-tracking approach which eases the reading of cardiac and vascular CTA datasets. Starting with a single seed point a local vessel-tracking is initialized and extended in both directions while the user "walks" along the vessel centerline. For a robust tracking of a wide variety of vessel diameters, from coronaries to the aorta, we combine a local A*-graph-search for tiny vessels and a model-based tracking for larger vessels to an hybrid model-based and graph-based approach. In order to further ease the reading of cardiac and vascular CTA datasets, we introduce a subdivision of the interactively acquired centerline into segments that can be approximated by a single plane. This subdivision allows the visualization of the vessel in optimally oriented multi-planar reformations (MPR). The proposed visualization combines the advantage of a curved planar reformation (CPR), showing a large part of the vessel in one view, with the benefits of a MPR, having a non distorted more trustable image.

  13. 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.…

  14. 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.…

  15. A combined crystal plasticity and graph-based vertex model of dynamic recrystallization at large deformations

    NASA Astrophysics Data System (ADS)

    Mellbin, Y.; Hallberg, H.; Ristinmaa, M.

    2015-06-01

    A mesoscale model of microstructure evolution is formulated in the present work by combining a crystal plasticity model with a graph-based vertex algorithm. This provides a versatile formulation capable of capturing finite-strain deformations, development of texture and microstructure evolution through recrystallization. The crystal plasticity model is employed in a finite element setting and allows tracing of stored energy build-up in the polycrystal microstructure and concurrent reorientation of the crystal lattices in the grains. This influences the progression of recrystallization as nucleation occurs at sites with sufficient stored energy and since the grain boundary mobility and energy is allowed to vary with crystallographic misorientation across the boundaries. The proposed graph-based vertex model describes the topological changes to the grain microstructure and keeps track of the grain inter-connectivity. Through homogenization, the macroscopic material response is also obtained. By the proposed modeling approach, grain structure evolution at large deformations as well as texture development are captured. This is in contrast to most other models of recrystallization which are usually limited by assumptions of one or the other of these factors. In simulation examples, the model is in the present study shown to capture the salient features of dynamic recrystallization, including the effects of varying initial grain size and strain rate on the transitions between single-peak and multiple-peak oscillating flow stress behavior. Also the development of recrystallization texture and the influence of different assumptions on orientation of recrystallization nuclei are investigated. Further, recrystallization kinetics are discussed and compared to classical JMAK theory. To promote computational efficiency, the polycrystal plasticity algorithm is parallelized through a GPU implementation that was recently proposed by the authors.

  16. 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)

  17. Combining computational models, semantic annotations and simulation experiments in a graph database.

    PubMed

    Henkel, Ron; Wolkenhauer, Olaf; Waltemath, Dagmar

    2015-01-01

    Model repositories such as the BioModels Database, the CellML Model Repository or JWS Online are frequently accessed to retrieve computational models of biological systems. However, their storage concepts support only restricted types of queries and not all data inside the repositories can be retrieved. In this article we present a storage concept that meets this challenge. It grounds on a graph database, reflects the models' structure, incorporates semantic annotations and simulation descriptions and ultimately connects different types of model-related data. The connections between heterogeneous model-related data and bio-ontologies enable efficient search via biological facts and grant access to new model features. The introduced concept notably improves the access of computational models and associated simulations in a model repository. This has positive effects on tasks such as model search, retrieval, ranking, matching and filtering. Furthermore, our work for the first time enables CellML- and Systems Biology Markup Language-encoded models to be effectively maintained in one database. We show how these models can be linked via annotations and queried. Database URL: https://sems.uni-rostock.de/projects/masymos/

  18. Representation of measured ejector characteristics by simple Eulerian bond graph models

    NASA Astrophysics Data System (ADS)

    Paynter, H. M.

    1985-12-01

    For some time, a purely fluidic type of pump or compressor has existed. This device possesses no solid moving parts. Such an ejector of jet-pump employs the momentum of a high velocity jet from the drive flow to entrain and pressurize a secondary suction flow stream. One application of such ejectors is related to an employment by the nuclear industry. Certain accidents have drawn attention to the grossly inadequate data base for ejectors operating under extreme pathological conditions including reverse flows. In connection with these developments, extensive tests were conducted. The present paper uses primarily data obtained in these tests. Attention is given to an analysis of the test results, aspects of bond graph representation, internal Eulerian flows satisfying a condition of Eulerian similitude, a canonical model, moduli functions, a near-perfect Eulerian device, and constant and variable paramter models. The considered tests and studies made it possible to establish a structured performance model for ejectors.

  19. Combining computational models, semantic annotations and simulation experiments in a graph database

    PubMed Central

    Henkel, Ron; Wolkenhauer, Olaf; Waltemath, Dagmar

    2015-01-01

    Model repositories such as the BioModels Database, the CellML Model Repository or JWS Online are frequently accessed to retrieve computational models of biological systems. However, their storage concepts support only restricted types of queries and not all data inside the repositories can be retrieved. In this article we present a storage concept that meets this challenge. It grounds on a graph database, reflects the models’ structure, incorporates semantic annotations and simulation descriptions and ultimately connects different types of model-related data. The connections between heterogeneous model-related data and bio-ontologies enable efficient search via biological facts and grant access to new model features. The introduced concept notably improves the access of computational models and associated simulations in a model repository. This has positive effects on tasks such as model search, retrieval, ranking, matching and filtering. Furthermore, our work for the first time enables CellML- and Systems Biology Markup Language-encoded models to be effectively maintained in one database. We show how these models can be linked via annotations and queried. Database URL: https://sems.uni-rostock.de/projects/masymos/ PMID:25754863

  20. On the mixing time of geographical threshold graphs

    SciTech Connect

    Bradonjic, Milan

    2009-01-01

    In this paper, we study the mixing time of 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). We specifically study the mixing times of random walks on 2-dimensional GTGs near the connectivity threshold. We provide a set of criteria on the distribution of vertex weights that guarantees that the mixing time is {Theta}(n log n).

  1. Menopause and big data: Word Adjacency Graph modeling of menopause-related ChaCha data.

    PubMed

    Carpenter, Janet S; Groves, Doyle; Chen, Chen X; Otte, Julie L; Miller, Wendy R

    2017-07-01

    To detect and visualize salient queries about menopause using Big Data from ChaCha. We used Word Adjacency Graph (WAG) modeling to detect clusters and visualize the range of menopause-related topics and their mutual proximity. The subset of relevant queries was fully modeled. We split each query into token words (ie, meaningful words and phrases) and removed stopwords (ie, not meaningful functional words). The remaining words were considered in sequence to build summary tables of words and two and three-word phrases. Phrases occurring at least 10 times were used to build a network graph model that was iteratively refined by observing and removing clusters of unrelated content. We identified two menopause-related subsets of queries by searching for questions containing menopause and menopause-related terms (eg, climacteric, hot flashes, night sweats, hormone replacement). The first contained 263,363 queries from individuals aged 13 and older and the second contained 5,892 queries from women aged 40 to 62 years. In the first set, we identified 12 topic clusters: 6 relevant to menopause and 6 less relevant. In the second set, we identified 15 topic clusters: 11 relevant to menopause and 4 less relevant. Queries about hormones were pervasive within both WAG models. Many of the queries reflected low literacy levels and/or feelings of embarrassment. We modeled menopause-related queries posed by ChaCha users between 2009 and 2012. ChaCha data may be used on its own or in combination with other Big Data sources to identify patient-driven educational needs and create patient-centered interventions.

  2. Automatic detection of inundation-related change areas in TerraSAR-X data using Markov image modeling on irregular graphs

    NASA Astrophysics Data System (ADS)

    Martinis, Sandro; Twele, André

    2010-05-01

    The worldwide increasing occurrence of flooding and the short-time monitoring capability of the new generation of high resolution synthetic aperture radar (SAR) sensors (TerraSAR-X, COSMO-SkyMed) require accurate and automatic methods for the detection of flood dynamics. This is especially important for operational rapid mapping purposes where the near-real time provision of precise information about the extent of a disaster and its spatio-temporal evolution is of key importance to support decision makers and humanitarian relief organizations. A split based parametric thresholding approach under the generalized Gaussian assumption is developed on normalized change index data to automatically solve the three-class change detection problem in large-size images with small class a priori probabilities. The thresholding result is used for the initialization of a hybrid Markov model which integrates both scale-dependent and spatial context into the classification process by combining hierarchical with noncausal Markov image modeling on irregular graphs. Hierarchical Markov modeling is accomplished by hierarchical maximum a posteriori (HMAP) estimation using Markov Chains in scale. Since this method requires only one bottom-up and one top-down pass on the graph, it offers high computational performance. To reduce the computational demand of the iterative optimization process related to noncausal Markov image models, we define a partial Markov Random Field (MRF) approach, which is applied on a restricted region of the lowest level of the graph. The selection of this region is based on a confidence map generated by combining the HMAP labeling result from the different graph levels. The proposed unsupervised change detection method is applied on a bi-temporal TerraSAR-X StripMap data set (3 m pixel spacing) of a real flood event. The effectiveness of the hybrid Markov image model in comparison to the sole application of the HMAP estimation is evaluated. Additionally, the

  3. The impact of home care nurses' numeracy and graph literacy on comprehension of visual display information: implications for dashboard design.

    PubMed

    Dowding, Dawn; Merrill, Jacqueline A; Onorato, Nicole; Barrón, Yolanda; Rosati, Robert J; Russell, David

    2017-04-27

    To explore home care nurses' numeracy and graph literacy and their relationship to comprehension of visualized data. A multifactorial experimental design using online survey software. Nurses were recruited from 2 Medicare-certified home health agencies. Numeracy and graph literacy were measured using validated scales. Nurses were randomized to 1 of 4 experimental conditions. Each condition displayed data for 1 of 4 quality indicators, in 1 of 4 different visualized formats (bar graph, line graph, spider graph, table). A mixed linear model measured the impact of numeracy, graph literacy, and display format on data understanding. In all, 195 nurses took part in the study. They were slightly more numerate and graph literate than the general population. Overall, nurses understood information presented in bar graphs most easily (88% correct), followed by tables (81% correct), line graphs (77% correct), and spider graphs (41% correct). Individuals with low numeracy and low graph literacy had poorer comprehension of information displayed across all formats. High graph literacy appeared to enhance comprehension of data regardless of numeracy capabilities. Clinical dashboards are increasingly used to provide information to clinicians in visualized format, under the assumption that visual display reduces cognitive workload. Results of this study suggest that nurses' comprehension of visualized information is influenced by their numeracy, graph literacy, and the display format of the data. Individual differences in numeracy and graph literacy skills need to be taken into account when designing dashboard technology.

  4. Error-Rate Estimation Based on Multi-Signal Flow Graph Model and Accelerated Radiation Tests

    PubMed Central

    Wang, Yueke; Xing, Kefei; Deng, Wei; Zhang, Zelong

    2016-01-01

    A method of evaluating the single-event effect soft-error vulnerability of space instruments before launched has been an active research topic in recent years. In this paper, a multi-signal flow graph model is introduced to analyze the fault diagnosis and meantime to failure (MTTF) for space instruments. A model for the system functional error rate (SFER) is proposed. In addition, an experimental method and accelerated radiation testing system for a signal processing platform based on the field programmable gate array (FPGA) is presented. Based on experimental results of different ions (O, Si, Cl, Ti) under the HI-13 Tandem Accelerator, the SFER of the signal processing platform is approximately 10−3(error/particle/cm2), while the MTTF is approximately 110.7 h. PMID:27583533

  5. Error-Rate Estimation Based on Multi-Signal Flow Graph Model and Accelerated Radiation Tests.

    PubMed

    He, Wei; Wang, Yueke; Xing, Kefei; Deng, Wei; Zhang, Zelong

    2016-01-01

    A method of evaluating the single-event effect soft-error vulnerability of space instruments before launched has been an active research topic in recent years. In this paper, a multi-signal flow graph model is introduced to analyze the fault diagnosis and meantime to failure (MTTF) for space instruments. A model for the system functional error rate (SFER) is proposed. In addition, an experimental method and accelerated radiation testing system for a signal processing platform based on the field programmable gate array (FPGA) is presented. Based on experimental results of different ions (O, Si, Cl, Ti) under the HI-13 Tandem Accelerator, the SFER of the signal processing platform is approximately 10-3(error/particle/cm2), while the MTTF is approximately 110.7 h.

  6. 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.

  7. 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.

  8. 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.

  9. Graph Theory Data Objects Applied to Stream Flow Network Representation in an Integrated Hydrological Model

    NASA Astrophysics Data System (ADS)

    Park, J.; Obeysekera, J.; Vanzee, R.

    2005-05-01

    The Management Simulation Engine (MSE) component of the Regional Simulation Model (RSM) incorporates a multi-level hierarchical control architecture which emphasizes the decoupling of hydrological state information from the management information processing applied to the states. A crucial aspect of effectively storing and accessing state information for water resource management purposes is the maintenance of an efficient storage mechanism which associates hydrological state information with the proper managerial abstractions. In the RSM this is done by storing hydrological and managerial information relevant to a water control unit (WCU) in a data storage object defined in the MSE Network. The MSE Network is an abstraction of the stream flow network and control structures suited to the needs of water resource routing and decisions. It is based on a standard graph theory representation of a flow network comprised of arcs and nodes. The MSE Network data objects serve as state and process information repositories for management processes. They maintain appropriately filtered state information, parameter storage relevant to WCU or hydraulic structure managerial constraints and variables, and serve as an integrated data source for any MSE algorithm. It also provides a mathematical representation of a constrained, interconnected flow network which facilitates efficient graph theory solutions of network connectivity and flow algorithms. This paper describes the MSE Network implementation in the RSM, an integrated hydrological computation engine aimed at meeting the needs for comprehensive integration of management features in coupled hydrological models [1]. [1] Belaineh, G., Peralta, R. C., Hughes, T. C., Simulation/ Optimization Modeling for Water Resources Management, ASCE Journal Water Resources Planning Management, 125(3), p 154-61, 1999

  10. On the assumption of cubic graphs of vascular networks

    NASA Astrophysics Data System (ADS)

    Cha, Sung-Hyuk; Chang, Sukmoon; Gargano, Michael L.

    2006-03-01

    A vascular network is often represented by a Reeb graph, which is a topological skeleton, and graph theory has been widely applied to analyze properties of a vascular network. A Reeb graph model for a vascular network is obtained by assigning the branch points of the network to be the vertices of the graph and the vessels between branch points to be the edges of the graph. Vascular networks develop by way of angiogenesis, a growth process that involves the biological mechanisms of vessel sprouting (budding) and splitting (intussusception). Vascular networks develop by way of two biological mechanisms of vessel sprouting (budding) and splitting (intussusception). According to a graph theory modeling of two vascular network growth mechanisms, all nodes in the Reeb graph must be cubic in degree except for two special nodes: the afferent (A) and efferent (E) nodes. We define that a vascular network is cubic if all internal nodes are cubic in degree. We consider six normal adult rat renal glomerular networks and use their reeb graphs already constructed and published in the literature. We observe that five of them contain internal vertices of degree higher than three. Branch points in vascular networks may appear to be of a higher degree if the imaging resolution cannot differentiate between blood vessels that are very close in proximity. Here, we propose a random graph theory model that edits a non-cubic vascular network into a cubic graph. We observe that the edited cubic graph from a non-cubic vascular network has the similar size and order as the one cubic vascular network.

  11. Learning graph matching.

    PubMed

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

    2009-06-01

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

  12. Assortativity of complementary graphs

    NASA Astrophysics Data System (ADS)

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

    2011-09-01

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

  13. A Graph Theoretic Approach for Hydraulic Fracturing and Wellbore Leakage Risk Modeling

    NASA Astrophysics Data System (ADS)

    Glosser, D.; Rose, K.; Bauer, J. R.; Warner, T.

    2016-12-01

    Recent large scale development of unconventional formations for fossil energy has raised concerns over the potential for fluid leakage between subsurface systems and wellbores. This is particularly true in regions with extensive drilling history, where spatial densities of wellbores are higher, and where significant uncertainties in the location and mechanical integrity of such wellbores exist. The generation of induced fracture networks during hydraulic fracturing may increase subsurface connectivity, and create the potential for unwanted fluid migration between operational and legacy wellbores and subsurface fracture networks. We present a graph theoretic approach for identifying geospatial regions and wellbores at increased risk for subsurface connectivity based on wellbore proximity and local geologic characteristics. The algorithm transforms user inputted geospatial data (geologic and wellbore x,y,z) to graph structure, where wellbores are represented as nodes, and where potential overlapping fracture network zones are represented as edges. The algorithm can be used to complement existing fracture models to better account for the reach of induced fractures, and to identify spatial extents at increased risk for unwanted subsurface connectivity. Additionally, the model can be used to identify regions in need of geophysical detection methods for locating undocumented wells. As a result, the method can be part of a cumulative strategy to reduce uncertainty inherent to combined geologic and engineered systems. The algorithm has been successfully tested against a known leakage scenario in Pennsylvania. In addition to identifying wells associated with the leakage event, the algorithm identified two other higher risk networks in the region. The algorithm output provides valuable information for industry to develop environmentally safe drilling and injection plans; and for regulators to identify specific wellbores at greater risk for leakage, and to develop targeted

  14. Learning molecular energies using localized graph kernels.

    PubMed

    Ferré, Grégoire; Haut, Terry; Barros, Kipton

    2017-03-21

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

  15. Learning molecular energies using localized graph kernels

    NASA Astrophysics Data System (ADS)

    Ferré, Grégoire; Haut, Terry; Barros, Kipton

    2017-03-01

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

  16. Global dynamic modeling of electro-hydraulic 3-UPS/S parallel stabilized platform by bond graph

    NASA Astrophysics Data System (ADS)

    Zhang, Lijie; Guo, Fei; Li, Yongquan; Lu, Wenjuan

    2016-08-01

    Dynamic modeling of a parallel manipulator(PM) is an important issue. A complete PM system is actually composed of multiple physical domains. As PMs are widely used in various fields, the importance of modeling the global dynamic model of the PM system becomes increasingly prominent. Currently there lacks further research in global dynamic modeling. A unified modeling approach for the multi-energy domains PM system is proposed based on bond graph and a global dynamic model of the 3-UPS/S parallel stabilized platform involving mechanical and electrical-hydraulic elements is built. Firstly, the screw bond graph theory is improved based on the screw theory, the modular joint model is modeled and the normalized dynamic model of the mechanism is established. Secondly, combined with the electro-hydraulic servo system model built by traditional bond graph, the global dynamic model of the system is obtained, and then the motion, force and power of any element can be obtained directly. Lastly, the experiments and simulations of the driving forces, pressure and flow are performed, and the results show that, the theoretical calculation results of the driving forces are in accord with the experimental ones, and the pressure and flow of the first limb and the third limb are symmetry with each other. The results are reasonable and verify the correctness and effectiveness of the model and the method. The proposed dynamic modeling method provides a reference for modeling of other multi-energy domains system which contains complex PM.

  17. Figure-Ground Segmentation Using Factor Graphs.

    PubMed

    Shen, Huiying; Coughlan, James; Ivanchenko, Volodymyr

    2009-06-04

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

  18. Highlighting the Structure-Function Relationship of the Brain with the Ising Model and Graph Theory

    PubMed Central

    Das, T. K.; Abeyasinghe, P. M.; Crone, J. S.; Sosnowski, A.; Laureys, S.; Owen, A. M.; Soddu, A.

    2014-01-01

    With the advent of neuroimaging techniques, it becomes feasible to explore the structure-function relationships in the brain. When the brain is not involved in any cognitive task or stimulated by any external output, it preserves important activities which follow well-defined spatial distribution patterns. Understanding the self-organization of the brain from its anatomical structure, it has been recently suggested to model the observed functional pattern from the structure of white matter fiber bundles. Different models which study synchronization (e.g., the Kuramoto model) or global dynamics (e.g., the Ising model) have shown success in capturing fundamental properties of the brain. In particular, these models can explain the competition between modularity and specialization and the need for integration in the brain. Graphing the functional and structural brain organization supports the model and can also highlight the strategy used to process and organize large amount of information traveling between the different modules. How the flow of information can be prevented or partially destroyed in pathological states, like in severe brain injured patients with disorders of consciousness or by pharmacological induction like in anaesthesia, will also help us to better understand how global or integrated behavior can emerge from local and modular interactions. PMID:25276772

  19. Highlighting the structure-function relationship of the brain with the Ising model and graph theory.

    PubMed

    Das, T K; Abeyasinghe, P M; Crone, J S; Sosnowski, A; Laureys, S; Owen, A M; Soddu, A

    2014-01-01

    With the advent of neuroimaging techniques, it becomes feasible to explore the structure-function relationships in the brain. When the brain is not involved in any cognitive task or stimulated by any external output, it preserves important activities which follow well-defined spatial distribution patterns. Understanding the self-organization of the brain from its anatomical structure, it has been recently suggested to model the observed functional pattern from the structure of white matter fiber bundles. Different models which study synchronization (e.g., the Kuramoto model) or global dynamics (e.g., the Ising model) have shown success in capturing fundamental properties of the brain. In particular, these models can explain the competition between modularity and specialization and the need for integration in the brain. Graphing the functional and structural brain organization supports the model and can also highlight the strategy used to process and organize large amount of information traveling between the different modules. How the flow of information can be prevented or partially destroyed in pathological states, like in severe brain injured patients with disorders of consciousness or by pharmacological induction like in anaesthesia, will also help us to better understand how global or integrated behavior can emerge from local and modular interactions.

  20. Agent-based simulation of building evacuation using a grid graph-based model

    NASA Astrophysics Data System (ADS)

    Tan, L.; Lin, H.; Hu, M.; Che, W.

    2014-02-01

    Shifting from macroscope models to microscope models, the agent-based approach has been widely used to model crowd evacuation as more attentions are paid on individualized behaviour. Since indoor evacuation behaviour is closely related to spatial features of the building, effective representation of indoor space is essential for the simulation of building evacuation. The traditional cell-based representation has limitations in reflecting spatial structure and is not suitable for topology analysis. Aiming at incorporating powerful topology analysis functions of GIS to facilitate agent-based simulation of building evacuation, we used a grid graph-based model in this study to represent the indoor space. Such model allows us to establish an evacuation network at a micro level. Potential escape routes from each node thus could be analysed through GIS functions of network analysis considering both the spatial structure and route capacity. This would better support agent-based modelling of evacuees' behaviour including route choice and local movements. As a case study, we conducted a simulation of emergency evacuation from the second floor of an official building using Agent Analyst as the simulation platform. The results demonstrate the feasibility of the proposed method, as well as the potential of GIS in visualizing and analysing simulation results.

  1. Generating GraphML XML Files for Graph Visualization of Architectures and Event Traces for the Monterey Phoenix Program

    DTIC Science & Technology

    2012-09-01

    files that conform to the Graph Markup Language (GraphML). MPGrapher compiles well-formed XML files that conform to the yEd GraphML schema. These...PLANARIZATION ........................................................................22 E. THE GRAPH MARKUP LANGUAGE ...26 F. ALTERNATIVES TO THE GRAPH MARKUP LANGUAGE ...............27 1. Graph Modelling Language (GML

  2. Model reduction for stochastic CaMKII reaction kinetics in synapses by graph-constrained correlation dynamics.

    PubMed

    Johnson, Todd; Bartol, Tom; Sejnowski, Terrence; Mjolsness, Eric

    2015-06-18

    A stochastic reaction network model of Ca(2+) dynamics in synapses (Pepke et al PLoS Comput. Biol. 6 e1000675) is expressed and simulated using rule-based reaction modeling notation in dynamical grammars and in MCell. The model tracks the response of calmodulin and CaMKII to calcium influx in synapses. Data from numerically intensive simulations is used to train a reduced model that, out of sample, correctly predicts the evolution of interaction parameters characterizing the instantaneous probability distribution over molecular states in the much larger fine-scale models. The novel model reduction method, 'graph-constrained correlation dynamics', requires a graph of plausible state variables and interactions as input. It parametrically optimizes a set of constant coefficients appearing in differential equations governing the time-varying interaction parameters that determine all correlations between variables in the reduced model at any time slice.

  3. Model reduction for stochastic CaMKII reaction kinetics in synapses by graph-constrained correlation dynamics

    PubMed Central

    Johnson, Todd; Bartol, Tom; Sejnowski, Terrence; Mjolsness, Eric

    2015-01-01

    Astochastic reaction network model of Ca2+ dynamics in synapses (Pepke et al PLoS Comput. Biol. 6 e1000675) is expressed and simulated using rule-based reaction modeling notation in dynamical grammars and in MCell. The model tracks the response of calmodulin and CaMKII to calcium influx in synapses. Data from numerically intensive simulations is used to train a reduced model that, out of sample, correctly predicts the evolution of interaction parameters characterizing the instantaneous probability distribution over molecular states in the much larger fine-scale models. The novel model reduction method, ‘graph-constrained correlation dynamics’, requires a graph of plausible state variables and interactions as input. It parametrically optimizes a set of constant coefficients appearing in differential equations governing the time-varying interaction parameters that determine all correlations between variables in the reduced model at any time slice. PMID:26086598

  4. Potts model partition functions for self-dual families of strip graphs

    NASA Astrophysics Data System (ADS)

    Chang, Shu-Chiuan; Shrock, Robert

    2001-12-01

    We consider the q-state Potts model on families of self-dual strip graphs GD of the square lattice of width Ly and arbitrarily great length Lx, with periodic longitudinal boundary conditions. The general partition function Z and the T=0 antiferromagnetic special case P (chromatic polynomial) have the respective forms ∑ j=1 NF, Ly, λcF, Ly, j( λF, Ly, j) Lx, with F= Z, P. For arbitrary Ly, we determine (i) the general coefficient cF, Ly, j in terms of Chebyshev polynomials, (ii) the number nF( Ly, d) of terms with each type of coefficient, and (iii) the total number of terms NF, Ly, λ. We point out interesting connections between the nZ( Ly, d) and Temperley-Lieb algebras, and between the NF, Ly, λ and enumerations of directed lattice animals. Exact calculations of P are presented for 2⩽ Ly⩽4. In the limit of infinite length, we calculate the ground state degeneracy per site (exponent of the ground state entropy), W( q). Generalizing q from Z+ to C, we determine the continuous locus B in the complex q plane where W( q) is singular. We find the interesting result that for all Ly values considered, the maximal point at which B crosses the real q-axis, denoted qc, is the same, and is equal to the value for the infinite square lattice, qc=3. This is the first family of strip graphs of which we are aware that exhibits this type of universality of qc.

  5. Neurally and ocularly informed graph-based models for searching 3D environments

    NASA Astrophysics Data System (ADS)

    Jangraw, David C.; Wang, Jun; Lance, Brent J.; Chang, Shih-Fu; Sajda, Paul

    2014-08-01

    Objective. As we move through an environment, we are constantly making assessments, judgments and decisions about the things we encounter. Some are acted upon immediately, but many more become mental notes or fleeting impressions—our implicit ‘labeling’ of the world. In this paper, we use physiological correlates of this labeling to construct a hybrid brain-computer interface (hBCI) system for efficient navigation of a 3D environment. Approach. First, we record electroencephalographic (EEG), saccadic and pupillary data from subjects as they move through a small part of a 3D virtual city under free-viewing conditions. Using machine learning, we integrate the neural and ocular signals evoked by the objects they encounter to infer which ones are of subjective interest to them. These inferred labels are propagated through a large computer vision graph of objects in the city, using semi-supervised learning to identify other, unseen objects that are visually similar to the labeled ones. Finally, the system plots an efficient route to help the subjects visit the ‘similar’ objects it identifies. Main results. We show that by exploiting the subjects’ implicit labeling to find objects of interest instead of exploring naively, the median search precision is increased from 25% to 97%, and the median subject need only travel 40% of the distance to see 84% of the objects of interest. We also find that the neural and ocular signals contribute in a complementary fashion to the classifiers’ inference of subjects’ implicit labeling. Significance. In summary, we show that neural and ocular signals reflecting subjective assessment of objects in a 3D environment can be used to inform a graph-based learning model of that environment, resulting in an hBCI system that improves navigation and information delivery specific to the user’s interests.

  6. A Systematic Composite Service Design Modeling Method Using Graph-Based Theory

    PubMed Central

    Elhag, Arafat Abdulgader Mohammed; Mohamad, Radziah; Aziz, Muhammad Waqar; Zeshan, Furkh

    2015-01-01

    The composite service design modeling is an essential process of the service-oriented software development life cycle, where the candidate services, composite services, operations and their dependencies are required to be identified and specified before their design. However, a systematic service-oriented design modeling method for composite services is still in its infancy as most of the existing approaches provide the modeling of atomic services only. For these reasons, a new method (ComSDM) is proposed in this work for modeling the concept of service-oriented design to increase the reusability and decrease the complexity of system while keeping the service composition considerations in mind. Furthermore, the ComSDM method provides the mathematical representation of the components of service-oriented design using the graph-based theoryto facilitate the design quality measurement. To demonstrate that the ComSDM method is also suitable for composite service design modeling of distributed embedded real-time systems along with enterprise software development, it is implemented in the case study of a smart home. The results of the case study not only check the applicability of ComSDM, but can also be used to validate the complexity and reusability of ComSDM. This also guides the future research towards the design quality measurement such as using the ComSDM method to measure the quality of composite service design in service-oriented software system. PMID:25928358

  7. A systematic composite service design modeling method using graph-based theory.

    PubMed

    Elhag, Arafat Abdulgader Mohammed; Mohamad, Radziah; Aziz, Muhammad Waqar; Zeshan, Furkh

    2015-01-01

    The composite service design modeling is an essential process of the service-oriented software development life cycle, where the candidate services, composite services, operations and their dependencies are required to be identified and specified before their design. However, a systematic service-oriented design modeling method for composite services is still in its infancy as most of the existing approaches provide the modeling of atomic services only. For these reasons, a new method (ComSDM) is proposed in this work for modeling the concept of service-oriented design to increase the reusability and decrease the complexity of system while keeping the service composition considerations in mind. Furthermore, the ComSDM method provides the mathematical representation of the components of service-oriented design using the graph-based theoryto facilitate the design quality measurement. To demonstrate that the ComSDM method is also suitable for composite service design modeling of distributed embedded real-time systems along with enterprise software development, it is implemented in the case study of a smart home. The results of the case study not only check the applicability of ComSDM, but can also be used to validate the complexity and reusability of ComSDM. This also guides the future research towards the design quality measurement such as using the ComSDM method to measure the quality of composite service design in service-oriented software system.

  8. Graphing Predictions

    ERIC Educational Resources Information Center

    Connery, Keely Flynn

    2007-01-01

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

  9. Graphing Predictions

    ERIC Educational Resources Information Center

    Connery, Keely Flynn

    2007-01-01

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

  10. Graph and circuit theory connectivity models of conservation biological control agents.

    PubMed

    Koh, Insu; Rowe, Helen I; Holland, Jeffrey D

    2013-10-01

    The control of agricultural pests is an important ecosystem service provided by predacious insects. In Midwestern USA, areas of remnant tallgrass prairie and prairie restorations may serve as relatively undisturbed sources of natural predators, and smaller areas of non-crop habitats such as seminatural areas and conservation plantings (CP) may serve as stepping stones across landscapes dominated by intensive agriculture. However, little is known about the flow of beneficial insects across large habitat networks. We measured abundance of soybean aphids and predators in 15 CP and adjacent soybean fields. We tested two hypotheses: (1) landscape connectivity enhances the flow of beneficial insects; and (2) prairies act as a source of sustaining populations of beneficial insects in well-connected habitats, by using adaptations of graph and circuit theory, respectively. For graph connectivity, incoming fluxes to the 15 CP from connected habitats were measured using an area- and distance-weighted flux metric with a range of negative exponential dispersal kernels. Distance was weighted by the percentage of seminatural area within ellipse-shaped landscapes, the shape of which was determined with correlated random walks. For circuit connectivity, effective conductance from the prairie to the individual 15 CP was measured by regarding the flux as conductance in a circuit. We used these two connectivity measures to predict the abundance of natural enemies in the selected sites. The most abundant predators were Anthocoridae, followed by exotic Coccinellidae, and native Coccinellidae. Predator abundances were explained well by aphid abundance. However, only native Coccinellidae were influenced by the flux and conductance. Interestingly, exotic Coccinellidae were negatively related to the flux, and native Coccinellidae were highly influenced by the interaction between exotic Coccinellidae and aphids. Our area- and distance-weighted flux and the conductance variables showed better

  11. Graph-based Data Modeling and Analysis for Data Fusion in Remote Sensing

    NASA Astrophysics Data System (ADS)

    Fan, Lei

    ., fusion of multi-source data can in principal produce more detailed information than each single source. On the other hand, besides the abundant spectral information contained in HSI data, features such as texture and shape may be employed to represent data points from a spatial perspective. Furthermore, feature fusion also includes the strategy of removing redundant and noisy features in the dataset. One of the major problems in machine learning and pattern recognition is to develop appropriate representations for complex nonlinear data. In HSI processing, a particular data point is usually described as a vector with coordinates corresponding to the intensities measured in the spectral bands. This vector representation permits the application of linear and nonlinear transformations with linear algebra to find an alternative representation of the data. More generally, HSI is multi-dimensional in nature and the vector representation may lose the contextual correlations. Tensor representation provides a more sophisticated modeling technique and a higher-order generalization to linear subspace analysis. In graph theory, data points can be generalized as nodes with connectivities measured from the proximity of a local neighborhood. The graph-based framework efficiently characterizes the relationships among the data and allows for convenient mathematical manipulation in many applications, such as data clustering, feature extraction, feature selection and data alignment. In this thesis, graph-based approaches applied in the field of multi-source feature and data fusion in remote sensing area are explored. We will mainly investigate the fusion of spatial, spectral and LiDAR information with linear and multilinear algebra under graph-based framework for data clustering and classification problems.

  12. Classification of signaling proteins based on molecular star graph descriptors using Machine Learning models.

    PubMed

    Fernandez-Lozano, Carlos; Cuiñas, Rubén F; Seoane, José A; Fernández-Blanco, Enrique; Dorado, Julian; Munteanu, Cristian R

    2015-11-07

    Signaling proteins are an important topic in drug development due to the increased importance of finding fast, accurate and cheap methods to evaluate new molecular targets involved in specific diseases. The complexity of the protein structure hinders the direct association of the signaling activity with the molecular structure. Therefore, the proposed solution involves the use of protein star graphs for the peptide sequence information encoding into specific topological indices calculated with S2SNet tool. The Quantitative Structure-Activity Relationship classification model obtained with Machine Learning techniques is able to predict new signaling peptides. The best classification model is the first signaling prediction model, which is based on eleven descriptors and it was obtained using the Support Vector Machines-Recursive Feature Elimination (SVM-RFE) technique with the Laplacian kernel (RFE-LAP) and an AUROC of 0.961. Testing a set of 3114 proteins of unknown function from the PDB database assessed the prediction performance of the model. Important signaling pathways are presented for three UniprotIDs (34 PDBs) with a signaling prediction greater than 98.0%. Copyright © 2015 Elsevier Ltd. All rights reserved.

  13. A mathematical model for generating bipartite graphs and its application to protein networks

    NASA Astrophysics Data System (ADS)

    Nacher, J. C.; Ochiai, T.; Hayashida, M.; Akutsu, T.

    2009-12-01

    Complex systems arise in many different contexts from large communication systems and transportation infrastructures to molecular biology. Most of these systems can be organized into networks composed of nodes and interacting edges. Here, we present a theoretical model that constructs bipartite networks with the particular feature that the degree distribution can be tuned depending on the probability rate of fundamental processes. We then use this model to investigate protein-domain networks. A protein can be composed of up to hundreds of domains. Each domain represents a conserved sequence segment with specific functional tasks. We analyze the distribution of domains in Homo sapiens and Arabidopsis thaliana organisms and the statistical analysis shows that while (a) the number of domain types shared by k proteins exhibits a power-law distribution, (b) the number of proteins composed of k types of domains decays as an exponential distribution. The proposed mathematical model generates bipartite graphs and predicts the emergence of this mixing of (a) power-law and (b) exponential distributions. Our theoretical and computational results show that this model requires (1) growth process and (2) copy mechanism.

  14. 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.

  15. Cascades on clique-based graphs.

    PubMed

    Hackett, Adam; Gleeson, James P

    2013-06-01

    We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly clustered random graphs introduced by Gleeson [J. P. Gleeson, Phys. Rev. E 80, 036107 (2009)]. A condition for the existence of global cascades is also derived. Applications of this approach include analyses of percolation, and Watts's model. We show how our techniques can be used to study the effects of in-group bias in cascades on social networks.

  16. Scenario Graphs and Attack Graphs

    DTIC Science & Technology

    2004-04-14

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

  17. 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.

  18. Supersymmetric SYK model and random matrix theory

    NASA Astrophysics Data System (ADS)

    Li, Tianlin; Liu, Junyu; Xin, Yuan; Zhou, Yehao

    2017-06-01

    In this paper, we investigate the effect of supersymmetry on the symmetry classification of random matrix theory ensembles. We mainly consider the random matrix behaviors in the N=1 supersymmetric generalization of Sachdev-Ye-Kitaev (SYK) model, a toy model for two-dimensional quantum black hole with supersymmetric constraint. Some analytical arguments and numerical results are given to show that the statistics of the supersymmetric SYK model could be interpreted as random matrix theory ensembles, with a different eight-fold classification from the original SYK model and some new features. The time-dependent evolution of the spectral form factor is also investigated, where predictions from random matrix theory are governing the late time behavior of the chaotic hamiltonian with supersymmetry.

  19. 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.

  20. Synchronization in the random-field Kuramoto model on complex networks

    NASA Astrophysics Data System (ADS)

    Lopes, M. A.; Lopes, E. M.; Yoon, S.; Mendes, J. F. F.; Goltsev, A. V.

    2016-07-01

    We study the impact of random pinning fields on the emergence of synchrony in the Kuramoto model on complete graphs and uncorrelated random complex networks. We consider random fields with uniformly distributed directions and homogeneous and heterogeneous (Gaussian) field magnitude distribution. In our analysis, we apply the Ott-Antonsen method and the annealed-network approximation to find the critical behavior of the order parameter. In the case of homogeneous fields, we find a tricritical point above which a second-order phase transition gives place to a first-order phase transition when the network is either fully connected or scale-free with the degree exponent γ >5 . Interestingly, for scale-free networks with 2 <γ ≤5 , the phase transition is of second-order at any field magnitude, except for degree distributions with γ =3 when the transition is of infinite order at Kc=0 independent of the random fields. Contrary to the Ising model, even strong Gaussian random fields do not suppress the second-order phase transition in both complete graphs and scale-free networks, although the fields increase the critical coupling for γ >3 . Our simulations support these analytical results.

  1. The Random-Effect DINA Model

    ERIC Educational Resources Information Center

    Huang, Hung-Yu; Wang, Wen-Chung

    2014-01-01

    The DINA (deterministic input, noisy, and gate) model has been widely used in cognitive diagnosis tests and in the process of test development. The outcomes known as slip and guess are included in the DINA model function representing the responses to the items. This study aimed to extend the DINA model by using the random-effect approach to allow…

  2. The Random-Effect DINA Model

    ERIC Educational Resources Information Center

    Huang, Hung-Yu; Wang, Wen-Chung

    2014-01-01

    The DINA (deterministic input, noisy, and gate) model has been widely used in cognitive diagnosis tests and in the process of test development. The outcomes known as slip and guess are included in the DINA model function representing the responses to the items. This study aimed to extend the DINA model by using the random-effect approach to allow…

  3. Graph-based modeling of tandem repeats improves global multiple sequence alignment

    PubMed Central

    Szalkowski, Adam M.; Anisimova, Maria

    2013-01-01

    Tandem repeats (TRs) are often present in proteins with crucial functions, responsible for resistance, pathogenicity and associated with infectious or neurodegenerative diseases. This motivates numerous studies of TRs and their evolution, requiring accurate multiple sequence alignment. TRs may be lost or inserted at any position of a TR region by replication slippage or recombination, but current methods assume fixed unit boundaries, and yet are of high complexity. We present a new global graph-based alignment method that does not restrict TR unit indels by unit boundaries. TR indels are modeled separately and penalized using the phylogeny-aware alignment algorithm. This ensures enhanced accuracy of reconstructed alignments, disentangling TRs and measuring indel events and rates in a biologically meaningful way. Our method detects not only duplication events but also all changes in TR regions owing to recombination, strand slippage and other events inserting or deleting TR units. We evaluate our method by simulation incorporating TR evolution, by either sampling TRs from a profile hidden Markov model or by mimicking strand slippage with duplications. The new method is illustrated on a family of type III effectors, a pathogenicity determinant in agriculturally important bacteria Ralstonia solanacearum. We show that TR indel rate variation contributes to the diversification of this protein family. PMID:23877246

  4. Modelling population processes with random initial conditions.

    PubMed

    Pollett, P K; Dooley, A H; Ross, J V

    2010-02-01

    Population dynamics are almost inevitably associated with two predominant sources of variation: the first, demographic variability, a consequence of chance in progenitive and deleterious events; the second, initial state uncertainty, a consequence of partial observability and reporting delays and errors. Here we outline a general method for incorporating random initial conditions in population models where a deterministic model is sufficient to describe the dynamics of the population. Additionally, we show that for a large class of stochastic models the overall variation is the sum of variation due to random initial conditions and variation due to random dynamics, and thus we are able to quantify the variation not accounted for when random dynamics are ignored. Our results are illustrated with reference to both simulated and real data. Copyright (c) 2009 Elsevier Inc. All rights reserved.

  5. Modeling alternative splicing variants from RNA-Seq data with isoform graphs.

    PubMed

    Beretta, Stefano; Bonizzoni, Paola; Vedova, Gianluca Della; Pirola, Yuri; Rizzi, Raffaella

    2014-01-01

    Next-generation sequencing (NGS) technologies need new methodologies for alternative splicing (AS) analysis. Current computational methods for AS analysis from NGS data are mainly based on aligning short reads against a reference genome, while methods that do not need a reference genome are mostly underdeveloped. In this context, the main developed tools for NGS data focus on de novo transcriptome assembly (Grabherr et al., 2011 ; Schulz et al., 2012). While these tools are extensively applied for biological investigations and often show intrinsic shortcomings from the obtained results, a theoretical investigation of the inherent computational limits of transcriptome analysis from NGS data, when a reference genome is unknown or highly unreliable, is still missing. On the other hand, we still lack methods for computing the gene structures due to AS events under the above assumptions--a problem that we start to tackle with this article. More precisely, based on the notion of isoform graph (Lacroix et al., 2008), we define a compact representation of gene structures--called splicing graph--and investigate the computational problem of building a splicing graph that is (i) compatible with NGS data and (ii) isomorphic to the isoform graph. We characterize when there is only one representative splicing graph compatible with input data, and we propose an efficient algorithmic approach to compute this graph.

  6. Random-effects models for longitudinal data

    SciTech Connect

    Laird, N.M.; Ware, J.H.

    1982-12-01

    Models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit. Multivariate models with general covariance structure are often difficult to apply to highly unbalanced data, whereas two-stage random-effects models can be used easily. In two-stage models, the probability distributions for the response vectors of different individuals belong to a single family, but some random-effects parameters vary across individuals, with a distribution specified at the second stage. A general family of models is discussed, which includes both growth models and repeated-measures models as special cases. A unified approach to fitting these models, based on a combination of empirical Bayes and maximum likelihood estimation of model parameters and using the EM algorithm, is discussed. Two examples are taken from a current epidemiological study of the health effects of air pollution.

  7. Exact Solution of the Markov Propagator for the Voter Model on the Complete Graph

    DTIC Science & Technology

    2014-07-01

    the generating function form of the Markov prop- agator of the random walk. This can be easily generalized to other models simply by specifying the...detailed information about the prop- agator than the bound on consensus. VI. CONCLUSIONS We have successfully derived exact solutions to the voter

  8. Enhancing multiple-point geostatistical modeling: 1. Graph theory and pattern adjustment

    NASA Astrophysics Data System (ADS)

    Tahmasebi, Pejman; Sahimi, Muhammad

    2016-03-01

    In recent years, higher-order geostatistical methods have been used for modeling of a wide variety of large-scale porous media, such as groundwater aquifers and oil reservoirs. Their popularity stems from their ability to account for qualitative data and the great flexibility that they offer for conditioning the models to hard (quantitative) data, which endow them with the capability for generating realistic realizations of porous formations with very complex channels, as well as features that are mainly a barrier to fluid flow. One group of such models consists of pattern-based methods that use a set of data points for generating stochastic realizations by which the large-scale structure and highly-connected features are reproduced accurately. The cross correlation-based simulation (CCSIM) algorithm, proposed previously by the authors, is a member of this group that has been shown to be capable of simulating multimillion cell models in a matter of a few CPU seconds. The method is, however, sensitive to pattern's specifications, such as boundaries and the number of replicates. In this paper the original CCSIM algorithm is reconsidered and two significant improvements are proposed for accurately reproducing large-scale patterns of heterogeneities in porous media. First, an effective boundary-correction method based on the graph theory is presented by which one identifies the optimal cutting path/surface for removing the patchiness and discontinuities in the realization of a porous medium. Next, a new pattern adjustment method is proposed that automatically transfers the features in a pattern to one that seamlessly matches the surrounding patterns. The original CCSIM algorithm is then combined with the two methods and is tested using various complex two- and three-dimensional examples. It should, however, be emphasized that the methods that we propose in this paper are applicable to other pattern-based geostatistical simulation methods.

  9. Automatic segmentation of lymph vessel wall using optimal surface graph cut and hidden Markov Models.

    PubMed

    Jones, Jonathan-Lee; Essa, Ehab; Xie, Xianghua

    2015-01-01

    We present a novel method to segment the lymph vessel wall in confocal microscopy images using Optimal Surface Segmentation (OSS) and hidden Markov Models (HMM). OSS is used to preform a pre-segmentation on the images, to act as the initial state for the HMM. We utilize a steerable filter to determine edge based filters for both of these segmentations, and use these features to build Gaussian probability distributions for both the vessel walls and the background. From this we infer the emission probability for the HMM, and the transmission probability is learned using a Baum-Welch algorithm. We transform the segmentation problem into one of cost minimization, with each node in the graph corresponding to one state, and the weight for each node being defined using its emission probability. We define the inter-relations between neighboring nodes using the transmission probability. Having constructed the problem, it is solved using the Viterbi algorithm, allowing the vessel to be reconstructed. The optimal solution can be found in polynomial time. We present qualitative and quantitative analysis to show the performance of the proposed method.

  10. A Study towards Building An Optimal Graph Theory Based Model For The Design of Tourism Website

    NASA Astrophysics Data System (ADS)

    Panigrahi, Goutam; Das, Anirban; Basu, Kajla

    2010-10-01

    Effective tourism website is a key to attract tourists from different parts of the world. Here we identify the factors of improving the effectiveness of website by considering it as a graph, where web pages including homepage are the nodes and hyperlinks are the edges between the nodes. In this model, the design constraints for building a tourism website are taken into consideration. Our objectives are to build a framework of an effective tourism website providing adequate level of information, service and also to enable the users to reach to the desired page by spending minimal loading time. In this paper an information hierarchy specifying the upper limit of outgoing link of a page has also been proposed. Following the hierarchy, the web developer can prepare an effective tourism website. Here loading time depends on page size and network traffic. We have assumed network traffic as uniform and the loading time is directly proportional with page size. This approach is done by quantifying the link structure of a tourism website. In this approach we also propose a page size distribution pattern of a tourism website.

  11. A Dexterous Optional Randomized Response Model

    ERIC Educational Resources Information Center

    Tarray, Tanveer A.; Singh, Housila P.; Yan, Zaizai

    2017-01-01

    This article addresses the problem of estimating the proportion Pi[subscript S] of the population belonging to a sensitive group using optional randomized response technique in stratified sampling based on Mangat model that has proportional and Neyman allocation and larger gain in efficiency. Numerically, it is found that the suggested model is…

  12. Medical image segmentation by combining graph cuts and oriented active appearance models.

    PubMed

    Chen, Xinjian; Udupa, Jayaram K; Bagci, Ulas; Zhuge, Ying; Yao, Jianhua

    2012-04-01

    In this paper, we propose a novel method based on a strategic combination of the active appearance model (AAM), live wire (LW), and graph cuts (GCs) for abdominal 3-D organ segmentation. The proposed method consists of three main parts: model building, object recognition, and delineation. In the model building part, we construct the AAM and train the LW cost function and GC parameters. In the recognition part, a novel algorithm is proposed for improving the conventional AAM matching method, which effectively combines the AAM and LW methods, resulting in the oriented AAM (OAAM). A multiobject strategy is utilized to help in object initialization. We employ a pseudo-3-D initialization strategy and segment the organs slice by slice via a multiobject OAAM method. For the object delineation part, a 3-D shape-constrained GC method is proposed. The object shape generated from the initialization step is integrated into the GC cost computation, and an iterative GC-OAAM method is used for object delineation. The proposed method was tested in segmenting the liver, kidneys, and spleen on a clinical CT data set and also on the MICCAI 2007 Grand Challenge liver data set. The results show the following: 1) The overall segmentation accuracy of true positive volume fraction TPVF > 94.3% and false positive volume fraction can be achieved; 2) the initialization performance can be improved by combining the AAM and LW; 3) the multiobject strategy greatly facilitates initialization; 4) compared with the traditional 3-D AAM method, the pseudo-3-D OAAM method achieves comparable performance while running 12 times faster; and 5) the performance of the proposed method is comparable to state-of-the-art liver segmentation algorithm. The executable version of the 3-D shape-constrained GC method with a user interface can be downloaded from http://xinjianchen.wordpress.com/research/.

  13. Evaluation of connectedness between the University courses of Physics and Chemistry basing on the graph model of intersubject links

    NASA Astrophysics Data System (ADS)

    Gnitetskaya, Tatyana; Ivanova, Elena

    2016-08-01

    An application of the graph model of inter-subject links to University courses of Physics and Chemistry is presented in this article. A part of inter-subject space with directions of inter-subject links from Physics to Chemistry in the group of physical concepts has been shown. The graph model of inter-subject links includes quantitative indicators. Its numerical values are given in the article. The degree of connectedness between the data of Physics and Chemistry courses is discussed for the courses considered. The effect of the courses placement within a curriculum on the value of their connectedness is shown. The placement of courses within a curriculum can provide the study of the courses at the same time or consecutive study, when one course precedes another.

  14. The Link Probability Model: A Network Simulation Alternative to the Exponential Random Graph Model

    DTIC Science & Technology

    2010-12-01

    This research is part of the Dynamics Networks project in CASOS (Center for Computational Analysis of Social and Organizational Systems, http...Technology, •ARL Telecordia: Communications and Networks Technology Collaborative Alliances, •Additional support on measures was provided by the

  15. Modeling Alternative Splicing Variants from RNA-Seq Data with Isoform Graphs

    PubMed Central

    Beretta, Stefano; Vedova, Gianluca Della; Pirola, Yuri; Rizzi, Raffaella

    2014-01-01

    Abstract Next-generation sequencing (NGS) technologies need new methodologies for alternative splicing (AS) analysis. Current computational methods for AS analysis from NGS data are mainly based on aligning short reads against a reference genome, while methods that do not need a reference genome are mostly underdeveloped. In this context, the main developed tools for NGS data focus on de novo transcriptome assembly (Grabherr et al., 2011; Schulz et al., 2012). While these tools are extensively applied for biological investigations and often show intrinsic shortcomings from the obtained results, a theoretical investigation of the inherent computational limits of transcriptome analysis from NGS data, when a reference genome is unknown or highly unreliable, is still missing. On the other hand, we still lack methods for computing the gene structures due to AS events under the above assumptions—a problem that we start to tackle with this article. More precisely, based on the notion of isoform graph (Lacroix et al., 2008), we define a compact representation of gene structures—called splicing graph—and investigate the computational problem of building a splicing graph that is (i) compatible with NGS data and (ii) isomorphic to the isoform graph. We characterize when there is only one representative splicing graph compatible with input data, and we propose an efficient algorithmic approach to compute this graph. PMID:24200390

  16. Evolutionary Dynamics on Degree-Heterogeneous Graphs

    NASA Astrophysics Data System (ADS)

    Antal, T.; Redner, S.; Sood, V.

    2006-05-01

    The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model dynamics) or by an individual giving birth to an offspring that takes over a random neighbor node (invasion process dynamics). The fixation probability for one species to take over a population of N individuals depends crucially on the dynamics and on the local environment. Starting with a single fitter mutant at a node of degree k, the fixation probability is proportional to k for voter model dynamics and to 1/k for invasion process dynamics.

  17. Random walk in degree space and the time-dependent Watts-Strogatz model.

    PubMed

    Casa Grande, H L; Cotacallapa, M; Hase, M O

    2017-01-01

    In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erdős-Rényi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.

  18. Random walk in degree space and the time-dependent Watts-Strogatz model

    NASA Astrophysics Data System (ADS)

    Casa Grande, H. L.; Cotacallapa, M.; Hase, M. O.

    2017-01-01

    In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erdős-Rényi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.

  19. Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings

    NASA Astrophysics Data System (ADS)

    Shrock, Robert; Xu, Yan

    2010-12-01

    We present exact results on the partition function of the q-state Potts model on various families of graphs G in a generalized external magnetic field that favors or disfavors spin values in a subset I s ={1,…, s} of the total set of possible spin values, Z( G, q, s, v, w), where v and w are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given for the interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial Ph( G, q, s, w) that counts the number of colorings of the vertices of G subject to the condition that colors of adjacent vertices are different, with a weighting w that favors or disfavors colors in the interval I s . We derive powerful new upper and lower bounds on Z( G, q, s, v, w) for the ferromagnetic case in terms of zero-field Potts partition functions with certain transformed arguments. We also prove general inequalities for Z( G, q, s, v, w) on different families of tree graphs. As part of our analysis, we elucidate how the field-dependent Potts partition function and weighted-set chromatic polynomial distinguish, respectively, between Tutte-equivalent and chromatically equivalent pairs of graphs.

  20. Randomly stopped sums: models and psychological applications

    PubMed Central

    Smithson, Michael; Shou, Yiyun

    2014-01-01

    This paper describes an approach to modeling the sums of a continuous random variable over a number of measurement occasions when the number of occasions also is a random variable. A typical example is summing the amounts of time spent attending to pieces of information in an information search task leading to a decision to obtain the total time taken to decide. Although there is a large literature on randomly stopped sums in financial statistics, it is largely absent from psychology. The paper begins with the standard modeling approaches used in financial statistics, and then extends them in two ways. First, the randomly stopped sums are modeled as “life distributions” such as the gamma or log-normal distribution. A simulation study investigates Type I error rate accuracy and power for gamma and log-normal versions of this model. Second, a Bayesian hierarchical approach is used for constructing an appropriate general linear model of the sums. Model diagnostics are discussed, and three illustrations are presented from real datasets. PMID:25426090

  1. Linear Wegner estimate for alloy-type Schrödinger operators on metric graphs

    NASA Astrophysics Data System (ADS)

    Helm, Mario; Veselić, Ivan

    2007-09-01

    We study spectra of alloy-type random Schrödinger operators on metric graphs. For finite edge subsets we prove a Wegner estimate which is linear in the volume (i.e., the total length of the edges) and the length of the energy interval. The single site potential needs to have fixed sign; the metric graph does not need to have a periodic structure. A further result is the existence of the integrated density of states for ergodic random Hamiltonians on metric graphs with a Zν structure. For certain models the two above results together imply the Lipschitz continuity of the integrated density of states.

  2. Prediction of Growth Factor-Dependent Cleft Formation During Branching Morphogenesis Using A Dynamic Graph-Based Growth Model.

    PubMed

    Dhulekar, Nimit; Ray, Shayoni; Yuan, Daniel; Baskaran, Abhirami; Oztan, Basak; Larsen, Melinda; Yener, Bulent

    2016-01-01

    This study considers the problem of describing and predicting cleft formation during the early stages of branching morphogenesis in mouse submandibular salivary glands (SMG) under the influence of varied concentrations of epidermal growth factors (EGF). Given a time-lapse video of a growing SMG, first we build a descriptive model that captures the underlying biological process and quantifies the ground truth. Tissue-scale (global) and morphological features related to regions of interest (local features) are used to characterize the biological ground truth. Second, we devise a predictive growth model that simulates EGF-modulated branching morphogenesis using a dynamic graph algorithm, which is driven by biological parameters such as EGF concentration, mitosis rate, and cleft progression rate. Given the initial configuration of the SMG, the evolution of the dynamic graph predicts the cleft formation, while maintaining the local structural characteristics of the SMG. We determined that higher EGF concentrations cause the formation of higher number of buds and comparatively shallow cleft depths. Third, we compared the prediction accuracy of our model to the Glazier-Graner-Hogeweg (GGH) model, an on-lattice Monte-Carlo simulation model, under a specific energy function parameter set that allows new rounds of de novo cleft formation. The results demonstrate that the dynamic graph model yields comparable simulations of gland growth to that of the GGH model with a significantly lower computational complexity. Fourth, we enhanced this model to predict the SMG morphology for an EGF concentration without the assistance of a ground truth time-lapse biological video data; this is a substantial benefit of our model over other similar models that are guided and terminated by information regarding the final SMG morphology. Hence, our model is suitable for testing the impact of different biological parameters involved with the process of branching morphogenesis in silico, while

  3. Prediction of Growth Factor Dependent Cleft Formation During Branching Morphogenesis Using A Dynamic Graph-Based Growth Model

    PubMed Central

    Dhulekar, Nimit; Ray, Shayoni; Yuan, Daniel; Baskaran, Abhirami; Oztan, Basak; Larsen, Melinda; Yener, Bülent

    2016-01-01

    This study considers the problem of describing and predicting cleft formation during the early stages of branching morphogenesis in mouse submandibular salivary glands (SMG) under the influence of varied concentrations of epidermal growth factors (EGF). Given a time-lapse video of a growing SMG, first we build a descriptive model that captures the underlying biological process and quantifies the ground truth. Tissue-scale (global) and morphological features related to regions of interest (local features) are used to characterize the biological ground truth. Second, we devise a predictive growth model that simulates EGF-modulated branching morphogenesis using a dynamic graph algorithm, which is driven by biological parameters such as EGF concentration, mitosis rate, and cleft progression rate. Given the initial configuration of the SMG, the evolution of the dynamic graph predicts the cleft formation, while maintaining the local structural characteristics of the SMG. We determined that higher EGF concentrations cause the formation of higher number of buds and comparatively shallow cleft depths. Third, we compared the prediction accuracy of our model to the Glazier-Graner-Hogeweg (GGH) model, an on-lattice Monte-Carlo simulation model, under a specific energy function parameter set that allows new rounds of de novo cleft formation. The results demonstrate that the dynamic graph model yields comparable simulations of gland growth to that of the GGH model with a significantly lower computational complexity. Fourth, we enhanced this model to predict the SMG morphology for an EGF concentration without the assistance of a ground truth time-lapse biological video data; this is a substantial benefit of our model over other similar models that are guided and terminated by information regarding the final SMG morphology. Hence, our model is suitable for testing the impact of different biological parameters involved with the process of branching morphogenesis in silico, while

  4. Graph Theory of Tower Tasks

    PubMed Central

    Hinz, Andreas M.

    2012-01-01

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

  5. An inventory model with random demand

    NASA Astrophysics Data System (ADS)

    Mitsel, A. A.; Kritski, O. L.; Stavchuk, LG

    2017-01-01

    The article describes a three-product inventory model with random demand at equal frequencies of delivery. A feature of this model is that the additional purchase of resources required is carried out within the scope of their deficit. This fact allows reducing their storage costs. A simulation based on the data on arrival of raw and materials at an enterprise in Kazakhstan has been prepared. The proposed model is shown to enable savings up to 40.8% of working capital.

  6. Bootstrapped models for intrinsic random functions

    SciTech Connect

    Campbell, K.

    1988-08-01

    Use of intrinsic random function stochastic models as a basis for estimation in geostatistical work requires the identification of the generalized covariance function of the underlying process. The fact that this function has to be estimated from data introduces an additional source of error into predictions based on the model. This paper develops the sample reuse procedure called the bootstrap in the context of intrinsic random functions to obtain realistic estimates of these errors. Simulation results support the conclusion that bootstrap distributions of functionals of the process, as well as their kriging variance, provide a reasonable picture of variability introduced by imperfect estimation of the generalized covariance function.

  7. Bootstrapped models for intrinsic random functions

    SciTech Connect

    Campbell, K.

    1987-01-01

    The use of intrinsic random function stochastic models as a basis for estimation in geostatistical work requires the identification of the generalized covariance function of the underlying process, and the fact that this function has to be estimated from the data introduces an additional source of error into predictions based on the model. This paper develops the sample reuse procedure called the ''bootstrap'' in the context of intrinsic random functions to obtain realistic estimates of these errors. Simulation results support the conclusion that bootstrap distributions of functionals of the process, as well as of their ''kriging variance,'' provide a reasonable picture of the variability introduced by imperfect estimation of the generalized covariance function.

  8. Critical properties of random Potts models

    NASA Astrophysics Data System (ADS)

    Kinzel, Wolfgang; Domany, Eytan

    1981-04-01

    The critical properties of Potts models with random bonds are considered in two dimensions. A position-space renormalization-group procedure, based on the Migdal-Kadanoff method, is developed. While all previous position-space calculations satisfied the Harris criterion and the resulting scaling relation only approximately, we found conditions under which these relations are exactly satisfied, and constructed our renormalization-group procedure accordingly. Numerical results for phase diagrams and thermodynamic functions for various random-bond Potts models are presented. In addition, some exact results obtained using a duality transformation, as well as an heuristic derivation of scaling properties that correspond to the percolation problem are given.

  9. A Structural Modeling Approach to a Multilevel Random Coefficients Model.

    ERIC Educational Resources Information Center

    Rovine, Michael J.; Molenaar, Peter C. M.

    2000-01-01

    Presents a method for estimating the random coefficients model using covariance structure modeling and allowing one to estimate both fixed and random effects. The method is applied to real and simulated data, including marriage data from J. Belsky and M. Rovine (1990). (SLD)

  10. Test of Graphing and Graph Interpretation Skills.

    ERIC Educational Resources Information Center

    Hermann, J.

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

  11. How mutation affects evolutionary games on graphs.

    PubMed

    Allen, Benjamin; Traulsen, Arne; Tarnita, Corina E; Nowak, Martin A

    2012-04-21

    Evolutionary dynamics are affected by population structure, mutation rates and update rules. Spatial or network structure facilitates the clustering of strategies, which represents a mechanism for the evolution of cooperation. Mutation dilutes this effect. Here we analyze how mutation influences evolutionary clustering on graphs. We introduce new mathematical methods to evolutionary game theory, specifically the analysis of coalescing random walks via generating functions. These techniques allow us to derive exact identity-by-descent (IBD) probabilities, which characterize spatial assortment on lattices and Cayley trees. From these IBD probabilities we obtain exact conditions for the evolution of cooperation and other game strategies, showing the dual effects of graph topology and mutation rate. High mutation rates diminish the clustering of cooperators, hindering their evolutionary success. Our model can represent either genetic evolution with mutation, or social imitation processes with random strategy exploration.

  12. Parabolic Anderson Model in a Dynamic Random Environment: Random Conductances

    NASA Astrophysics Data System (ADS)

    Erhard, D.; den Hollander, F.; Maillard, G.

    2016-06-01

    The parabolic Anderson model is defined as the partial differential equation ∂ u( x, t)/ ∂ t = κ Δ u( x, t) + ξ( x, t) u( x, t), x ∈ ℤ d , t ≥ 0, where κ ∈ [0, ∞) is the diffusion constant, Δ is the discrete Laplacian, and ξ is a dynamic random environment that drives the equation. The initial condition u( x, 0) = u 0( x), x ∈ ℤ d , is typically taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump at rate 2 d κ, split into two at rate ξ ∨ 0, and die at rate (- ξ) ∨ 0. In earlier work we looked at the Lyapunov exponents λ p(κ ) = limlimits _{tto ∞} 1/t log {E} ([u(0,t)]p)^{1/p}, quad p in {N} , qquad λ 0(κ ) = limlimits _{tto ∞} 1/2 log u(0,t). For the former we derived quantitative results on the κ-dependence for four choices of ξ : space-time white noise, independent simple random walks, the exclusion process and the voter model. For the latter we obtained qualitative results under certain space-time mixing conditions on ξ. In the present paper we investigate what happens when κΔ is replaced by Δ𝓚, where 𝓚 = {𝓚( x, y) : x, y ∈ ℤ d , x ˜ y} is a collection of random conductances between neighbouring sites replacing the constant conductances κ in the homogeneous model. We show that the associated annealed Lyapunov exponents λ p (𝓚), p ∈ ℕ, are given by the formula λ p({K} ) = {sup} {λ p(κ ) : κ in {Supp} ({K} )}, where, for a fixed realisation of 𝓚, Supp(𝓚) is the set of values taken by the 𝓚-field. We also show that for the associated quenched Lyapunov exponent λ 0(𝓚) this formula only provides a lower bound, and we conjecture that an upper bound holds when Supp(𝓚) is replaced by its convex hull. Our proof is valid for three classes of reversible ξ, and for all 𝓚

  13. Two-Stage Modelling Of Random Phenomena

    NASA Astrophysics Data System (ADS)

    Barańska, Anna

    2015-12-01

    The main objective of this publication was to present a two-stage algorithm of modelling random phenomena, based on multidimensional function modelling, on the example of modelling the real estate market for the purpose of real estate valuation and estimation of model parameters of foundations vertical displacements. The first stage of the presented algorithm includes a selection of a suitable form of the function model. In the classical algorithms, based on function modelling, prediction of the dependent variable is its value obtained directly from the model. The better the model reflects a relationship between the independent variables and their effect on the dependent variable, the more reliable is the model value. In this paper, an algorithm has been proposed which comprises adjustment of the value obtained from the model with a random correction determined from the residuals of the model for these cases which, in a separate analysis, were considered to be the most similar to the object for which we want to model the dependent variable. The effect of applying the developed quantitative procedures for calculating the corrections and qualitative methods to assess the similarity on the final outcome of the prediction and its accuracy, was examined by statistical methods, mainly using appropriate parametric tests of significance. The idea of the presented algorithm has been designed so as to approximate the value of the dependent variable of the studied phenomenon to its value in reality and, at the same time, to have it "smoothed out" by a well fitted modelling function.

  14. Filling in the Gaps: Modelling Incomplete CBL Data Using a Graphing Calculator.

    ERIC Educational Resources Information Center

    Swingle, David A.; Pachnowski, Lynne M.

    2003-01-01

    Discusses a real-world problem-solving lesson that emerged when a high school math teacher used a motion detector with a CBL and graphing calculator to obtain the bounce data of a ping-pong ball. Describes the lesson in which students collect bad data then fill in the missing parabolas that result using critical components of parabolas and…

  15. Extracting Between-Pathway Models from E-MAP Interactions Using Expected Graph Compression

    NASA Astrophysics Data System (ADS)

    Kelley, David R.; Kingsford, Carl

    Genetic interactions (such as synthetic lethal interactions) have become quantifiable on a large-scale using the epistatic miniarray profile (E-MAP) method. An E-MAP allows the construction of a large, weighted network of both aggravating and alleviating genetic interactions between genes. By clustering genes into modules and establishing relationships between those modules, we can discover compensatory pathways. We introduce a general framework for applying greedy clustering heuristics to probabilistic graphs. We use this framework to apply a graph clustering method called graph summarization to an E-MAP that targets yeast chromosome biology. This results in a new method for clustering E-MAP data that we call Expected Graph Compression (EGC). We validate modules and compensatory pathways using enriched Gene Ontology annotations and a novel method based on correlated gene expression. EGC finds a number of modules that are not found by any previous methods to cluster E-MAP data. EGC also uncovers core submodules contained within several previously found modules, suggesting that EGC can reveal the finer structure of E-MAP networks.

  16. Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

    SciTech Connect

    Purvine, Emilie AH; Monson, Kyle E.; Jurrus, Elizabeth R.; Star, Keith T.; Baker, Nathan A.

    2016-09-01

    There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of maximum flow-minimum cut graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.

  17. Filling in the Gaps: Modelling Incomplete CBL Data Using a Graphing Calculator.

    ERIC Educational Resources Information Center

    Swingle, David A.; Pachnowski, Lynne M.

    2003-01-01

    Discusses a real-world problem-solving lesson that emerged when a high school math teacher used a motion detector with a CBL and graphing calculator to obtain the bounce data of a ping-pong ball. Describes the lesson in which students collect bad data then fill in the missing parabolas that result using critical components of parabolas and…

  18. Static cooperator-defector patterns in models of the snowdrift game played on cycle graphs.

    PubMed

    Laird, Robert A

    2013-07-01

    Evolutionary graph theory is an extension of evolutionary game theory in which each individual agent, represented by a node, interacts only with a subset of the entire population to which it belongs (i.e., those to which it is connected by edges). In the context of the evolution of cooperation, in which individuals playing the cooperator strategy interact with individuals playing the defector strategy and game payoffs are equated with fitness, evolutionary games on graphs lead to global standoffs (i.e., static patterns) when all cooperators in a population have the same payoff as any defectors with which they share an edge. I consider the simplest type of regular-connected graph, the cycle graph, in which every node has exactly two edges (k = 2), for the prisoner's dilemma game and the snowdrift game, the two most important pairwise games in cooperation theory. I show that for simplified payoff structures associated with these games, standoffs are only possible for two valid cost-benefit ratios in the snowdrift game. I further show that only the greater of these two cost-benefit ratios is likely to be attracting in most situations (i.e., likely to spontaneously result in a global standoff when starting from nonstandoff conditions). Numerical simulations confirm this prediction. This work contributes to our understanding of the evolution of pattern formation in games played in finite, sparsely connected populations.

  19. Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

    PubMed Central

    Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A.

    2016-01-01

    There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of “maximum flow-minimum cut” graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered. PMID:27089174

  20. Energy Minimization of Discrete Protein Titration State Models Using Graph Theory.

    PubMed

    Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A

    2016-08-25

    There are several applications in computational biophysics that require the optimization of discrete interacting states, for example, amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of "maximum flow-minimum cut" graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.

  1. Inhomogeneous random phase approximation: A solvable model

    SciTech Connect

    Lemm, J.C.

    1995-11-15

    A recently developed method to include particle-hole correlations into the time-independent mean field theory for scattering (TIMF) by an inhomogeneous random phase approximation (IRPA) is applied to a numerically solvable model. Having adapted the procedure according to numerical requirements, IRPA calculations turn out to be tractable. The obtained results improve TIMF results. 8 refs., 28 figs., 3 tabs.

  2. Improving randomness characterization through Bayesian model selection.

    PubMed

    Díaz Hernández Rojas, Rafael; Solís, Aldo; Angulo Martínez, Alí M; U'Ren, Alfred B; Hirsch, Jorge G; Marsili, Matteo; Pérez Castillo, Isaac

    2017-06-08

    Random number generation plays an essential role in technology with important applications in areas ranging from cryptography to Monte Carlo methods, and other probabilistic algorithms. All such applications require high-quality sources of random numbers, yet effective methods for assessing whether a source produce truly random sequences are still missing. Current methods either do not rely on a formal description of randomness (NIST test suite) on the one hand, or are inapplicable in principle (the characterization derived from the Algorithmic Theory of Information), on the other, for they require testing all the possible computer programs that could produce the sequence to be analysed. Here we present a rigorous method that overcomes these problems based on Bayesian model selection. We derive analytic expressions for a model's likelihood which is then used to compute its posterior distribution. Our method proves to be more rigorous than NIST's suite and Borel-Normality criterion and its implementation is straightforward. We applied our method to an experimental device based on the process of spontaneous parametric downconversion to confirm it behaves as a genuine quantum random number generator. As our approach relies on Bayesian inference our scheme transcends individual sequence analysis, leading to a characterization of the source itself.

  3. Random matrices and holographic tensor models

    NASA Astrophysics Data System (ADS)

    Krishnan, Chethan; Kumar, K. V. Pavan; Sanyal, Sambuddha

    2017-06-01

    We further explore the connection between holographic O( n) tensor models and random matrices. First, we consider the simplest non-trivial uncolored tensor model and show that the results for the density of states, level spacing and spectral form factor are qualitatively identical to the colored case studied in arXiv:1612.06330. We also explain an overall 16-fold degeneracy by identifying various symmetries, some of which were unavailable in SYK and the colored models. Secondly, and perhaps more interestingly, we systematically identify the Spectral Mirror Symmetry and the Time-Reversal Symmetry of both the colored and uncolored models for all values of n, and use them to identify the Andreev ensembles that control their random matrix behavior. We find that the ensembles that arise exhibit a refined version of Bott periodicity in n.

  4. Tests of Hypotheses Arising In the Correlated Random Coefficient Model*

    PubMed Central

    Heckman, James J.; Schmierer, Daniel

    2010-01-01

    This paper examines the correlated random coefficient model. It extends the analysis of Swamy (1971), who pioneered the uncorrelated random coefficient model in economics. We develop the properties of the correlated random coefficient model and derive a new representation of the variance of the instrumental variable estimator for that model. We develop tests of the validity of the correlated random coefficient model against the null hypothesis of the uncorrelated random coefficient model. PMID:21170148

  5. Tests of Hypotheses Arising In the Correlated Random Coefficient Model.

    PubMed

    Heckman, James J; Schmierer, Daniel

    2010-11-01

    This paper examines the correlated random coefficient model. It extends the analysis of Swamy (1971), who pioneered the uncorrelated random coefficient model in economics. We develop the properties of the correlated random coefficient model and derive a new representation of the variance of the instrumental variable estimator for that model. We develop tests of the validity of the correlated random coefficient model against the null hypothesis of the uncorrelated random coefficient model.

  6. Bio-AIMS Collection of Chemoinformatics Web Tools based on Molecular Graph Information and Artificial Intelligence Models.

    PubMed

    Munteanu, Cristian R; Gonzalez-Diaz, Humberto; Garcia, Rafael; Loza, Mabel; Pazos, Alejandro

    2015-01-01

    The molecular information encoding into molecular descriptors is the first step into in silico Chemoinformatics methods in Drug Design. The Machine Learning methods are a complex solution to find prediction models for specific biological properties of molecules. These models connect the molecular structure information such as atom connectivity (molecular graphs) or physical-chemical properties of an atom/group of atoms to the molecular activity (Quantitative Structure - Activity Relationship, QSAR). Due to the complexity of the proteins, the prediction of their activity is a complicated task and the interpretation of the models is more difficult. The current review presents a series of 11 prediction models for proteins, implemented as free Web tools on an Artificial Intelligence Model Server in Biosciences, Bio-AIMS (http://bio-aims.udc.es/TargetPred.php). Six tools predict protein activity, two models evaluate drug - protein target interactions and the other three calculate protein - protein interactions. The input information is based on the protein 3D structure for nine models, 1D peptide amino acid sequence for three tools and drug SMILES formulas for two servers. The molecular graph descriptor-based Machine Learning models could be useful tools for in silico screening of new peptides/proteins as future drug targets for specific treatments.

  7. Graph search: active appearance model based automated segmentation of retinal layers for optic nerve head centered OCT images

    NASA Astrophysics Data System (ADS)

    Gao, Enting; Shi, Fei; Zhu, Weifang; Jin, Chao; Sun, Min; Chen, Haoyu; Chen, Xinjian

    2017-02-01

    In this paper, a novel approach combining the active appearance model (AAM) and graph search is proposed to segment retinal layers for optic nerve head(ONH) centered optical coherence tomography(OCT) images. The method includes two parts: preprocessing and layer segmentation. During the preprocessing phase, images is first filtered for denoising, then the B-scans are flattened. During layer segmentation, the AAM is first used to obtain the coarse segmentation results. Then a multi-resolution GS-AAM algorithm is applied to further refine the results, in which AAM is efficiently integrated into the graph search segmentation process. The proposed method was tested on a dataset which contained113-D SD-OCT images, and compared to the manual tracings of two observers on all the volumetric scans. The overall mean border positioning error for layer segmentation was found to be 7.09 +/- 6.18μm for normal subjects. It was comparable to the results of traditional graph search method (8.03+/-10.47μm) and mean inter-observer variability (6.35+/-6.93μm).The preliminary results demonstrated the feasibility and efficiency of the proposed method.

  8. GraphBench

    SciTech Connect

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

    2016-06-01

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

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

    SciTech Connect

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

    2016-01-01

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

  10. Conformational transitions in random heteropolymer models

    NASA Astrophysics Data System (ADS)

    Blavatska, Viktoria; Janke, Wolfhard

    2014-01-01

    We study the conformational properties of heteropolymers containing two types of monomers A and B, modeled as self-attracting self-avoiding random walks on a regular lattice. Such a model can describe in particular the sequences of hydrophobic and hydrophilic residues in proteins [K. F. Lau and K. A. Dill, Macromolecules 22, 3986 (1989)] and polyampholytes with oppositely charged groups [Y. Kantor and M. Kardar, Europhys. Lett. 28, 169 (1994)]. Treating the sequences of the two types of monomers as quenched random variables, we provide a systematic analysis of possible generalizations of this model. To this end we apply the pruned-enriched Rosenbluth chain-growth algorithm, which allows us to obtain the phase diagrams of extended and compact states coexistence as function of both the temperature and fraction of A and B monomers along the heteropolymer chain.

  11. Testing the Correlated Random Coefficient Model*

    PubMed Central

    Heckman, James J.; Schmierer, Daniel; Urzua, Sergio

    2010-01-01

    The recent literature on instrumental variables (IV) features models in which agents sort into treatment status on the basis of gains from treatment as well as on baseline-pretreatment levels. Components of the gains known to the agents and acted on by them may not be known by the observing economist. Such models are called correlated random coe cient models. Sorting on unobserved components of gains complicates the interpretation of what IV estimates. This paper examines testable implications of the hypothesis that agents do not sort into treatment based on gains. In it, we develop new tests to gauge the empirical relevance of the correlated random coe cient model to examine whether the additional complications associated with it are required. We examine the power of the proposed tests. We derive a new representation of the variance of the instrumental variable estimator for the correlated random coefficient model. We apply the methods in this paper to the prototypical empirical problem of estimating the return to schooling and nd evidence of sorting into schooling based on unobserved components of gains. PMID:21057649

  12. Effect of random field disorder on the first order transition in p-spin interaction model

    NASA Astrophysics Data System (ADS)

    Sumedha; Singh, Sushant K.

    2016-01-01

    We study the random field p-spin model with Ising spins on a fully connected graph using the theory of large deviations in this paper. This is a good model to study the effect of quenched random field on systems which have a sharp first order transition in the pure state. For p = 2, the phase-diagram of the model, for bimodal distribution of the random field, has been well studied and is known to undergo a continuous transition for lower values of the random field (h) and a first order transition beyond a threshold, htp(≈ 0.439) . We find the phase diagram of the model, for all p ≥ 2, with bimodal random field distribution, using large deviation techniques. We also look at the fluctuations in the system by calculating the magnetic susceptibility. For p = 2, beyond the tricritical point in the regime of first order transition, we find that for htp < h < 0.447, magnetic susceptibility increases rapidly (even though it never diverges) as one approaches the transition from the high temperature side. On the other hand, for 0.447 < h ≤ 0.5, the high temperature behaviour is well described by the Curie-Weiss law. For all p ≥ 2, we find that for larger magnitudes of the random field (h >ho = 1 / p!), the system does not show ferromagnetic order even at zero temperature. We find that the magnetic susceptibility for p ≥ 3 is discontinuous at the transition point for h

  13. Line graphs for fractals

    NASA Astrophysics Data System (ADS)

    Warchalowski, Wiktor; Krawczyk, Malgorzata J.

    2017-03-01

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

  14. "Improved Geometric Network Model" (IGNM): a novel approach for deriving Connectivity Graphs for Indoor Navigation

    NASA Astrophysics Data System (ADS)

    Mortari, F.; Zlatanova, S.; Liu, L.; Clementini, E.

    2014-04-01

    Over the past few years Personal Navigation Systems have become an established tool for route planning, but they are mainly designed for outdoor environments. Indoor navigation is still a challenging research area for several reasons: positioning is not very accurate, users can freely move between the interior boundaries of buildings, path network construction process may not be easy and straightforward due to complexity of indoor space configurations. Therefore the creation of a good network is essential for deriving overall connectivity of a building and for representing position of objects within the environment. This paper reviews current approaches to automatic derivation of route graphs for indoor navigation and discusses some of their limitations. Then, it introduces a novel algorithmic strategy for extracting a 3D connectivity graph for indoor navigation based on 2D floor plans.

  15. Modelling graph dynamics of flaring active regions using SDO/HMI data

    NASA Astrophysics Data System (ADS)

    Lukyanov, A. D.; Makarenko, N. G.; Knyazeva, I. S.

    2017-01-01

    Large solar flares define parameters of space weather near the Earth and normal operation of spacecrafts substantially depends on the cosmic particles flux of solar wind. Therefore, search for large flares predictors is an important problem. We propose to approximate topology of the magnetic field of active region by graph, whose vertices are minima and maxima of a scalar field and edges form a so-called critical net. Localization and number of critical points change during the process of evolution and, therefore, it is possible to track dynamic regimes of active region by considering dynamics of graphs. Numerical characteristic of the critical net is a spectrum of eigenvalues of its discrete Laplacian. We present examples which show that, apparently, Laplacian spectrum is closely related to flaring activity. It will allow us to use critical net in prognostic systems for prediction of large solar flares.

  16. High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials

    NASA Astrophysics Data System (ADS)

    >Jesper Lykke Jacobsen,

    2014-04-01

    The critical curves of the q-state Potts model can be determined exactly for regular two-dimensional lattices G that are of the three-terminal type. This comprises the square, triangular, hexagonal and bow-tie lattices. Jacobsen and Scullard have defined a graph polynomial PB(q, v) that gives access to the critical manifold for general lattices. It depends on a finite repeating part of the lattice, called the basis B, and its real roots in the temperature variable v = eK - 1 provide increasingly accurate approximations to the critical manifolds upon increasing the size of B. Using transfer matrix techniques, these authors computed PB(q, v) for large bases (up to 243 edges), obtaining determinations of the ferromagnetic critical point vc > 0 for the (4, 82), kagome, and (3, 122) lattices to a precision (of the order 10-8) slightly superior to that of the best available Monte Carlo simulations. In this paper we describe a more efficient transfer matrix approach to the computation of PB(q, v) that relies on a formulation within the periodic Temperley-Lieb algebra. This makes possible computations for substantially larger bases (up to 882 edges), and the precision on vc is hence taken to the range 10-13. We further show that a large variety of regular lattices can be cast in a form suitable for this approach. This includes all Archimedean lattices, their duals and their medials. For all these lattices we tabulate high-precision estimates of the bond percolation thresholds pc and Potts critical points vc. We also trace and discuss the full Potts critical manifold in the (q, v) plane, paying special attention to the antiferromagnetic region v < 0. Finally, we adapt the technique to site percolation as well, and compute the polynomials PB(p) for certain Archimedean and dual lattices (those having only cubic and quartic vertices), using very large bases (up to 243 vertices). This produces the site percolation thresholds pc to a precision of the order of 10-9.

  17. Multi-class Graph Mumford-Shah Model for Plume Detection using the MBO Scheme

    DTIC Science & Technology

    2014-10-01

    Theoretical analysis is developed and a Lyapunov functional is proven to decrease as the algorithm proceeds. Furthermore, to reduce the com...dynamics. Theoretical analysis is developed and a Lyapunov functional is proven to decrease as the algorithm proceeds. Furthermore, to reduce the...for the multi-class case. An analogous discussion in a graph setting is given in [23]. Inspired by the work of [7, 23], we develop a Lyapunov

  18. Entropy, complexity, and Markov diagrams for random walk cancer models

    NASA Astrophysics Data System (ADS)

    Newton, Paul K.; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

    2014-12-01

    The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.

  19. Entropy, complexity, and Markov diagrams for random walk cancer models

    PubMed Central

    Newton, Paul K.; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

    2014-01-01

    The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential. PMID:25523357

  20. Entropy, complexity, and Markov diagrams for random walk cancer models.

    PubMed

    Newton, Paul K; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

    2014-12-19

    The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.

  1. A novel model for DNA sequence similarity analysis based on graph theory.

    PubMed

    Qi, Xingqin; Wu, Qin; Zhang, Yusen; Fuller, Eddie; Zhang, Cun-Quan

    2011-01-01

    Determination of sequence similarity is one of the major steps in computational phylogenetic studies. As we know, during evolutionary history, not only DNA mutations for individual nucleotide but also subsequent rearrangements occurred. It has been one of major tasks of computational biologists to develop novel mathematical descriptors for similarity analysis such that various mutation phenomena information would be involved simultaneously. In this paper, different from traditional methods (eg, nucleotide frequency, geometric representations) as bases for construction of mathematical descriptors, we construct novel mathematical descriptors based on graph theory. In particular, for each DNA sequence, we will set up a weighted directed graph. The adjacency matrix of the directed graph will be used to induce a representative vector for DNA sequence. This new approach measures similarity based on both ordering and frequency of nucleotides so that much more information is involved. As an application, the method is tested on a set of 0.9-kb mtDNA sequences of twelve different primate species. All output phylogenetic trees with various distance estimations have the same topology, and are generally consistent with the reported results from early studies, which proves the new method's efficiency; we also test the new method on a simulated data set, which shows our new method performs better than traditional global alignment method when subsequent rearrangements happen frequently during evolutionary history.

  2. A graph edit dictionary for correcting errors in roof topology graphs reconstructed from point clouds

    NASA Astrophysics Data System (ADS)

    Xiong, B.; Oude Elberink, S.; Vosselman, G.

    2014-07-01

    In the task of 3D building model reconstruction from point clouds we face the problem of recovering a roof topology graph in the presence of noise, small roof faces and low point densities. Errors in roof topology graphs will seriously affect the final modelling results. The aim of this research is to automatically correct these errors. We define the graph correction as a graph-to-graph problem, similar to the spelling correction problem (also called the string-to-string problem). The graph correction is more complex than string correction, as the graphs are 2D while strings are only 1D. We design a strategy based on a dictionary of graph edit operations to automatically identify and correct the errors in the input graph. For each type of error the graph edit dictionary stores a representative erroneous subgraph as well as the corrected version. As an erroneous roof topology graph may contain several errors, a heuristic search is applied to find the optimum sequence of graph edits to correct the errors one by one. The graph edit dictionary can be expanded to include entries needed to cope with errors that were previously not encountered. Experiments show that the dictionary with only fifteen entries already properly corrects one quarter of erroneous graphs in about 4500 buildings, and even half of the erroneous graphs in one test area, achieving as high as a 95% acceptance rate of the reconstructed models.

  3. 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.

  4. Random matrix model for chiral symmetry breaking

    SciTech Connect

    Jackson, A.D.; Verbaarschot, J.J.

    1996-06-01

    We formulate a random matrix model which mimics the chiral phase transition in QCD with two light flavors. Two critical exponents are calculated. We obtain the mean-field values {beta}=1/2 and {delta}=3. We also find that the chiral phase transition can be characterized by the dynamics of the smallest eigenvalue of the Dirac operator. This suggests an alternative order parameter which may be of relevance for lattice QCD simulations. {copyright} {ital 1996 The American Physical Society.}

  5. 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.

  6. Quantum ergodicity on graphs.

    PubMed

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

    2008-12-31

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

  7. Quantum Ergodicity on Graphs

    SciTech Connect

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

    2008-12-31

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

  8. Detecting labor using graph theory on connectivity matrices of uterine EMG.

    PubMed

    Al-Omar, S; Diab, A; Nader, N; Khalil, M; Karlsson, B; Marque, C

    2015-08-01

    Premature labor is one of the most serious health problems in the developed world. One of the main reasons for this is that no good way exists to distinguish true labor from normal pregnancy contractions. The aim of this paper is to investigate if the application of graph theory techniques to multi-electrode uterine EMG signals can improve the discrimination between pregnancy contractions and labor. To test our methods we first applied them to synthetic graphs where we detected some differences in the parameters results and changes in the graph model from pregnancy-like graphs to labor-like graphs. Then, we applied the same methods to real signals. We obtained the best differentiation between pregnancy and labor through the same parameters. Major improvements in differentiating between pregnancy and labor were obtained using a low pass windowing preprocessing step. Results show that real graphs generally became more organized when moving from pregnancy, where the graph showed random characteristics, to labor where the graph became a more small-world like graph.

  9. DNA Rearrangements through Spatial Graphs

    NASA Astrophysics Data System (ADS)

    Jonoska, Nataša; Saito, Masahico

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

  10. Random Walks in Model Brain Tissue

    NASA Astrophysics Data System (ADS)

    Grinberg, Farida; Farrher, Ezequiel; Oros-Peusquens, Ana-Maria; Shah, N. Jon

    2011-03-01

    The propagation of water molecules in the brain and the corresponding NMR response are affected by many factors such as compartmentalization, restrictions and anisotropy imposed by the cellular microstructure. Interfacial interactions with cell membranes and exchange additionally come into play. Due to the complexity of the underlying factors, a differentiation between the various contributions to the average NMR signal in in vivo studies represents a difficult task. In this work we perform random-walk Monte Carlo simulations in well-defined model systems aiming at establishing quantitative relations between dynamics and microstructure. The results are compared with experimental data obtained for artificial anisotropic model systems.

  11. Multiple graph regularized protein domain ranking

    PubMed Central

    2012-01-01

    Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. PMID:23157331

  12. A study of structural properties of gene network graphs for mathematical modeling of integrated mosaic gene networks.

    PubMed

    Petrovskaya, Olga V; Petrovskiy, Evgeny D; Lavrik, Inna N; Ivanisenko, Vladimir A

    2017-04-01

    Gene network modeling is one of the widely used approaches in systems biology. It allows for the study of complex genetic systems function, including so-called mosaic gene networks, which consist of functionally interacting subnetworks. We conducted a study of a mosaic gene networks modeling method based on integration of models of gene subnetworks by linear control functionals. An automatic modeling of 10,000 synthetic mosaic gene regulatory networks was carried out using computer experiments on gene knockdowns/knockouts. Structural analysis of graphs of generated mosaic gene regulatory networks has revealed that the most important factor for building accurate integrated mathematical models, among those analyzed in the study, is data on expression of genes corresponding to the vertices with high properties of centrality.

  13. Blind Identification of Graph Filters

    NASA Astrophysics Data System (ADS)

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

    2017-03-01

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

  14. Generating graphs for visual analytics through interactive sketching.

    PubMed

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

    2006-01-01

    We introduce an interactive graph generator, GreenSketch, designed to facilitate the creation of descriptive graphs required for different visual analytics tasks. The human-centric design approach of GreenSketch enables users to master the creation process without specific training or prior knowledge of graph model theory. The customized user interface encourages users to gain insight into the connection between the compact matrix representation and the topology of a graph layout when they sketch their graphs. Both the human-enforced and machine-generated randomnesses supported by GreenSketch provide the flexibility needed to address the uncertainty factor in many analytical tasks. This paper describes more than two dozen examples that cover a wide variety of graph creations from a single line of nodes to a real-life small-world network that describes a snapshot of telephone connections. While the discussion focuses mainly on the design of GreenSketch, we include a case study that applies the technology in a visual analytics environment and a usability study that evaluates the strengths and weaknesses of our design approach.

  15. A Clustering Graph Generator

    SciTech Connect

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

    2015-10-26

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

  16. Conceptual graphs for semantics and knowledge processing

    SciTech Connect

    Fargues, J.; Landau, M.C.; Dugourd, A.; Catach, L.

    1986-01-01

    This paper discusses the representational and algorithmic power of the conceptual graph model for natural language semantics and knowledge processing. Also described is a Prolog-like resolution method for conceptual graphs, which allows to perform deduction on very large semantic domains. The interpreter developed is similar to a Prolog interpreter in which the terms are any conceptual graphs and in which the unification algorithm is replaced by a specialized algorithm for conceptual graphs.

  17. Mechatronic modeling of a 750kW fixed-speed wind energy conversion system using the Bond Graph Approach.

    PubMed

    Khaouch, Zakaria; Zekraoui, Mustapha; Bengourram, Jamaa; Kouider, Nourreeddine; Mabrouki, Mustapha

    2016-11-01

    In this paper, we would like to focus on modeling main parts of the wind turbines (blades, gearbox, tower, generator and pitching system) from a mechatronics viewpoint using the Bond-Graph Approach (BGA). Then, these parts are combined together in order to simulate the complete system. Moreover, the real dynamic behavior of the wind turbine is taken into account and with the new model; final load simulation is more realistic offering benefits and reliable system performance. This model can be used to develop control algorithms to reduce fatigue loads and enhance power production. Different simulations are carried-out in order to validate the proposed wind turbine model, using real data provided in the open literature (blade profile and gearbox parameters for a 750 kW wind turbine).

  18. Approximate Graph Edit Distance in Quadratic Time.

    PubMed

    Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst

    2015-09-14

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

  19. 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.

  20. Mild traumatic brain injury: graph-model characterization of brain networks for episodic memory.

    PubMed

    Tsirka, Vasso; Simos, Panagiotis G; Vakis, Antonios; Kanatsouli, Kassiani; Vourkas, Michael; Erimaki, Sofia; Pachou, Ellie; Stam, Cornelis Jan; Micheloyannis, Sifis

    2011-02-01

    Episodic memory is among the cognitive functions that can be affected in the acute phase following mild traumatic brain injury (MTBI). The present study used EEG recordings to evaluate global synchronization and network organization of rhythmic activity during the encoding and recognition phases of an episodic memory task varying in stimulus type (kaleidoscope images, pictures, words, and pseudowords). Synchronization of oscillatory activity was assessed using a linear and nonlinear connectivity estimator and network analyses were performed using algorithms derived from graph theory. Twenty five MTBI patients (tested within days post-injury) and healthy volunteers were closely matched on demographic variables, verbal ability, psychological status variables, as well as on overall task performance. Patients demonstrated sub-optimal network organization, as reflected by changes in graph parameters in the theta and alpha bands during both encoding and recognition. There were no group differences in spectral energy during task performance or on network parameters during a control condition (rest). Evidence of less optimally organized functional networks during memory tasks was more prominent for pictorial than for verbal stimuli.

  1. Cascades on clique-based graphs

    NASA Astrophysics Data System (ADS)

    Hackett, Adam; Gleeson, James P.

    2013-06-01

    We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly clustered random graphs introduced by Gleeson [J. P. Gleeson, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.80.036107 80, 036107 (2009)]. A condition for the existence of global cascades is also derived. Applications of this approach include analyses of percolation, and Watts's model. We show how our techniques can be used to study the effects of in-group bias in cascades on social networks.

  2. Reducing RANS Model Error Using Random Forest

    NASA Astrophysics Data System (ADS)

    Wang, Jian-Xun; Wu, Jin-Long; Xiao, Heng; Ling, Julia

    2016-11-01

    Reynolds-Averaged Navier-Stokes (RANS) models are still the work-horse tools in the turbulence modeling of industrial flows. However, the model discrepancy due to the inadequacy of modeled Reynolds stresses largely diminishes the reliability of simulation results. In this work we use a physics-informed machine learning approach to improve the RANS modeled Reynolds stresses and propagate them to obtain the mean velocity field. Specifically, the functional forms of Reynolds stress discrepancies with respect to mean flow features are trained based on an offline database of flows with similar characteristics. The random forest model is used to predict Reynolds stress discrepancies in new flows. Then the improved Reynolds stresses are propagated to the velocity field via RANS equations. The effects of expanding the feature space through the use of a complete basis of Galilean tensor invariants are also studied. The flow in a square duct, which is challenging for standard RANS models, is investigated to demonstrate the merit of the proposed approach. The results show that both the Reynolds stresses and the propagated velocity field are improved over the baseline RANS predictions. SAND Number: SAND2016-7437 A

  3. Gestational Age Assessment in the Ghana Randomized Air Pollution and Health Study (GRAPHS): Ultrasound Capacity Building, Fetal Biometry Protocol Development, and Ongoing Quality Control

    PubMed Central

    Boamah, Ellen A; Asante, KP; Ae-Ngibise, KA; Kinney, Patrick L; Jack, Darby W; Manu, Grace; Azindow, Irene T; Owusu-Agyei, Seth

    2014-01-01

    Background Four million premature deaths occur yearly as a result of smoke from cooking fires. The Ghana Randomized Air Pollution and Health Study (GRAPHS) is underway in the Kintampo North municipality and South district of rural Ghana to evaluate the impact of improved cook stoves introduced during pregnancy on birth weight and childhood pneumonia. These hypotheses are being tested in a cluster-randomized intervention trial among 1415 maternal-infant pairs within 35 communities assigned to a control arm (traditional cooking) or one of two intervention arms (cooking with an improved biomass stove; cooking with liquefied petroleum gas stoves). Objective The trial is designed to ensure delivery of the stove intervention prior to the period of maximal fetal growth. To answer questions about the impact of household air pollution on pregnancy outcome, accurate gestational age assessment is critical. This manuscript describes in detail the development of the gestational dating protocol, intensive ultrasound training involved, ultrasound capacity building, and ultrasound quality control program. Methods Ultrasound training occurred in several phases over the course of 2 years. Training included a basic obstetric ultrasound course offered to all midwives performing antenatal care at the two study hospitals, followed by a more intense period of hands-on training focused on fetal biometry for a select group of providers demonstrating aptitude in the basic course. A standard operating procedure was developed describing how to obtain all fetal biometric measurements. Consensus was obtained on how biometric images are used in the trial to establish gestational age and estimate the delivery date. An ongoing ultrasound quality control program including the use of an image scorecard was also designed. Results Publication of trial results is anticipated in late 2016. Conclusions Use of ultrasound should be strongly considered in field-based trials involving pregnant women to

  4. Models construction for acetone-butanol-ethanol fermentations with acetate/butyrate consecutively feeding by graph theory.

    PubMed

    Li, Zhigang; Shi, Zhongping; Li, Xin

    2014-05-01

    Several fermentations with consecutively feeding of acetate/butyrate were conducted in a 7 L fermentor and the results indicated that exogenous acetate/butyrate enhanced solvents productivities by 47.1% and 39.2% respectively, and changed butyrate/acetate ratios greatly. Then extracellular butyrate/acetate ratios were utilized for calculation of acids rates and the results revealed that acetate and butyrate formation pathways were almost blocked by corresponding acids feeding. In addition, models for acetate/butyrate feeding fermentations were constructed by graph theory based on calculation results and relevant reports. Solvents concentrations and butanol/acetone ratios of these fermentations were also calculated and the results of models calculation matched fermentation data accurately which demonstrated that models were constructed in a reasonable way. Copyright © 2014 Elsevier Ltd. All rights reserved.

  5. Reliable ABC model choice via random forests.

    PubMed

    Pudlo, Pierre; Marin, Jean-Michel; Estoup, Arnaud; Cornuet, Jean-Marie; Gautier, Mathieu; Robert, Christian P

    2016-03-15

    Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior probabilities may be poorly evaluated by standard ABC techniques. We propose a novel approach based on a machine learning tool named random forests (RF) to conduct selection among the highly complex models covered by ABC algorithms. We thus modify the way Bayesian model selection is both understood and operated, in that we rephrase the inferential goal as a classification problem, first predicting the model that best fits the data with RF and postponing the approximation of the posterior probability of the selected model for a second stage also relying on RF. Compared with earlier implementations of ABC model choice, the ABC RF approach offers several potential improvements: (i) it often has a larger discriminative power among the competing models, (ii) it is more robust against the number and choice of statistics summarizing the data, (iii) the computing effort is drastically reduced (with a gain in computation efficiency of at least 50) and (iv) it includes an approximation of the posterior probability of the selected model. The call to RF will undoubtedly extend the range of size of datasets and complexity of models that ABC can handle. We illustrate the power of this novel methodology by analyzing controlled experiments as well as genuine population genetics datasets. The proposed methodology is implemented in the R package abcrf available on the CRAN. jean-michel.marin@umontpellier.fr Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

  6. Disentangling giant component and finite cluster contributions in sparse random matrix spectra.

    PubMed

    Kühn, Reimer

    2016-04-01

    We describe a method for disentangling giant component and finite cluster contributions to sparse random matrix spectra, using sparse symmetric random matrices defined on Erdős-Rényi graphs as an example and test bed. Our methods apply to sparse matrices defined in terms of arbitrary graphs in the configuration model class, as long as they have finite mean degree.

  7. What is the difference between the breakpoint graph and the de Bruijn graph?

    PubMed

    Lin, Yu; Nurk, Sergey; Pevzner, Pavel A

    2014-01-01

    The breakpoint graph and the de Bruijn graph are two key data structures in the studies of genome rearrangements and genome assembly. However, the classical breakpoint graphs are defined on two genomes (represented as sequences of synteny blocks), while the classical de Bruijn graphs are defined on a single genome (represented as DNA strings). Thus, the connection between these two graph models is not explicit. We generalize the notions of both the breakpoint graph and the de Bruijn graph, and make it transparent that the breakpoint graph and the de Bruijn graph are mathematically equivalent. The explicit description of the connection between these important data structures provides a bridge between two previously separated bioinformatics communities studying genome rearrangements and genome assembly.

  8. Kinetic Models with Randomly Perturbed Binary Collisions

    NASA Astrophysics Data System (ADS)

    Bassetti, Federico; Ladelli, Lucia; Toscani, Giuseppe

    2011-02-01

    We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules which, in some special cases, identify models for granular gases with a background heat bath (Carrillo et al. in Discrete Contin. Dyn. Syst. 24(1):59-81, 2009), and models for wealth redistribution in an agent-based market (Bisi et al. in Commun. Math. Sci. 7:901-916, 2009). Conditions on these collisional rules which guarantee both the existence and uniqueness of equilibrium profiles and their main properties are found. The characterization of these stationary states is of independent interest, since we show that they are stationary solutions of different evolution problems, both in the kinetic theory of rarefied gases (Cercignani et al. in J. Stat. Phys. 105:337-352, 2001; Villani in J. Stat. Phys. 124:781-822, 2006) and in the econophysical context (Bisi et al. in Commun. Math. Sci. 7:901-916, 2009).

  9. Multibody graph transformations and analysis

    PubMed Central

    2013-01-01

    This two-part paper uses graph transformation methods to develop methods for partitioning, aggregating, and constraint embedding for multibody systems. This first part focuses on tree-topology systems and reviews the key notion of spatial kernel operator (SKO) models for such systems. It develops systematic and rigorous techniques for partitioning SKO models in terms of the SKO models of the component subsystems based on the path-induced property of the component subgraphs. It shows that the sparsity structure of key matrix operators and the mass matrix for the multibody system can be described using partitioning transformations. Subsequently, the notions of node contractions and subgraph aggregation and their role in coarsening graphs are discussed. It is shown that the tree property of a graph is preserved after subgraph aggregation if and only if the subgraph satisfies an aggregation condition. These graph theory ideas are used to develop SKO models for the aggregated tree multibody systems. PMID:24288438

  10. 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.

  11. A Directed Acyclic Graph-Large Margin Distribution Machine Model for Music Symbol Classification.

    PubMed

    Wen, Cuihong; Zhang, Jing; Rebelo, Ana; Cheng, Fanyong

    2016-01-01

    Optical Music Recognition (OMR) has received increasing attention in recent years. In this paper, we propose a classifier based on a new method named Directed Acyclic Graph-Large margin Distribution Machine (DAG-LDM). The DAG-LDM is an improvement of the Large margin Distribution Machine (LDM), which is a binary classifier that optimizes the margin distribution by maximizing the margin mean and minimizing the margin variance simultaneously. We modify the LDM to the DAG-LDM to solve the multi-class music symbol classification problem. Tests are conducted on more than 10000 music symbol images, obtained from handwritten and printed images of music scores. The proposed method provides superior classification capability and achieves much higher classification accuracy than the state-of-the-art algorithms such as Support Vector Machines (SVMs) and Neural Networks (NNs).

  12. A random effects epidemic-type aftershock sequence model.

    PubMed

    Lin, Feng-Chang

    2011-04-01

    We consider an extension of the temporal epidemic-type aftershock sequence (ETAS) model with random effects as a special case of a well-known doubly stochastic self-exciting point process. The new model arises from a deterministic function that is randomly scaled by a nonnegative random variable, which is unobservable but assumed to follow either positive stable or one-parameter gamma distribution with unit mean. Both random effects models are of interest although the one-parameter gamma random effects model is more popular when modeling associated survival times. Our estimation is based on the maximum likelihood approach with marginalized intensity. The methods are shown to perform well in simulation experiments. When applied to an earthquake sequence on the east coast of Taiwan, the extended model with positive stable random effects provides a better model fit, compared to the original ETAS model and the extended model with one-parameter gamma random effects.

  13. Universal spectral statistics in quantum graphs.

    PubMed

    Gnutzmann, Sven; Altland, Alexander

    2004-11-05

    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.

  14. Cayley Bipolar Fuzzy Graphs

    PubMed Central

    Alshehri, Noura O.

    2013-01-01

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

  15. Preserving Differential Privacy in Degree-Correlation based Graph Generation

    PubMed Central

    Wang, Yue; Wu, Xintao

    2014-01-01

    Enabling accurate analysis of social network data while preserving differential privacy has been challenging since graph features such as cluster coefficient often have high sensitivity, which is different from traditional aggregate functions (e.g., count and sum) on tabular data. In this paper, we study the problem of enforcing edge differential privacy in graph generation. The idea is to enforce differential privacy on graph model parameters learned from the original network and then generate the graphs for releasing using the graph model with the private parameters. In particular, we develop a differential privacy preserving graph generator based on the dK-graph generation model. We first derive from the original graph various parameters (i.e., degree correlations) used in the dK-graph model, then enforce edge differential privacy on the learned parameters, and finally use the dK-graph model with the perturbed parameters to generate graphs. For the 2K-graph model, we enforce the edge differential privacy by calibrating noise based on the smooth sensitivity, rather than the global sensitivity. By doing this, we achieve the strict differential privacy guarantee with smaller magnitude noise. We conduct experiments on four real networks and compare the performance of our private dK-graph models with the stochastic Kronecker graph generation model in terms of utility and privacy tradeoff. Empirical evaluations show the developed private dK-graph generation models significantly outperform the approach based on the stochastic Kronecker generation model. PMID:24723987

  16. Preserving Differential Privacy in Degree-Correlation based Graph Generation.

    PubMed

    Wang, Yue; Wu, Xintao

    2013-08-01

    Enabling accurate analysis of social network data while preserving differential privacy has been challenging since graph features such as cluster coefficient often have high sensitivity, which is different from traditional aggregate functions (e.g., count and sum) on tabular data. In this paper, we study the problem of enforcing edge differential privacy in graph generation. The idea is to enforce differential privacy on graph model parameters learned from the original network and then generate the graphs for releasing using the graph model with the private parameters. In particular, we develop a differential privacy preserving graph generator based on the dK-graph generation model. We first derive from the original graph various parameters (i.e., degree correlations) used in the dK-graph model, then enforce edge differential privacy on the learned parameters, and finally use the dK-graph model with the perturbed parameters to generate graphs. For the 2K-graph model, we enforce the edge differential privacy by calibrating noise based on the smooth sensitivity, rather than the global sensitivity. By doing this, we achieve the strict differential privacy guarantee with smaller magnitude noise. We conduct experiments on four real networks and compare the performance of our private dK-graph models with the stochastic Kronecker graph generation model in terms of utility and privacy tradeoff. Empirical evaluations show the developed private dK-graph generation models significantly outperform the approach based on the stochastic Kronecker generation model.

  17. Mechanical device for determining the stiffness and the viscous friction coefficient of shock absorber elements modelled by bond graph

    NASA Astrophysics Data System (ADS)

    Ibănescu, R.; Ibănescu, M.

    2016-11-01

    The present paper presents a mechanical device for the assessment of the fundamental parameters of a shock absorber: the spring stiffness and the viscous friction coefficient, without disassembling the absorber. The device produces an oscillatory motion of the shock absorber and can measure its amplitude and angular velocities. The dynamic model of the system, consisting of the mechanical device and the shock absorber, is performed by using the bond- graph method. Based on this model, the motion equations are obtained, which by integration lead to the motion law. The two previously mentioned parameters are determined by using this law and the measured values of two amplitudes and of their corresponding angular velocities. They result as solutions of a system of two non-linear algebraic equations.

  18. AptRank: an adaptive PageRank model for protein function prediction on   bi-relational graphs.

    PubMed

    Jiang, Biaobin; Kloster, Kyle; Gleich, David F; Gribskov, Michael

    2017-06-15

    Diffusion-based network models are widely used for protein function prediction using protein network data and have been shown to outperform neighborhood-based and module-based methods. Recent studies have shown that integrating the hierarchical structure of the Gene Ontology (GO) data dramatically improves prediction accuracy. However, previous methods usually either used the GO hierarchy to refine the prediction results of multiple classifiers, or flattened the hierarchy into a function-function similarity kernel. No study has taken the GO hierarchy into account together with the protein network as a two-layer network model. We first construct a Bi-relational graph (Birg) model comprised of both protein-protein association and function-function hierarchical networks. We then propose two diffusion-based methods, BirgRank and AptRank, both of which use PageRank to diffuse information on this two-layer graph model. BirgRank is a direct application of traditional PageRank with fixed decay parameters. In contrast, AptRank utilizes an adaptive diffusion mechanism to improve the performance of BirgRank. We evaluate the ability of both methods to predict protein function on yeast, fly and human protein datasets, and compare with four previous methods: GeneMANIA, TMC, ProteinRank and clusDCA. We design four different validation strategies: missing function prediction, de novo function prediction, guided function prediction and newly discovered function prediction to comprehensively evaluate predictability of all six methods. We find that both BirgRank and AptRank outperform the previous methods, especially in missing function prediction when using only 10% of the data for training. The MATLAB code is available at https://github.rcac.purdue.edu/mgribsko/aptrank . gribskov@purdue.edu. Supplementary data are available at Bioinformatics online.

  19. Positive and Unlabeled Multi-Graph Learning.

    PubMed

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

    2016-03-23

    In this paper, we advance graph classification to handle multi-graph learning for complicated objects, where each object is represented as a bag of graphs and the label is only available to each bag but not individual graphs. In addition, when training classifiers, users are only given a handful of positive bags and many unlabeled bags, and the learning objective is to train models to classify previously unseen graph bags with maximum accuracy. To achieve the goal, we propose a positive and unlabeled multi-graph learning (puMGL) framework to first select informative subgraphs to convert graphs into a feature space. To utilize unlabeled bags for learning, puMGL assigns a confidence weight to each bag and dynamically adjusts its weight value to select "reliable negative bags." A number of representative graphs, selected from positive bags and identified reliable negative graph bags, form a "margin graph pool" which serves as the base for deriving subgraph patterns, training graph classifiers, and further updating the bag weight values. A closed-loop iterative process helps discover optimal subgraphs from positive and unlabeled graph bags for learning. Experimental comparisons demonstrate the performance of puMGL for classifying real-world complicated objects.

  20. The effects of neuron morphology on graph theoretic measures of network connectivity: the analysis of a two-level statistical model.

    PubMed

    Aćimović, Jugoslava; Mäki-Marttunen, Tuomo; Linne, Marja-Leena

    2015-01-01

    We developed a two-level statistical model that addresses the question of how properties of neurite morphology shape the large-scale network connectivity. We adopted a low-dimensional statistical description of neurites. From the neurite model description we derived the expected number of synapses, node degree, and the effective radius, the maximal distance between two neurons expected to form at least one synapse. We related these quantities to the network connectivity described using standard measures from graph theory, such as motif counts, clustering coefficient, minimal path length, and small-world coefficient. These measures are used in a neuroscience context to study phenomena from synaptic connectivity in the small neuronal networks to large scale functional connectivity in the cortex. For these measures we provide analytical solutions that clearly relate different model properties. Neurites that sparsely cover space lead to a small effective radius. If the effective radius is small compared to the overall neuron size the obtained networks share similarities with the uniform random networks as each neuron connects to a small number of distant neurons. Large neurites with densely packed branches lead to a large effective radius. If this effective radius is large compared to the neuron size, the obtained networks have many local connections. In between these extremes, the networks maximize the variability of connection repertoires. The presented approach connects the properties of neuron morphology with large scale network properties without requiring heavy simulations with many model parameters. The two-steps procedure provides an easier interpretation of the role of each modeled parameter. The model is flexible and each of its components can be further expanded. We identified a range of model parameters that maximizes variability in network connectivity, the property that might affect network capacity to exhibit different dynamical regimes.

  1. The effects of neuron morphology on graph theoretic measures of network connectivity: the analysis of a two-level statistical model

    PubMed Central

    Aćimović, Jugoslava; Mäki-Marttunen, Tuomo; Linne, Marja-Leena

    2015-01-01

    We developed a two-level statistical model that addresses the question of how properties of neurite morphology shape the large-scale network connectivity. We adopted a low-dimensional statistical description of neurites. From the neurite model description we derived the expected number of synapses, node degree, and the effective radius, the maximal distance between two neurons expected to form at least one synapse. We related these quantities to the network connectivity described using standard measures from graph theory, such as motif counts, clustering coefficient, minimal path length, and small-world coefficient. These measures are used in a neuroscience context to study phenomena from synaptic connectivity in the small neuronal networks to large scale functional connectivity in the cortex. For these measures we provide analytical solutions that clearly relate different model properties. Neurites that sparsely cover space lead to a small effective radius. If the effective radius is small compared to the overall neuron size the obtained networks share similarities with the uniform random networks as each neuron connects to a small number of distant neurons. Large neurites with densely packed branches lead to a large effective radius. If this effective radius is large compared to the neuron size, the obtained networks have many local connections. In between these extremes, the networks maximize the variability of connection repertoires. The presented approach connects the properties of neuron morphology with large scale network properties without requiring heavy simulations with many model parameters. The two-steps procedure provides an easier interpretation of the role of each modeled parameter. The model is flexible and each of its components can be further expanded. We identified a range of model parameters that maximizes variability in network connectivity, the property that might affect network capacity to exhibit different dynamical regimes. PMID:26113811

  2. Differentials on graph complexes II: hairy graphs

    NASA Astrophysics Data System (ADS)

    Khoroshkin, Anton; Willwacher, Thomas; Živković, Marko

    2017-10-01

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

  3. 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.

  4. Learning molecular energies using localized graph kernels

    DOE PAGES

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

    2017-03-21

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

  5. Quantifying randomness in real networks

    NASA Astrophysics Data System (ADS)

    Orsini, Chiara; Dankulov, Marija M.; Colomer-de-Simón, Pol; Jamakovic, Almerima; Mahadevan, Priya; Vahdat, Amin; Bassler, Kevin E.; Toroczkai, Zoltán; Boguñá, Marián; Caldarelli, Guido; Fortunato, Santo; Krioukov, Dmitri

    2015-10-01

    Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks--the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain--and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate dk-random graphs.

  6. Quantifying randomness in real networks

    PubMed Central

    Orsini, Chiara; Dankulov, Marija M.; Colomer-de-Simón, Pol; Jamakovic, Almerima; Mahadevan, Priya; Vahdat, Amin; Bassler, Kevin E.; Toroczkai, Zoltán; Boguñá, Marián; Caldarelli, Guido; Fortunato, Santo; Krioukov, Dmitri

    2015-01-01

    Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks—the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain—and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate dk-random graphs. PMID:26482121

  7. Quantifying randomness in real networks.

    PubMed

    Orsini, Chiara; Dankulov, Marija M; Colomer-de-Simón, Pol; Jamakovic, Almerima; Mahadevan, Priya; Vahdat, Amin; Bassler, Kevin E; Toroczkai, Zoltán; Boguñá, Marián; Caldarelli, Guido; Fortunato, Santo; Krioukov, Dmitri

    2015-10-20

    Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks--the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain--and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate dk-random graphs.

  8. Handling Correlations between Covariates and Random Slopes in Multilevel Models

    ERIC Educational Resources Information Center

    Bates, Michael David; Castellano, Katherine E.; Rabe-Hesketh, Sophia; Skrondal, Anders

    2014-01-01

    This article discusses estimation of multilevel/hierarchical linear models that include cluster-level random intercepts and random slopes. Viewing the models as structural, the random intercepts and slopes represent the effects of omitted cluster-level covariates that may be correlated with included covariates. The resulting correlations between…

  9. Handling Correlations between Covariates and Random Slopes in Multilevel Models

    ERIC Educational Resources Information Center

    Bates, Michael David; Castellano, Katherine E.; Rabe-Hesketh, Sophia; Skrondal, Anders

    2014-01-01

    This article discusses estimation of multilevel/hierarchical linear models that include cluster-level random intercepts and random slopes. Viewing the models as structural, the random intercepts and slopes represent the effects of omitted cluster-level covariates that may be correlated with included covariates. The resulting correlations between…

  10. Left-ventricle segmentation in real-time 3D echocardiography using a hybrid active shape model and optimal graph search approach

    NASA Astrophysics Data System (ADS)

    Zhang, Honghai; Abiose, Ademola K.; Campbell, Dwayne N.; Sonka, Milan; Martins, James B.; Wahle, Andreas

    2010-03-01

    Quantitative analysis of the left ventricular shape and motion patterns associated with left ventricular mechanical dyssynchrony (LVMD) is essential for diagnosis and treatment planning in congestive heart failure. Real-time 3D echocardiography (RT3DE) used for LVMD analysis is frequently limited by heavy speckle noise or partially incomplete data, thus a segmentation method utilizing learned global shape knowledge is beneficial. In this study, the endocardial surface of the left ventricle (LV) is segmented using a hybrid approach combining active shape model (ASM) with optimal graph search. The latter is used to achieve landmark refinement in the ASM framework. Optimal graph search translates the 3D segmentation into the detection of a minimum-cost closed set in a graph and can produce a globally optimal result. Various information-gradient, intensity distributions, and regional-property terms-are used to define the costs for the graph search. The developed method was tested on 44 RT3DE datasets acquired from 26 LVMD patients. The segmentation accuracy was assessed by surface positioning error and volume overlap measured for the whole LV as well as 16 standard LV regions. The segmentation produced very good results that were not achievable using ASM or graph search alone.

  11. 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.

  12. Aligning graphs and finding substructures by a cavity approach

    NASA Astrophysics Data System (ADS)

    Bradde, S.; Braunstein, A.; Mahmoudi, H.; Tria, F.; Weigt, M.; Zecchina, R.

    2010-02-01

    We introduce a new distributed algorithm for aligning graphs or finding substructures within a given graph. It is based on the cavity method and is used to study the maximum-clique and the graph-alignment problems in random graphs. The algorithm allows to analyze large graphs and may find applications in fields such as computational biology. As a proof of concept we use our algorithm to align the similarity graphs of two interacting protein families involved in bacterial signal transduction, and to predict actually interacting protein partners between these families.

  13. Multi-channel MRI segmentation with graph cuts using spectral gradient and multidimensional Gaussian mixture model

    NASA Astrophysics Data System (ADS)

    Lecoeur, Jérémy; Ferré, Jean-Christophe; Collins, D. Louis; Morrisey, Sean P.; Barillot, Christian

    2009-02-01

    A new segmentation framework is presented taking advantage of multimodal image signature of the different brain tissues (healthy and/or pathological). This is achieved by merging three different modalities of gray-level MRI sequences into a single RGB-like MRI, hence creating a unique 3-dimensional signature for each tissue by utilising the complementary information of each MRI sequence. Using the scale-space spectral gradient operator, we can obtain a spatial gradient robust to intensity inhomogeneity. Even though it is based on psycho-visual color theory, it can be very efficiently applied to the RGB colored images. More over, it is not influenced by the channel assigment of each MRI. Its optimisation by the graph cuts paradigm provides a powerful and accurate tool to segment either healthy or pathological tissues in a short time (average time about ninety seconds for a brain-tissues classification). As it is a semi-automatic method, we run experiments to quantify the amount of seeds needed to perform a correct segmentation (dice similarity score above 0.85). Depending on the different sets of MRI sequences used, this amount of seeds (expressed as a relative number in pourcentage of the number of voxels of the ground truth) is between 6 to 16%. We tested this algorithm on brainweb for validation purpose (healthy tissue classification and MS lesions segmentation) and also on clinical data for tumours and MS lesions dectection and tissues classification.

  14. Design of a flexible component gathering algorithm for converting cell-based models to graph representations for use in evolutionary search

    PubMed Central

    2014-01-01

    Background The ability of science to produce experimental data has outpaced the ability to effectively visualize and integrate the data into a conceptual framework that can further higher order understanding. Multidimensional and shape-based observational data of regenerative biology presents a particularly daunting challenge in this regard. Large amounts of data are available in regenerative biology, but little progress has been made in understanding how organisms such as planaria robustly achieve and maintain body form. An example of this kind of data can be found in a new repository (PlanformDB) that encodes descriptions of planaria experiments and morphological outcomes using a graph formalism. Results We are developing a model discovery framework that uses a cell-based modeling platform combined with evolutionary search to automatically search for and identify plausible mechanisms for the biological behavior described in PlanformDB. To automate the evolutionary search we developed a way to compare the output of the modeling platform to the morphological descriptions stored in PlanformDB. We used a flexible connected component algorithm to create a graph representation of the virtual worm from the robust, cell-based simulation data. These graphs can then be validated and compared with target data from PlanformDB using the well-known graph-edit distance calculation, which provides a quantitative metric of similarity between graphs. The graph edit distance calculation was integrated into a fitness function that was able to guide automated searches for unbiased models of planarian regeneration. We present a cell-based model of planarian that can regenerate anatomical regions following bisection of the organism, and show that the automated model discovery framework is capable of searching for and finding models of planarian regeneration that match experimental data stored in PlanformDB. Conclusion The work presented here, including our algorithm for converting cell

  15. 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.

  16. Random matrix model of adiabatic quantum computing

    SciTech Connect

    Mitchell, David R.; Adami, Christoph; Lue, Waynn; Williams, Colin P.

    2005-05-15

    We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of random matrix theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances - i.e., those having a critical ratio of clauses to variables - the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathematical model of the probability of avoided level crossings and concomitant failure rate of the adiabatic algorithm due to nonadiabatic Landau-Zener-type transitions. Our model predicts that if the interpolation is performed at a uniform rate, the average failure rate of the quantum adiabatic algorithm, when averaged over hard problem instances, scales exponentially with increasing problem size.

  17. Interacting particle systems on graphs

    NASA Astrophysics Data System (ADS)

    Sood, Vishal

    In this dissertation, the dynamics of socially or biologically interacting populations are investigated. The individual members of the population are treated as particles that interact via links on a social or biological network represented as a graph. The effect of the structure of the graph on the properties of the interacting particle system is studied using statistical physics techniques. In the first chapter, the central concepts of graph theory and social and biological networks are presented. Next, interacting particle systems that are drawn from physics, mathematics and biology are discussed in the second chapter. In the third chapter, the random walk on a graph is studied. The mean time for a random walk to traverse between two arbitrary sites of a random graph is evaluated. Using an effective medium approximation it is found that the mean first-passage time between pairs of sites, as well as all moments of this first-passage time, are insensitive to the density of links in the graph. The inverse of the mean-first passage time varies non-monotonically with the density of links near the percolation transition of the random graph. Much of the behavior can be understood by simple heuristic arguments. Evolutionary dynamics, by which mutants overspread an otherwise uniform population on heterogeneous graphs, are studied in the fourth chapter. Such a process underlies' epidemic propagation, emergence of fads, social cooperation or invasion of an ecological niche by a new species. The first part of this chapter is devoted to neutral dynamics, in which the mutant genotype does not have a selective advantage over the resident genotype. The time to extinction of one of the two genotypes is derived. In the second part of this chapter, selective advantage or fitness is introduced such that the mutant genotype has a higher birth rate or a lower death rate. This selective advantage leads to a dynamical competition in which selection dominates for large populations

  18. 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…

  19. Using a CBL Unit, a Temperature Sensor, and a Graphing Calculator to Model the Kinetics of Consecutive First-Order Reactions as Safe In-Class Demonstrations

    ERIC Educational Resources Information Center

    Moore-Russo, Deborah A.; Cortes-Figueroa, Jose E.; Schuman, Michael J.

    2006-01-01

    The use of Calculator-Based Laboratory (CBL) technology, the graphing calculator, and the cooling and heating of water to model the behavior of consecutive first-order reactions is presented, where B is the reactant, I is the intermediate, and P is the product for an in-class demonstration. The activity demonstrates the spontaneous and consecutive…

  20. Using a CBL Unit, a Temperature Sensor, and a Graphing Calculator to Model the Kinetics of Consecutive First-Order Reactions as Safe In-Class Demonstrations

    ERIC Educational Resources Information Center

    Moore-Russo, Deborah A.; Cortes-Figueroa, Jose E.; Schuman, Michael J.

    2006-01-01

    The use of Calculator-Based Laboratory (CBL) technology, the graphing calculator, and the cooling and heating of water to model the behavior of consecutive first-order reactions is presented, where B is the reactant, I is the intermediate, and P is the product for an in-class demonstration. The activity demonstrates the spontaneous and consecutive…

  1. Effects of Modeling, Story Templates, and Self-Graphing in the Use of Story Elements by Students with Moderate Intellectual Disability

    ERIC Educational Resources Information Center

    Pennington, Robert; Koehler, Mallory

    2017-01-01

    There is limited research on teaching narrative writing skills to students with moderate to severe intellectual disability. In the current study, we used a multiple probe across participants single case design to evaluate the effects of an intervention package comprised of modeling, story templates, and self-graphing, on the inclusion of story…

  2. Flow graphs: interweaving dynamics and structure.

    PubMed

    Lambiotte, R; Sinatra, R; Delvenne, J-C; Evans, T S; Barahona, M; Latora, V

    2011-07-01

    The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential because different dynamical processes may be affected very differently by network topology. A full characterization of such systems thus requires a formalization that encompasses both aspects simultaneously, rather than relying only on the topological adjacency matrix. To achieve this, we introduce the concept of flow graphs, namely weighted networks where dynamical flows are embedded into the link weights. Flow graphs provide an integrated representation of the structure and dynamics of the system, which can then be analyzed with standard tools from network theory. Conversely, a structural network feature of our choice can also be used as the basis for the construction of a flow graph that will then encompass a dynamics biased by such a feature. We illustrate the ideas by focusing on the mathematical properties of generic linear processes on complex networks that can be represented as biased random walks and their dual consensus dynamics, and show how our framework improves our understanding of these processes.

  3. Study of Double-Weighted Graph Model and Optimal Path Planning for Tourist Scenic Area Oriented Intelligent Tour Guide

    NASA Astrophysics Data System (ADS)

    Shi, Y.; Long, Y.; Wi, X. L.

    2014-04-01

    When tourists visiting multiple tourist scenic spots, the travel line is usually the most effective road network according to the actual tour process, and maybe the travel line is different from planned travel line. For in the field of navigation, a proposed travel line is normally generated automatically by path planning algorithm, considering the scenic spots' positions and road networks. But when a scenic spot have a certain area and have multiple entrances or exits, the traditional described mechanism of single point coordinates is difficult to reflect these own structural features. In order to solve this problem, this paper focuses on the influence on the process of path planning caused by scenic spots' own structural features such as multiple entrances or exits, and then proposes a doubleweighted Graph Model, for the weight of both vertexes and edges of proposed Model can be selected dynamically. And then discusses the model building method, and the optimal path planning algorithm based on Dijkstra algorithm and Prim algorithm. Experimental results show that the optimal planned travel line derived from the proposed model and algorithm is more reasonable, and the travelling order and distance would be further optimized.

  4. Multi-target QPDR classification model for human breast and colon cancer-related proteins using star graph topological indices.

    PubMed

    Munteanu, Cristian Robert; Magalhães, Alexandre L; Uriarte, Eugenio; González-Díaz, Humberto

    2009-03-21

    The cancer diagnostic is a complex process and, sometimes, the specific markers can interfere or produce negative results. Thus, new simple and fast theoretical models are required. One option is the complex network graphs theory that permits us to describe any real system, from the small molecules to the complex genetic, neural or social networks by transforming real properties in topological indices. This work converts the protein primary structure data in specific Randic's star networks topological indices using the new sequence to star networks (S2SNet) application. A set of 1054 proteins were selected from previous works and contains proteins related or not with two types of cancer, human breast cancer (HBC) and human colon cancer (HCC). The general discriminant analysis method generates an input-coded multi-target classification model with the training/predicting set accuracies of 90.0% for the forward stepwise model type. In addition, a protein subset was modified by single amino acid mutations with higher log-odds PAM250 values and tested with the new classification if can be related with HBC or HCC. In conclusion, we shown that, using simple input data such is the primary protein sequence and the simples linear analysis, it is possible to obtain accurate classification models that can predict if a new protein related with two types of cancer. These results promote the use of the S2SNet in clinical proteomics.

  5. Model ecosystems with random nonlinear interspecies interactions

    NASA Astrophysics Data System (ADS)

    Santos, Danielle O. C.; Fontanari, José F.

    2004-12-01

    The principle of competitive exclusion in ecology establishes that two species living together cannot occupy the same ecological niche. Here we present a model ecosystem in which the species are described by a series of phenotypic characters and the strength of the competition between two species is given by a nondecreasing (modulating) function of the number of common characters. Using analytical tools of statistical mechanics we find that the ecosystem diversity, defined as the fraction of species that coexist at equilibrium, decreases as the complexity (i.e., number of characters) of the species increases, regardless of the modulating function. By considering both selective and random elimination of the links in the community web, we show that ecosystems composed of simple species are more robust than those composed of complex species. In addition, we show that the puzzling result that there exists either rich or poor ecosystems for a linear modulating function is not typical of communities in which the interspecies interactions are determined by a complementarity rule.

  6. Model ecosystems with random nonlinear interspecies interactions.

    PubMed

    Santos, Danielle O C; Fontanari, José F

    2004-12-01

    The principle of competitive exclusion in ecology establishes that two species living together cannot occupy the same ecological niche. Here we present a model ecosystem in which the species are described by a series of phenotypic characters and the strength of the competition between two species is given by a nondecreasing (modulating) function of the number of common characters. Using analytical tools of statistical mechanics we find that the ecosystem diversity, defined as the fraction of species that coexist at equilibrium, decreases as the complexity (i.e., number of characters) of the species increases, regardless of the modulating function. By considering both selective and random elimination of the links in the community web, we show that ecosystems composed of simple species are more robust than those composed of complex species. In addition, we show that the puzzling result that there exists either rich or poor ecosystems for a linear modulating function is not typical of communities in which the interspecies interactions are determined by a complementarity rule.

  7. Random-walk model of homologous recombination

    NASA Astrophysics Data System (ADS)

    Fujitani, Youhei; Kobayashi, Ichizo

    1995-12-01

    Interaction between two homologous (i.e., identical or nearly identical) DNA sequences leads to their homologous recombination in the cell. We present the following stochastic model to explain the dependence of the frequency of homologous recombination on the length of the homologous region. The branch point connecting the two DNAs in a reaction intermediate follows the random-walk process along the homology (N base-pairs). If the branch point reaches either of the homology ends, it bounds back to the homologous region at a probability of γ (reflection coefficient) and is destroyed at a probability of 1-γ. When γ is small, the frequency of homologous recombination is found to be proportional to N3 for smaller N and a linear function of N for larger N. The exponent of the nonlinear dependence for smaller N decreases from three as γ increases. When γ=1, only the linear dependence is left. These theoretical results can explain many experimental data in various systems. (c) 1995 The American Physical Society

  8. 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.

  9. GPD: A Graph Pattern Diffusion Kernel for Accurate Graph Classification with Applications in Cheminformatics

    PubMed Central

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

    2011-01-01

    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. PMID:20431140

  10. 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.

  11. Exactly solvable interacting two-particle quantum graphs

    NASA Astrophysics Data System (ADS)

    Bolte, Jens; Garforth, George

    2017-03-01

    We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing compatibility with the Bethe ansatz method, we calculate quantisation conditions in the form of secular equations from which the spectra can be deduced. We compare spectral statistics of some examples to well known results in random matrix theory, analysing the chaotic properties of their classical counterparts.

  12. The Random-Effect Generalized Rating Scale Model

    ERIC Educational Resources Information Center

    Wang, Wen-Chung; Wu, Shiu-Lien

    2011-01-01

    Rating scale items have been widely used in educational and psychological tests. These items require people to make subjective judgments, and these subjective judgments usually involve randomness. To account for this randomness, Wang, Wilson, and Shih proposed the random-effect rating scale model in which the threshold parameters are treated as…

  13. The Random-Effect Generalized Rating Scale Model

    ERIC Educational Resources Information Center

    Wang, Wen-Chung; Wu, Shiu-Lien

    2011-01-01

    Rating scale items have been widely used in educational and psychological tests. These items require people to make subjective judgments, and these subjective judgments usually involve randomness. To account for this randomness, Wang, Wilson, and Shih proposed the random-effect rating scale model in which the threshold parameters are treated as…

  14. Random effects logistic models for analysing efficacy of a longitudinal randomized treatment with non-adherence.

    PubMed

    Small, Dylan S; Ten Have, Thomas R; Joffe, Marshall M; Cheng, Jing

    2006-06-30

    We present a random effects logistic approach for estimating the efficacy of treatment for compliers in a randomized trial with treatment non-adherence and longitudinal binary outcomes. We use our approach to analyse a primary care depression intervention trial. The use of a random effects model to estimate efficacy supplements intent-to-treat longitudinal analyses based on random effects logistic models that are commonly used in primary care depression research. Our estimation approach is an extension of Nagelkerke et al.'s instrumental variables approximation for cross-sectional binary outcomes. Our approach is easily implementable with standard random effects logistic regression software. We show through a simulation study that our approach provides reasonably accurate inferences for the setting of the depression trial under model assumptions. We also evaluate the sensitivity of our approach to model assumptions for the depression trial. Copyright (c) 2005 John Wiley & Sons, Ltd.

  15. Assistance to neurosurgical planning: using a fuzzy spatial graph model of the brain for locating anatomical targets in MRI

    NASA Astrophysics Data System (ADS)

    Villéger, Alice; Ouchchane, Lemlih; Lemaire, Jean-Jacques; Boire, Jean-Yves

    2007-03-01

    Symptoms of neurodegenerative pathologies such as Parkinson's disease can be relieved through Deep Brain Stimulation. This neurosurgical technique relies on high precision positioning of electrodes in specific areas of the basal ganglia and the thalamus. These subcortical anatomical targets must be located at pre-operative stage, from a set of MRI acquired under stereotactic conditions. In order to assist surgical planning, we designed a semi-automated image analysis process for extracting anatomical areas of interest. Complementary information, provided by both patient's data and expert knowledge, is represented as fuzzy membership maps, which are then fused by means of suitable possibilistic operators in order to achieve the segmentation of targets. More specifically, theoretical prior knowledge on brain anatomy is modelled within a 'virtual atlas' organised as a spatial graph: a list of vertices linked by edges, where each vertex represents an anatomical structure of interest and contains relevant information such as tissue composition, whereas each edge represents a spatial relationship between two structures, such as their relative directions. The model is built using heterogeneous sources of information such as qualitative descriptions from the expert, or quantitative information from prelabelled images. For each patient, tissue membership maps are extracted from MR data through a classification step. Prior model and patient's data are then matched by using a research algorithm (or 'strategy') which simultaneously computes an estimation of the location of every structures. The method was tested on 10 clinical images, with promising results. Location and segmentation results were statistically assessed, opening perspectives for enhancements.

  16. Non-parametric Bayesian graph models reveal community structure in resting state fMRI.

    PubMed

    Andersen, Kasper Winther; Madsen, Kristoffer H; Siebner, Hartwig Roman; Schmidt, Mikkel N; Mørup, Morten; Hansen, Lars Kai

    2014-10-15

    Modeling of resting state functional magnetic resonance imaging (rs-fMRI) data using network models is of increasing interest. It is often desirable to group nodes into clusters to interpret the communication patterns between nodes. In this study we consider three different nonparametric Bayesian models for node clustering in complex networks. In particular, we test their ability to predict unseen data and their ability to reproduce clustering across datasets. The three generative models considered are the Infinite Relational Model (IRM), Bayesian Community Detection (BCD), and the Infinite Diagonal Model (IDM). The models define probabilities of generating links within and between clusters and the difference between the models lies in the restrictions they impose upon the between-cluster link probabilities. IRM is the most flexible model with no restrictions on the probabilities of links between clusters. BCD restricts the between-cluster link probabilities to be strictly lower than within-cluster link probabilities to conform to the community structure typically seen in social networks. IDM only models a single between-cluster link probability, which can be interpreted as a background noise probability. These probabilistic models are compared against three other approaches for node clustering, namely Infomap, Louvain modularity, and hierarchical clustering. Using 3 different datasets comprising healthy volunteers' rs-fMRI we found that the BCD model was in general the most predictive and reproducible model. This suggests that rs-fMRI data exhibits community structure and furthermore points to the significance of modeling heterogeneous between-cluster link probabilities.

  17. Molecular graph convolutions: moving beyond fingerprints

    PubMed Central

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

    2016-01-01

    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

  18. 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.

  19. Constructing and sampling graphs with a given joint degree distribution.

    SciTech Connect

    Pinar, Ali; Stanton, Isabelle

    2010-09-01

    One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent work has shown that while these generative models do have the right degree distribution, they are not good models for real life networks due to their differences on other important metrics like conductance. We believe this is, in part, because many of these real-world networks have very different joint degree distributions, i.e. the probability that a randomly selected edge will be between nodes of degree k and l. Assortativity is a sufficient statistic of the joint degree distribution, and it has been previously noted that social networks tend to be assortative, while biological and technological networks tend to be disassortative. We suggest understanding the relationship between network structure and the joint degree distribution of graphs is an interesting avenue of further research. An important tool for such studies are algorithms that can generate random instances of graphs with the same joint degree distribution. This is the main topic of this paper and we study the problem from both a theoretical and practical perspective. We provide an algorithm for constructing simple graphs from a given joint degree distribution, and a Monte Carlo Markov Chain method for sampling them. We also show that the state space of simple graphs with a fixed degree distribution is connected via end point switches. We empirically evaluate the mixing time of this Markov Chain by using experiments based on the autocorrelation of each edge. These experiments show that our Markov Chain mixes quickly on real graphs, allowing for utilization of our techniques in practice.

  20. Comparing pedigree graphs.

    PubMed

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

    2012-09-01

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