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Sample records for random graph model

  1. Models of random graph hierarchies

    NASA Astrophysics Data System (ADS)

    Paluch, Robert; Suchecki, Krzysztof; Hołyst, Janusz A.

    2015-10-01

    We introduce two models of inclusion hierarchies: random graph hierarchy (RGH) and limited random graph hierarchy (LRGH). In both models a set of nodes at a given hierarchy level is connected randomly, as in the Erdős-Rényi random graph, with a fixed average degree equal to a system parameter c. Clusters of the resulting network are treated as nodes at the next hierarchy level and they are connected again at this level and so on, until the process cannot continue. In the RGH model we use all clusters, including those of size 1, when building the next hierarchy level, while in the LRGH model clusters of size 1 stop participating in further steps. We find that in both models the number of nodes at a given hierarchy level h decreases approximately exponentially with h. The height of the hierarchy H, i.e. the number of all hierarchy levels, increases logarithmically with the system size N, i.e. with the number of nodes at the first level. The height H decreases monotonically with the connectivity parameter c in the RGH model and it reaches a maximum for a certain c max in the LRGH model. The distribution of separate cluster sizes in the LRGH model is a power law with an exponent about - 1.25. The above results follow from approximate analytical calculations and have been confirmed by numerical simulations.

  2. The weighted random graph model

    NASA Astrophysics Data System (ADS)

    Garlaschelli, Diego

    2009-07-01

    We introduce the weighted random graph (WRG) model, which represents the weighted counterpart of the Erdos-Renyi random graph and provides fundamental insights into more complicated weighted networks. We find analytically that the WRG is characterized by a geometric weight distribution, a binomial degree distribution and a negative binomial strength distribution. We also characterize exactly the percolation phase transitions associated with edge removal and with the appearance of weighted subgraphs of any order and intensity. We find that even this completely null model displays a percolation behaviour similar to what is observed in real weighted networks, implying that edge removal cannot be used to detect community structure empirically. By contrast, the analysis of clustering successfully reveals different patterns between the WRG and real networks.

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

    PubMed

    Jena, Siddhartha G

    2016-03-01

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

  4. 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. PMID:26353253

  5. Visual Tracking via Random Walks on Graph Model.

    PubMed

    Li, Xiaoli; Han, Zhifeng; Wang, Lijun; Lu, Huchuan

    2016-09-01

    In this paper, we formulate visual tracking as random walks on graph models with nodes representing superpixels and edges denoting relationships between superpixels. We integrate two novel graphs with the theory of Markov random walks, resulting in two Markov chains. First, an ergodic Markov chain is enforced to globally search for the candidate nodes with similar features to the template nodes. Second, an absorbing Markov chain is utilized to model the temporal coherence between consecutive frames. The final confidence map is generated by a structural model which combines both appearance similarity measurement derived by the random walks and internal spatial layout demonstrated by different target parts. The effectiveness of the proposed Markov chains as well as the structural model is evaluated both qualitatively and quantitatively. Experimental results on challenging sequences show that the proposed tracking algorithm performs favorably against state-of-the-art methods. PMID:26292358

  6. Exponential random graph models for networks with community structure

    NASA Astrophysics Data System (ADS)

    Fronczak, Piotr; Fronczak, Agata; Bujok, Maksymilian

    2013-09-01

    Although the community structure organization is an important characteristic of real-world networks, most of the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for testing community detection algorithms. They are also inadequate to predict various properties of real networks. With this paper we intend to fill the gap. We develop an exponential random graph approach to networks with community structure. To this end we mainly built upon the idea of blockmodels. We consider both the classical blockmodel and its degree-corrected counterpart and study many of their properties analytically. We show that in the degree-corrected blockmodel, node degrees display an interesting scaling property, which is reminiscent of what is observed in real-world fractal networks. A short description of Monte Carlo simulations of the models is also given in the hope of being useful to others working in the field.

  7. Random Walks on Random Graphs

    NASA Astrophysics Data System (ADS)

    Cooper, Colin; Frieze, Alan

    The aim of this article is to discuss some of the notions and applications of random walks on finite graphs, especially as they apply to random graphs. In this section we give some basic definitions, in Section 2 we review applications of random walks in computer science, and in Section 3 we focus on walks in random graphs.

  8. 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

  9. Random graphs with hidden color.

    PubMed

    Söderberg, Bo

    2003-07-01

    We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, random graphs with a given degree distribution, in a way that admits a nontrivial correlation structure in the resulting graphs. The approach unifies a number of existing random graph ensembles within a common general formalism, and allows for the analytic calculation of observable graph characteristics. In particular, generating function techniques are used to derive the size distribution of connected components (clusters) as well as the location of the percolation threshold where a giant component appears. PMID:12935185

  10. Information geometry of the ising model on planar random graphs.

    PubMed

    Janke, W; Johnston, D A; Malmini, Ranasinghe P K C

    2002-11-01

    It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterization of the phase structure, particularly in the case where there are two such parameters, such as the Ising model with inverse temperature beta and external field h. In various two-parameter calculable models, the scalar curvature R of the information metric has been found to diverge at the phase transition point beta(c) and a plausible scaling relation postulated: R approximately |beta-beta(c)|(alpha-2). For spin models the necessity of calculating in nonzero field has limited analytic consideration to one-dimensional, mean-field and Bethe lattice Ising models. In this paper we use the solution in field of the Ising model on an ensemble of planar random graphs (where alpha=-1, beta=1/2, gamma=2) to evaluate the scaling behavior of the scalar curvature, and find R approximately |beta-beta(c)|(-2). The apparent discrepancy is traced back to the effect of a negative alpha. PMID:12513568

  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. Coloring random graphs.

    PubMed

    Mulet, R; Pagnani, A; Weigt, M; Zecchina, R

    2002-12-23

    We study the graph coloring problem over random graphs of finite average connectivity c. Given a number q of available colors, we find that graphs with low connectivity admit almost always a proper coloring, whereas graphs with high connectivity are uncolorable. Depending on q, we find the precise value of the critical average connectivity c(q). Moreover, we show that below c(q) there exists a clustering phase c in [c(d),c(q)] in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity in local search algorithms. PMID:12484862

  13. Statistical Inference for Valued-Edge Networks: The Generalized Exponential Random Graph Model

    PubMed Central

    Desmarais, Bruce A.; Cranmer, Skyler J.

    2012-01-01

    Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks based on both endogenous and exogenous factors, exponential random graph models are a ubiquitous means of analysis. However, they are limited by an inability to model networks with valued edges. We address this problem by introducing a class of generalized exponential random graph models capable of modeling networks whose edges have continuous values (bounded or unbounded), thus greatly expanding the scope of networks applied researchers can subject to statistical analysis. PMID:22276151

  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. 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.

  16. On the critical parameters of the q ≤ 4 random-cluster model on isoradial graphs

    NASA Astrophysics Data System (ADS)

    Beffara, V.; Duminil-Copin, H.; Smirnov, S.

    2015-12-01

    The critical surface for the random-cluster model with cluster-weight q≥slant 4 on isoradial graphs is identified using parafermionic observables. Correlations are also shown to decay exponentially fast in the subcritical regime. While this result is restricted to random-cluster models with q≥slant 4, it extends the recent theorem of (Beffara and Duminil-Copin 2012 Probl. Theory Relat. Fields 153 511-42) to a large class of planar graphs. In particular, the anisotropic random-cluster model on the square lattice is shown to be critical if \\frac{{p}{{v}}{p}{{h}}}{(1-{p}{{v}})(1-{p}{{h}})}=q, where p v and p h denote the horizontal and vertical edge-weights respectively. We also mention consequences for Potts models.

  17. Bayesian Analysis for Exponential Random Graph Models Using the Adaptive Exchange Sampler*

    PubMed Central

    Jin, Ick Hoon; Yuan, Ying; Liang, Faming

    2014-01-01

    Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the intractable normalizing constant and model degeneracy. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the intractable normalizing constant and model degeneracy issues encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency. PMID:24653788

  18. Fast generation of sparse random kernel graphs

    DOE PAGESBeta

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

    2015-09-10

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

  19. 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.

  20. Fast Generation of Sparse Random Kernel Graphs

    PubMed Central

    2015-01-01

    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 𝒪(n(logn)2). As a practical example we show how to generate samples of power-law degree distribution graphs with tunable assortativity. PMID:26356296

  1. Multi-body quenched disordered X Y and p -clock models on random graphs

    NASA Astrophysics Data System (ADS)

    Marruzzo, Alessia; Leuzzi, Luca

    2016-03-01

    The X Y model with four-body quenched disordered interactions and its discrete p -clock proxy are studied on bipartite random graphs by means of the cavity method. The phase diagrams are determined from the ordered case to the spin-glass case. Dynamic, spinodal, and thermodynamic transition lines are identified by analyzing free energy, complexity, and tree reconstruction functions as temperature and disorder are changed. The study of the convergence of the p -clock model to the X Y model is performed down to temperature low enough to determine all relevant transition points for different node connectivity.

  2. A reexamination of connectivity trends via exponential random graph modeling in two IDU risk networks.

    PubMed

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

    2013-12-01

    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

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

    PubMed

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

    2011-07-01

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

  4. Mean-field behavior of the negative-weight percolation model on random regular graphs.

    PubMed

    Melchert, Oliver; Hartmann, Alexander K; Mézard, Marc

    2011-10-01

    We investigate both analytically and numerically the ensemble of minimum-weight loops in the negative-weight percolation model on random graphs with fixed connectivity and bimodal weight distribution. This allows us to study the mean-field behavior of this model. The analytical study is based on a conjectured equivalence with the problem of self-avoiding walks in a random medium. The numerical study is based on a mapping to a standard minimum-weight matching problem for which fast algorithms exist. Both approaches yield results that are in agreement on the location of the phase transition, on the value of critical exponents, and on the absence of any sizable indications of a glass phase. By these results, the previously conjectured upper critical dimension of d(u)=6 is confirmed. PMID:22181086

  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. Random graphs containing arbitrary distributions of subgraphs

    NASA Astrophysics Data System (ADS)

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

    2010-12-01

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

  8. Component Evolution in General Random Intersection Graphs

    NASA Astrophysics Data System (ADS)

    Bradonjić, Milan; Hagberg, Aric; Hengartner, Nicolas W.; Percus, Allon G.

    Random intersection graphs (RIGs) are an important random structure with algorithmic applications in social networks, epidemic networks, blog readership, and wireless sensor networks. RIGs can be interpreted as a model for large randomly formed non-metric data sets. We analyze the component evolution in general RIGs, giving conditions on the existence and uniqueness of the giant component. Our techniques generalize existing methods for analysis of component evolution: 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 of the study of component evolution in Erdős-Rényi graphs. The major challenge comes from the underlying structure of RIGs, which involves both a set of nodes and a set of attributes, with different probabilities associated with each attribute.

  9. 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.

  10. Consensus dynamics on random rectangular graphs

    NASA Astrophysics Data System (ADS)

    Estrada, Ernesto; Sheerin, Matthew

    2016-06-01

    A random rectangular graph (RRG) is a generalization of the random geometric graph (RGG) in which the nodes are embedded into a rectangle with side lengths a and b = 1 / a, instead of on a unit square [ 0 , 1 ] 2. Two nodes are then connected if and only if they are separated at a Euclidean distance smaller than or equal to a certain threshold radius r. When a = 1 the RRG is identical to the RGG. Here we apply the consensus dynamics model to the RRG. Our main result is a lower bound for the time of consensus, i.e., the time at which the network reaches a global consensus state. To prove this result we need first to find an upper bound for the algebraic connectivity of the RRG, i.e., the second smallest eigenvalue of the combinatorial Laplacian of the graph. This bound is based on a tight lower bound found for the graph diameter. Our results prove that as the rectangle in which the nodes are embedded becomes more elongated, the RRG becomes a 'large-world', i.e., the diameter grows to infinity, and a poorly-connected graph, i.e., the algebraic connectivity decays to zero. The main consequence of these findings is the proof that the time of consensus in RRGs grows to infinity as the rectangle becomes more elongated. In closing, consensus dynamics in RRGs strongly depend on the geometric characteristics of the embedding space, and reaching the consensus state becomes more difficult as the rectangle is more elongated.

  11. Random geometric graphs with general connection functions

    NASA Astrophysics Data System (ADS)

    Dettmann, Carl P.; Georgiou, Orestis

    2016-03-01

    In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H (r ) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.

  12. Scale-invariant geometric random graphs

    NASA Astrophysics Data System (ADS)

    Xie, Zheng; Rogers, Tim

    2016-03-01

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

  13. A Detailed Investigation into Near Degenerate Exponential Random Graphs

    NASA Astrophysics Data System (ADS)

    Yin, Mei

    2016-07-01

    The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better understand how phases transition between one another as tuning parameters vary. As the parameters cross certain lines, the model asymptotically transitions from a very sparse graph to a very dense graph, completely skipping all intermediate structures. We delve deeper into this near degenerate tendency and give an explicit characterization of the asymptotic graph structure as a function of the parameters.

  14. A Detailed Investigation into Near Degenerate Exponential Random Graphs

    NASA Astrophysics Data System (ADS)

    Yin, Mei

    2016-05-01

    The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better understand how phases transition between one another as tuning parameters vary. As the parameters cross certain lines, the model asymptotically transitions from a very sparse graph to a very dense graph, completely skipping all intermediate structures. We delve deeper into this near degenerate tendency and give an explicit characterization of the asymptotic graph structure as a function of the parameters.

  15. 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.

  16. Coloring random graphs and maximizing local diversity.

    PubMed

    Bounkong, S; van Mourik, J; Saad, D

    2006-11-01

    We study a variation of the graph coloring problem on random graphs of finite average connectivity. Given the number of colors, we aim to maximize the number of different colors at neighboring vertices (i.e., one edge distance) of any vertex. Two efficient algorithms, belief propagation and Walksat, are adapted to carry out this task. We present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution. The problem and the suggested algorithms have practical relevance since various applications, such as distributed storage, can be mapped onto this problem. PMID:17280022

  17. 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…

  18. 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

  19. 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.

  20. 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. PMID:26565177

  1. 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.

  2. 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. PMID:11136023

  3. Bootstrap Percolation in Power-Law Random Graphs

    NASA Astrophysics Data System (ADS)

    Amini, Hamed; Fountoulakis, Nikolaos

    2014-04-01

    A bootstrap percolation process on a graph is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least infected neighbours becomes infected and remains so forever. The parameter is fixed. Such processes have been used as models for the spread of ideas or trends within a network of individuals. We analyse this process in the case where the underlying graph is an inhomogeneous random graph, which exhibits a power-law degree distribution, and initially there are randomly infected nodes. The main focus of this paper is the number of vertices that will have been infected by the end of the process. The main result of this work is that if the degree sequence of the random graph follows a power law with exponent , where , then a sublinear number of initially infected vertices is enough to spread the infection over a linear fraction of the nodes of the random graph, with high probability. More specifically, we determine explicitly a critical function such that with the following property. Assuming that is the number of vertices of the underlying random graph, if , then the process does not evolve at all, with high probability as grows, whereas if , then there is a constant such that, with high probability, the final set of infected vertices has size at least . This behaviour is in sharp contrast with the case where the underlying graph is a random graph with . It follows from an observation of Balogh and Bollobás that in this case if the number of initially infected vertices is sublinear, then there is lack of evolution of the process. It turns out that when the maximum degree is , then depends also on . But when the maximum degree is , then.

  4. Random graph coloring: statistical physics approach.

    PubMed

    van Mourik, J; Saad, D

    2002-11-01

    The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte Carlo simulations. We critically discuss the merits and shortcomings of the various methods, and interpret the results obtained. We present an exact analytical expression for the two-coloring problem as well as general replica symmetric approximated solutions for the thermodynamics of the graph coloring problem with p colors and K-body edges. PMID:12513569

  5. 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.

  6. Regular graphs maximize the variability of random neural networks

    NASA Astrophysics Data System (ADS)

    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.

  7. 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.

  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. PMID:25616091

  9. 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).

  10. 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.

  11. Connectivity of Soft Random Geometric Graphs over Annuli

    NASA Astrophysics Data System (ADS)

    Giles, Alexander P.; Georgiou, Orestis; Dettmann, Carl P.

    2016-02-01

    Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present analytic formulas for the connection probability of these spatially embedded graphs, describing the connectivity behaviour as a dense-network limit is approached. This extends recent work modelling ad hoc networks in non-convex domains.

  12. Graph models of habitat mosaics.

    PubMed

    Urban, Dean L; Minor, Emily S; Treml, Eric A; Schick, Robert S

    2009-03-01

    Graph theory is a body of mathematics dealing with problems of connectivity, flow, and routing in networks ranging from social groups to computer networks. Recently, network applications have erupted in many fields, and graph models are now being applied in landscape ecology and conservation biology, particularly for applications couched in metapopulation theory. In these applications, graph nodes represent habitat patches or local populations and links indicate functional connections among populations (i.e. via dispersal). Graphs are models of more complicated real systems, and so it is appropriate to review these applications from the perspective of modelling in general. Here we review recent applications of network theory to habitat patches in landscape mosaics. We consider (1) the conceptual model underlying these applications; (2) formalization and implementation of the graph model; (3) model parameterization; (4) model testing, insights, and predictions available through graph analyses; and (5) potential implications for conservation biology and related applications. In general, and for a variety of ecological systems, we find the graph model a remarkably robust framework for applications concerned with habitat connectivity. We close with suggestions for further work on the parameterization and validation of graph models, and point to some promising analytic insights. PMID:19161432

  13. A program generating homogeneous random graphs with given weights

    NASA Astrophysics Data System (ADS)

    Bogacz, L.; Burda, Z.; Janke, W.; Waclaw, B.

    2005-12-01

    We present a program package to generate homogeneous random graphs with probabilities prescribed by the user. The statistical weight of a labeled graph α is given in the form W(α)=∏i=1Np(q), where p(q) is an arbitrary user function and q are the degrees of the graph nodes. The program can be used to generate two types of graphs (simple graphs and pseudo-graphs) from three types of ensembles (micro-canonical, canonical and grand-canonical). Program summaryTitle of the program:GraphGen Catalogue identifier:ADWL Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWL Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: PC, Alpha workstation Operating systems or monitors under which the program has been tested:Linux, Unix, MS Windows XP Programing language used:C Memory required to execute with typical data:300 k words for a graph with 1000 nodes and up to 50 000 links No. of bits in a word:32 No. of processor used:1 Has the code been vectorized or parallelized:No No. of lines in distributed program, including test data, etc.:2253 No. of bytes in distributed program, including test data, etc.:14 330 Distribution format:tar.gz Keywords:Random graphs, complex networks, Markov process, Monte Carlo method Nature of the problem:The program generates random graphs. The probabilities of graph occurrence are proportional to their statistical weight, dependent on node degrees defined by arbitrary distributions Method of solution:The starting graph is taken arbitrary and then a sequence of graphs is generated. Each graph is obtained from the previous one by means of a simple modification. The probability of accepting or rejecting the new graph results from a detailed balance condition realized as Metropolis algorithm. When the length of the generated Markov chain increases, the probabilities of graph occurrence approach the stationary distribution given by

  14. 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…

  15. 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.

  16. 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. PMID:23166818

  17. The Einstein Relation for RandomWalks on Graphs

    NASA Astrophysics Data System (ADS)

    Telcs, András

    2006-05-01

    This paper investigates the Einstein relation; the connection between the volume growth, the resistance growth and the expected time a random walk needs to leave a ball on a weighted graph. The Einstein relation is proved under different set of conditions. In the simplest case it is shown under the volume doubling and time comparison principles. This and the other set of conditions provide the basic framework for the study of (sub-) diffusive behavior of the random walks on weighted graphs.

  18. The Einstein Relation for Random Walks on Graphs

    NASA Astrophysics Data System (ADS)

    Telcs, András

    2006-02-01

    This paper investigates the Einstein relation; the connection between the volume growth, the resistance growth and the expected time a random walk needs to leave a ball on a weighted graph. The Einstein relation is proved under different set of conditions. In the simplest case it is shown under the volume doubling and time comparison principles. This and the other set of conditions provide the basic framework for the study of (sub-) diffusive behavior of the random walks on weighted graphs.

  19. Polynomial iterative algorithms for coloring and analyzing random graphs.

    PubMed

    Braunstein, A; Mulet, R; Pagnani, A; Weigt, M; Zecchina, R

    2003-09-01

    We study the graph coloring problem over random graphs of finite average connectivity c. Given a number q of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable. Depending on q, we find with a one-step replica-symmetry breaking approximation the precise value of the critical average connectivity c(q). Moreover, we show that below c(q) there exists a clustering phase c in [c(d),c(q)] in which ground states spontaneously divide into an exponential number of clusters. Furthermore, we extended our considerations to the case of single instances showing consistent results. This leads us to propose a different algorithm that is able to color in polynomial time random graphs in the hard but colorable region, i.e., when c in [c(d),c(q)]. PMID:14524921

  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. PMID:23005389

  1. 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.

  2. Graph modeling systems and methods

    DOEpatents

    Neergaard, Mike

    2015-10-13

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

  3. Intergroup networks as random threshold graphs

    NASA Astrophysics Data System (ADS)

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

    2014-04-01

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

  4. 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.

  5. Opinion dynamics and influencing on random geometric graphs.

    PubMed

    Zhang, Weituo; Lim, Chjan C; Korniss, G; Szymanski, Boleslaw K

    2014-01-01

    We investigate the two-word Naming Game on two-dimensional random geometric graphs. Studying this model advances our understanding of the spatial distribution and propagation of opinions in social dynamics. A main feature of this model is the spontaneous emergence of spatial structures called opinion domains which are geographic regions with clear boundaries within which all individuals share the same opinion. We provide the mean-field equation for the underlying dynamics and discuss several properties of the equation such as the stationary solutions and two-time-scale separation. For the evolution of the opinion domains we find that the opinion domain boundary propagates at a speed proportional to its curvature. Finally we investigate the impact of committed agents on opinion domains and find the scaling of consensus time. PMID:24993655

  6. Opinion Dynamics and Influencing on Random Geometric Graphs

    PubMed Central

    Zhang, Weituo; Lim, Chjan C.; Korniss, G.; Szymanski, Boleslaw K.

    2014-01-01

    We investigate the two-word Naming Game on two-dimensional random geometric graphs. Studying this model advances our understanding of the spatial distribution and propagation of opinions in social dynamics. A main feature of this model is the spontaneous emergence of spatial structures called opinion domains which are geographic regions with clear boundaries within which all individuals share the same opinion. We provide the mean-field equation for the underlying dynamics and discuss several properties of the equation such as the stationary solutions and two-time-scale separation. For the evolution of the opinion domains we find that the opinion domain boundary propagates at a speed proportional to its curvature. Finally we investigate the impact of committed agents on opinion domains and find the scaling of consensus time. PMID:24993655

  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. 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.

  9. Noninteracting multiparticle quantum random walks applied to the graph isomorphism problem for strongly regular graphs

    NASA Astrophysics Data System (ADS)

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

    2012-08-01

    We investigate the quantum dynamics of particles on graphs (“quantum random walks”), with the aim of developing quantum algorithms for determining if two graphs are isomorphic (related to each other by a relabeling of vertices). We focus on quantum random walks of multiple noninteracting particles on strongly regular graphs (SRGs), a class of graphs with high symmetry that is known to have pairs of graphs that are hard to distinguish. Previous work has already demonstrated analytically that two-particle noninteracting quantum walks cannot distinguish nonisomorphic SRGs of the same family. Here, we demonstrate numerically that three-particle noninteracting quantum walks have significant, but not universal, distinguishing power for pairs of SRGs, proving a fundamental difference between the distinguishing power of two-particle and three-particle noninteracting walks. We show analytically why this distinguishing power is possible, whereas it is forbidden for two-particle noninteracting walks. Based on sampling of SRGs with up to 64 vertices, we find no difference in the distinguishing power of bosonic and fermionic walks. In addition, we find that the four-fermion noninteracting walk has greater distinguishing power than the three-particle walk on SRGs, showing that increasing the particle number increases the distinguishing power. However, we also show analytically that no noninteracting walk with a fixed number of particles can distinguish all SRGs, thus demonstrating a potential fundamental difference in the distinguishing power of interacting versus noninteracting walks.

  10. 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.

  11. 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.

  12. 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. PMID:19905386

  13. 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…

  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. 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)

  16. Unimodular lattice triangulations as small-world and scale-free random graphs

    NASA Astrophysics Data System (ADS)

    Krüger, B.; Schmidt, E. M.; Mecke, K.

    2015-02-01

    Real-world networks, e.g., the social relations or world-wide-web graphs, exhibit both small-world and scale-free behaviour. We interpret lattice triangulations as planar graphs by identifying triangulation vertices with graph nodes and one-dimensional simplices with edges. Since these triangulations are ergodic with respect to a certain Pachner flip, applying different Monte Carlo simulations enables us to calculate average properties of random triangulations, as well as canonical ensemble averages, using an energy functional that is approximately the variance of the degree distribution. All considered triangulations have clustering coefficients comparable with real-world graphs; for the canonical ensemble there are inverse temperatures with small shortest path length independent of system size. Tuning the inverse temperature to a quasi-critical value leads to an indication of scale-free behaviour for degrees k≥slant 5. Using triangulations as a random graph model can improve the understanding of real-world networks, especially if the actual distance of the embedded nodes becomes important.

  17. Generic criticality of community structure in random graphs

    NASA Astrophysics Data System (ADS)

    Lipowski, Adam; Lipowska, Dorota

    2014-09-01

    We examine a community structure in random graphs of size n and link probability p /n determined with the Newman greedy optimization of modularity. Calculations show that for p <1 communities are nearly identical with clusters. For p =1 the average sizes of a community sav and of the giant community sg show a power-law increase sav˜nα' and sg˜nα. From numerical results we estimate α'≈0.26(1) and α ≈0.50(1) and using the probability distribution of sizes of communities we suggest that α'=α/2 should hold. For p >1 the community structure remains critical: (i) sav and sg have a power-law increase with α'≈α<1 and (ii) the probability distribution of sizes of communities is very broad and nearly flat for all sizes up to sg. For large p the modularity Q decays as Q˜p-0.55, which is intermediate between some previous estimations. To check the validity of the results, we also determine the community structure using another method, namely, a nongreedy optimization of modularity. Tests with some benchmark networks show that the method outperforms the greedy version. For random graphs, however, the characteristics of the community structure determined using both greedy and nongreedy optimizations are, within small statistical fluctuations, the same.

  18. Phase transitions in the coloring of random graphs.

    PubMed

    Zdeborová, Lenka; Krzakała, Florent

    2007-09-01

    We consider the problem of coloring the vertices of a large sparse random graph with a given number of colors so that no adjacent vertices have the same color. Using the cavity method, we present a detailed and systematic analytical study of the space of proper colorings (solutions). We show that for a fixed number of colors and as the average vertex degree (number of constraints) increases, the set of solutions undergoes several phase transitions similar to those observed in the mean field theory of glasses. First, at the clustering transition, the entropically dominant part of the phase space decomposes into an exponential number of pure states so that beyond this transition a uniform sampling of solutions becomes hard. Afterward, the space of solutions condenses over a finite number of the largest states and consequently the total entropy of solutions becomes smaller than the annealed one. Another transition takes place when in all the entropically dominant states a finite fraction of nodes freezes so that each of these nodes is allowed a single color in all the solutions inside the state. Eventually, above the coloring threshold, no more solutions are available. We compute all the critical connectivities for Erdos-Rényi and regular random graphs and determine their asymptotic values for a large number of colors. Finally, we discuss the algorithmic consequences of our findings. We argue that the onset of computational hardness is not associated with the clustering transition and we suggest instead that the freezing transition might be the relevant phenomenon. We also discuss the performance of a simple local Walk-COL algorithm and of the belief propagation algorithm in the light of our results. PMID:17930223

  19. 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.

  20. Replica theory for learning curves for Gaussian processes on random graphs

    NASA Astrophysics Data System (ADS)

    Urry, M. J.; Sollich, P.

    2012-10-01

    We use a statistical physics approach to derive accurate predictions for the challenging problem of predicting the performance of Gaussian process regression. Performance is quantified by the learning curve, defined as the average error versus number of training examples. We assume the Gaussian process prior is defined by a random walk kernel, inputs are vertices on a random graph and the outputs are noisy function values. We show that replica techniques can be used to obtain exact performance predictions in the limit of large graphs, after first rewriting the average error in terms of a graphical model. Conventionally, the Gaussian process kernel is only globally normalized, so that the prior variance can differ between vertices. As a more principled alternative we also consider local normalization, where the prior variance is uniform. The normalization constants for the prior then have to be defined as thermal averages in an unnormalized model and this requires the introduction of a second, auxiliary set of replicas. Our results for both types of kernel normalization apply generically to all random graph ensembles constrained by a fixed but arbitrary degree distribution. We compare with numerically simulated learning curves and find excellent agreement, a significant improvement over existing approximations.

  1. 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.

  2. 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.

  3. 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.

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

    DOE PAGESBeta

    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 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

  5. 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.

  6. Graph based model to support nurses' work.

    PubMed

    Benedik, Peter; Rajkovič, Uroš; Sušteršič, Olga; Prijatelj, Vesna; Rajkovič, Vladislav

    2014-01-01

    Health care is a knowledge-based community that critically depends on knowledge management activities in order to ensure quality. Nurses are primary stakeholders and need to ensure that their information and knowledge needs are being met in such ways that enable them, to improve the quality and efficiency of health care service delivery for all subjects of health care. This paper describes a system to help nurses to create nursing care plan. It supports focusing nurse's attention on those resources/solutions that are likely to be most relevant to their particular situation/problem in nursing domain. System is based on multi-relational property graph representing a flexible modeling construct. Graph allows modeling a nursing domain (ontology) and the indices that partition domain into an efficient, searchable space where the solution to a problem is seen as abstractly defined traversals through its vertices and edges. PMID:24943559

  7. Quantum decomposition of random walk on Cayley graph of finite group

    NASA Astrophysics Data System (ADS)

    Kang, Yuanbao

    2016-09-01

    In the paper, A quantum decomposition (QD, for short) of random walk on Cayley graph of finite group is introduced, which contains two cases. One is QD of quantum random walk operator (QRWO, for short), another is QD of Quantum random walk state (QRWS, for short). Using these findings, I finally obtain some applications for quantum random walk (QRW, for short), which are of interest in the study of QRW, highlighting the role played by QRWO and QRWS.

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. Personalized PageRank Clustering: A graph clustering algorithm based on random walks

    NASA Astrophysics Data System (ADS)

    A. Tabrizi, Shayan; Shakery, Azadeh; Asadpour, Masoud; Abbasi, Maziar; Tavallaie, Mohammad Ali

    2013-11-01

    Graph clustering has been an essential part in many methods and thus its accuracy has a significant effect on many applications. In addition, exponential growth of real-world graphs such as social networks, biological networks and electrical circuits demands clustering algorithms with nearly-linear time and space complexity. In this paper we propose Personalized PageRank Clustering (PPC) that employs the inherent cluster exploratory property of random walks to reveal the clusters of a given graph. We combine random walks and modularity to precisely and efficiently reveal the clusters of a graph. PPC is a top-down algorithm so it can reveal inherent clusters of a graph more accurately than other nearly-linear approaches that are mainly bottom-up. It also gives a hierarchy of clusters that is useful in many applications. PPC has a linear time and space complexity and has been superior to most of the available clustering algorithms on many datasets. Furthermore, its top-down approach makes it a flexible solution for clustering problems with different requirements.

  18. 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

  19. Ising-like models on arbitrary graphs: The Hadamard way

    NASA Astrophysics Data System (ADS)

    Mosseri, Rémy

    2015-01-01

    We propose a generic framework to describe classical Ising-like models defined on arbitrary graphs. The energy spectrum is shown to be the Hadamard transform of a suitably defined sparse "coding" vector associated with the graph. We expect that the existence of a fast Hadamard transform algorithm (used, for instance, in image compression processes), together with the sparseness of the coding vector, may provide ways to fasten the spectrum computation. Applying this formalism to regular graphs, such as hypercubic graphs, we obtain a simple recurrence relation for the spectrum, which significantly speeds up its determination. First attempts to analyze partition functions and transfer matrices are also presented.

  20. Interpreting Unfamiliar Graphs: A Generative, Activity Theoretic Model

    ERIC Educational Resources Information Center

    Roth, Wolff-Michael; Lee, Yew Jin

    2004-01-01

    Research on graphing presents its results as if knowing and understanding were something stored in peoples' minds independent of the situation that they find themselves in. Thus, there are no models that situate interview responses to graphing tasks. How, then, we question, are the interview texts produced? How do respondents begin and end…

  1. 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 {{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.

  2. 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.

  3. 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

  4. 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.

  5. Graph Matching Algorithms for Business Process Model Similarity Search

    NASA Astrophysics Data System (ADS)

    Dijkman, Remco; Dumas, Marlon; García-Bañuelos, Luciano

    We investigate the problem of ranking all process models in a repository according to their similarity with respect to a given process model. We focus specifically on the application of graph matching algorithms to this similarity search problem. Since the corresponding graph matching problem is NP-complete, we seek to find a compromise between computational complexity and quality of the computed ranking. Using a repository of 100 process models, we evaluate four graph matching algorithms, ranging from a greedy one to a relatively exhaustive one. The results show that the mean average precision obtained by a fast greedy algorithm is close to that obtained with the most exhaustive algorithm.

  6. 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'.

  7. 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.

  8. 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. PMID:24453857

  9. 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

  10. 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

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

    PubMed

    Altarelli, Fabrizio; Braunstein, Alfredo; Dall'Asta, Luca; De Bacco, Caterina; Franz, Silvio

    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

  12. 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. PMID:25122337

  13. 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.

  14. 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.

  15. A conceptual graphs modeling of UMLS components.

    PubMed

    Joubert, M; Miton, F; Fieschi, M; Robert, J J

    1995-01-01

    The Unified Medical Language System (UMLS) of the U.S. National Library of Medicine is a complex collection of terms, concepts, and relationships derived from standard classifications. Potential applications would benefit from a high level representation of its components. This paper proposes a conceptual representation of both the Metathesaurus and the Semantic Network of the UMLS based on conceptual graphs. It shows that the addition of a dictionary of concepts to the UMLS knowledge base allows the capability to exploit it pertinently. This dictionary defines more precisely the core concepts and adds constraints on their use. Constraints are dedicated to guide an "intelligent" browsing of the UMLS knowledge sources. PMID:8591348

  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. Corona graphs as a model of small-world networks

    NASA Astrophysics Data System (ADS)

    Lv, Qian; Yi, Yuhao; Zhang, Zhongzhi

    2015-11-01

    We introduce recursive corona graphs as a model of small-world networks. We investigate analytically the critical characteristics of the model, including order and size, degree distribution, average path length, clustering coefficient, and the number of spanning trees, as well as Kirchhoff index. Furthermore, we study the spectra for the adjacency matrix and the Laplacian matrix for the model. We obtain explicit results for all the quantities of the recursive corona graphs, which are similar to those observed in real-life networks.

  18. User-friendly graph editing for procedural modeling of buildings.

    PubMed

    Patow, Gustavo

    2012-01-01

    A proposed rule-based editing metaphor intuitively lets artists create buildings without changing their workflow. It's based on the realization that the rule base represents a directed acyclic graph and on a shift in the development paradigm from product-based to rule-based representations. Users can visually add or edit rules, connect them to control the workflow, and easily create commands that expand the artist's toolbox (for example, Boolean operations or local controlling operators). This approach opens new possibilities, from model verification to model editing through graph rewriting. PMID:24804948

  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. Circulant Graph Modeling Deterministic Small-World Networks

    NASA Astrophysics Data System (ADS)

    Zhao, Chenggui

    In recent years, many research works have revealed some technological networks including internet to be small-world networks, which is attracting attention from computer scientists. One can decide if or not a real network is Small-world by whether it has high local clustering and small average path distance which are the two distinguishing characteristics of small-world networks. So far, researchers have presented many small-world models by dynamically evolving a deterministic network into a small world one by stochastic adding vertices and edges to original networks. Rather few works focused on deterministic models. In this paper, as a important kind of Cayley graph, the circulant graph is proposed as models of deterministic small-world networks, thinking if its simple structures and significant adaptability. It shows circulant graph constructed in this document takes on the two expected characteristics of small word. This work should be useful because circulant graph has serviced as some models of communication and computer networks. The small world characteristic will be helpful to design and analysis of structure and performance.

  1. 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

  2. Random Item IRT Models

    ERIC Educational Resources Information Center

    De Boeck, Paul

    2008-01-01

    It is common practice in IRT to consider items as fixed and persons as random. Both, continuous and categorical person parameters are most often random variables, whereas for items only continuous parameters are used and they are commonly of the fixed type, although exceptions occur. It is shown in the present article that random item parameters…

  3. Fatigue strength reduction model: RANDOM3 and RANDOM4 user manual, appendix 2

    NASA Technical Reports Server (NTRS)

    Boyce, Lola; Lovelace, Thomas B.

    1989-01-01

    The FORTRAN programs RANDOM3 and RANDOM4 are documented. They are based on fatigue strength reduction, using a probabilistic constitutive model. They predict the random lifetime of an engine component to reach a given fatigue strength. Included in this user manual are details regarding the theoretical backgrounds of RANDOM3 and RANDOM4. Appendix A gives information on the physical quantities, their symbols, FORTRAN names, and both SI and U.S. Customary units. Appendix B and C include photocopies of the actual computer printout corresponding to the sample problems. Appendices D and E detail the IMSL, Version 10(1), subroutines and functions called by RANDOM3 and RANDOM4 and SAS/GRAPH(2) programs that can be used to plot both the probability density functions (p.d.f.) and the cumulative distribution functions (c.d.f.).

  4. 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.

  5. 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.

  6. A Multi-Teacher Learning Automata Computing Model for Graph Partitioning Problems

    NASA Astrophysics Data System (ADS)

    Ikebo, Shigeya; Qian, Fei; Hirata, Hironori

    Graph partitioning is an important problem that has extensive applications in many areas, including VLSI design, scientific computing, data mining, geographical information systems and job scheduling. The graph partitioning problem (GPP) is NP-complete. There are several heuristic algorithms developed finding a reasonably good resolution. The most famous partitioning methods are simulated annealing (SA) and mean field algorithm (MFA) known to produce good partition for a wide class of problems, and they are used quite extensively. However these methods are very expensive in time and very sensitive in parameters tuning methods. In this paper, a new parameter-free algorithm for GPP has been proposed. The algorithm has been constructed using the S-model learning automata with multi-teacher random environments. As shown in our experiments, the proposed algorithm has some advantages superior to SA, MFA and ParMeTiS.

  7. 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. PMID:16442849

  8. 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.

  9. 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.

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

    NASA Astrophysics Data System (ADS)

    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 , Nature (London)NATUAS0028-083610.1038/nature03248 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/N0→0 in the limit of large systems (where N0 is the initial size of the graph and N its size at a given RSR step). In contrast, it happens at finite N/N0 in sparse ER graphs and in the annealed model, while it happens for N/N0→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 [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.101.148701 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

  11. 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.

  12. A Graph Based Framework to Model Virus Integration Sites.

    PubMed

    Fronza, Raffaele; Vasciaveo, Alessandro; Benso, Alfredo; Schmidt, Manfred

    2016-01-01

    With next generation sequencing thousands of virus and viral vector integration genome targets are now under investigation to uncover specific integration preferences and to define clusters of integration, termed common integration sites (CIS), that may allow to assess gene therapy safety or to detect disease related genomic features such as oncogenes. Here, we addressed the challenge to: 1) define the notion of CIS on graph models, 2) demonstrate that the structure of CIS enters in the category of scale-free networks and 3) show that our network approach analyzes CIS dynamically in an integrated systems biology framework using the Retroviral Transposon Tagged Cancer Gene Database (RTCGD) as a testing dataset. PMID:27257470

  13. Quantum Random Walks of Non-Interacting Bosons on Strongly Regular Graphs

    NASA Astrophysics Data System (ADS)

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

    2011-03-01

    We investigate the quantum dynamics of particles on graphs (``quantum walks"), with the aim of developing quantum algorithms for determining if two graphs are isomorphic and show that there are fundamental differences between the distinguishing power of two-particle and three-particle non-interacting quantum walks. We investigate quantum walks on strongly regular graphs (SRGs), a class of graphs with high symmetry. We show analytically that the two-particle walk always fails to distinguish non-isomorphic members of the same SRG family. We show numerically that the three-boson walk is able to distinguish 99.6% of 70,712 SRG comparisons made and that this distinguishing power comes from different multiplicities of certain graph substructures in non-isomorphic graphs. We identify certain distinguishing substructures and examine ones that appear in the four-boson walk, discovering they are able to distinguish almost all of the graphs that the three-boson walk failed on. This indicates a positive correlation between number of bosons in the walk and distinguishing power. This work was supported by ARO and DOD (W911NF-09-1-0439) and NSF (CCF-0635355). J.K.G. acknowledges support from the NSF.

  14. Quantum spins on star graphs and the Kondo model

    NASA Astrophysics Data System (ADS)

    Crampé, N.; Trombettoni, A.

    2013-06-01

    We study the XX model for quantum spins on the star graph with three legs (i.e., on a Y-junction). By performing a Jordan-Wigner transformation supplemented by the introduction of an auxiliary space we find a Kondo Hamiltonian of fermions, in the spin 1 representation of su(2), locally coupled with a magnetic impurity. In the continuum limit our model is shown to be equivalent to the 4-channel Kondo model coupling spin-1/2 fermions with a spin-1/2 impurity and exhibiting a non-Fermi liquid behavior. We also show that it is possible to find an XY model such that - after the Jordan-Wigner transformation - one obtains a quadratic fermionic Hamiltonian directly diagonalizable.

  15. 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

  16. 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).

  17. 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

  18. A random matrix model with localization and ergodic transitions

    NASA Astrophysics Data System (ADS)

    Kravtsov, V. E.; Khaymovich, I. M.; Cuevas, E.; Amini, M.

    2015-12-01

    Motivated by the problem of many-body localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig-Porter random matrix model is suggested that possesses two transitions. One of them is the Anderson localization transition from the localized to the extended states. The other one is the ergodic transition from the extended non-ergodic (multifractal) states to the extended ergodic states. We confirm the existence of both transitions by computing the two-level spectral correlation function, the spectrum of multifractality f(α ) and the wave function overlap which consistently demonstrate these two transitions.

  19. Randomized Item Response Theory Models

    ERIC Educational Resources Information Center

    Fox, Jean-Paul

    2005-01-01

    The randomized response (RR) technique is often used to obtain answers on sensitive questions. A new method is developed to measure latent variables using the RR technique because direct questioning leads to biased results. Within the RR technique is the probability of the true response modeled by an item response theory (IRT) model. The RR…

  20. Bridges in the random-cluster model

    NASA Astrophysics Data System (ADS)

    Elçi, Eren Metin; Weigel, Martin; Fytas, Nikolaos G.

    2016-02-01

    The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By introducing a classification of edges based on their relevance to the connectivity we study the stability of clusters in this model. We prove several exact relations for general graphs that allow us to derive unambiguously the finite-size scaling behavior of the density of bridges and non-bridges. For percolation, we are also able to characterize the point for which clusters become maximally fragile and show that it is connected to the concept of the bridge load. Combining our exact treatment with further results from conformal field theory, we uncover a surprising behavior of the (normalized) variance of the number of (non-)bridges, showing that it diverges in two dimensions below the value 4cos2 ⁡ (π /√{ 3}) = 0.2315891 ⋯ of the cluster coupling q. Finally, we show that a partial or complete pruning of bridges from clusters enables estimates of the backbone fractal dimension that are much less encumbered by finite-size corrections than more conventional approaches.

  1. Cauchy graph embedding based diffusion model for salient object detection.

    PubMed

    Tan, Yihua; Li, Yansheng; Chen, Chen; Yu, Jin-Gang; Tian, Jinwen

    2016-05-01

    Salient object detection has been a rather hot research topic recently, due to its potential applications in image compression, scene classification, image registration, and so forth. The overwhelming majority of existing computational models are designed based on computer vision techniques by using lots of image cues and priors. Actually, salient object detection is derived from the biological perceptual mechanism, and biological evidence shows that the spread of the spatial attention generates the object attention. Inspired by this, we attempt to utilize the emerging spread mechanism of object attention to construct a new computational model. A novel Cauchy graph embedding based diffusion (CGED) model is proposed to fulfill the spread process. Combining the diffusion model and attention prediction model, a salient object detection approach is presented through perceptually grouping the multiscale diffused attention maps. The effectiveness of the proposed approach is validated on the salient object dataset. The experimental results show that the CGED process can obviously improve the performance of salient object detection compared with the input spatial attention map, and the proposed approach can achieve performance comparable to that of state-of-the-art approaches. PMID:27140886

  2. 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

  3. Random modelling of contagious diseases.

    PubMed

    Demongeot, J; Hansen, O; Hessami, H; Jannot, A S; Mintsa, J; Rachdi, M; Taramasco, C

    2013-03-01

    Modelling contagious diseases needs to include a mechanistic knowledge about contacts between hosts and pathogens as specific as possible, e.g., by incorporating in the model information about social networks through which the disease spreads. The unknown part concerning the contact mechanism can be modelled using a stochastic approach. For that purpose, we revisit SIR models by introducing first a microscopic stochastic version of the contacts between individuals of different populations (namely Susceptible, Infective and Recovering), then by adding a random perturbation in the vicinity of the endemic fixed point of the SIR model and eventually by introducing the definition of various types of random social networks. We propose as example of application to contagious diseases the HIV, and we show that a micro-simulation of individual based modelling (IBM) type can reproduce the current stable incidence of the HIV epidemic in a population of HIV-positive men having sex with men (MSM). PMID:23525763

  4. 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. PMID:18003206

  5. Random trinomial tree models and vanilla options

    NASA Astrophysics Data System (ADS)

    Ganikhodjaev, Nasir; Bayram, Kamola

    2013-09-01

    In this paper we introduce and study random trinomial model. The usual trinomial model is prescribed by triple of numbers (u, d, m). We call the triple (u, d, m) an environment of the trinomial model. A triple (Un, Dn, Mn), where {Un}, {Dn} and {Mn} are the sequences of independent, identically distributed random variables with 0 < Dn < 1 < Un and Mn = 1 for all n, is called a random environment and trinomial tree model with random environment is called random trinomial model. The random trinomial model is considered to produce more accurate results than the random binomial model or usual trinomial model.

  6. Coloring geographical threshold graphs

    SciTech Connect

    Bradonjic, Milan; Percus, Allon; Muller, Tobias

    2008-01-01

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

  7. A parallel graph coloring heuristic

    SciTech Connect

    Jones, M.T.; Plassmann, P.E. )

    1993-05-01

    The problem of computing good graph colorings arises in many diverse applications, such as in the estimation of sparse Jacobians and in the development of efficient, parallel iterative methods for solving sparse linear systems. This paper presents an asynchronous graph coloring heuristic well suited to distributed memory parallel computers. Experimental results obtained on an Intel iPSC/860 are presented, which demonstrate that, for graphs arising from finite element applications, the heuristic exhibits scalable performance and generates colorings usually within three or four colors of the best-known linear time sequential heuristics. For bounded degree graphs, it is shown that the expected running time of the heuristic under the P-Ram computation model is bounded by EO(log(n)/log log(n)). This bound is an improvement over the previously known best upper bound for the expected running time of a random heuristic for the graph coloring problem.

  8. 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.

  9. Graph-matching model using Gibbsian modeling: application to map/SPOT image road networks for map updating

    NASA Astrophysics Data System (ADS)

    Descombes, Xavier; Hivernat, Christine; Randriamasy, Sabine; Zerubia, Josiane B.

    1999-06-01

    We consider herein the matching between two graphs representing road networks. This problem is embedded into a labeling framework. One graph is taken as a reference. A Gibbsian model is proposed to label the other graph. The labels are defined by the noes of the second graph. The potentials are defined by the angle between the nodes and the length of the associated features. Therefore, the model is invariant by translation and rotation. We apply this model to match a road network extracted from a SPOT image on the road network of a cartographic database. This matching provides some information for map updating.

  10. A model of random sequences for de novo peptide sequencing

    SciTech Connect

    Jarman, Kenneth D.; Cannon, William R.; Jarman, Kristin H.; Heredia-Langner, Alejandro

    2003-04-15

    We present a model for the probability of random sequences appearing in product ion spectra obtained from tandem mass spectrometry experiments using collision-induced dissociation. We demonstrate the use of these probabilities for ranking candidate peptide sequences obtained using a de novo algorithm. Sequence candidates are obtained from a spectrum graph that is greatly reduced in size from those in previous graph-theoretical de novo approaches. Evidence of multiple instances of subsequences of each candidate, due to different fragment ion type series as well as isotopic peaks, is incorporated in a hierarchical scoring scheme. This approach is shown to be useful for confirming results from database search and as a first step towards a statistically rigorous de novo algorithm.

  11. Computational Graph Model for 3D Cells Tracking in Zebra Fish Datasets

    NASA Astrophysics Data System (ADS)

    Zhang, Lelin; Xiong, Hongkai; Zhao, Yang; Zhang, Kai; Zhou, Xiaobo

    2007-11-01

    This paper leads to a novel technique for tracking and identification of zebra-fish cells in 3D image sequences, extending graph-based multi-objects tracking algorithm to 3D applications. As raised in previous work of 2D graph-based method, separated cells are modeled as vertices that connected by edges. Then the tracking work is simplified to that of vertices matching between graphs generated from consecutive frames. Graph-based tracking is composed of three steps: graph generation, initial source vertices selection and graph saturation. To satisfy demands in this work separated cell records are segmented from original datasets using 3D level-set algorithms. Besides, advancements are achieved in each of the step including graph regulations, multi restrictions on source vertices and enhanced flow quantifications. Those strategies make a good compensation for graph-based multi-objects tracking method in 2D space. Experiments are carried out in 3D datasets sampled from zebra fish, results of which shows that this enhanced method could be potentially applied to tracking of objects with diverse features.

  12. 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. PMID:17913139

  13. 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.

  14. A universal form of slow dynamics in zero-temperature random-field Ising model

    NASA Astrophysics Data System (ADS)

    Ohta, H.; Sasa, S.

    2010-04-01

    The zero-temperature Glauber dynamics of the random-field Ising model describes various ubiquitous phenomena such as avalanches, hysteresis, and related critical phenomena. Here, for a model on a random graph with a special initial condition, we derive exactly an evolution equation for an order parameter. Through a bifurcation analysis of the obtained equation, we reveal a new class of cooperative slow dynamics with the determination of critical exponents.

  15. Eigenfunction statistics on quantum graphs

    SciTech Connect

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

    2010-12-15

    We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric {sigma} model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.

  16. 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.…

  17. A graph theoretic approach to global earthquake sequencing: A Markov chain model

    NASA Astrophysics Data System (ADS)

    Vasudevan, K.; Cavers, M. S.

    2012-12-01

    We construct a directed graph to represent a Markov chain of global earthquake sequences and analyze the statistics of transition probabilities linked to earthquake zones. For earthquake zonation, we consider the simplified plate boundary template of Kagan, Bird, and Jackson (KBJ template, 2010). We demonstrate the applicability of the directed graph approach to hazard-related forecasting using some of the properties of graphs that represent the finite Markov chain. We extend the present study to consider Bird's 52-plate zonation (2003) describing the global earthquakes at and within plate boundaries to gain further insight into the usefulness of digraphs corresponding to a Markov chain model.

  18. 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…

  19. Modeling and simulation of hydraulic vibration system based on bond graph and Matlab/Simulink

    NASA Astrophysics Data System (ADS)

    Lian, Hongzhen; Kou, Ziming

    2008-10-01

    The hydraulic vibration system controlled by wave exciter is a mechanic-electric-fluid integration system, and it has high dynamic characteristics. Modeling and simulation for it has come to professional's attention in the field of hydraulic vibration industry, because it is nonlinear and complex. In this paper, a method has been proposed. By using power bond graph method, the bond graph model for it can be established, meanwhile, it is proposed that controlled parameters are considered to join the model, in order to control power flow alternated; and the mathematical model(state equations) of this system can be built according to bond graph theory and controlled relations; then simulation model can be built by using Matlab/Simulink software, the model can intuitively express system's power flow direction and controlled relations. To the question that stiff equation appears easily in model of hydraulic system, we can choose the adapting algorithm offered by Matlab software to obtain the more precise simulation results.

  20. 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

  1. Evolutionary Games of Multiplayer Cooperation on Graphs.

    PubMed

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

    2016-08-01

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

  2. 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. PMID:26544962

  3. 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…

  4. 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

  5. Bond graph modeling and validation of an energy regenerative system for emulsion pump tests.

    PubMed

    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

  6. ECM-Aware Cell-Graph Mining for Bone Tissue Modeling and Classification.

    PubMed

    Bilgin, Cemal Cagatay; Bullough, Peter; Plopper, George E; Yener, Bülent

    2009-10-21

    Pathological examination of a biopsy is the most reliable and widely used technique to diagnose bone cancer. However, it suffers from both inter- and intra- observer subjectivity. Techniques for automated tissue modeling and classification can reduce this subjectivity and increases the accuracy of bone cancer diagnosis. This paper presents a graph theoretical method, called extracellular matrix (ECM)-aware cell-graph mining, that combines the ECM formation with the distribution of cells in hematoxylin and eosin (H&E) stained histopathological images of bone tissues samples. This method can identify different types of cells that coexist in the same tissue as a result of its functional state. Thus, it models the structure-function relationships more precisely and classifies bone tissue samples accurately for cancer diagnosis. The tissue images are segmented, using the eigenvalues of the Hessian matrix, to compute spatial coordinates of cell nuclei as the nodes of corresponding cell-graph. Upon segmentation a color code is assigned to each node based on the composition of its surrounding ECM. An edge is hypothesized (and established) between a pair of nodes if the corresponding cell membranes are in physical contact and if they share the same color. Hence, multiple colored-cell-graphs coexist in a tissue each modeling a different cell-type organization. Both topological and spectral features of ECM-aware cell-graphs are computed to quantify the structural properties of tissue samples and classify their different functional states as healthy, fractured, or cancerous using support vector machines. Classification accuracy comparison to related work shows that ECM-aware cell-graph approach yields 90.0% whereas Delaunay triangulation and simple cell-graph approach achieves 75.0% and 81.1% accuracy, respectively. PMID:20543911

  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. SIRS Dynamics on Random Networks: Simulations and Analytical Models

    NASA Astrophysics Data System (ADS)

    Rozhnova, Ganna; Nunes, Ana

    The standard pair approximation equations (PA) for the Susceptible-Infective-Recovered-Susceptible (SIRS) model of infection spread on a network of homogeneous degree k predict a thin phase of sustained oscillations for parameter values that correspond to diseases that confer long lasting immunity. Here we present a study of the dependence of this oscillatory phase on the parameter k and of its relevance to understand the behaviour of simulations on networks. For k = 4, we compare the phase diagram of the PA model with the results of simulations on regular random graphs (RRG) of the same degree. We show that for parameter values in the oscillatory phase, and even for large system sizes, the simulations either die out or exhibit damped oscillations, depending on the initial conditions. This failure of the standard PA model to capture the qualitative behaviour of the simulations on large RRGs is currently being investigated.

  10. Modeling Randomness in Judging Rating Scales with a Random-Effects Rating Scale Model

    ERIC Educational Resources Information Center

    Wang, Wen-Chung; Wilson, Mark; Shih, Ching-Lin

    2006-01-01

    This study presents the random-effects rating scale model (RE-RSM) which takes into account randomness in the thresholds over persons by treating them as random-effects and adding a random variable for each threshold in the rating scale model (RSM) (Andrich, 1978). The RE-RSM turns out to be a special case of the multidimensional random…

  11. A graph isomorphism algorithm using signatures computed via quantum walk search model

    NASA Astrophysics Data System (ADS)

    Wang, Huiquan; Wu, Junjie; Yang, Xuejun; Yi, Xun

    2015-03-01

    In this paper, we propose a new algorithm based on a quantum walk search model to distinguish strongly similar graphs. Our algorithm computes a signature for each graph via the quantum walk search model and uses signatures to distinguish non-isomorphic graphs. Our method is less complex than those of previous works. In addition, our algorithm can be extended by raising the signature levels. The higher the level adopted, the stronger the distinguishing ability and the higher the complexity of the algorithm. Our algorithm was tested with standard benchmarks from four databases. We note that the weakest signature at level 1 can distinguish all similar graphs, with a time complexity of O({{N}3.5}), which that outperforms the previous best work except when it comes to strongly regular graphs (SRGs). Once the signature is raised to level 3, all SRGs tested can be distinguished successfully. In this case, the time complexity is O({{N}5.5}), also better than the previous best work.

  12. Error Threshold of Fully Random Eigen Model

    NASA Astrophysics Data System (ADS)

    Li, Duo-Fang; Cao, Tian-Guang; Geng, Jin-Peng; Qiao, Li-Hua; Gu, Jian-Zhong; Zhan, Yong

    2015-01-01

    Species evolution is essentially a random process of interaction between biological populations and their environments. As a result, some physical parameters in evolution models are subject to statistical fluctuations. In this work, two important parameters in the Eigen model, the fitness and mutation rate, are treated as Gaussian distributed random variables simultaneously to examine the property of the error threshold. Numerical simulation results show that the error threshold in the fully random model appears as a crossover region instead of a phase transition point, and as the fluctuation strength increases the crossover region becomes smoother and smoother. Furthermore, it is shown that the randomization of the mutation rate plays a dominant role in changing the error threshold in the fully random model, which is consistent with the existing experimental data. The implication of the threshold change due to the randomization for antiviral strategies is discussed.

  13. 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.

  14. 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).

  15. 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.

  16. 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…

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

    PubMed

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

    2016-09-01

    We present a novel synergistic methodology for the spatio-temporal analysis of single Electroencephalogram (EEG) trials. This new methodology is based on the novel synergy of Local Global Graph (LG graph) to characterize define the structural features of the EEG topography as a global descriptor for robust comparison of dominant topographies (microstates) and Hidden Markov Models (HMM) to model the topographic sequence in a unique way. In particular, the LG graph descriptor defines similarity and distance measures that can be successfully used for the difficult comparison of the extracted LG graphs in the presence of noise. In addition, hidden states represent periods of stationary distribution of topographies that constitute the equivalent of the microstates in the model. The transitions between the different microstates and the formed syntactic patterns can reveal differences in the processing of the input stimulus between different pathologies. We train the HMM model to learn the transitions between the different microstates and express the syntactic patterns that appear in the single trials in a compact and efficient way. We applied this methodology in single trials consisting of normal subjects and patients with Progressive Mild Cognitive Impairment (PMCI) to discriminate these two groups. The classification results show that this approach is capable to efficiently discriminate between control and Progressive MCI single trials. Results indicate that HMMs provide physiologically meaningful results that can be used in the syntactic analysis of Event Related Potentials. PMID:27255799

  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. Parametric models for samples of random functions

    SciTech Connect

    Grigoriu, M.

    2015-09-15

    A new class of parametric models, referred to as sample parametric models, is developed for random elements that match sample rather than the first two moments and/or other global properties of these elements. The models can be used to characterize, e.g., material properties at small scale in which case their samples represent microstructures of material specimens selected at random from a population. The samples of the proposed models are elements of finite-dimensional vector spaces spanned by samples, eigenfunctions of Karhunen–Loève (KL) representations, or modes of singular value decompositions (SVDs). The implementation of sample parametric models requires knowledge of the probability laws of target random elements. Numerical examples including stochastic processes and random fields are used to demonstrate the construction of sample parametric models, assess their accuracy, and illustrate how these models can be used to solve efficiently stochastic equations.

  20. Applications of Vertex Coloring Problems for Graphs. Applications of Graph Theory in Model Construction. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 442.

    ERIC Educational Resources Information Center

    Malkevitch, Joseph

    One of the great strengths of mathematics is viewed as the fact that apparently diverse real-world questions translate into that same mathematical question. It is felt that studying a mathematical problem can often bring about a tool of surprisingly diverse usability. The module is geared to help users know how to use graph theory to model simple…

  1. Graphing Reality

    NASA Astrophysics Data System (ADS)

    Beeken, Paul

    2014-11-01

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

  2. Spectral statistics of nearly unidirectional quantum graphs

    NASA Astrophysics Data System (ADS)

    Akila, Maram; Gutkin, Boris

    2015-08-01

    The energy levels of a quantum graph with time reversal symmetry and unidirectional classical dynamics are doubly degenerate and obey the spectral statistics of the Gaussian unitary ensemble. These degeneracies, however, are lifted when the unidirectionality is broken in one of the graph’s vertices by a singular perturbation. Based on a random matrix model we derive an analytic expression for the nearest neighbour distribution between energy levels of such systems. As we demonstrate the result agrees excellently with the actual statistics for graphs with a uniform distribution of eigenfunctions. Yet, it exhibits quite substantial deviations for classes of graphs which show strong scarring.

  3. Graphing Reality

    ERIC Educational Resources Information Center

    Beeken, Paul

    2014-01-01

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

  4. A spectral graph regression model for learning brain connectivity of Alzheimer's disease.

    PubMed

    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

  5. 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

  6. 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.

  7. 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

  8. Impossible Graphs.

    ERIC Educational Resources Information Center

    Noble, Tracy; And Others

    Graphs without a time axis, such as velocity-versus-position graphs, offer interesting possibilities for exploring graphing and motion. Relations depicted by these graphs are not limited to functions. Interviews with a high school student named Olivia, who uses a motion detector to create such graphs, indicate that she uses thought experiments as…

  9. Stochastic data-flow graph models for the reliability analysis of communication networks and computer systems

    SciTech Connect

    Chen, D.J.

    1988-01-01

    The literature is abundant with combinatorial reliability analysis of communication networks and fault-tolerant computer systems. However, it is very difficult to formulate reliability indexes using combinatorial methods. These limitations have led to the development of time-dependent reliability analysis using stochastic processes. In this research, time-dependent reliability-analysis techniques using Dataflow Graphs (DGF) are developed. The chief advantages of DFG models over other models are their compactness, structural correspondence with the systems, and general amenability to direct interpretation. This makes the verification of the correspondence of the data-flow graph representation to the actual system possible. Several DGF models are developed and used to analyze the reliability of communication networks and computer systems. Specifically, Stochastic Dataflow graphs (SDFG), both the discrete-time and the continuous time models are developed and used to compute time-dependent reliability of communication networks and computer systems. The repair and coverage phenomenon of communication networks is also analyzed using SDFG models.

  10. 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.

  11. 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…

  12. A bond graph approach to modeling the anuran vocal production system.

    PubMed

    Kime, Nicole M; Ryan, Michael J; Wilson, Preston S

    2013-06-01

    Air-driven vocal production systems such as those found in mammals, birds, and anurans (frogs and toads) combine pneumatic and mechanical elements in species-specific ways to produce a diversity of communication signals. This study uses bond graphs to model a generalized anuran vocal production system. Bond graphs allow an incremental approach to modeling dynamic physical systems involving different domains. Anurans provide an example of how signal diversity results from variation in the structure and behavior of vocal system elements. This paper first proposes a bond graph model of the integrated anuran vocal system as a framework for future study. It then presents a simulated submodel of the anuran sound source that produces sustained oscillations in vocal fold displacement and air flow through the larynx. The modeling approach illustrated here should prove of general applicability to other biological sound production systems, and will allow researchers to study the biomechanics of vocal production as well as the functional congruence and evolution of groups of traits within integrated vocal systems. PMID:23742365

  13. The Ising Model on a Quenched Ensemble of c=-5 Gravity Graphs

    NASA Astrophysics Data System (ADS)

    Anagnostopoulos, K. N.; Bialas, P.; Thorleifsson, G.

    1999-02-01

    We study with Monte Carlo methods an ensemble of c=-5 gravity graphs, generated by coupling a conformal field theory with central charge c=-5 to two-dimensional quantum gravity. We measure the fractal properties of the ensemble, such as the string susceptibility exponent γ s and the intrinsic fractal dimension d H. We find γ s=-1.5(1) and d H=3.36(4), in reasonable agreement with theoretical predictions. In addition, we study the critical behavior of an Ising model on a quenched ensemble of the c=-5 graphs and show that it agrees, within numerical accuracy, with theoretical predictions for the critical behavior of an Ising model coupled dynamically to two-dimensional quantum gravity, with a total central charge of the matter sector c=-5.

  14. Modeling and mitigating noise in graph and manifold representations of hyperspectral imagery

    NASA Astrophysics Data System (ADS)

    Jin, Can; Bachmann, Charles M.

    2015-05-01

    Over the past decade, manifold and graph representations of hyperspectral imagery (HSI) have been explored widely in HSI applications. There are a large number of data-driven approaches to deriving manifold coordinate representations including Isometric Mapping (ISOMAP)1, Local Linear Embedding (LLE)2, Laplacian Eigenmaps (LE)3, Diffusion Kernels (DK)4, and many related methods. Improvements to specific algorithms have been developed to ease computational burden or otherwise improve algorithm performance. For example, the best way to estimate the size of the locally linear neighborhoods used in graph construction have been addressed6 as well as the best method of linking the manifold representation with classifiers in applications. However, the problem of how to model and mitigate noise in manifold representations of hyperspectral imagery has not been well studied and remains a challenge for graph and manifold representations of hyperspectral imagery and their application. It is relatively easy to apply standard linear methods to remove noise from the data in advance of further processing, however, these approaches by and large treat the noise model in a global sense, using statistics derived from the entire data set and applying the results globally over the data set. Graph and manifold representations by their nature attempt to find an intrinsic representation of the local data structure, so it is natural to ask how can one best represent the noise model in a local sense. In this paper, we explore the approaches to modeling and mitigating noise at a local level, using manifold coordinates of local spectral subsets. The issue of landmark selection of the current landmark ISOMAP algorithm5 is addressed and a workflow is proposed to make use of manifold coordinates of local spectral subsets to make optimal landmark selection and minimize the effect of local noise.

  15. 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.

  16. Graphing the Model or Modeling the Graph? Not-so-Subtle Problems in Linear IS-LM Analysis.

    ERIC Educational Resources Information Center

    Alston, Richard M.; Chi, Wan Fu

    1989-01-01

    Outlines the differences between the traditional and modern theoretical models of demand for money. States that the two models are often used interchangeably in textbooks, causing ambiguity. Argues against the use of linear specifications that imply that income velocity can increase without limit and that autonomous components of aggregate demand…

  17. 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.

  18. Ranking Medical Subject Headings using a factor graph model

    PubMed Central

    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. PMID:26306236

  19. Random-diluted triangular plaquette model: Study of phase transitions in a kinetically constrained model

    NASA Astrophysics Data System (ADS)

    Franz, Silvio; Gradenigo, Giacomo; Spigler, Stefano

    2016-03-01

    We study how the thermodynamic properties of the triangular plaquette model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in kinetically constrained models. As soon as we generalize the model to include additional interactions, a thermodynamic phase transition appears in the system. The additional interactions we consider are either short ranged, forming a regular lattice in the plane, or long ranged of the small-world kind. In the case of long-range interactions we call the new model the random-diluted TPM. We provide arguments that the model so modified should undergo a thermodynamic phase transition, and that in the long-range case this is a glass transition of the "random first-order" kind. Finally, we give support to our conjectures studying the finite-temperature phase diagram of the random-diluted TPM in the Bethe approximation. This corresponds to the exact calculation on the random regular graph, where free energy and configurational entropy can be computed by means of the cavity equations.

  20. Random-diluted triangular plaquette model: Study of phase transitions in a kinetically constrained model.

    PubMed

    Franz, Silvio; Gradenigo, Giacomo; Spigler, Stefano

    2016-03-01

    We study how the thermodynamic properties of the triangular plaquette model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in kinetically constrained models. As soon as we generalize the model to include additional interactions, a thermodynamic phase transition appears in the system. The additional interactions we consider are either short ranged, forming a regular lattice in the plane, or long ranged of the small-world kind. In the case of long-range interactions we call the new model the random-diluted TPM. We provide arguments that the model so modified should undergo a thermodynamic phase transition, and that in the long-range case this is a glass transition of the "random first-order" kind. Finally, we give support to our conjectures studying the finite-temperature phase diagram of the random-diluted TPM in the Bethe approximation. This corresponds to the exact calculation on the random regular graph, where free energy and configurational entropy can be computed by means of the cavity equations. PMID:27078408

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

    PubMed

    Shang, Yilun

    2015-01-01

    Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices. PMID:25822506

  2. Laplacian Estrada and Normalized Laplacian Estrada Indices of Evolving Graphs

    PubMed Central

    Shang, Yilun

    2015-01-01

    Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices. PMID:25822506

  3. A graph-theoretic algorithm for comparative modeling of protein structure.

    PubMed

    Samudrala, R; Moult, J

    1998-05-29

    The interconnected nature of interactions in protein structures appears to be the major hurdle in preventing the construction of accurate comparative models. We present an algorithm that uses graph theory to handle this problem. Each possible conformation of a residue in an amino acid sequence is represented using the notion of a node in a graph. Each node is given a weight based on the degree of the interaction between its side-chain atoms and the local main-chain atoms. Edges are then drawn between pairs of residue conformations/nodes that are consistent with each other (i.e. clash-free and satisfying geometrical constraints). The edges are weighted based on the interactions between the atoms of the two nodes. Once the entire graph is constructed, all the maximal sets of completely connected nodes (cliques) are found using a clique-finding algorithm. The cliques with the best weights represent the optimal combinations of the various main-chain and side-chain possibilities, taking the respective environments into account. The algorithm is used in a comparative modeling scenario to build side-chains, regions of main chain, and mix and match between different homologs in a context-sensitive manner. The predictive power of this method is assessed by applying it to cases where the experimental structure is not known in advance. PMID:9636717

  4. 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. PMID:26978821

  5. 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

  6. 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.

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

    PubMed

    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 K_{c}=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. PMID:27575149

  8. 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.

  9. 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.

  10. 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.

  11. Software reliability growth models dominated by randomness

    NASA Technical Reports Server (NTRS)

    Shen, Wenhui; Wilson, Larry

    1989-01-01

    The Jelinski-Moranda and Geometric models for software reliability failed the consistency test which was proposed. These models were challenged to take data which comes from a process which they have correctly modeled and to make predictions about the reliability of that process. It was found that either model, given data precisely from a process it correctly models, will usually fail to make good predictions. These problems are attributed to randomness in the data used as input to the models and a remedy is indicated for this lack of robustness, namely replication of data.

  12. 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

  13. Graph model for calculating the properties of saturated monoalcohols based on the additivity of energy terms

    NASA Astrophysics Data System (ADS)

    Grebeshkov, V. V.; Smolyakov, V. M.

    2012-05-01

    A 16-constant additive scheme was derived for calculating the physicochemical properties of saturated monoalcohols CH4O-C9H20O and decomposing the triangular numbers of the Pascal triangle based on the similarity of subgraphs in the molecular graphs (MGs) of the homologous series of these alcohols. It was shown, using this scheme for calculation of properties of saturated monoalcohols as an example, that each coefficient of the scheme (in other words, the number of methods to impose a chain of a definite length i 1, i 2, … on a molecular graph) is the result of the decomposition of the triangular numbers of the Pascal triangle. A linear dependence was found within the adopted classification of structural elements. Sixteen parameters of the schemes were recorded as linear combinations of 17 parameters. The enthalpies of vaporization L {298/K 0} of the saturated monoalcohols CH4O-C9H20O, for which there were no experimental data, were calculated. It was shown that the parameters are not chosen randomly when using the given procedure for constructing an additive scheme by decomposing the triangular numbers of the Pascal triangle.

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

    USGS Publications Warehouse

    Grace, James B.; Schoolmaster, Donald R., Jr.; 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

  15. 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.

  16. 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

  17. 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).

  18. 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.

  19. Random sphere packing model of heterogeneous propellants

    NASA Astrophysics Data System (ADS)

    Kochevets, Sergei Victorovich

    It is well recognized that combustion of heterogeneous propellants is strongly dependent on the propellant morphology. Recent developments in computing systems make it possible to start three-dimensional modeling of heterogeneous propellant combustion. A key component of such large scale computations is a realistic model of industrial propellants which retains the true morphology---a goal never achieved before. The research presented develops the Random Sphere Packing Model of heterogeneous propellants and generates numerical samples of actual industrial propellants. This is done by developing a sphere packing algorithm which randomly packs a large number of spheres with a polydisperse size distribution within a rectangular domain. First, the packing code is developed, optimized for performance, and parallelized using the OpenMP shared memory architecture. Second, the morphology and packing fraction of two simple cases of unimodal and bimodal packs are investigated computationally and analytically. It is shown that both the Loose Random Packing and Dense Random Packing limits are not well defined and the growth rate of the spheres is identified as the key parameter controlling the efficiency of the packing. For a properly chosen growth rate, computational results are found to be in excellent agreement with experimental data. Third, two strategies are developed to define numerical samples of polydisperse heterogeneous propellants: the Deterministic Strategy and the Random Selection Strategy. Using these strategies, numerical samples of industrial propellants are generated. The packing fraction is investigated and it is shown that the experimental values of the packing fraction can be achieved computationally. It is strongly believed that this Random Sphere Packing Model of propellants is a major step forward in the realistic computational modeling of heterogeneous propellant of combustion. In addition, a method of analysis of the morphology of heterogeneous

  20. 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.

  1. 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.

  2. Conformational transitions in random heteropolymer models.

    PubMed

    Blavatska, Viktoria; Janke, Wolfhard

    2014-01-21

    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. PMID:25669411

  3. 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.

  4. 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.

  5. Model of twelve properties of a set of organic solvents with graph-theoretical and/or experimental parameters.

    PubMed

    Pogliani, Lionello

    2010-01-30

    Twelve properties of a highly heterogeneous class of organic solvents have been modeled with a graph-theoretical molecular connectivity modified (MC) method, which allows to encode the core electrons and the hydrogen atoms. The graph-theoretical method uses the concepts of simple, general, and complete graphs, where these last types of graphs are used to encode the core electrons. The hydrogen atoms have been encoded by the aid of a graph-theoretical perturbation parameter, which contributes to the definition of the valence delta, delta(v), a key parameter in molecular connectivity studies. The model of the twelve properties done with a stepwise search algorithm is always satisfactory, and it allows to check the influence of the hydrogen content of the solvent molecules on the choice of the type of descriptor. A similar argument holds for the influence of the halogen atoms on the type of core electron representation. In some cases the molar mass, and in a minor way, special "ad hoc" parameters have been used to improve the model. A very good model of the surface tension could be obtained by the aid of five experimental parameters. A mixed model method based on experimental parameters plus molecular connectivity indices achieved, instead, to consistently improve the model quality of five properties. To underline is the importance of the boiling point temperatures as descriptors in these last two model methodologies. PMID:19462460

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

    PubMed

    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

  7. 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

  8. 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

  9. 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.

  10. A Gestalt rules and graph-cut-based simplification framework for urban building models

    NASA Astrophysics Data System (ADS)

    Wang, Yuebin; Zhang, Liqiang; Mathiopoulos, P. Takis; Deng, Hao

    2015-03-01

    To visualize large urban models efficiently, this paper presents a framework for generalizing urban building footprints and facade textures by using multiple Gestalt rules and a graph-cut-based energy function. First, an urban scene is divided into different blocks by main road networks. In each block, the building footprints are partitioned into potential Gestalt groups. A footprint may satisfy several Gestalt principles. We employ the graph-cut-based optimization function to obtain a consistent segmentation of the buildings into optimal Gestalt groups with minimal energy. The building footprints in each Gestalt group are aggregated into different levels of detail (LODs). Building facade textures are also abstracted and simplified into multiple LODs using the same approach as the building footprint simplification. An effective data structure termed SceneTree is introduced to manage these aggregated building footprints and facade textures. Combined with the parallelization scheme, the rendering efficiency of large-scale urban buildings is improved. Compared with other methods, our presented method can efficiently visualize large urban models and maintain the city's image.

  11. 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.

  12. 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.

  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. 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

  15. 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

  16. Deformable Graph Model for Tracking Epithelial Cell Sheets in Fluorescence Microscopy.

    PubMed

    Zou, Roger S; Tomasi, Carlo

    2016-07-01

    We propose a novel method for tracking cells that are connected through a visible network of membrane junctions. Tissues of this form are common in epithelial cell sheets and resemble planar graphs where each face corresponds to a cell. We leverage this structure and develop a method to track the entire tissue as a deformable graph. This coupled model in which vertices inform the optimal placement of edges and vice versa captures global relationships between tissue components and leads to accurate and robust cell tracking. We compare the performance of our method with that of four reference tracking algorithms on four data sets that present unique tracking challenges. Our method exhibits consistently superior performance in tracking all cells accurately over all image frames, and is robust over a wide range of image intensity and cell shape profiles. This may be an important tool for characterizing tissues of this type especially in the field of developmental biology where automated cell analysis can help elucidate the mechanisms behind controlled cell-shape changes. PMID:26829784

  17. Graphs on uniform points in [0,1]d

    NASA Astrophysics Data System (ADS)

    Appel, Martin J. B.; Russo, Ralph P.; Yang, King J.

    1995-06-01

    Statistical problems in pattern or structure recognition for a random multidimensional point set may be addressed by variations on the random graph model of Erdos and Renyui. The imposition of graph structure with a variable edge criterion on a large random point set allows a search for signature quantities or behavior under the given distributional hypothesis. The work is motivated by the question of how to make statistical inferences from sensed mine field data. This article describes recent results obtained in the following special cases. On independent random points U1,...,Un distributed uniformly on [0,1]d, a random graph Gn(x) is constructed in which two distinct such points are joined by an edge if the l(infinity )-distance between them is at most some prescribed value 0 graph are described. Almost-sure asymptotic rates of convergence/divergence are obtained for various quantities, including the maximum and minimum vertex degree of the random graph, its clique number, chromatic number, and independence number, as the number n of points becomes large and the edge distance x is allowed to vary with n. The connectivity distance cn, the smallest x such that Gn(x) is connected, and the largest nearest neighbor link dn, the smallest x such that Gn(x) has no vertices of degree zero, are asymptotic in ratio, as n becomes large, for d >= 2.

  18. 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. PMID:27583533

  19. Study on the Model of Consensus Formation in Internet Based on the Directed Graph

    NASA Astrophysics Data System (ADS)

    Hu, Chaolang; Wu, Rongjun; Liu, Jiayong

    2012-06-01

    This paper constructs a model of the consensus formation in Internet based on the directed graph after analyzing the classical models of the social consensus formation, sets up the rules for the evolvement of opinions of agents and induces the evolving algorithm of consensus in Internet. The paper presents some key parameters such as the influence area of the mainstream media, the average influence of the mainstream media, the average self-persisting ability of agents and etc. Simulation results on a small-world networks show that the less the average self-persisting capability of the agents is, the easier the guidance of the media will be. The stronger the average influence of the main stream media is, the easier the mainstream media guides the consensus. These results reflect the formation law of the network consensus and are consistent approximately with the real circumstance.

  20. Chain Graph Models to Elicit the Structure of a Bayesian Network

    PubMed Central

    Stefanini, Federico M.

    2014-01-01

    Bayesian networks are possibly the most successful graphical models to build decision support systems. Building the structure of large networks is still a challenging task, but Bayesian methods are particularly suited to exploit experts' degree of belief in a quantitative way while learning the network structure from data. In this paper details are provided about how to build a prior distribution on the space of network structures by eliciting a chain graph model on structural reference features. Several structural features expected to be often useful during the elicitation are described. The statistical background needed to effectively use this approach is summarized, and some potential pitfalls are illustrated. Finally, a few seminal contributions from the literature are reformulated in terms of structural features. PMID:24688427

  1. Graph hierarchies for phylogeography.

    PubMed

    Cybis, Gabriela B; Sinsheimer, Janet S; Lemey, Philippe; Suchard, Marc A

    2013-03-19

    Bayesian phylogeographic methods simultaneously integrate geographical and evolutionary modelling, and have demonstrated value in assessing spatial spread patterns of measurably evolving organisms. We improve on existing phylogeographic methods by combining information from multiple phylogeographic datasets in a hierarchical setting. Consider N exchangeable datasets or strata consisting of viral sequences and locations, each evolving along its own phylogenetic tree and according to a conditionally independent geographical process. At the hierarchical level, a random graph summarizes the overall dispersion process by informing which migration rates between sampling locations are likely to be relevant in the strata. This approach provides an efficient and improved framework for analysing inherently hierarchical datasets. We first examine the evolutionary history of multiple serotypes of dengue virus in the Americas to showcase our method. Additionally, we explore an application to intrahost HIV evolution across multiple patients. PMID:23382428

  2. Modeling superhydrophobic surfaces comprised of random roughness

    NASA Astrophysics Data System (ADS)

    Samaha, M. A.; Vahedi Tafreshi, H.; Gad-El-Hak, M.

    2011-11-01

    We model the performance of superhydrophobic surfaces comprised of randomly distributed roughness that resembles natural surfaces, or those produced via random deposition of hydrophobic particles. Such a fabrication method is far less expensive than ordered-microstructured fabrication. The present numerical simulations are aimed at improving our understanding of the drag reduction effect and the stability of the air-water interface in terms of the microstructure parameters. For comparison and validation, we have also simulated the flow over superhydrophobic surfaces made up of aligned or staggered microposts for channel flows as well as streamwise or spanwise ridge configurations for pipe flows. The present results are compared with other theoretical and experimental studies. The numerical simulations indicate that the random distribution of surface roughness has a favorable effect on drag reduction, as long as the gas fraction is kept the same. The stability of the meniscus, however, is strongly influenced by the average spacing between the roughness peaks, which needs to be carefully examined before a surface can be recommended for fabrication. Financial support from DARPA, contract number W91CRB-10-1-0003, is acknowledged.

  3. Matching structural, effective, and functional connectivity: a comparison between structural equation modeling and ancestral graphs.

    PubMed

    Bringmann, Laura F; Scholte, H Steven; Waldorp, Lourens J

    2013-01-01

    In this study, we examined the accuracy of ancestral graphs (AGs) to study effective connectivity in the brain. Unlike most other methods that estimate effective connectivity, an AG is able to explicitly model missing brain regions in a network model. We compared AGs with the conventional structural equation models (SEM). We used both methods to estimate connection strengths between six regions of interest of the visual cortex based on functional magnetic resonance imaging data of a motion perception task. In order to examine which method is more accurate to estimate effective connectivity, we compared the connection strengths of the AG and SEM models with connection probabilities resulting from probabilistic tractography obtained from diffusion tensor images. This was done by correlating the connection strengths of the best fitting AG and SEM models with the connection probabilities of the probabilistic tractography models. We show that, in general, AGs result in more accurate models to estimate effective connectivity than SEM. The reason for this is that missing regions are taken into account when modeling with AG but not when modeling with SEM: AG can be used to explicitly test the assumption of missing regions. If the set of regions is complete, SEM and AG perform about equally well. PMID:23662916

  4. 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.

  5. 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

  6. 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.

  7. Discriminatively Trained And-Or Graph Models for Object Shape Detection.

    PubMed

    Lin, Liang; Wang, Xiaolong; Yang, Wei; Lai, Jian-Huang

    2015-05-01

    In this paper, we investigate a novel reconfigurable part-based model, namely And-Or graph model, to recognize object shapes in images. Our proposed model consists of four layers: leaf-nodes at the bottom are local classifiers for detecting contour fragments; or-nodes above the leaf-nodes function as the switches to activate their child leaf-nodes, making the model reconfigurable during inference; and-nodes in a higher layer capture holistic shape deformations; one root-node on the top, which is also an or-node, activates one of its child and-nodes to deal with large global variations (e.g. different poses and views). We propose a novel structural optimization algorithm to discriminatively train the And-Or model from weakly annotated data. This algorithm iteratively determines the model structures (e.g. the nodes and their layouts) along with the parameter learning. On several challenging datasets, our model demonstrates the effectiveness to perform robust shape-based object detection against background clutter and outperforms the other state-of-the-art approaches. We also release a new shape database with annotations, which includes more than 1500 challenging shape instances, for recognition and detection. PMID:26353321

  8. 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. PMID:24039322

  9. 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

  10. 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.

  11. 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. PMID:25276772

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

    NASA Astrophysics Data System (ADS)

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

    2015-07-01

    A stochastic 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.

  13. 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

  14. Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks

    NASA Astrophysics Data System (ADS)

    Krasnytska, M.; Berche, B.; Holovatch, Yu; Kenna, R.

    2016-04-01

    We analyse the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as P(k) ˜ k -λ . We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee-Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case λ > 5, reproduces the zeros for the Ising model on a complete graph. For 3 < λ < 5 we derive the λ-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the λ-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when 3 < λ < 5. Whereas in the former case the zeros are purely imaginary, they have a non zero real part in latter case, so that the celebrated Lee-Yang circle theorem is violated.

  15. 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

  16. 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. PMID:25928358

  17. 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.

  18. 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.

  19. 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.

  20. 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…

  1. Modeling macroscopic response of random composites

    SciTech Connect

    Aidun, J.B.; Rintoul, M.D.; Lo, D.C.S.

    1998-02-01

    Preliminary work is presented on an effort to generate synthetic constitutive data for random composite materials. The long-ranged goal is to use the overall response determined from finite element simulations of representative volumes (RV) of the heterogeneous material to construct a homogenized constitutive model. A simple composite of a matrix containing polydispersed spheres was chosen as the first configuration to simulate. Here the accuracy of the numerical simulation tools is tested by determining effective elastic constants of the ordered elastic composite in which equal-sized spheres are arranged in each of three cubic lattice configurations. The resulting anisotropic effective elastic constant values agree with theoretical results to better than 10%, with typical agreement being better than 4%.

  2. 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

    2015-11-01

    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%. PMID:26297890

  3. 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.

  4. 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…

  5. A phase plane graph based model of the ovulatory cycle lacking the "positive feedback" phenomenon

    PubMed Central

    2012-01-01

    When hormones during the ovulatory cycle are shown in phase plane graphs, reported FSH and estrogen values form a specific pattern that resembles the leaning “&" symbol, while LH and progesterone (Pg) values form a "boomerang" shape. Graphs in this paper were made using data reported by Stricker et al. [Clin Chem Lab Med 2006;44:883–887]. These patterns were used to construct a simplistic model of the ovulatory cycle without the conventional "positive feedback" phenomenon. The model is based on few well-established relations: hypothalamic GnRH secretion is increased under estrogen exposure during two weeks that start before the ovulatory surge and lasts till lutheolysis. the pituitary GnRH receptors are so prone to downregulation through ligand binding that this must be important for their function. in several estrogen target tissue progesterone receptor (PgR) expression depends on previous estrogen binding to functional estrogen receptors (ER), while Pg binding to the expressed PgRs reduces both ER and PgR expression. Some key features of the presented model are here listed: High GnRH secretion induced by the recovered estrogen exposure starts in the late follicular phase and lasts till lutheolysis. The LH and FSH surges start due to combination of accumulated pituitary GnRH receptors and increased GnRH secretion. The surges quickly end due to partial downregulation of the pituitary GnRH receptors (64% reduction of the follicular phase pituitary GnRH receptors is needed to explain the reported LH drop after the surge). A strong increase in the lutheal Pg blood level, despite modest decline in LH levels, is explained as delayed expression of pituitary PgRs. Postponed pituitary PgRs expression enforces a negative feedback loop between Pg levels and LH secretions not before the mid lutheal phase. Lutheolysis is explained as a consequence of Pg binding to hypothalamic and pituitary PgRs that reduces local ER expression. When hypothalamic sensitivity to estrogen is

  6. A bond graph model for the sample extraction/injection system of a microsized gas chromatographic instrument

    NASA Astrophysics Data System (ADS)

    Lin, Jie; Wang, Wanjun; Murphy, Michael C.; Overton, Edward

    1996-09-01

    A bond graph model of the sample extraction/injection system of a prototype portable gas chromatographic instrument has been developed. In addition to performing the same functions as current portable gas chromatographs (GCs), the new generation of GC instruments is designed to perform extraction of analytes from liquid and solid samples. The prototype instrument achieves these improvements by taking of advantage of microfabrication technologies and microprocessor control in the design. A novel sample extraction/injection module is essential to the improved performance of the portable instrument, which will include microfabricated components such as inlets, interface chips, fluid channels, control valves, optimal heater/sensor combinations, and multiport connectors. In order to achieve the desired analytical performance, all of the major components are heated to 250 °C during different stages of a sample analysis. Predicting the performance of the system in this operating regime requires the modeling and analysis of system behavior in two interacting energy domains, fluid and thermal. This article represents the first effort to understand the dynamic behavior of the thermofluid aspect of micro-GC instruments and one of the first attempts to apply the widely-used bond graph technique to modeling and analysis of microsized thermofluid systems. Simulation results using the bond graph model closely match available experimental data, with differences typically less than 10%. This demonstrates that fluid dynamic theory for macroscale systems, and the bond graph method based on it, can be readily applied to microscale systems with these dimensions. The bond graph method can be a useful computer-aided design tool for the development of a new generation of truly integrated micro-GC instruments and sensors fabricated with micromachining technology.

  7. Exact Solution of the Gauge Symmetric p-Spin Glass Model on a Complete Graph

    NASA Astrophysics Data System (ADS)

    Korada, Satish Babu; Macris, Nicolas

    2009-07-01

    We consider a gauge symmetric version of the p-spin glass model on a complete graph. The gauge symmetry guarantees the absence of replica symmetry breaking and allows to fully use the interpolation scheme of Guerra (Fields Inst. Commun. 30:161, 2001) to rigorously compute the free energy. In the case of pairwise interactions ( p=2), where we have a gauge symmetric version of the Sherrington-Kirkpatrick model, we get the free energy and magnetization for all values of external parameters. Our analysis also works for even p≥4 except in a range of parameters surrounding the phase transition line, and for odd p≥3 in a more restricted region. We also obtain concentration estimates for the magnetization and overlap parameter that play a crucial role in the proofs for odd p and justify the absence of replica symmetry breaking. Our initial motivation for considering this model came from problems related to communication over a noisy channel, and is briefly explained.

  8. 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.

  9. An accessibility graph-based model to optimize tsunami evacuation sites and routes in Martinique, France

    NASA Astrophysics Data System (ADS)

    Péroche, M.; Leone, F.; Gutton, R.

    2014-01-01

    The risk of tsunami threatens the whole Caribbean coastline especially the Lesser Antilles. The first available models of tsunami propagation estimate that the travel time from the closest seismic sources would only take few minutes to impact the Martinique Island. Considering this threat, the most effective measure is a planned and organized evacuation of the coastal population. This requires an efficient regional warning system, estimation of the maximum expected tsunami flood height, preparation of the population to evacuate, and drawing up of local and regional emergency plans. In order to produce an efficient evacuation plan, we have to assess the number of people at risk, the potential evacuation routes, the safe areas and the available time to evacuate. However, this essential information is still lacking in the French West Indies emergency plans. This paper proposes a model of tsunami evacuation sites accessibility for Martinique directly addressed to decision makers. It is based on a population database at a local scale, the development of connected graphs of roads, the identification of potential safe areas and the velocity setting for pedestrians. Evacuation routes are calculated using the Dijkstra's algorithm which gives the shortest path between areas at risk and designated evacuation sites. The first results allow us to map the theoretical times and routes to keep the exposed population safe and to compare these results with a tsunami travel time scenario.

  10. 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.

  11. 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…

  12. Ancestry assessment using random forest modeling.

    PubMed

    Hefner, Joseph T; Spradley, M Kate; Anderson, Bruce

    2014-05-01

    A skeletal assessment of ancestry relies on morphoscopic traits and skeletal measurements. Using a sample of American Black (n = 38), American White (n = 39), and Southwest Hispanics (n = 72), the present study investigates whether these data provide similar biological information and combines both data types into a single classification using a random forest model (RFM). Our results indicate that both data types provide similar information concerning the relationships among population groups. Also, by combining both in an RFM, the correct allocation of ancestry for an unknown cranium increases. The distribution of cross-validated grouped cases correctly classified using discriminant analyses and RFMs ranges between 75.4% (discriminant function analysis, morphoscopic data only) and 89.6% (RFM). Unlike the traditional, experience-based approach using morphoscopic traits, the inclusion of both data types in a single analysis is a quantifiable approach accounting for more variation within and between groups, reducing misclassification rates, and capturing aspects of cranial shape, size, and morphology. PMID:24502438

  13. A recursive model-reduction method for approximate inference in Gaussian Markov random fields.

    PubMed

    Johnson, Jason K; Willsky, Alan S

    2008-01-01

    This paper presents recursive cavity modeling--a principled, tractable approach to approximate, near-optimal inference for large Gauss-Markov random fields. The main idea is to subdivide the random field into smaller subfields, constructing cavity models which approximate these subfields. Each cavity model is a concise, yet faithful, model for the surface of one subfield sufficient for near-optimal inference in adjacent subfields. This basic idea leads to a tree-structured algorithm which recursively builds a hierarchy of cavity models during an "upward pass" and then builds a complementary set of blanket models during a reverse "downward pass." The marginal statistics of individual variables can then be approximated using their blanket models. Model thinning plays an important role, allowing us to develop thinned cavity and blanket models thereby providing tractable approximate inference. We develop a maximum-entropy approach that exploits certain tractable representations of Fisher information on thin chordal graphs. Given the resulting set of thinned cavity models, we also develop a fast preconditioner, which provides a simple iterative method to compute optimal estimates. Thus, our overall approach combines recursive inference, variational learning and iterative estimation. We demonstrate the accuracy and scalability of this approach in several challenging, large-scale remote sensing problems. PMID:18229805

  14. 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.

  15. Graph-based unsupervised segmentation algorithm for cultured neuronal networks' structure characterization and modeling.

    PubMed

    de Santos-Sierra, Daniel; Sendiña-Nadal, Irene; Leyva, Inmaculada; Almendral, Juan A; Ayali, Amir; Anava, Sarit; Sánchez-Ávila, Carmen; Boccaletti, Stefano

    2015-06-01

    Large scale phase-contrast images taken at high resolution through the life of a cultured neuronal network are analyzed by a graph-based unsupervised segmentation algorithm with a very low computational cost, scaling linearly with the image size. The processing automatically retrieves the whole network structure, an object whose mathematical representation is a matrix in which nodes are identified neurons or neurons' clusters, and links are the reconstructed connections between them. The algorithm is also able to extract any other relevant morphological information characterizing neurons and neurites. More importantly, and at variance with other segmentation methods that require fluorescence imaging from immunocytochemistry techniques, our non invasive measures entitle us to perform a longitudinal analysis during the maturation of a single culture. Such an analysis furnishes the way of individuating the main physical processes underlying the self-organization of the neurons' ensemble into a complex network, and drives the formulation of a phenomenological model yet able to describe qualitatively the overall scenario observed during the culture growth. PMID:25393432

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

    PubMed

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

    2015-08-01

    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. PMID:26736778

  17. 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.

  18. 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

  19. 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.

  20. 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

    2015-01-01

    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

  1. Disentangling giant component and finite cluster contributions in sparse random matrix spectra

    NASA Astrophysics Data System (ADS)

    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.

  2. 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. PMID:27176257

  3. Discrete Signal Processing on Graphs: Sampling Theory

    NASA Astrophysics Data System (ADS)

    Chen, Siheng; Varma, Rohan; Sandryhaila, Aliaksei; Kovacevic, Jelena

    2015-12-01

    We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that perfect recovery is possible for graph signals bandlimited under the graph Fourier transform. The sampled signal coefficients form a new graph signal, whose corresponding graph structure preserves the first-order difference of the original graph signal. For general graphs, an optimal sampling operator based on experimentally designed sampling is proposed to guarantee perfect recovery and robustness to noise; for graphs whose graph Fourier transforms are frames with maximal robustness to erasures as well as for Erd\\H{o}s-R\\'enyi graphs, random sampling leads to perfect recovery with high probability. We further establish the connection to the sampling theory of finite discrete-time signal processing and previous work on signal recovery on graphs. To handle full-band graph signals, we propose a graph filter bank based on sampling theory on graphs. Finally, we apply the proposed sampling theory to semi-supervised classification on online blogs and digit images, where we achieve similar or better performance with fewer labeled samples compared to previous work.

  4. Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable

    ERIC Educational Resources Information Center

    du Toit, Stephen H. C.; Cudeck, Robert

    2009-01-01

    A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution…

  5. A Markov Random Field Model-Based Approach To Image Interpretation

    NASA Astrophysics Data System (ADS)

    Zhang, Jun; Modestino, James W.

    1989-11-01

    In this paper, a Markov random field (MRF) model-based approach to automated image interpretation is described and demonstrated as a region-based scheme. In this approach, an image is first segmented into a collection of disjoint regions which form the nodes of an adjacency graph. Image interpretation is then achieved through assigning object labels, or interpretations, to the segmented regions, or nodes, using domain knowledge, extracted feature measurements and spatial relationships between the various regions. The interpretation labels are modeled as a MRF on the corresponding adjacency graph and the image interpretation problem is formulated as a maximum a posteriori (MAP) estimation rule. Simulated annealing is used to find the best realization, or optimal MAP interpretation. Through the MRF model, this approach also provides a systematic method for organizing and representing domain knowledge through the clique functions of the pdf of the underlying MRF. Results of image interpretation experiments performed on synthetic and real-world images using this approach are described and appear promising.

  6. 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

  7. 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

  8. Random effects and shrinkage estimation in capture-recapture models

    USGS Publications Warehouse

    Royle, J. Andrew; Link, W.A.

    2002-01-01

    We discuss the analysis of random effects in capture-recapture models, and outline Bayesian and frequentists approaches to their analysis. Under a normal model, random effects estimators derived from Bayesian or frequentist considerations have a common form as shrinkage estimators. We discuss some of the difficulties of analysing random effects using traditional methods, and argue that a Bayesian formulation provides a rigorous framework for dealing with these difficulties. In capture-recapture models, random effects may provide a parsimonious compromise between constant and completely time-dependent models for the parameters (e.g. survival probability). We consider application of random effects to band-recovery models, although the principles apply to more general situations, such as Cormack-Jolly-Seber models. We illustrate these ideas using a commonly analysed band recovery data set.

  9. Using random forest to model the domain applicability of another random forest model.

    PubMed

    Sheridan, Robert P

    2013-11-25

    In QSAR, a statistical model is generated from a training set of molecules (represented by chemical descriptors) and their biological activities. We will call this traditional type of QSAR model an "activity model". The activity model can be used to predict the activities of molecules not in the training set. A relatively new subfield for QSAR is domain applicability. The aim is to estimate the reliability of prediction of a specific molecule on a specific activity model. A number of different metrics have been proposed in the literature for this purpose. It is desirable to build a quantitative model of reliability against one or more of these metrics. We can call this an "error model". A previous publication from our laboratory (Sheridan J. Chem. Inf. Model., 2012, 52, 814-823.) suggested the simultaneous use of three metrics would be more discriminating than any one metric. An error model could be built in the form of a three-dimensional set of bins. When the number of metrics exceeds three, however, the bin paradigm is not practical. An obvious solution for constructing an error model using multiple metrics is to use a QSAR method, in our case random forest. In this paper we demonstrate the usefulness of this paradigm, specifically for determining whether a useful error model can be built and which metrics are most useful for a given problem. For the ten data sets and for the seven metrics we examine here, it appears that it is possible to construct a useful error model using only two metrics (TREE_SD and PREDICTED). These do not require calculating similarities/distances between the molecules being predicted and the molecules used to build the activity model, which can be rate-limiting. PMID:24152204

  10. Simulation of 3D infrared scenes using random fields model

    NASA Astrophysics Data System (ADS)

    Shao, Xiaopeng; Zhang, Jianqi

    2001-09-01

    Analysis and simulation of smart munitions requires imagery for the munition's sensor to view. The traditional infrared background simulations are always limited in the plane scene studies. A new method is described to synthesize the images in 3D view and with various terrains texture. We develop the random fields model and temperature fields to simulate 3D infrared scenes. Generalized long-correlation (GLC) model, one of random field models, will generate both the 3D terrains skeleton data and the terrains texture in this work. To build the terrain mesh with the random fields, digital elevation models (DEM) are introduced in the paper. And texture mapping technology will perform the task of pasting the texture in the concavo-convex surfaces of the 3D scene. The simulation using random fields model is a very available method to produce 3D infrared scene with great randomicity and reality.

  11. A Model for Random Student Drug Testing

    ERIC Educational Resources Information Center

    Nelson, Judith A.; Rose, Nancy L.; Lutz, Danielle

    2011-01-01

    The purpose of this case study was to examine random student drug testing in one school district relevant to: (a) the perceptions of students participating in competitive extracurricular activities regarding drug use and abuse; (b) the attitudes and perceptions of parents, school staff, and community members regarding student drug involvement; (c)…

  12. 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.

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

    NASA Astrophysics Data System (ADS)

    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.

  14. 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. PMID:23944412

  15. 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…

  16. 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. PMID:27089174

  17. Finding long cycles in graphs

    NASA Astrophysics Data System (ADS)

    Marinari, Enzo; Semerjian, Guilhem; van Kerrebroeck, Valery

    2007-06-01

    We analyze the problem of discovering long cycles inside a graph. We propose and test two algorithms for this task. The first one is based on recent advances in statistical mechanics and relies on a message passing procedure. The second follows a more standard Monte Carlo Markov chain strategy. Special attention is devoted to Hamiltonian cycles of (nonregular) random graphs of minimal connectivity equal to 3.

  18. Phase Structure of the Random Zq Models in 2D

    NASA Astrophysics Data System (ADS)

    Sasamoto, T.; Nishimori, H.

    We discuss the phase diagram of the random Zq models in two dimensions. It is argued that, when q is large enough, there exist three phases in the phase diagram with two axes being the temperature and the strength of randomness. Our conlusions are derived based on the application of the duality arguments for random systems, which have been formulated recently by Maillard et al.

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

    SciTech Connect

    Hong, Seokyong; Sukumar, Sreenivas Rangan; Vatsavai, Raju

    2016-01-01

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

  20. Sums of random matrices and the Potts model on random planar maps

    NASA Astrophysics Data System (ADS)

    Atkin, Max R.; Niedner, Benjamin; Wheater, John F.

    2016-05-01

    We compute the partition function of the q-states Potts model on a random planar lattice with p≤slant q allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix model representation in the planar limit, generalising a result by Voiculescu for the addition of random matrices to a situation beyond free probability theory. We show that the partition functions with p and q - p colours on the boundary are related algebraically. Finally, we investigate the phase diagram of the model when 0≤slant q≤slant 4 and comment on the conformal field theory description of the critical points.

  1. 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. PMID:26736726

  2. Signal Detection Models with Random Participant and Item Effects

    ERIC Educational Resources Information Center

    Rouder, Jeffrey N.; Lu, Jun; Sun, Dongchu; Speckman, Paul; Morey, Richard; Naveh-Benjamin, Moshe

    2007-01-01

    The theory of signal detection is convenient for measuring mnemonic ability in recognition memory paradigms. In these paradigms, randomly selected participants are asked to study randomly selected items. In practice, researchers aggregate data across items or participants or both. The signal detection model is nonlinear; consequently, analysis…

  3. Analog model for quantum gravity effects: phonons in random fluids.

    PubMed

    Krein, G; Menezes, G; Svaiter, N F

    2010-09-24

    We describe an analog model for quantum gravity effects in condensed matter physics. The situation discussed is that of phonons propagating in a fluid with a random velocity wave equation. We consider that there are random fluctuations in the reciprocal of the bulk modulus of the system and study free phonons in the presence of Gaussian colored noise with zero mean. We show that, in this model, after performing the random averages over the noise function a free conventional scalar quantum field theory describing free phonons becomes a self-interacting model. PMID:21230759

  4. Estimating the minimum control count of random network models

    PubMed Central

    Ruths, Derek; Ruths, Justin

    2016-01-01

    The study of controllability of complex networks has introduced the minimum number of controls required for full controllability as a new network measure of interest. This network measure, like many others, is non-trivial to compute. As a result, establishing the significance of minimum control counts (MCCs) in real networks using random network null models is expensive. Here we derive analytic estimates for the expected MCCs of networks drawn from three commonly-used random network models. Our estimates show good agreement with exact control counts. Furthermore, the analytic expressions we derive offer insights into the structures within each random network model that induce the need for controls. PMID:26817434

  5. A numerical study of the 3D random interchange and random loop models

    NASA Astrophysics Data System (ADS)

    Barp, Alessandro; Barp, Edoardo Gabriele; Briol, François-Xavier; Ueltschi, Daniel

    2015-08-01

    We have studied numerically the random interchange model and related loop models on the three-dimensional cubic lattice. We have determined the transition time for the occurrence of long loops. The joint distribution of the lengths of long loops is Poisson-Dirichlet with parameter 1 or \\frac{1}{2}.

  6. 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.

  7. "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.

  8. 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.

  9. An instrumental variable random-coefficients model for binary outcomes

    PubMed Central

    Chesher, Andrew; Rosen, Adam M

    2014-01-01

    In this paper, we study a random-coefficients model for a binary outcome. We allow for the possibility that some or even all of the explanatory variables are arbitrarily correlated with the random coefficients, thus permitting endogeneity. We assume the existence of observed instrumental variables Z that are jointly independent with the random coefficients, although we place no structure on the joint determination of the endogenous variable X and instruments Z, as would be required for a control function approach. The model fits within the spectrum of generalized instrumental variable models, and we thus apply identification results from our previous studies of such models to the present context, demonstrating their use. Specifically, we characterize the identified set for the distribution of random coefficients in the binary response model with endogeneity via a collection of conditional moment inequalities, and we investigate the structure of these sets by way of numerical illustration. PMID:25798048

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

    NASA Astrophysics Data System (ADS)

    Ziemann, Amanda K.; Messinger, David W.

    2014-06-01

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

  11. Human sexual contact network as a bipartite graph

    NASA Astrophysics Data System (ADS)

    Ergün, Güler

    2002-05-01

    A simple model to encapsulate the essential growth properties of the web of human sexual contacts is presented. In the model only heterosexual connection is considered and represented by a random growing bipartite graph where both male-female contact networks grow simultaneously. The time evolution of the model is analysed by a rate equation approach leading to confirm that male and female sexual contact distributions decay as power laws with exponents depending on influx and charisma of the sexes.

  12. Quantum Ergodicity for Quantum Graphs without Back-Scattering

    NASA Astrophysics Data System (ADS)

    Brammall, Matthew; Winn, B.

    2016-06-01

    We give an estimate of the quantum variance for $d$-regular graphs quantised with boundary scattering matrices that prohibit back-scattering. For families of graphs that are expanders, with few short cycles, our estimate leads to quantum ergodicity for these families of graphs. Our proof is based on a uniform control of an associated random walk on the bonds of the graph. We show that recent constructions of Ramanujan graphs, and asymptotically almost surely, random $d$-regular graphs, satisfy the necessary conditions to conclude that quantum ergodicity holds.

  13. Weighted Hybrid Decision Tree Model for Random Forest Classifier

    NASA Astrophysics Data System (ADS)

    Kulkarni, Vrushali Y.; Sinha, Pradeep K.; Petare, Manisha C.

    2016-06-01

    Random Forest is an ensemble, supervised machine learning algorithm. An ensemble generates many classifiers and combines their results by majority voting. Random forest uses decision tree as base classifier. In decision tree induction, an attribute split/evaluation measure is used to decide the best split at each node of the decision tree. The generalization error of a forest of tree classifiers depends on the strength of the individual trees in the forest and the correlation among them. The work presented in this paper is related to attribute split measures and is a two step process: first theoretical study of the five selected split measures is done and a comparison matrix is generated to understand pros and cons of each measure. These theoretical results are verified by performing empirical analysis. For empirical analysis, random forest is generated using each of the five selected split measures, chosen one at a time. i.e. random forest using information gain, random forest using gain ratio, etc. The next step is, based on this theoretical and empirical analysis, a new approach of hybrid decision tree model for random forest classifier is proposed. In this model, individual decision tree in Random Forest is generated using different split measures. This model is augmented by weighted voting based on the strength of individual tree. The new approach has shown notable increase in the accuracy of random forest.

  14. Application of Poisson random effect models for highway network screening.

    PubMed

    Jiang, Ximiao; Abdel-Aty, Mohamed; Alamili, Samer

    2014-02-01

    In recent years, Bayesian random effect models that account for the temporal and spatial correlations of crash data became popular in traffic safety research. This study employs random effect Poisson Log-Normal models for crash risk hotspot identification. Both the temporal and spatial correlations of crash data were considered. Potential for Safety Improvement (PSI) were adopted as a measure of the crash risk. Using the fatal and injury crashes that occurred on urban 4-lane divided arterials from 2006 to 2009 in the Central Florida area, the random effect approaches were compared to the traditional Empirical Bayesian (EB) method and the conventional Bayesian Poisson Log-Normal model. A series of method examination tests were conducted to evaluate the performance of different approaches. These tests include the previously developed site consistence test, method consistence test, total rank difference test, and the modified total score test, as well as the newly proposed total safety performance measure difference test. Results show that the Bayesian Poisson model accounting for both temporal and spatial random effects (PTSRE) outperforms the model that with only temporal random effect, and both are superior to the conventional Poisson Log-Normal model (PLN) and the EB model in the fitting of crash data. Additionally, the method evaluation tests indicate that the PTSRE model is significantly superior to the PLN model and the EB model in consistently identifying hotspots during successive time periods. The results suggest that the PTSRE model is a superior alternative for road site crash risk hotspot identification. PMID:24269863

  15. Fluorescence microscopy image noise reduction using a stochastically-connected random field model

    PubMed Central

    Haider, S. A.; Cameron, A.; Siva, P.; Lui, D.; Shafiee, M. J.; Boroomand, A.; Haider, N.; Wong, A.

    2016-01-01

    Fluorescence microscopy is an essential part of a biologist’s toolkit, allowing assaying of many parameters like subcellular localization of proteins, changes in cytoskeletal dynamics, protein-protein interactions, and the concentration of specific cellular ions. A fundamental challenge with using fluorescence microscopy is the presence of noise. This study introduces a novel approach to reducing noise in fluorescence microscopy images. The noise reduction problem is posed as a Maximum A Posteriori estimation problem, and solved using a novel random field model called stochastically-connected random field (SRF), which combines random graph and field theory. Experimental results using synthetic and real fluorescence microscopy data show the proposed approach achieving strong noise reduction performance when compared to several other noise reduction algorithms, using quantitative metrics. The proposed SRF approach was able to achieve strong performance in terms of signal-to-noise ratio in the synthetic results, high signal to noise ratio and contrast to noise ratio in the real fluorescence microscopy data results, and was able to maintain cell structure and subtle details while reducing background and intra-cellular noise. PMID:26884148

  16. 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.

  17. 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.

  18. A graph model, ParaDiGM, and a software tool, VISA, for the representation, design, and simulation of parallel, distributed computations

    SciTech Connect

    Demeure, I.M.

    1989-01-01

    The research presented here is concerned with representation techniques and tools to support the design, prototyping, simulation, and evaluation of message-based parallel, distributed computations. The author describes ParaDiGM-Parallel, Distributed computation Graph Model-a visual representation technique for parallel, message-based distributed computations. ParaDiGM provides several views of a computation depending on the aspect of concern. It is made of two complementary submodels, the DCPG-Distributed Computing Precedence Graph-model, and the PAM-Process Architecture Model-model. DCPGs are precedence graphs used to express the functionality of a computation in terms of tasks, message-passing, and data. PAM graphs are used to represent the partitioning of a computation into schedulable units or processes, and the pattern of communication among those units. There is a natural mapping between the two models. He illustrates the utility of ParaDiGM as a representation technique by applying it to various computations (e.g., an adaptive global optimization algorithm, the client-server model). ParaDiGM representations are concise. They can be used in documenting the design and the implementation of parallel, distributed computations, in describing such computations to colleagues, and in comparing and contrasting various implementations of the same computation. He then describes VISA-VISual Assistant, a software tool to support the design, prototyping, and simulation of message-based parallel, distributed computations. VISA is based on the ParaDiGM model. In particular, it supports the editing of ParaDiGM graphs to describe the computations of interest, and the animation of these graphs to provide visual feedback during simulations. The graphs are supplemented with various attributes, simulation parameters, and interpretations which are procedures that can be executed by VISA.

  19. Disorder Identification in Hysteresis Data: Recognition Analysis of the Random-Bond-Random-Field Ising Model

    SciTech Connect

    Ovchinnikov, O. S.; Jesse, S.; Kalinin, S. V.; Bintacchit, P.; Trolier-McKinstry, S.

    2009-10-09

    An approach for the direct identification of disorder type and strength in physical systems based on recognition analysis of hysteresis loop shape is developed. A large number of theoretical examples uniformly distributed in the parameter space of the system is generated and is decorrelated using principal component analysis (PCA). The PCA components are used to train a feed-forward neural network using the model parameters as targets. The trained network is used to analyze hysteresis loops for the investigated system. The approach is demonstrated using a 2D random-bond-random-field Ising model, and polarization switching in polycrystalline ferroelectric capacitors.

  20. 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.

  1. Quantum Ergodicity on Graphs

    NASA Astrophysics Data System (ADS)

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

    2008-12-01

    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 σ 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.

  2. A Gompertzian model with random effects to cervical cancer growth

    NASA Astrophysics Data System (ADS)

    Mazlan, Mazma Syahidatul Ayuni; Rosli, Norhayati

    2015-05-01

    In this paper, a Gompertzian model with random effects is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via maximum likehood estimation. We apply 4-stage Runge-Kutta (SRK4) for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of the cervical cancer growth. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits.

  3. A Gompertzian model with random effects to cervical cancer growth

    SciTech Connect

    Mazlan, Mazma Syahidatul Ayuni; Rosli, Norhayati

    2015-05-15

    In this paper, a Gompertzian model with random effects is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via maximum likehood estimation. We apply 4-stage Runge-Kutta (SRK4) for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of the cervical cancer growth. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits.

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

    PubMed

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

    2016-01-01

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

  5. Topology regulates pattern formation capacity of binary cellular automata on graphs

    NASA Astrophysics Data System (ADS)

    Marr, Carsten; Hütt, Marc-Thorsten

    2005-08-01

    We study the effect of topology variation on the dynamic behavior of a system with local update rules. We implement one-dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree-dependent rules, each containing a single parameter. We observe that changes in graph topology induce transitions between different dynamic domains (Wolfram classes) without a formal change in the update rule. Along with topological variations, we study the pattern formation capacities of regular, random, small-world and scale-free graphs. Pattern formation capacity is quantified in terms of two entropy measures, which for standard cellular automata allow a qualitative distinction between the four Wolfram classes. A mean-field model explains the dynamic behavior of random graphs. Implications for our understanding of information transport through complex, network-based systems are discussed.

  6. Probabilistic solution of random SI-type epidemiological models using the Random Variable Transformation technique

    NASA Astrophysics Data System (ADS)

    Casabán, M.-C.; Cortés, J.-C.; Romero, J.-V.; Roselló, M.-D.

    2015-07-01

    This paper presents a full probabilistic description of the solution of random SI-type epidemiological models which are based on nonlinear differential equations. This description consists of determining: the first probability density function of the solution in terms of the density functions of the diffusion coefficient and the initial condition, which are assumed to be independent random variables; the expectation and variance functions of the solution as well as confidence intervals and, finally, the distribution of time until a given proportion of susceptibles remains in the population. The obtained formulas are general since they are valid regardless the probability distributions assigned to the random inputs. We also present a pair of illustrative examples including in one of them the application of the theoretical results to model the diffusion of a technology using real data.

  7. Variational Bounds for the Generalized Random Energy Model

    NASA Astrophysics Data System (ADS)

    Giardinà, Cristian; Starr, Shannon

    2007-04-01

    We compute the pressure of the random energy model (REM) and generalized random energy model (GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra's "broken replica symmetry bounds," and identify the random probability cascade as the appropriate random overlap structure for the model. For the REM the lower bound is obtained, in the high temperature regime using Talagrand's concentration of measure inequality, and in the low temperature regime using convexity and the high temperature formula. The lower bound for the GREM follows from the lower bound for the REM by induction. While the argument for the lower bound is fairly standard, our proof of the upper bound is new.

  8. Modelling Of Random Vertical Irregularities Of Railway Tracks

    NASA Astrophysics Data System (ADS)

    Podwórna, M.

    2015-08-01

    The study presents state-of-the-art in analytical and numerical modelling of random vertical irregularities of continuously welded ballasted railway tracks. The common model of railway track irregularity vertical profiles is applied, in the form of a stationary and ergodic Gaussian process in space. Random samples of track irregularity vertical profiles are generated with the Monte-Carlo method. Based on the numerical method developed in the study, the minimum and recommended sampling number required in the random analysis of railway bridges and number of frequency increments (harmonic components) in track irregularity vertical profiles simulation are determined. The lower and upper limits of wavelengths are determined based on the literature studies. The approach yields track irregularity random samples close to reality. The track irregularity model developed in the study can be used in the dynamic analysis of railway bridge / track structure / highspeed train systems.

  9. A random spatial network model based on elementary postulates

    USGS Publications Warehouse

    Karlinger, M.R.; Troutman, B.M.

    1989-01-01

    In contrast to the random topology model, this model ascribes a unique spatial specification to generated drainage networks, a distinguishing property of some network growth models. The simplicity of the postulates creates an opportunity for potential analytic investigations of the probabilistic structure of the drainage networks, while the spatial specification enables analyses of spatially dependent network properties. In the random topology model all drainage networks, conditioned on magnitude (number of first-order streams), are equally likely, whereas in this model all spanning trees of a grid, conditioned on area and drainage density, are equally likely. As a result, link lengths in the generated networks are not independent, as usually assumed in the random topology model. -from Authors

  10. 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.

  11. Random walks on networks

    NASA Astrophysics Data System (ADS)

    Donnelly, Isaac

    Random walks on lattices are a well used model for diffusion on continuum. They have been to model subdiffusive systems, systems with forcing and reactions as well as a combination of the three. We extend the traditional random walk framework to the network to obtain novel results. As an example due to the small graph diameter, the early time behaviour of subdiffusive dynamics dominates the observed system which has implications for models of the brain or airline networks. I would like to thank the Australian American Fulbright Association.

  12. Hyperspectral Data Classification Using Factor Graphs

    NASA Astrophysics Data System (ADS)

    Makarau, A.; Müller, R.; Palubinskas, G.; Reinartz, P.

    2012-07-01

    Accurate classification of hyperspectral data is still a competitive task and new classification methods are developed to achieve desired tasks of hyperspectral data use. The objective of this paper is to develop a new method for hyperspectral data classification ensuring the classification model properties like transferability, generalization, probabilistic interpretation, etc. While factor graphs (undirected graphical models) are unfortunately not widely employed in remote sensing tasks, these models possess important properties such as representation of complex systems to model estimation/decision making tasks. In this paper we present a new method for hyperspectral data classification using factor graphs. Factor graph (a bipartite graph consisting of variables and factor vertices) allows factorization of a more complex function leading to definition of variables (employed to store input data), latent variables (allow to bridge abstract class to data), and factors (defining prior probabilities for spectral features and abstract classes; input data mapping to spectral features mixture and further bridging of the mixture to an abstract class). Latent variables play an important role by defining two-level mapping of the input spectral features to a class. Configuration (learning) on training data of the model allows calculating a parameter set for the model to bridge the input data to a class. The classification algorithm is as follows. Spectral bands are separately pre-processed (unsupervised clustering is used) to be defined on a finite domain (alphabet) leading to a representation of the data on multinomial distribution. The represented hyperspectral data is used as input evidence (evidence vector is selected pixelwise) in a configured factor graph and an inference is run resulting in the posterior probability. Variational inference (Mean field) allows to obtain plausible results with a low calculation time. Calculating the posterior probability for each class

  13. Using graph models to find transcription factor modules: the hitting set problem and an exact algorithm.

    PubMed

    Lu, Songjian; Lu, Xinghua

    2013-01-01

    : Systematically perturbing a cellular system and monitoring the effects of the perturbations on gene expression provide a powerful approach to study signal transduction in gene expression systems. A critical step of revealing a signal transduction pathway regulating gene expression is to identify transcription factors transmitting signals in the system. In this paper, we address the task of identifying modules of cooperative transcription factors based on results derived from systems-biology experiments at two levels: First, a graph algorithm is developed to identify a minimum set of co-operative TFs that covers the differentially expressed genes under each systematic perturbation. Second, using a clique-finding approach, modules of TFs that tend to consistently cooperate together under various perturbations are further identified. Our results indicate that this approach is capable of identifying many known TF modules based on the individual experiment; thus we provide a novel graph-based method of identifying context-specific and highly reused TF-modules. PMID:23324335

  14. A population growth model forced by random, episodic disturbances

    NASA Astrophysics Data System (ADS)

    Peckham, S. D.

    2011-12-01

    As a first step to quantify and better understand the nature of thresholds in ecosystems, a prototype population dynamics model has been developed and analyzed for the case where a population is subjected to random, episodic disturbances. This model assumes that disturbances occur at random times (following a Poisson event process) and have random magnitudes that determine the fraction of the population that survives the disturbance. Disturbances may be events such as fire, drought, disease or infestation. Between disturbances, the model assumes that population growth is deterministic and can be modeled by an exponential or logistic equation. The model is characterized by time, t, and four other parameters: the initial population size, N0, the per capita growth rate, r, the expected number of disturbance events per unit time, λ , and μ = E(X), where X is the random fraction (between 0 and 1) of the population that survives a given disturbance. What is nice about this simple, stochastic model is that it is mathematically tractable and clearly exhibits threshold behavior that can be computed explicitly in terms of the model parameters. In particular, the long-term behavior of the model is characterized by an easily-computed indicator that is a function of the model parameters. Whenever the model parameters are such that this indicator is less than zero, the expected value of the random population size declines over time and is unsustainable. But whenever it is greater than zero, the expected population size grows, despite the random disturbances. The case where the indicator is zero therefore represents a type of critical threshold for this problem that determines whether or not the population is likely to survive the disturbances. A number of analytic results will be presented along with numerical results from a large number of simulations.

  15. The melting phenomenon in random-walk model of DNA

    SciTech Connect

    Hayrapetyan, G. N.; Mamasakhlisov, E. Sh.; Papoyan, Vl. V.; Poghosyan, S. S.

    2012-10-15

    The melting phenomenon in a double-stranded homopolypeptide is considered. The relative distance between the corresponding monomers of two polymer chains is modeled by the two-dimensional random walk on the square lattice. Returns of the random walk to the origin describe the formation of hydrogen bonds between complementary units. To take into account the two competing interactions of monomers inside the chains, we obtain a completely denatured state at finite temperature T{sub c}.

  16. Simulation of Radar Rainfall Fields: A Random Error Model

    NASA Astrophysics Data System (ADS)

    Aghakouchak, A.; Habib, E.; Bardossy, A.

    2008-12-01

    Precipitation is a major input in hydrological and meteorological models. It is believed that uncertainties due to input data will propagate in modeling hydrologic processes. Stochastically generated rainfall data are used as input to hydrological and meteorological models to assess model uncertainties and climate variability in water resources systems. The superposition of random errors of different sources is one of the main factors in uncertainty of radar estimates. One way to express these uncertainties is to stochastically generate random error fields to impose them on radar measurements in order to obtain an ensemble of radar rainfall estimates. In the method introduced here, the random error consists of two components: purely random error and dependent error on the indicator variable. Model parameters of the error model are estimated using a heteroscedastic maximum likelihood model in order to account for variance heterogeneity in radar rainfall error estimates. When reflectivity values are considered, the exponent and multiplicative factor of the Z-R relationship are estimated simultaneously with the model parameters. The presented model performs better compared to the previous approaches that generally result in unaccounted heteroscedasticity in error fields and thus radar ensemble.

  17. 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. PMID:26113811

  18. 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

  19. Stability and dynamical properties of material flow systems on random networks

    NASA Astrophysics Data System (ADS)

    Anand, K.; Galla, T.

    2009-04-01

    The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are characteristic of flow networks in economic, ecological and biological systems. Based on results from random matrix theory, we work out the phase diagram of such systems defined on extensively connected random graphs, and study in detail how the choice of control policies and the network structure affects stability. We also present results for more complex topologies of the underlying graph, focussing on finitely connected Erdös-Réyni graphs, Small-World Networks and Barabási-Albert scale-free networks. Results indicate that variability of input-output matrix elements, and random structures of the underlying graph tend to make the system less stable, while fast price dynamics or strong responsiveness to stock accumulation promote stability.

  20. A conceptual model for quantifying connectivity using graph theory and cellular (per-pixel) approach

    NASA Astrophysics Data System (ADS)

    Singh, Manudeo; Sinha, Rajiv; Tandon, Sampat K.

    2016-04-01

    pathways will show changes under different LULC conditions even if the slope remains the same. The graphical approach provides the statistics of connected and disconnected graph elements (edges, nodes) and graph components, thereby allowing the quantification of structural connectivity. This approach also quantifies the dynamic connectivity by allowing the measurement of the fluxes (e.g. via hydrographs or sedimentographs) at any node as well as at any system outlet. The contribution of any sub-system can be understood by removing the remaining sub-systems which can be conveniently achieved by masking associated graph elements.

  1. Fitting Partially Nonlinear Random Coefficient Models as SEMs

    ERIC Educational Resources Information Center

    Harring, Jeffrey R.; Cudeck, Robert; du Toit, Stephen H. C.

    2006-01-01

    The nonlinear random coefficient model has become increasingly popular as a method for describing individual differences in longitudinal research. Although promising, the nonlinear model it is not utilized as often as it might be because software options are still somewhat limited. In this article we show that a specialized version of the model…

  2. A new efficient algorithm generating all minimal S-T cut-sets in a graph-modeled network

    NASA Astrophysics Data System (ADS)

    Malinowski, Jacek

    2016-06-01

    A new algorithm finding all minimal s-t cut-sets in a graph-modeled network with failing links and nodes is presented. It is based on the analysis of the tree of acyclic s-t paths connecting a given pair of nodes in the considered structure. The construction of such a tree is required by many existing algorithms for s-t cut-sets generation in order to eliminate "stub" edges or subgraphs through which no acyclic path passes. The algorithm operates on the acyclic paths tree alone, i.e. no other analysis of the network's topology is necessary. It can be applied to both directed and undirected graphs, as well as partly directed ones. It is worth noting that the cut-sets can be composed of both links and failures, while many known algorithms do not take nodes into account, which is quite restricting from the practical point of view. The developed cut-sets generation technique makes the algorithm significantly faster than most of the previous methods, as proved by the experiments.

  3. 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). PMID:26985826

  4. A Directed Acyclic Graph-Large Margin Distribution Machine Model for Music Symbol Classification

    PubMed Central

    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). PMID:26985826

  5. QSAR as a random event: modeling of nanoparticles uptake in PaCa2 cancer cells.

    PubMed

    Toropov, Andrey A; Toropova, Alla P; Puzyn, Tomasz; Benfenati, Emilio; Gini, Giuseppina; Leszczynska, Danuta; Leszczynski, Jerzy

    2013-06-01

    Quantitative structure-property/activity relationships (QSPRs/QSARs) are a tool to predict various endpoints for various substances. The "classic" QSPR/QSAR analysis is based on the representation of the molecular structure by the molecular graph. However, simplified molecular input-line entry system (SMILES) gradually becomes most popular representation of the molecular structure in the databases available on the Internet. Under such circumstances, the development of molecular descriptors calculated directly from SMILES becomes attractive alternative to "classic" descriptors. The CORAL software (http://www.insilico.eu/coral) is provider of SMILES-based optimal molecular descriptors which are aimed to correlate with various endpoints. We analyzed data set on nanoparticles uptake in PaCa2 pancreatic cancer cells. The data set includes 109 nanoparticles with the same core but different surface modifiers (small organic molecules). The concept of a QSAR as a random event is suggested in opposition to "classic" QSARs which are based on the only one distribution of available data into the training and the validation sets. In other words, five random splits into the "visible" training set and the "invisible" validation set were examined. The SMILES-based optimal descriptors (obtained by the Monte Carlo technique) for these splits are calculated with the CORAL software. The statistical quality of all these models is good. PMID:23566368

  6. 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.

  7. Random and Targeted Interventions for Epidemic Control in Metapopulation Models

    NASA Astrophysics Data System (ADS)

    Tanaka, Gouhei; Urabe, Chiyori; Aihara, Kazuyuki

    2014-07-01

    In general, different countries and communities respond to epidemics in accordance with their own control plans and protocols. However, owing to global human migration and mobility, strategic planning for epidemic control measures through the collaboration of relevant public health administrations is gaining importance for mitigating and containing large-scale epidemics. Here, we present a framework to evaluate the effectiveness of random (non-strategic) and targeted (strategic) epidemic interventions for spatially separated patches in metapopulation models. For a random intervention, we analytically derive the critical fraction of patches that receive epidemic interventions, above which epidemics are successfully contained. The analysis shows that the heterogeneity of patch connectivity makes it difficult to contain epidemics under the random intervention. We demonstrate that, particularly in such heterogeneously connected networks, targeted interventions are considerably effective compared to the random intervention. Our framework is useful for identifying the target areas where epidemic control measures should be focused.

  8. 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

  9. Insight into earthquake sequencing: analysis and interpretation of time-series constructed from the directed graph of the Markov chain model

    NASA Astrophysics Data System (ADS)

    Cavers, M. S.; Vasudevan, K.

    2015-02-01

    Directed graph representation of a Markov chain model to study global earthquake sequencing leads to a time-series of state-to-state transition probabilities that includes the spatio-temporally linked recurrent events in the record-breaking sense. A state refers to a configuration comprised of zones with either the occurrence or non-occurrence of an earthquake in each zone in a pre-determined time interval. Since the time-series is derived from non-linear and non-stationary earthquake sequencing, we use known analysis methods to glean new information. We apply decomposition procedures such as ensemble empirical mode decomposition (EEMD) to study the state-to-state fluctuations in each of the intrinsic mode functions. We subject the intrinsic mode functions, the orthogonal basis set derived from the time-series using the EEMD, to a detailed analysis to draw information-content of the time-series. Also, we investigate the influence of random-noise on the data-driven state-to-state transition probabilities. We consider a second aspect of earthquake sequencing that is closely tied to its time-correlative behavior. Here, we extend the Fano factor and Allan factor analysis to the time-series of state-to state transition frequencies of a Markov chain. Our results support not only the usefulness the intrinsic mode functions in understanding the time-series but also the presence of power-law behaviour exemplified by the Fano factor and the Allan factor.

  10. The Volume Regulation Graph versus the Ejection Fraction as Metrics of Left Ventricular Performance in Heart Failure with and without a Preserved Ejection Fraction: A Mathematical Model Study

    PubMed Central

    Faes, Theo JC; Kerkhof, Peter LM

    2015-01-01

    In left ventricular heart failure, often a distinction is made between patients with a reduced and a preserved ejection fraction (EF). As EF is a composite metric of both the end-diastolic volume (EDV) and the end-systolic ventricular volume (ESV), the lucidity of the EF is sometimes questioned. As an alternative, the ESV–EDV graph is advocated. This study identifies the dependence of the EF and the EDV–ESV graph on the major determinants of ventricular performance. Numerical simulations were made using a model of the systemic circulation, consisting of an atrium–ventricle valves combination; a simple constant pressure as venous filling system; and a three-element Windkessel extended with a venous system. ESV–EDV graphs and EFs were calculated using this model while varying one by one the filling pressure, diastolic and systolic ventricular elastances, and diastolic pressure in the aorta. In conclusion, the ESV–EDV graph separates between diastolic and systolic dysfunction while the EF encompasses these two pathologies. Therefore, the ESV–EDV graph can provide an advantage over EF in heart failure studies. PMID:26052232

  11. Using Random Forest Models to Predict Organizational Violence

    NASA Technical Reports Server (NTRS)

    Levine, Burton; Bobashev, Georgly

    2012-01-01

    We present a methodology to access the proclivity of an organization to commit violence against nongovernment personnel. We fitted a Random Forest model using the Minority at Risk Organizational Behavior (MAROS) dataset. The MAROS data is longitudinal; so, individual observations are not independent. We propose a modification to the standard Random Forest methodology to account for the violation of the independence assumption. We present the results of the model fit, an example of predicting violence for an organization; and finally, we present a summary of the forest in a "meta-tree,"

  12. Random-anisotropy Blume-Emery-Griffiths model

    NASA Technical Reports Server (NTRS)

    Maritan, Amos; Cieplak, Marek; Swift, Michael R.; Toigo, Flavio; Banavar, Jayanth R.

    1992-01-01

    The results are described of studies of a random-anisotropy Blume-Emery-Griffiths spin-1 Ising model using mean-field theory, transfer-matrix calculations, and position-space renormalization-group calculations. The interplay between the quenched randomness of the anisotropy and the annealed disorder introduced by the spin-1 model leads to a rich phase diagram with a variety of phase transitions and reentrant behavior. The results may be relevant to the study of the phase separation of He-3 - He-4 mixtures in porous media in the vicinity of the superfluid transition.

  13. Confining bond rearrangement in the random center vortex model

    NASA Astrophysics Data System (ADS)

    Altarawneh, Derar; Höllwieser, Roman; Engelhardt, Michael

    2016-03-01

    We present static meson-meson and baryon-antibaryon potentials in Z (2 ) and Z (3 ) random center vortex models for the infrared sector of Yang-Mills theory, i.e., hypercubic lattice models of random vortex world surfaces. In particular, we calculate multiple Polyakov loop correlators corresponding to static meson-meson or baryon-antibaryon configurations in a center vortex background and observe that their expectation values follow the minimal area law, displaying bond rearrangement behavior, a characteristic expected for the confining dynamics of the strong interaction. The static meson-meson and baryon-antibaryon potentials are compared with theoretical predictions and lattice QCD simulations.

  14. A discrete time random walk model for anomalous diffusion

    NASA Astrophysics Data System (ADS)

    Angstmann, C. N.; Donnelly, I. C.; Henry, B. I.; Nichols, J. A.

    2015-07-01

    The continuous time random walk, introduced in the physics literature by Montroll and Weiss, has been widely used to model anomalous diffusion in external force fields. One of the features of this model is that the governing equations for the evolution of the probability density function, in the diffusion limit, can generally be simplified using fractional calculus. This has in turn led to intensive research efforts over the past decade to develop robust numerical methods for the governing equations, represented as fractional partial differential equations. Here we introduce a discrete time random walk that can also be used to model anomalous diffusion in an external force field. The governing evolution equations for the probability density function share the continuous time random walk diffusion limit. Thus the discrete time random walk provides a novel numerical method for solving anomalous diffusion equations in the diffusion limit, including the fractional Fokker-Planck equation. This method has the clear advantage that the discretisation of the diffusion limit equation, which is necessary for numerical analysis, is itself a well defined physical process. Some examples using the discrete time random walk to provide numerical solutions of the probability density function for anomalous subdiffusion, including forcing, are provided.

  15. 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.

  16. Bead-rod-spring models in random flows

    NASA Astrophysics Data System (ADS)

    Plan, Emmanuel Lance Christopher Medillo, VI; Ali, Aamir; Vincenzi, Dario

    2016-08-01

    Bead-rod-spring models are the foundation of the kinetic theory of polymer solutions. We derive the diffusion equation for the probability density function of the configuration of a general bead-rod-spring model in short-correlated Gaussian random flows. Under isotropic conditions, we solve this equation analytically for the elastic rhombus model introduced by Curtiss, Bird, and Hassager [Adv. Chem. Phys. 35, 31 (1976)].

  17. Bead-rod-spring models in random flows.

    PubMed

    Plan, Emmanuel Lance Christopher Vi Medillo; Ali, Aamir; Vincenzi, Dario

    2016-08-01

    Bead-rod-spring models are the foundation of the kinetic theory of polymer solutions. We derive the diffusion equation for the probability density function of the configuration of a general bead-rod-spring model in short-correlated Gaussian random flows. Under isotropic conditions, we solve this equation analytically for the elastic rhombus model introduced by Curtiss, Bird, and Hassager [Adv. Chem. Phys. 35, 31 (1976)]. PMID:27627227

  18. 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

  19. 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.

  20. 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.

  1. Performance of Random Effects Model Estimators under Complex Sampling Designs

    ERIC Educational Resources Information Center

    Jia, Yue; Stokes, Lynne; Harris, Ian; Wang, Yan

    2011-01-01

    In this article, we consider estimation of parameters of random effects models from samples collected via complex multistage designs. Incorporation of sampling weights is one way to reduce estimation bias due to unequal probabilities of selection. Several weighting methods have been proposed in the literature for estimating the parameters of…

  2. A discrete impulsive model for random heating and Brownian motion

    NASA Astrophysics Data System (ADS)

    Ramshaw, John D.

    2010-01-01

    The energy of a mechanical system subjected to a random force with zero mean increases irreversibly and diverges with time in the absence of friction or dissipation. This random heating effect is usually encountered in phenomenological theories formulated in terms of stochastic differential equations, the epitome of which is the Langevin equation of Brownian motion. We discuss a simple discrete impulsive model that captures the essence of random heating and Brownian motion. The model may be regarded as a discrete analog of the Langevin equation, although it is developed ab initio. Its analysis requires only simple algebraic manipulations and elementary averaging concepts, but no stochastic differential equations (or even calculus). The irreversibility in the model is shown to be a consequence of a natural causal stochastic condition that is closely analogous to Boltzmann's molecular chaos hypothesis in the kinetic theory of gases. The model provides a simple introduction to several ostensibly more advanced topics, including random heating, molecular chaos, irreversibility, Brownian motion, the Langevin equation, and fluctuation-dissipation theorems.

  3. 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.

  4. 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

  5. The Abelian Sandpile Model on a Random Binary Tree

    NASA Astrophysics Data System (ADS)

    Redig, F.; Ruszel, W. M.; Saada, E.

    2012-06-01

    We study the abelian sandpile model on a random binary tree. Using a transfer matrix approach introduced by Dhar and Majumdar, we prove exponential decay of correlations, and in a small supercritical region (i.e., where the branching process survives with positive probability) exponential decay of avalanche sizes. This shows a phase transition phenomenon between exponential decay and power law decay of avalanche sizes. Our main technical tools are: (1) A recursion for the ratio between the numbers of weakly and strongly allowed configurations which is proved to have a well-defined stochastic solution; (2) quenched and annealed estimates of the eigenvalues of a product of n random transfer matrices.

  6. 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…

  7. 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.

  8. 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.

  9. Inference for blocked randomization under a selection bias model.

    PubMed

    Kennes, Lieven N; Rosenberger, William F; Hilgers, Ralf-Dieter

    2015-12-01

    We provide an asymptotic test to analyze randomized clinical trials that may be subject to selection bias. For normally distributed responses, and under permuted block randomization, we derive a likelihood ratio test of the treatment effect under a selection bias model. A likelihood ratio test of the presence of selection bias arises from the same formulation. We prove that the test is asymptotically chi-square on one degree of freedom. These results correlate well with the likelihood ratio test of Ivanova et al. (2005, Statistics in Medicine 24, 1537-1546) for binary responses, for which they established by simulation that the asymptotic distribution is chi-square. Simulations also show that the test is robust to departures from normality and under another randomization procedure. We illustrate the test by reanalyzing a clinical trial on retinal detachment. PMID:26099068

  10. Quantum walk coherences on a dynamical percolation graph

    NASA Astrophysics Data System (ADS)

    Elster, Fabian; Barkhofen, Sonja; Nitsche, Thomas; Novotný, Jaroslav; Gábris, Aurél; Jex, Igor; Silberhorn, Christine

    2015-08-01

    Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In particular, quantum walks on percolation structures constitute an attractive platform for studying open system dynamics of random media. Here, we present an implementation of quantum walks differing from the previous experiments by achieving dynamical control of the underlying graph structure. We demonstrate the evolution of an optical time-multiplexed quantum walk over six double steps, revealing the intricate interplay between the internal and external degrees of freedom. The observation of clear non-Markovian signatures in the coin space testifies the high coherence of the implementation and the extraordinary degree of control of all system parameters. Our work is the proof-of-principle experiment of a quantum walk on a dynamical percolation graph, paving the way towards complex simulation of quantum transport in random media.

  11. 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…

  12. Path Separability of Graphs

    NASA Astrophysics Data System (ADS)

    Diot, Emilie; Gavoille, Cyril

    In this paper we investigate the structural properties of k-path separable graphs, that are the graphs that can be separated by a set of k shortest paths. We identify several graph families having such path separability, and we show that this property is closed under minor taking. In particular we establish a list of forbidden minors for 1-path separable graphs.

  13. Graphing for Any Grade.

    ERIC Educational Resources Information Center

    Nibbelink, William

    1982-01-01

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

  14. A monoecious and diploid Moran model of random mating.

    PubMed

    Hössjer, Ola; Tyvand, Peder A

    2016-04-01

    An exact Markov chain is developed for a Moran model of random mating for monoecious diploid individuals with a given probability of self-fertilization. The model captures the dynamics of genetic variation at a biallelic locus. We compare the model with the corresponding diploid Wright-Fisher (WF) model. We also develop a novel diffusion approximation of both models, where the genotype frequency distribution dynamics is described by two partial differential equations, on different time scales. The first equation captures the more slowly varying allele frequencies, and it is the same for the Moran and WF models. The other equation captures departures of the fraction of heterozygous genotypes from a large population equilibrium curve that equals Hardy-Weinberg proportions in the absence of selfing. It is the distribution of a continuous time Ornstein-Uhlenbeck process for the Moran model and a discrete time autoregressive process for the WF model. One application of our results is to capture dynamics of the degree of non-random mating of both models, in terms of the fixation index fIS. Although fIS has a stable fixed point that only depends on the degree of selfing, the normally distributed oscillations around this fixed point are stochastically larger for the Moran than for the WF model. PMID:26807805

  15. A generalized model via random walks for information filtering

    NASA Astrophysics Data System (ADS)

    Ren, Zhuo-Ming; Kong, Yixiu; Shang, Ming-Sheng; Zhang, Yi-Cheng

    2016-08-01

    There could exist a simple general mechanism lurking beneath collaborative filtering and interdisciplinary physics approaches which have been successfully applied to online E-commerce platforms. Motivated by this idea, we propose a generalized model employing the dynamics of the random walk in the bipartite networks. Taking into account the degree information, the proposed generalized model could deduce the collaborative filtering, interdisciplinary physics approaches and even the enormous expansion of them. Furthermore, we analyze the generalized model with single and hybrid of degree information on the process of random walk in bipartite networks, and propose a possible strategy by using the hybrid degree information for different popular objects to toward promising precision of the recommendation.

  16. 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.

  17. 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.

  18. Inference of random walk models to describe leukocyte migration

    NASA Astrophysics Data System (ADS)

    Jones, Phoebe J. M.; Sim, Aaron; Taylor, Harriet B.; Bugeon, Laurence; Dallman, Magaret J.; Pereira, Bernard; Stumpf, Michael P. H.; Liepe, Juliane

    2015-12-01

    While the majority of cells in an organism are static and remain relatively immobile in their tissue, migrating cells occur commonly during developmental processes and are crucial for a functioning immune response. The mode of migration has been described in terms of various types of random walks. To understand the details of the migratory behaviour we rely on mathematical models and their calibration to experimental data. Here we propose an approximate Bayesian inference scheme to calibrate a class of random walk models characterized by a specific, parametric particle re-orientation mechanism to observed trajectory data. We elaborate the concept of transition matrices (TMs) to detect random walk patterns and determine a statistic to quantify these TM to make them applicable for inference schemes. We apply the developed pipeline to in vivo trajectory data of macrophages and neutrophils, extracted from zebrafish that had undergone tail transection. We find that macrophage and neutrophils exhibit very distinct biased persistent random walk patterns, where the strengths of the persistence and bias are spatio-temporally regulated. Furthermore, the movement of macrophages is far less persistent than that of neutrophils in response to wounding.

  19. Inference of random walk models to describe leukocyte migration.

    PubMed

    Jones, Phoebe J M; Sim, Aaron; Taylor, Harriet B; Bugeon, Laurence; Dallman, Magaret J; Pereira, Bernard; Stumpf, Michael P H; Liepe, Juliane

    2015-12-01

    While the majority of cells in an organism are static and remain relatively immobile in their tissue, migrating cells occur commonly during developmental processes and are crucial for a functioning immune response. The mode of migration has been described in terms of various types of random walks. To understand the details of the migratory behaviour we rely on mathematical models and their calibration to experimental data. Here we propose an approximate Bayesian inference scheme to calibrate a class of random walk models characterized by a specific, parametric particle re-orientation mechanism to observed trajectory data. We elaborate the concept of transition matrices (TMs) to detect random walk patterns and determine a statistic to quantify these TM to make them applicable for inference schemes. We apply the developed pipeline to in vivo trajectory data of macrophages and neutrophils, extracted from zebrafish that had undergone tail transection. We find that macrophage and neutrophils exhibit very distinct biased persistent random walk patterns, where the strengths of the persistence and bias are spatio-temporally regulated. Furthermore, the movement of macrophages is far less persistent than that of neutrophils in response to wounding. PMID:26403334

  20. 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. PMID:20431140

  1. Generalized random sign and alert delay models for imperfect maintenance.

    PubMed

    Dijoux, Yann; Gaudoin, Olivier

    2014-04-01

    This paper considers the modelling of the process of Corrective and condition-based Preventive Maintenance, for complex repairable systems. In order to take into account the dependency between both types of maintenance and the possibility of imperfect maintenance, Generalized Competing Risks models have been introduced in "Doyen and Gaudoin (J Appl Probab 43:825-839, 2006)". In this paper, we study two classes of these models, the Generalized Random Sign and Generalized Alert Delay models. A Generalized Competing Risks model can be built as a generalization of a particular Usual Competing Risks model, either by using a virtual age framework or not. The models properties are studied and their parameterizations are discussed. Finally, simulation results and an application to real data are presented. PMID:23460491

  2. Many-body localization in the quantum random energy model

    NASA Astrophysics Data System (ADS)

    Laumann, Chris; Pal, Arijeet

    2014-03-01

    The quantum random energy model is a canonical toy model for a quantum spin glass with a well known phase diagram. We show that the model exhibits a many-body localization-delocalization transition at finite energy density which significantly alters the interpretation of the statistical ``frozen'' phase at lower temperature in isolated quantum systems. The transition manifests in many-body level statistics as well as the long time dynamics of on-site observables. CRL thanks the Perimeter Institute for hospitality and support.

  3. 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.

  4. A graph-dynamic model of the power law of practice and the problem-solving fan-effect.

    PubMed

    Shrager, J; Hogg, T; Huberman, B A

    1988-10-21

    Numerous human learning phenomena have been observed and captured by individual laws, but no unified theory of learning has succeeded in accounting for these observations. A theory and model are proposed that account for two of these phenomena: the power law of practice and the problem-solving fan-effect. The power law of practice states that the speed of performance of a task will improve as a power of the number of times that the task is performed. The power law resulting from two sorts of problem-solving changes, addition of operators to the problem-space graph and alterations in the decision procedure used to decide which operator to apply at a particular state, is empirically demonstrated. The model provides an analytic account for both of these sources of the power law. The model also predicts a problem-solving fan-effect, slowdown during practice caused by an increase in the difficulty of making useful decisions between possible paths, which is also found empirically. PMID:3175664

  5. Statistical Modeling of Robotic Random Walks on Different Terrain

    NASA Astrophysics Data System (ADS)

    Naylor, Austin; Kinnaman, Laura

    Issues of public safety, especially with crowd dynamics and pedestrian movement, have been modeled by physicists using methods from statistical mechanics over the last few years. Complex decision making of humans moving on different terrains can be modeled using random walks (RW) and correlated random walks (CRW). The effect of different terrains, such as a constant increasing slope, on RW and CRW was explored. LEGO robots were programmed to make RW and CRW with uniform step sizes. Level ground tests demonstrated that the robots had the expected step size distribution and correlation angles (for CRW). The mean square displacement was calculated for each RW and CRW on different terrains and matched expected trends. The step size distribution was determined to change based on the terrain; theoretical predictions for the step size distribution were made for various simple terrains. It's Dr. Laura Kinnaman, not sure where to put the Prefix.

  6. Modelling wildland fire propagation by tracking random fronts

    NASA Astrophysics Data System (ADS)

    Pagnini, G.; Mentrelli, A.

    2013-11-01

    Wildland fire propagation is studied in literature by two alternative approaches, namely the reaction-diffusion equation and the level-set method. These two approaches are considered alternative each other because the solution of the reaction-diffusion equation is generally a continuous smooth function that has an exponential decay and an infinite support, while the level-set method, which is a front tracking technique, generates a sharp function with a finite support. However, these two approaches can indeed be considered complementary and reconciled. Turbulent hot-air transport and fire spotting are phenomena with a random character that are extremely important in wildland fire propagation. As a consequence the fire front gets a random character, too. Hence a tracking method for random fronts is needed. In particular, the level-set contourn is here randomized accordingly to the probability density function of the interface particle displacement. Actually, when the level-set method is developed for tracking a front interface with a random motion, the resulting averaged process emerges to be governed by an evolution equation of the reaction-diffusion type. In this reconciled approach, the rate of spread of the fire keeps the same key and characterizing role proper to the level-set approach. The resulting model emerges to be suitable to simulate effects due to turbulent convection as fire flank and backing fire, the faster fire spread because of the actions by hot air pre-heating and by ember landing, and also the fire overcoming a firebreak zone that is a case not resolved by models based on the level-set method. Moreover, from the proposed formulation it follows a correction for the rate of spread formula due to the mean jump-length of firebrands in the downwind direction for the leeward sector of the fireline contour.

  7. Random Resistor Network Model of Minimal Conductivity in Graphene

    NASA Astrophysics Data System (ADS)

    Cheianov, Vadim V.; Fal'Ko, Vladimir I.; Altshuler, Boris L.; Aleiner, Igor L.

    2007-10-01

    Transport in undoped graphene is related to percolating current patterns in the networks of n- and p-type regions reflecting the strong bipolar charge density fluctuations. Finite transparency of the p-n junctions is vital in establishing the macroscopic conductivity. We propose a random resistor network model to analyze scaling dependencies of the conductance on the doping and disorder, the quantum magnetoresistance and the corresponding dephasing rate.

  8. Spatially random models, estimation theory, and robot arm dynamics

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.

    1987-01-01

    Spatially random models provide an alternative to the more traditional deterministic models used to describe robot arm dynamics. These alternative models can be used to establish a relationship between the methodologies of estimation theory and robot dynamics. A new class of algorithms for many of the fundamental robotics problems of inverse and forward dynamics, inverse kinematics, etc. can be developed that use computations typical in estimation theory. The algorithms make extensive use of the difference equations of Kalman filtering and Bryson-Frazier smoothing to conduct spatial recursions. The spatially random models are very easy to describe and are based on the assumption that all of the inertial (D'Alembert) forces in the system are represented by a spatially distributed white-noise model. The models can also be used to generate numerically the composite multibody system inertia matrix. This is done without resorting to the more common methods of deterministic modeling involving Lagrangian dynamics, Newton-Euler equations, etc. These methods make substantial use of human knowledge in derivation and minipulation of equations of motion for complex mechanical systems.

  9. Identification of dynamical biological systems based on random effects models.

    PubMed

    Batista, Levy; Bastogne, Thierry; Djermoune, El-Hadi

    2015-01-01

    System identification is a data-driven modeling approach more and more used in biology and biomedicine. In this application context, each assay is always repeated to estimate the response variability. The inference of the modeling conclusions to the whole population requires to account for the inter-individual variability within the modeling procedure. One solution consists in using random effects models but up to now no similar approach exists in the field of dynamical system identification. In this article, we propose a new solution based on an ARX (Auto Regressive model with eXternal inputs) structure using the EM (Expectation-Maximisation) algorithm for the estimation of the model parameters. Simulations show the relevance of this solution compared with a classical procedure of system identification repeated for each subject. PMID:26736981

  10. A model of the holographic principle: Randomness and additional dimension

    NASA Astrophysics Data System (ADS)

    Boyarsky, Abraham; Góra, Paweł; Proppe, Harald

    2010-01-01

    In recent years an idea has emerged that a system in a 3-dimensional space can be described from an information point of view by a system on its 2-dimensional boundary. This mysterious correspondence is called the Holographic Principle and has had profound effects in string theory and our perception of space-time. In this note we describe a purely mathematical model of the Holographic Principle using ideas from nonlinear dynamical systems theory. We show that a random map on the surface S of a 3-dimensional open ball B has a natural counterpart in B, and the two maps acting in different dimensional spaces have the same entropy. We can reverse this construction if we start with a special 3-dimensional map in B called a skew product. The key idea is to use the randomness, as imbedded in the parameter of the 2-dimensional random map, to define a third dimension. The main result shows that if we start with an arbitrary dynamical system in B with entropy E we can construct a random map on S whose entropy is arbitrarily close to E.

  11. Social Aggregation in Pea Aphids: Experiment and Random Walk Modeling

    PubMed Central

    Nilsen, Christa; Paige, John; Warner, Olivia; Mayhew, Benjamin; Sutley, Ryan; Lam, Matthew; Bernoff, Andrew J.; Topaz, Chad M.

    2013-01-01

    From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid's nearest neighbor. For large nearest neighbor distances, when an aphid is essentially isolated, its motion is ballistic with aphids moving faster, turning less, and being less likely to stop. In contrast, for short nearest neighbor distances, aphids move more slowly, turn more, and are more likely to become stationary; this behavior constitutes an aggregation mechanism. From the experimental data, we estimate the state transition probabilities and correlated random walk parameters as a function of nearest neighbor distance. With the individual-level model established, we assess whether it reproduces the macroscopic patterns of movement at the group level. To do so, we consider three distributions, namely distance to nearest neighbor, angle to nearest neighbor, and percentage of population moving at any given time. For each of these three distributions, we compare our experimental data to the output of numerical simulations of our nearest neighbor model, and of a control model in which aphids do not interact socially. Our stochastic, social nearest neighbor model reproduces salient features of the experimental data that are not captured by the control. PMID:24376691

  12. Social aggregation in pea aphids: experiment and random walk modeling.

    PubMed

    Nilsen, Christa; Paige, John; Warner, Olivia; Mayhew, Benjamin; Sutley, Ryan; Lam, Matthew; Bernoff, Andrew J; Topaz, Chad M

    2013-01-01

    From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid's nearest neighbor. For large nearest neighbor distances, when an aphid is essentially isolated, its motion is ballistic with aphids moving faster, turning less, and being less likely to stop. In contrast, for short nearest neighbor distances, aphids move more slowly, turn more, and are more likely to become stationary; this behavior constitutes an aggregation mechanism. From the experimental data, we estimate the state transition probabilities and correlated random walk parameters as a function of nearest neighbor distance. With the individual-level model established, we assess whether it reproduces the macroscopic patterns of movement at the group level. To do so, we consider three distributions, namely distance to nearest neighbor, angle to nearest neighbor, and percentage of population moving at any given time. For each of these three distributions, we compare our experimental data to the output of numerical simulations of our nearest neighbor model, and of a control model in which aphids do not interact socially. Our stochastic, social nearest neighbor model reproduces salient features of the experimental data that are not captured by the control. PMID:24376691

  13. SpectralNET – an application for spectral graph analysis and visualization

    PubMed Central

    Forman, Joshua J; Clemons, Paul A; Schreiber, Stuart L; Haggarty, Stephen J

    2005-01-01

    Background Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices) and interactions (edges) that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks. Results Available both as a standalone .NET executable and as an ASP.NET web application, SpectralNET was designed specifically with the analysis of graph-theoretic metrics in mind, a computational task not easily accessible using currently available applications. Users can choose either to upload a network for analysis using a variety of input formats, or to have SpectralNET generate an idealized random network for comparison to a real-world dataset. Whichever graph-generation method is used, SpectralNET displays detailed information about each connected component of the graph, including graphs of degree distribution, clustering coefficient by degree, and average distance by degree. In addition, extensive information about the selected vertex is shown, including degree, clustering coefficient, various distance metrics, and the corresponding components of the adjacency, Laplacian, and normalized Laplacian eigenvectors. SpectralNET also displays several graph visualizations, including a linear dimensionality reduction for uploaded datasets (Principal Components Analysis) and a non-linear dimensionality reduction that provides an elegant view of global graph structure (Laplacian eigenvectors). Conclusion SpectralNET provides an easily accessible means of analyzing graph-theoretic metrics for data modeling and dimensionality reduction. SpectralNET is publicly available as both a .NET application and an ASP.NET web application from . Source code is available upon request. PMID:16236170

  14. Random-field Ising model on isometric lattices: Ground states and non-Porod scattering

    NASA Astrophysics Data System (ADS)

    Bupathy, Arunkumar; Banerjee, Varsha; Puri, Sanjay

    2016-01-01

    We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δc at zero temperature with high accuracy. For the SC lattice, our estimate (Δc=2.278 ±0.002 ) is consistent with earlier reports. For the BCC and FCC lattices, Δc=3.316 ±0.002 and 5.160 ±0.002 , respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α =0.5 ±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy Ei(L ) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.

  15. Cascading failures in bi-partite graphs: model for systemic risk propagation.

    PubMed

    Huang, Xuqing; Vodenska, Irena; Havlin, Shlomo; Stanley, H Eugene

    2013-01-01

    As economic entities become increasingly interconnected, a shock in a financial network can provoke significant cascading failures throughout the system. To study the systemic risk of financial systems, we create a bi-partite banking network model composed of banks and bank assets and propose a cascading failure model to describe the risk propagation process during crises. We empirically test the model with 2007 US commercial banks balance sheet data and compare the model prediction of the failed banks with the real failed banks after 2007. We find that our model efficiently identifies a significant portion of the actual failed banks reported by Federal Deposit Insurance Corporation. The results suggest that this model could be useful for systemic risk stress testing for financial systems. The model also identifies that commercial rather than residential real estate assets are major culprits for the failure of over 350 US commercial banks during 2008-2011. PMID:23386974

  16. Cascading Failures in Bi-partite Graphs: Model for Systemic Risk Propagation

    PubMed Central

    Huang, Xuqing; Vodenska, Irena; Havlin, Shlomo; Stanley, H. Eugene

    2013-01-01

    As economic entities become increasingly interconnected, a shock in a financial network can provoke significant cascading failures throughout the system. To study the systemic risk of financial systems, we create a bi-partite banking network model composed of banks and bank assets and propose a cascading failure model to describe the risk propagation process during crises. We empirically test the model with 2007 US commercial banks balance sheet data and compare the model prediction of the failed banks with the real failed banks after 2007. We find that our model efficiently identifies a significant portion of the actual failed banks reported by Federal Deposit Insurance Corporation. The results suggest that this model could be useful for systemic risk stress testing for financial systems. The model also identifies that commercial rather than residential real estate assets are major culprits for the failure of over 350 US commercial banks during 2008–2011. PMID:23386974

  17. Incremental checking of Master Data Management model based on contextual graphs

    NASA Astrophysics Data System (ADS)

    Lamolle, Myriam; Menet, Ludovic; Le Duc, Chan

    2015-10-01

    The validation of models is a crucial step in distributed heterogeneous systems. In this paper, an incremental validation method is proposed in the scope of a Model Driven Engineering (MDE) approach, which is used to develop a Master Data Management (MDM) field represented by XML Schema models. The MDE approach presented in this paper is based on the definition of an abstraction layer using UML class diagrams. The validation method aims to minimise the model errors and to optimisethe process of model checking. Therefore, the notion of validation contexts is introduced allowing the verification of data model views. Description logics specify constraints that the models have to check. An experimentation of the approach is presented through an application developed in ArgoUML IDE.

  18. 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. PMID:24914522

  19. Randomized shortest-path problems: two related models.

    PubMed

    Saerens, Marco; Achbany, Youssef; Fouss, François; Yen, Luh

    2009-08-01

    This letter addresses the problem of designing the transition probabilities of a finite Markov chain (the policy) in order to minimize the expected cost for reaching a destination node from a source node while maintaining a fixed level of entropy spread throughout the network (the exploration). It is motivated by the following scenario. Suppose you have to route agents through a network in some optimal way, for instance, by minimizing the total travel cost-nothing particular up to now-you could use a standard shortest-path algorithm. Suppose, however, that you want to avoid pure deterministic routing policies in order, for instance, to allow some continual exploration of the network, avoid congestion, or avoid complete predictability of your routing strategy. In other words, you want to introduce some randomness or unpredictability in the routing policy (i.e., the routing policy is randomized). This problem, which will be called the randomized shortest-path problem (RSP), is investigated in this work. The global level of randomness of the routing policy is quantified by the expected Shannon entropy spread throughout the network and is provided a priori by the designer. Then, necessary conditions to compute the optimal randomized policy-minimizing the expected routing cost-are derived. Iterating these necessary conditions, reminiscent of Bellman's value iteration equations, allows computing an optimal policy, that is, a set of transition probabilities in each node. Interestingly and surprisingly enough, this first model, while formulated in a totally different framework, is equivalent to Akamatsu's model ( 1996 ), appearing in transportation science, for a special choice of the entropy constraint. We therefore revisit Akamatsu's model by recasting it into a sum-over-paths statistical physics formalism allowing easy derivation of all the quantities of interest in an elegant, unified way. For instance, it is shown that the unique optimal policy can be obtained by

  20. Discrete Random Media Techniques for Microwave Modeling of Vegetated Terrain

    NASA Technical Reports Server (NTRS)

    Lang, R. H.

    1984-01-01

    Microwave remote sensing of agricultural crops and forested regions is studied. Long term goals of the research involve modeling vegetation so that radar signatures can be used to infer the parameters which characterize the vegetation and underlying ground. Vegetation is modeled by discrete scatterers viz, leaves, stems, branches and trunks. These are replaced by glossy dielectric discs and cylinders. Rough surfaces are represented by their mean and spectral characteristics. Average scattered power is then calculated by employing discrete random media methodology such as the distorted Born approximation or transport theory. Both coherent and incoherent multiple scattering techniques are explored. Once direct methods are developed, inversion techniques can be investigated.

  1. Experiments on parallel graph coloring and applications

    SciTech Connect

    Lewandowski, G.; Condon, A.

    1994-12-31

    The graph coloring problem is an NP-Complete problem with a wide array of applications, such as course scheduling, exam scheduling, register allocation, and parallelizing solutions for sparse systems of linear equations. Much theoretical effort has been put into designing heuristics that perform well on randomly generated graphs. The best sequential heuristics require large amounts of time and tuning of various parameters in the heuristics. We have used parallelism to combine exhaustive search with successful heuristic strategies to create a new heuristic, Hybrid, which does well on a wide variety of graphs, without any tuning of parameters. We have also gathered real application data and tested several heuristics on this data. Our study of real data points out some flaws in studying only random graphs and also suggests interesting new problems for study.

  2. Multilevel models for survival analysis with random effects.

    PubMed

    Yau, K K

    2001-03-01

    A method for modeling survival data with multilevel clustering is described. The Cox partial likelihood is incorporated into the generalized linear mixed model (GLMM) methodology. Parameter estimation is achieved by maximizing a log likelihood analogous to the likelihood associated with the best linear unbiased prediction (BLUP) at the initial step of estimation and is extended to obtain residual maximum likelihood (REML) estimators of the variance component. Estimating equations for a three-level hierarchical survival model are developed in detail, and such a model is applied to analyze a set of chronic granulomatous disease (CGD) data on recurrent infections as an illustration with both hospital and patient effects being considered as random. Only the latter gives a significant contribution. A simulation study is carried out to evaluate the performance of the REML estimators. Further extension of the estimation procedure to models with an arbitrary number of levels is also discussed. PMID:11252624

  3. A stochastic model of randomly accelerated walkers for human mobility.

    PubMed

    Gallotti, Riccardo; Bazzani, Armando; Rambaldi, Sandro; Barthelemy, Marc

    2016-01-01

    Recent studies of human mobility largely focus on displacements patterns and power law fits of empirical long-tailed distributions of distances are usually associated to scale-free superdiffusive random walks called Lévy flights. However, drawing conclusions about a complex system from a fit, without any further knowledge of the underlying dynamics, might lead to erroneous interpretations. Here we show, on the basis of a data set describing the trajectories of 780,000 private vehicles in Italy, that the Lévy flight model cannot explain the behaviour of travel times and speeds. We therefore introduce a class of accelerated random walks, validated by empirical observations, where the velocity changes due to acceleration kicks at random times. Combining this mechanism with an exponentially decaying distribution of travel times leads to a short-tailed distribution of distances which could indeed be mistaken with a truncated power law. These results illustrate the limits of purely descriptive models and provide a mechanistic view of mobility. PMID:27573984

  4. Occupation time statistics of the random acceleration model

    NASA Astrophysics Data System (ADS)

    Joël Ouandji Boutcheng, Hermann; Bouetou Bouetou, Thomas; Burkhardt, Theodore W.; Rosso, Alberto; Zoia, Andrea; Timoleon Crepin, Kofane

    2016-05-01

    The random acceleration model is one of the simplest non-Markovian stochastic systems and has been widely studied in connection with applications in physics and mathematics. However, the occupation time and related properties are non-trivial and not yet completely understood. In this paper we consider the occupation time T + of the one-dimensional random acceleration model on the positive half-axis. We calculate the first two moments of T + analytically and also study the statistics of T + with Monte Carlo simulations. One goal of our work was to ascertain whether the occupation time T + and the time T m at which the maximum of the process is attained are statistically equivalent. For regular Brownian motion the distributions of T + and T m coincide and are given by Lévy’s arcsine law. We show that for randomly accelerated motion the distributions of T + and T m are quite similar but not identical. This conclusion follows from the exact results for the moments of the distributions and is also consistent with our Monte Carlo simulations.

  5. A new test statistic for climate models that includes field and spatial dependencies using Gaussian Markov random fields

    DOE PAGESBeta

    Nosedal-Sanchez, Alvaro; Jackson, Charles S.; Huerta, Gabriel

    2016-07-20

    A new test statistic for climate model evaluation has been developed that potentially mitigates some of the limitations that exist for observing and representing field and space dependencies of climate phenomena. Traditionally such dependencies have been ignored when climate models have been evaluated against observational data, which makes it difficult to assess whether any given model is simulating observed climate for the right reasons. The new statistic uses Gaussian Markov random fields for estimating field and space dependencies within a first-order grid point neighborhood structure. We illustrate the ability of Gaussian Markov random fields to represent empirical estimates of fieldmore » and space covariances using "witch hat" graphs. We further use the new statistic to evaluate the tropical response of a climate model (CAM3.1) to changes in two parameters important to its representation of cloud and precipitation physics. Overall, the inclusion of dependency information did not alter significantly the recognition of those regions of parameter space that best approximated observations. However, there were some qualitative differences in the shape of the response surface that suggest how such a measure could affect estimates of model uncertainty.« less

  6. A new test statistic for climate models that includes field and spatial dependencies using Gaussian Markov random fields

    NASA Astrophysics Data System (ADS)

    Nosedal-Sanchez, Alvaro; Jackson, Charles S.; Huerta, Gabriel

    2016-07-01

    A new test statistic for climate model evaluation has been developed that potentially mitigates some of the limitations that exist for observing and representing field and space dependencies of climate phenomena. Traditionally such dependencies have been ignored when climate models have been evaluated against observational data, which makes it difficult to assess whether any given model is simulating observed climate for the right reasons. The new statistic uses Gaussian Markov random fields for estimating field and space dependencies within a first-order grid point neighborhood structure. We illustrate the ability of Gaussian Markov random fields to represent empirical estimates of field and space covariances using "witch hat" graphs. We further use the new statistic to evaluate the tropical response of a climate model (CAM3.1) to changes in two parameters important to its representation of cloud and precipitation physics. Overall, the inclusion of dependency information did not alter significantly the recognition of those regions of parameter space that best approximated observations. However, there were some qualitative differences in the shape of the response surface that suggest how such a measure could affect estimates of model uncertainty.

  7. Image synthesis with graph cuts: a fast model proposal mechanism in probabilistic inversion

    NASA Astrophysics Data System (ADS)

    Zahner, Tobias; Lochbühler, Tobias; Mariethoz, Grégoire; Linde, Niklas

    2016-02-01

    Geophysical inversion should ideally produce geologically realistic subsurface models that explain the available data. Multiple-point statistics is a geostatistical approach to construct subsurface models that are consistent with site-specific data, but also display the same type of patterns as those found in a training image. The training image can be seen as a conceptual model of the subsurface and is used as a non-parametric model of spatial variability. Inversion based on multiple-point statistics is challenging due to high nonlinearity and time-consuming geostatistical resimulation steps that are needed to create new model proposals. We propose an entirely new model proposal mechanism for geophysical inversion that is inspired by texture synthesis in computer vision. Instead of resimulating pixels based on higher-order patterns in the training image, we identify a suitable patch of the training image that replace a corresponding patch in the current model without breaking the patterns found in the training image, that is, remaining consistent with the given prior. We consider three cross-hole ground-penetrating radar examples in which the new model proposal mechanism is employed within an extended Metropolis Markov chain Monte Carlo (MCMC) inversion. The model proposal step is about 40 times faster than state-of-the-art multiple-point statistics resimulation techniques, the number of necessary MCMC steps is lower and the quality of the final model realizations is of similar quality. The model proposal mechanism is presently limited to 2-D fields, but the method is general and can be applied to a wide range of subsurface settings and geophysical data types.

  8. Computing Information Value from RDF Graph Properties

    SciTech Connect

    al-Saffar, Sinan; Heileman, Gregory

    2010-11-08

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

  9. Random Predictor Models for Rigorous Uncertainty Quantification: Part 1

    NASA Technical Reports Server (NTRS)

    Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

    2015-01-01

    This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean and the variance of the model's parameters, thus of the predicted output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, can be bounded tightly and rigorously.

  10. A new phase of disordered phonons modelled by random matrices

    NASA Astrophysics Data System (ADS)

    Schmittner, Sebastian; Zirnbauer, Martin

    2015-03-01

    Starting from the clean harmonic crystal and not invoking two-level systems, we propose a model for phonons in a disordered solid. In this model the strength of mass and spring constant disorder can be increased separately. Both types of disorder are modelled by random matrices that couple the degrees of freedom locally. Treated in coherent potential approximation (CPA), the speed of sound decreases with increasing disorder until it reaches zero at finite disorder strength. There, a critical transition to a strong disorder phase occurs. In this novel phase, we find the density of states at zero energy in three dimensions to be finite, leading to a linear temperature dependence of the heat capacity, as observed experimentally for vitreous systems. For any disorder strength, our model is stable, i.e. masses and spring constants are positive, and there are no runaway dynamics. This is ensured by using appropriate probability distributions, inspired by Wishart ensembles, for the random matrices. The CPA self-consistency equations are derived in a very accessible way using planar diagrams. The talk focuses on the model and the results. The first author acknowledges financial support by the Deutsche Telekom Stiftung.

  11. Random Predictor Models for Rigorous Uncertainty Quantification: Part 2

    NASA Technical Reports Server (NTRS)

    Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

    2015-01-01

    This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean, the variance, and the range of the model's parameter, thus of the output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, is bounded rigorously.

  12. Interval process model and non-random vibration analysis

    NASA Astrophysics Data System (ADS)

    Jiang, C.; Ni, B. Y.; Liu, N. Y.; Han, X.; Liu, J.

    2016-07-01

    This paper develops an interval process model for time-varying or dynamic uncertainty analysis when information of the uncertain parameter is inadequate. By using the interval process model to describe a time-varying uncertain parameter, only its upper and lower bounds are required at each time point rather than its precise probability distribution, which is quite different from the traditional stochastic process model. A correlation function is defined for quantification of correlation between the uncertain-but-bounded variables at different times, and a matrix-decomposition-based method is presented to transform the original dependent interval process into an independent one for convenience of subsequent uncertainty analysis. More importantly, based on the interval process model, a non-random vibration analysis method is proposed for response computation of structures subjected to time-varying uncertain external excitations or loads. The structural dynamic responses thus can be derived in the form of upper and lower bounds, providing an important guidance for practical safety analysis and reliability design of structures. Finally, two numerical examples and one engineering application are investigated to demonstrate the feasibility of the interval process model and corresponding non-random vibration analysis method.

  13. Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory

    PubMed Central

    van Wijk, Bernadette C. M.; Stam, Cornelis J.; Daffertshofer, Andreas

    2010-01-01

    Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) non-significant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others. PMID:21060892

  14. Optimizing spread dynamics on graphs by message passing

    NASA Astrophysics Data System (ADS)

    Altarelli, F.; Braunstein, A.; Dall'Asta, L.; Zecchina, R.

    2013-09-01

    Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully applied to describe cascades in a large variety of contexts. Over the past decades, much effort has been devoted to understanding the typical behavior of the cascades arising from initial conditions extracted at random from some given ensemble. However, the problem of optimizing the trajectory of the system, i.e. of identifying appropriate initial conditions to maximize (or minimize) the final number of active nodes, is still considered to be practically intractable, with the only exception being models that satisfy a sort of diminishing returns property called submodularity. Submodular models can be approximately solved by means of greedy strategies, but by definition they lack cooperative characteristics which are fundamental in many real systems. Here we introduce an efficient algorithm based on statistical physics for the optimization of trajectories in cascade processes on graphs. We show that for a wide class of irreversible dynamics, even in the absence of submodularity, the spread optimization problem can be solved efficiently on large networks. Analytic and algorithmic results on random graphs are complemented by the solution of the spread maximization problem on a real-world network (the Epinions consumer reviews network).

  15. Relating Cortical Atrophy in Temporal Lobe Epilepsy with Graph Diffusion-Based Network Models

    PubMed Central

    Abdelnour, Farras; Mueller, Susanne; Raj, Ashish

    2015-01-01

    Mesial temporal lobe epilepsy (TLE) is characterized by stereotyped origination and spread pattern of epileptogenic activity, which is reflected in stereotyped topographic distribution of neuronal atrophy on magnetic resonance imaging (MRI). Both epileptogenic activity and atrophy spread appear to follow white matter connections. We model the networked spread of activity and atrophy in TLE from first principles via two simple first order network diffusion models. Atrophy distribution is modeled as a simple consequence of the propagation of epileptogenic activity in one model, and as a progressive degenerative process in the other. We show that the network models closely reproduce the regional volumetric gray matter atrophy distribution of two epilepsy cohorts: 29 TLE subjects with medial temporal sclerosis (TLE-MTS), and 50 TLE subjects with normal appearance on MRI (TLE-no). Statistical validation at the group level suggests high correlation with measured atrophy (R = 0.586 for TLE-MTS, R = 0.283 for TLE-no). We conclude that atrophy spread model out-performs the hyperactivity spread model. These results pave the way for future clinical application of the proposed model on individual patients, including estimating future spread of atrophy, identification of seizure onset zones and surgical planning. PMID:26513579

  16. Thermodynamical Limit for Correlated Gaussian Random Energy Models

    NASA Astrophysics Data System (ADS)

    Contucci, P.; Esposti, M. Degli; Giardinà, C.; Graffi, S.

    Let {EΣ(N)}ΣΣN be a family of |ΣN|=2N centered unit Gaussian random variables defined by the covariance matrix CN of elements cN(Σ,τ):=Av(EΣ(N)Eτ(N)) and the corresponding random Hamiltonian. Then the quenched thermodynamical limit exists if, for every decomposition N=N1+N2, and all pairs (Σ,τ)ΣN×ΣN: where πk(Σ),k=1,2 are the projections of ΣΣN into ΣNk. The condition is explicitly verified for the Sherrington-Kirkpatrick, the even p-spin, the Derrida REM and the Derrida-Gardner GREM models.

  17. Blood Clot Simulation Model by Using the Bond-Graph Technique

    PubMed Central

    Martinez, M. Luisa

    2013-01-01

    The World Health Organization estimates that 17 million people die of cardiovascular disease, particularly heart attacks and strokes, every year. Most strokes are caused by a blood clot that occludes an artery in the cerebral circulation and the process concerning the removal of this obstruction involves catheterisation. The fundamental object of the presented study consists in determining and optimizing the necessary simulation model corresponding with the blood clot zone to be implemented jointly with other Mechanical Thrombectomy Device simulation models, which have become more widely used during the last decade. To do so, a multidomain technique is used to better explain the different aspects of the attachment to the artery wall and between the existing platelets, it being possible to obtain the mathematical equations that define the full model. For a better understanding, a consecutive approximation to the definitive model will be presented, analyzing the different problems found during the study. The final presented model considers an elastic characterization of the blood clot composition and the possibility of obtaining a consecutive detachment process from the artery wall. In conclusion, the presented model contains the necessary behaviour laws to be implemented in future blood clot simulation models. PMID:24453867

  18. Isometric graphing and multidimensional scaling for reaction-diffusion modeling on regular and fractal surfaces with spatiotemporal pattern recognition

    NASA Astrophysics Data System (ADS)

    Kuriakose, Jainy; Ghosh, Anandamohan; Ravi Kumar, V.; Kulkarni, B. D.

    2004-03-01

    Heterogeneous surface reactions exhibiting complex spatiotemporal dynamics and patterns can be studied as processes involving reaction-diffusion mechanisms. In many realistic situations, the surface has fractal characteristics. This situation is studied by isometric graphing and multidimensional scaling (IGMDS) of fractal surfaces for extracting geodesic distances (i.e., shortest scaled distances that obtain edges of neighboring surface nodes and their interconnections) and the results obtained used to model effects of surface diffusion with nonlinear reactions. Further analysis of evolved spatiotemporal patterns may be carried out by IGMDS because high-dimensional snapshot data can be efficiently projected to a transformed subspace with reduced dimensions. Validation of the IGMDS methodology is carried out by comparing results with reduction capabilities of conventional principal component analysis for simple situations of reaction and diffusion on surfaces. The usefulness of the IGMDS methodology is shown for analysis of complex patterns formed on both regular and fractal surfaces, and using generic nonlinear reaction-diffusion systems following FitzHugh Nagumo and cubic reaction kinetics. The studies of these systems with nonlinear kinetics and noise show that effects of surface disorder due to fractality can become very relevant. The relevance is shown by studying properties of dynamical invariants in IGMDS component space, viz., the Lyapunov exponents and the KS entropy for interesting situations of spiral formation and turbulent patterns.

  19. Contact graphs of disk packings as a model of spatial planar networks

    NASA Astrophysics Data System (ADS)

    Zhang, Zhongzhi; Guan, Jihong; Ding, Bailu; Chen, Lichao; Zhou, Shuigeng

    2009-08-01

    Spatially constrained planar networks are frequently encountered in real-life systems. In this paper, based on a space-filling disk packing we propose a minimal model for spatial maximal planar networks, which is similar to but different from the model for Apollonian networks (Andrade et al 2005 Phys. Rev. Lett. 94 018702). We present an exhaustive analysis of various properties of our model, and obtain the analytic solutions for most of the features, including degree distribution, clustering coefficient, average path length and degree correlations. The model recovers some striking generic characteristics observed in most real networks. To address the robustness of the relevant network properties, we compare the structural features between the investigated network and the Apollonian networks. We show that topological properties of the two networks are encoded in the way of disk packing. We argue that spatial constraints of nodes are relevant to the structure of the networks.

  20. Connectivity properties of the random-cluster model

    NASA Astrophysics Data System (ADS)

    Weigel, Martin; Metin Elci, Eren; Fytas, Nikolaos G.

    2016-02-01

    We investigate the connectivity properties of the random-cluster model mediated by bridge bonds that, if removed, lead to the generation of new connected components. We study numerically the density of bridges and the fragmentation kernel, i.e., the relative sizes of the generated fragments, and find that these quantities follow a scaling description. The corresponding scaling exponents are related to well known equilibrium critical exponents of the model. Using the Russo-Margulis formalism, we derive an exact relation between the expected density of bridges and the number of active edges. The same approach allows us to study the fluctuations in the numbers of bridges, thereby uncovering a new singularity in the random- cluster model as q < 4 cos2 (π/√3) in two dimensions. For numerical simulations of the model directly in the language of individual bonds, known as Sweeny's algorithm, the prevalence of bridges and the scaling of the sizes of clusters connected by bridges and candidate-bridges play a pivotal role. We discuss several different implementations of the necessary connectivity algorithms and assess their relative performance.

  1. API Requirements for Dynamic Graph Prediction

    SciTech Connect

    Gallagher, B; Eliassi-Rad, T

    2006-10-13

    Given a large-scale time-evolving multi-modal and multi-relational complex network (a.k.a., a large-scale dynamic semantic graph), we want to implement algorithms that discover patterns of activities on the graph and learn predictive models of those discovered patterns. This document outlines the application programming interface (API) requirements for fast prototyping of feature extraction, learning, and prediction algorithms on large dynamic semantic graphs. Since our algorithms must operate on large-scale dynamic semantic graphs, we have chosen to use the graph API developed in the CASC Complex Networks Project. This API is supported on the back end by a semantic graph database (developed by Scott Kohn and his team). The advantages of using this API are (i) we have full-control of its development and (ii) the current API meets almost all of the requirements outlined in this document.

  2. Marginal and Random Intercepts Models for Longitudinal Binary Data with Examples from Criminology

    ERIC Educational Resources Information Center

    Long, Jeffrey D.; Loeber, Rolf; Farrington, David P.

    2009-01-01

    Two models for the analysis of longitudinal binary data are discussed: the marginal model and the random intercepts model. In contrast to the linear mixed model (LMM), the two models for binary data are not subsumed under a single hierarchical model. The marginal model provides group-level information whereas the random intercepts model provides…

  3. SAR-based change detection using hypothesis testing and Markov random field modelling

    NASA Astrophysics Data System (ADS)

    Cao, W.; Martinis, S.

    2015-04-01

    The objective of this study is to automatically detect changed areas caused by natural disasters from bi-temporal co-registered and calibrated TerraSAR-X data. The technique in this paper consists of two steps: Firstly, an automatic coarse detection step is applied based on a statistical hypothesis test for initializing the classification. The original analytical formula as proposed in the constant false alarm rate (CFAR) edge detector is reviewed and rewritten in a compact form of the incomplete beta function, which is a builtin routine in commercial scientific software such as MATLAB and IDL. Secondly, a post-classification step is introduced to optimize the noisy classification result in the previous step. Generally, an optimization problem can be formulated as a Markov random field (MRF) on which the quality of a classification is measured by an energy function. The optimal classification based on the MRF is related to the lowest energy value. Previous studies provide methods for the optimization problem using MRFs, such as the iterated conditional modes (ICM) algorithm. Recently, a novel algorithm was presented based on graph-cut theory. This method transforms a MRF to an equivalent graph and solves the optimization problem by a max-flow/min-cut algorithm on the graph. In this study this graph-cut algorithm is applied iteratively to improve the coarse classification. At each iteration the parameters of the energy function for the current classification are set by the logarithmic probability density function (PDF). The relevant parameters are estimated by the method of logarithmic cumulants (MoLC). Experiments are performed using two flood events in Germany and Australia in 2011 and a forest fire on La Palma in 2009 using pre- and post-event TerraSAR-X data. The results show convincing coarse classifications and considerable improvement by the graph-cut post-classification step.

  4. Numerical modeling of seismogram envelopes in 2-D random media

    NASA Astrophysics Data System (ADS)

    Fehler, Michael

    2002-11-01

    Several portions of seismograms recorded from regional earthquakes cannot be easily explained as resulting from waves propagating along deterministic paths within the Earth. For example, seismic coda, which is the tail portion of the seismogram of an earthquake recorded at distances of less than 100 km, is considered as resulting from waves that are multiply scattered from random heterogeneities in the Earth's lithosphere. At greater distances, observations that the duration of the initial arriving wave packet is much longer than the source-time duration is explained as being due to multiple forward scattering along the path between the source and the receiver. To investigate these phenomena, we use a finite difference method to numerically simulate 2-D scalar-waves that propagate through random media characterized by a von Karman autocorrelation function. Such media are considered to be appropriate models for the random component of the structure of the Earth's lithosphere. We investigate the characteristics of the resulting wavefields and compare them with those of observed seismograms.

  5. Critical behavior of the Ising model on random fractals

    NASA Astrophysics Data System (ADS)

    Monceau, Pascal

    2011-11-01

    We study the critical behavior of the Ising model in the case of quenched disorder constrained by fractality on random Sierpinski fractals with a Hausdorff dimension df≃1.8928. This is a first attempt to study a situation between the borderline cases of deterministic self-similarity and quenched randomness. Intensive Monte Carlo simulations were carried out. Scaling corrections are much weaker than in the deterministic cases, so that our results enable us to ensure that finite-size scaling holds, and that the critical behavior is described by a new universality class. The hyperscaling relation is compatible with an effective dimension equal to the Hausdorff one; moreover the two eigenvalues exponents of the renormalization flows are shown to be different from the ones calculated from ɛ expansions, and from the ones obtained for fourfold symmetric deterministic fractals. Although the space dimensionality is not integer, lack of self-averaging properties exhibits some features very close to the ones of a random fixed point associated with a relevant disorder.

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

    SciTech Connect

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

    2015-09-30

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

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

    SciTech Connect

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

    2015-11-15

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

  8. Fatigue strength reduction model: RANDOM3 and RANDOM4 user manual. Appendix 2: Development of advanced methodologies for probabilistic constitutive relationships of material strength models

    NASA Technical Reports Server (NTRS)

    Boyce, Lola; Lovelace, Thomas B.

    1989-01-01

    FORTRAN programs RANDOM3 and RANDOM4 are documented in the form of a user's manual. Both programs are based on fatigue strength reduction, using a probabilistic constitutive model. The programs predict the random lifetime of an engine component to reach a given fatigue strength. The theoretical backgrounds, input data instructions, and sample problems illustrating the use of the programs are included.

  9. USE OF A GRAPH THEORETIC SIMILARITY INDEX IN PREDICTION STUDIES OF LINEAR DISCRIMINANTS AND MODELS

    EPA Science Inventory

    A goal of many structure-activity and structure-property studies is to develop the capability to predict the activity or property of interest for previously untested compounds. A quantitative model or a discriminant is developed from a training set of molecules with known activit...

  10. Markov-random-field modeling for linear seismic tomography.

    PubMed

    Kuwatani, Tatsu; Nagata, Kenji; Okada, Masato; Toriumi, Mitsuhiro

    2014-10-01

    We apply the Markov-random-field model to linear seismic tomography and propose a method to estimate the hyperparameters for the smoothness and the magnitude of the noise. Optimal hyperparameters can be determined analytically by minimizing the free energy function, which is defined by marginalizing the evaluation function. In synthetic inversion tests under various settings, the assumed velocity structures are successfully reconstructed, which shows the effectiveness and robustness of the proposed method. The proposed mathematical framework can be applied to inversion problems in various fields in the natural sciences. PMID:25375468

  11. Bouchaud-Mézard model on a random network

    NASA Astrophysics Data System (ADS)

    Ichinomiya, Takashi

    2012-09-01

    We studied the Bouchaud-Mézard (BM) model, which was introduced to explain Pareto's law in a real economy, on a random network. Using “adiabatic and independent” assumptions, we analytically obtained the stationary probability distribution function of wealth. The results show that wealth condensation, indicated by the divergence of the variance of wealth, occurs at a larger J than that obtained by the mean-field theory, where J represents the strength of interaction between agents. We compared our results with numerical simulation results and found that they were in good agreement.

  12. Mining Discriminative Patterns from Graph Data with Multiple Labels and Its Application to Quantitative Structure-Activity Relationship (QSAR) Models.

    PubMed

    Shao, Zheng; Hirayama, Yuya; Yamanishi, Yoshihiro; Saigo, Hiroto

    2015-12-28

    Graph data are becoming increasingly common in machine learning and data mining, and its application field pervades to bioinformatics and cheminformatics. Accordingly, as a method to extract patterns from graph data, graph mining recently has been studied and developed rapidly. Since the number of patterns in graph data is huge, a central issue is how to efficiently collect informative patterns suitable for subsequent tasks such as classification or regression. In this paper, we consider mining discriminative subgraphs from graph data with multiple labels. The resulting task has important applications in cheminformatics, such as finding common functional groups that trigger multiple drug side effects, or identifying ligand functional groups that hit multiple targets. In computational experiments, we first verify the effectiveness of the proposed approach in synthetic data, then we apply it to drug adverse effect prediction problem. In the latter dataset, we compared the proposed method with L1-norm logistic regression in combination with the PubChem/Open Babel fingerprint, in that the proposed method showed superior performance with a much smaller number of subgraph patterns. Software is available from https://github.com/axot/GLP. PMID:26549421

  13. Random-effects models for serial observations with binary response

    SciTech Connect

    Stiratelli, R.; Laird, N.; Ware, J.H.

    1984-12-01

    This paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants. Each subject's serial responses are assumed to arise from a logistic model, but with regression coefficients that vary between subjects. The logistic regression parameters are assumed to be normally distributed in the population. Inference is based upon maximum likelihood estimation of fixed effects and variance components, and empirical Bayes estimation of random effects. Exact solutions are analytically and computationally infeasible, but an approximation based on the mode of the posterior distribution of the random parameters is proposed, and is implemented by means of the EM algorithm. This approximate method is compared with a simpler two-step method proposed by Korn and Whittemore, using data from a panel study of asthmatics originally described in that paper. One advantage of the estimation strategy described here is the ability to use all of the data, including that from subjects with insufficient data to permit fitting of a separate logistic regression model, as required by the Korn and Whittemore method. However, the new method is computationally intensive.

  14. Comprehensive analytical model to characterize randomness in optical waveguides.

    PubMed

    Zhou, Junhe; Gallion, Philippe

    2016-04-01

    In this paper, the coupled mode theory (CMT) is used to derive the corresponding stochastic differential equations (SDEs) for the modal amplitude evolution inside optical waveguides with random refractive index variations. Based on the SDEs, the ordinary differential equations (ODEs) are derived to analyze the statistics of the modal amplitudes, such as the optical power and power variations as well as the power correlation coefficients between the different modal powers. These ODEs can be solved analytically and therefore, it greatly simplifies the analysis. It is demonstrated that the ODEs for the power evolution of the modes are in excellent agreement with the Marcuse' coupled power model. The higher order statistics, such as the power variations and power correlation coefficients, which are not exactly analyzed in the Marcuse' model, are discussed afterwards. Monte-Carlo simulations are performed to demonstrate the validity of the analytical model. PMID:27136981

  15. Box graphs and resolutions I

    NASA Astrophysics Data System (ADS)

    Braun, Andreas P.; Schäfer-Nameki, Sakura

    2016-04-01

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

  16. Are Graphs Finally Surfacing?

    ERIC Educational Resources Information Center

    Beineke, Lowell W.

    1989-01-01

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

  17. Graph-Plotting Routine

    NASA Technical Reports Server (NTRS)

    Kantak, Anil V.

    1987-01-01

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

  18. Graphing Important People

    ERIC Educational Resources Information Center

    Reading Teacher, 2012

    2012-01-01

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

  19. Graphing Inequalities, Connecting Meaning

    ERIC Educational Resources Information Center

    Switzer, J. Matt

    2014-01-01

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

  20. Reconstructing patient-specific cardiac models from contours via Delaunay triangulation and graph-cuts.

    PubMed

    Wan, Min; Lim, Calvin; Zhang, Junmei; Su, Yi; Yeo, Si Yong; Wang, Desheng; Tan, Ru San; Zhong, Liang

    2013-01-01

    This study proposes a novel method to reconstruct the left cardiac structure from contours. Given the contours representing left ventricle (LV), left atrium (LA), and aorta (AO), re-orientation, contour matching, extrapolation, and interpolation are performed sequentially. The processed data are then reconstructed via a variational method. The weighted minimal surface model is revised to handle the multi-phase cases, which happens at the LV-LA-AO junction. A Delaunay-based tetrahedral mesh is generated to discretize the domain while the max-flow/min-cut algorithm is utilized as the minimization tool. The reconstructed model including LV, LA, and AO structure is extracted from the mesh and post-processed further. Numerical examples show the robustness and effectiveness of the proposed method. PMID:24110352

  1. Experimental quantum annealing: case study involving the graph isomorphism problem

    PubMed Central

    Zick, Kenneth M.; Shehab, Omar; French, Matthew

    2015-01-01

    Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N2 to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers. PMID:26053973

  2. Experimental quantum annealing: case study involving the graph isomorphism problem

    NASA Astrophysics Data System (ADS)

    Zick, Kenneth M.; Shehab, Omar; French, Matthew

    2015-06-01

    Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N2 to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers.

  3. Vortices and superfields on a graph

    SciTech Connect

    Kan, Nahomi; Kobayashi, Koichiro; Shiraishi, Kiyoshi

    2009-08-15

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

  4. Vortices and superfields on a graph

    NASA Astrophysics Data System (ADS)

    Kan, Nahomi; Kobayashi, Koichiro; Shiraishi, Kiyoshi

    2009-08-01

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

  5. Graph-Based Data Selection for the Construction of Genomic Prediction Models

    PubMed Central

    Maenhout, Steven; De Baets, Bernard; Haesaert, Geert

    2010-01-01

    Efficient genomic selection in animals or crops requires the accurate prediction of the agronomic performance of individuals from their high-density molecular marker profiles. Using a training data set that contains the genotypic and phenotypic information of a large number of individuals, each marker or marker allele is associated with an estimated effect on the trait under study. These estimated marker effects are subsequently used for making predictions on individuals for which no phenotypic records are available. As most plant and animal breeding programs are currently still phenotype driven, the continuously expanding collection of phenotypic records can only be used to construct a genomic prediction model if a dense molecular marker fingerprint is available for each phenotyped individual. However, as the genotyping budget is generally limited, the genomic prediction model can only be constructed using a subset of the tested individuals and possibly a genome-covering subset of the molecular markers. In this article, we demonstrate how an optimal selection of individuals can be made with respect to the quality of their available phenotypic data. We also demonstrate how the total number of molecular markers can be reduced while a maximum genome coverage is ensured. The third selection problem we tackle is specific to the construction of a genomic prediction model for a hybrid breeding program where only molecular marker fingerprints of the homozygous parents are available. We show how to identify the set of parental inbred lines of a predefined size that has produced the highest number of progeny. These three selection approaches are put into practice in a simulation study where we demonstrate how the trade-off between sample size and sample quality affects the prediction accuracy of genomic prediction models for hybrid maize. PMID:20479144

  6. Integrating Sediment Connectivity into Water Resources Management Trough a Graph Theoretic, Stochastic Modeling Framework.

    NASA Astrophysics Data System (ADS)

    Schmitt, R. J. P.; Castelletti, A.; Bizzi, S.

    2014-12-01

    Understanding sediment transport processes at the river basin scale, their temporal spectra and spatial patterns is key to identify and minimize morphologic risks associated to channel adjustments processes. This work contributes a stochastic framework for modeling bed-load connectivity based on recent advances in the field (e.g., Bizzi & Lerner, 2013; Czubas & Foufoulas-Georgiu, 2014). It presents river managers with novel indicators from reach scale vulnerability to channel adjustment in large river networks with sparse hydrologic and sediment observations. The framework comprises three steps. First, based on a distributed hydrological model and remotely sensed information, the framework identifies a representative grain size class for each reach. Second, sediment residence time distributions are calculated for each reach in a Monte-Carlo approach applying standard sediment transport equations driven by local hydraulic conditions. Third, a network analysis defines the up- and downstream connectivity for various travel times resulting in characteristic up/downstream connectivity signatures for each reach. Channel vulnerability indicators quantify the imbalance between up/downstream connectivity for each travel time domain, representing process dependent latency of morphologic response. Last, based on the stochastic core of the model, a sensitivity analysis identifies drivers of change and major sources of uncertainty in order to target key detrimental processes and to guide effective gathering of additional data. The application, limitation and integration into a decision analytic framework is demonstrated for a major part of the Red River Basin in Northern Vietnam (179.000 km2). Here, a plethora of anthropic alterations ranging from large reservoir construction to land-use changes results in major downstream deterioration and calls for deriving concerted sediment management strategies to mitigate current and limit future morphologic alterations.

  7. Identifying common components across biological network graphs using a bipartite data model

    PubMed Central

    2014-01-01

    The GeneWeaver bipartite data model provides an efficient means to evaluate shared molecular components from sets derived across diverse species, disease states and biological processes. In order to adapt this model for examining related molecular components and biological networks, such as pathway or gene network data, we have developed a means to leverage the bipartite data structure to extract and analyze shared edges. Using the Pathway Commons database we demonstrate the ability to rapidly identify shared connected components among a diverse set of pathways. In addition, we illustrate how results from maximal bipartite discovery can be decomposed into hierarchical relationships, allowing shared pathway components to be mapped through various parent-child relationships to help visualization and discovery of emergent kernel driven relationships. Interrogating common relationships among biological networks and conventional GeneWeaver gene lists will increase functional specificity and reliability of the shared biological components. This approach enables self-organization of biological processes through shared biological networks. PMID:25374613

  8. Contact Graph Routing

    NASA Technical Reports Server (NTRS)

    Burleigh, Scott C.

    2011-01-01

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

  9. RIM: A Random Item Mixture Model to Detect Differential Item Functioning

    ERIC Educational Resources Information Center

    Frederickx, Sofie; Tuerlinckx, Francis; De Boeck, Paul; Magis, David

    2010-01-01

    In this paper we present a new methodology for detecting differential item functioning (DIF). We introduce a DIF model, called the random item mixture (RIM), that is based on a Rasch model with random item difficulties (besides the common random person abilities). In addition, a mixture model is assumed for the item difficulties such that the…

  10. Modeling crash spatial heterogeneity: random parameter versus geographically weighting.

    PubMed

    Xu, Pengpeng; Huang, Helai

    2015-02-01

    The widely adopted techniques for regional crash modeling include the negative binomial model (NB) and Bayesian negative binomial model with conditional autoregressive prior (CAR). The outputs from both models consist of a set of fixed global parameter estimates. However, the impacts of predicting variables on crash counts might not be stationary over space. This study intended to quantitatively investigate this spatial heterogeneity in regional safety modeling using two advanced approaches, i.e., random parameter negative binomial model (RPNB) and semi-parametric geographically weighted Poisson regression model (S-GWPR). Based on a 3-year data set from the county of Hillsborough, Florida, results revealed that (1) both RPNB and S-GWPR successfully capture the spatially varying relationship, but the two methods yield notably different sets of results; (2) the S-GWPR performs best with the highest value of Rd(2) as well as the lowest mean absolute deviance and Akaike information criterion measures. Whereas the RPNB is comparable to the CAR, in some cases, it provides less accurate predictions; (3) a moderately significant spatial correlation is found in the residuals of RPNB and NB, implying the inadequacy in accounting for the spatial correlation existed across adjacent zones. As crash data are typically collected with reference to location dimension, it is desirable to firstly make use of the geographical component to explore explicitly spatial aspects of the crash data (i.e., the spatial heterogeneity, or the spatially structured varying relationships), then is the unobserved heterogeneity by non-spatial or fuzzy techniques. The S-GWPR is proven to be more appropriate for regional crash modeling as the method outperforms the global models in capturing the spatial heterogeneity occurring in the relationship that is model, and compared with the non-spatial model, it is capable of accounting for the spatial correlation in crash data. PMID:25460087

  11. Methods of visualizing graphs

    DOEpatents

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

    2008-12-23

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

  12. On designing heteroclinic networks from graphs

    NASA Astrophysics Data System (ADS)

    Ashwin, Peter; Postlethwaite, Claire

    2013-12-01

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

  13. Continuous percolation transition in suppressed random cluster growth model

    NASA Astrophysics Data System (ADS)

    Roy, Bappaditya; Santra, S. B.

    2016-05-01

    A new suppressed cluster growth model on 2D square lattice combining Hoshen-Kopelman and Leath approaches is studied here. The lattice sites are initially occupied randomly with probability (ρ). The empty perimeter sites of the clusters of occupied sites are grown with a cluster size dependent probability. The growth probability is then lowest for the largest cluster and highest for the smallest cluster. At the end of growth process all the cluster related quantities are estimated and they are found to display power law scaling as in percolation transition. However, the values of the critical exponents vary continuously with ρ, the initial seed concentration. At higher values of ρ, the model belongs the percolation universality class.

  14. A random interacting network model for complex networks

    NASA Astrophysics Data System (ADS)

    Goswami, Bedartha; Shekatkar, Snehal M.; Rheinwalt, Aljoscha; Ambika, G.; Kurths, Jürgen

    2015-12-01

    We propose a RAndom Interacting Network (RAIN) model to study the interactions between a pair of complex networks. The model involves two major steps: (i) the selection of a pair of nodes, one from each network, based on intra-network node-based characteristics, and (ii) the placement of a link between selected nodes based on the similarity of their relative importance in their respective networks. Node selection is based on a selection fitness function and node linkage is based on a linkage probability defined on the linkage scores of nodes. The model allows us to relate within-network characteristics to between-network structure. We apply the model to the interaction between the USA and Schengen airline transportation networks (ATNs). Our results indicate that two mechanisms: degree-based preferential node selection and degree-assortative link placement are necessary to replicate the observed inter-network degree distributions as well as the observed inter-network assortativity. The RAIN model offers the possibility to test multiple hypotheses regarding the mechanisms underlying network interactions. It can also incorporate complex interaction topologies. Furthermore, the framework of the RAIN model is general and can be potentially adapted to various real-world complex systems.

  15. A random interacting network model for complex networks

    PubMed Central

    Goswami, Bedartha; Shekatkar, Snehal M.; Rheinwalt, Aljoscha; Ambika, G.; Kurths, Jürgen

    2015-01-01

    We propose a RAndom Interacting Network (RAIN) model to study the interactions between a pair of complex networks. The model involves two major steps: (i) the selection of a pair of nodes, one from each network, based on intra-network node-based characteristics, and (ii) the placement of a link between selected nodes based on the similarity of their relative importance in their respective networks. Node selection is based on a selection fitness function and node linkage is based on a linkage probability defined on the linkage scores of nodes. The model allows us to relate within-network characteristics to between-network structure. We apply the model to the interaction between the USA and Schengen airline transportation networks (ATNs). Our results indicate that two mechanisms: degree-based preferential node selection and degree-assortative link placement are necessary to replicate the observed inter-network degree distributions as well as the observed inter-network assortativity. The RAIN model offers the possibility to test multiple hypotheses regarding the mechanisms underlying network interactions. It can also incorporate complex interaction topologies. Furthermore, the framework of the RAIN model is general and can be potentially adapted to various real-world complex systems. PMID:26657032

  16. A random interacting network model for complex networks.

    PubMed

    Goswami, Bedartha; Shekatkar, Snehal M; Rheinwalt, Aljoscha; Ambika, G; Kurths, Jürgen

    2015-01-01

    We propose a RAndom Interacting Network (RAIN) model to study the interactions between a pair of complex networks. The model involves two major steps: (i) the selection of a pair of nodes, one from each network, based on intra-network node-based characteristics, and (ii) the placement of a link between selected nodes based on the similarity of their relative importance in their respective networks. Node selection is based on a selection fitness function and node linkage is based on a linkage probability defined on the linkage scores of nodes. The model allows us to relate within-network characteristics to between-network structure. We apply the model to the interaction between the USA and Schengen airline transportation networks (ATNs). Our results indicate that two mechanisms: degree-based preferential node selection and degree-assortative link placement are necessary to replicate the observed inter-network degree distributions as well as the observed inter-network assortativity. The RAIN model offers the possibility to test multiple hypotheses regarding the mechanisms underlying network interactions. It can also incorporate complex interaction topologies. Furthermore, the framework of the RAIN model is general and can be potentially adapted to various real-world complex systems. PMID:26657032

  17. Modelling wildland fire propagation by tracking random fronts

    NASA Astrophysics Data System (ADS)

    Pagnini, G.; Mentrelli, A.

    2014-08-01

    Wildland fire propagation is studied in the literature by two alternative approaches, namely the reaction-diffusion equation and the level-set method. These two approaches are considered alternatives to each other because the solution of the reaction-diffusion equation is generally a continuous smooth function that has an exponential decay, and it is not zero in an infinite domain, while the level-set method, which is a front tracking technique, generates a sharp function that is not zero inside a compact domain. However, these two approaches can indeed be considered complementary and reconciled. Turbulent hot-air transport and fire spotting are phenomena with a random nature and they are extremely important in wildland fire propagation. Consequently, the fire front gets a random character, too; hence, a tracking method for random fronts is needed. In particular, the level-set contour is randomised here according to the probability density function of the interface particle displacement. Actually, when the level-set method is developed for tracking a front interface with a random motion, the resulting averaged process emerges to be governed by an evolution equation of the reaction-diffusion type. In this reconciled approach, the rate of spread of the fire keeps the same key and characterising role that is typical of the level-set approach. The resulting model emerges to be suitable for simulating effects due to turbulent convection, such as fire flank and backing fire, the faster fire spread being because of the actions by hot-air pre-heating and by ember landing, and also due to the fire overcoming a fire-break zone, which is a case not resolved by models based on the level-set method. Moreover, from the proposed formulation, a correction follows for the formula of the rate of spread which is due to the mean jump length of firebrands in the downwind direction for the leeward sector of the fireline contour. The presented study constitutes a proof of concept, and it

  18. Modeling Temporal Variation in Social Network: An Evolutionary Web Graph Approach

    NASA Astrophysics Data System (ADS)

    Mitra, Susanta; Bagchi, Aditya

    A social network is a social structure between actors (individuals, organization or other social entities) and indicates the ways in which they are connected through various social relationships like friendships, kinships, professional, academic etc. Usually, a social network represents a social community, like a club and its members or a city and its citizens etc. or a research group communicating over Internet. In seventies Leinhardt [1] first proposed the idea of representing a social community by a digraph. Later, this idea became popular among other research workers like, network designers, web-service application developers and e-learning modelers. It gave rise to a rapid proliferation of research work in the area of social network analysis. Some of the notable structural properties of a social network are connectedness between actors, reachability between a source and a target actor, reciprocity or pair-wise connection between actors with bi-directional links, centrality of actors or the important actors having high degree or more connections and finally the division of actors into sub-structures or cliques or strongly-connected components. The cycles present in a social network may even be nested [2, 3]. The formal definition of these structural properties will be provided in Sect. 8.2.1. The division of actors into cliques or sub-groups can be a very important factor for understanding a social structure, particularly the degree of cohesiveness in a community. The number, size, and connections among the sub-groups in a network are useful in understanding how the network, as a whole, is likely to behave.

  19. Graph theory for analyzing pair-wise data: application to geophysical model parameters estimated from interferometric synthetic aperture radar data at Okmok volcano, Alaska

    NASA Astrophysics Data System (ADS)

    Reinisch, Elena C.; Cardiff, Michael; Feigl, Kurt L.

    2016-07-01

    Graph theory is useful for analyzing time-dependent model parameters estimated from interferometric synthetic aperture radar (InSAR) data in the temporal domain. Plotting acquisition dates (epochs) as vertices and pair-wise interferometric combinations as edges defines an incidence graph. The edge-vertex incidence matrix and the normalized edge Laplacian matrix are factors in the covariance matrix for the pair-wise data. Using empirical measures of residual scatter in the pair-wise observations, we estimate the relative variance at each epoch by inverting the covariance of the pair-wise data. We evaluate the rank deficiency of the corresponding least-squares problem via the edge-vertex incidence matrix. We implement our method in a MATLAB software package called GraphTreeTA available on GitHub (https://github.com/feigl/gipht). We apply temporal adjustment to the data set described in Lu et al. (Geophys Res Solid Earth 110, 2005) at Okmok volcano, Alaska, which erupted most recently in 1997 and 2008. The data set contains 44 differential volumetric changes and uncertainties estimated from interferograms between 1997 and 2004. Estimates show that approximately half of the magma volume lost during the 1997 eruption was recovered by the summer of 2003. Between June 2002 and September 2003, the estimated rate of volumetric increase is (6.2 ± 0.6) × 10^6~m^3/year . Our preferred model provides a reasonable fit that is compatible with viscoelastic relaxation in the five years following the 1997 eruption. Although we demonstrate the approach using volumetric rates of change, our formulation in terms of incidence graphs applies to any quantity derived from pair-wise differences, such as range change, range gradient, or atmospheric delay.

  20. Mechanisms of evolution of avalanches in regular graphs

    NASA Astrophysics Data System (ADS)

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

    2013-06-01

    A mapping of avalanches occurring in the zero-temperature random-field Ising model to life periods of a population experiencing immigration is established. Such a mapping allows the microscopic criteria for the occurrence of an infinite avalanche in a q-regular graph to be determined. A key factor for an avalanche of spin flips to become infinite is that it interacts in an optimal way with previously flipped spins. Based on these criteria, we explain why an infinite avalanche can occur in q-regular graphs only for q>3 and suggest that this criterion might be relevant for other systems. The generating function techniques developed for branching processes are applied to obtain analytical expressions for the durations, pulse shapes, and power spectra of the avalanches. The results show that only very long avalanches exhibit a significant degree of universality.

  1. Graph Theory Enables Drug Repurposing – How a Mathematical Model Can Drive the Discovery of Hidden Mechanisms of Action

    PubMed Central

    Gramatica, Ruggero; Di Matteo, T.; Giorgetti, Stefano; Barbiani, Massimo; Bevec, Dorian; Aste, Tomaso

    2014-01-01

    We introduce a methodology to efficiently exploit natural-language expressed biomedical knowledge for repurposing existing drugs towards diseases for which they were not initially intended. Leveraging on developments in Computational Linguistics and Graph Theory, a methodology is defined to build a graph representation of knowledge, which is automatically analysed to discover hidden relations between any drug and any disease: these relations are specific paths among the biomedical entities of the graph, representing possible Modes of Action for any given pharmacological compound. We propose a measure for the likeliness of these paths based on a stochastic process on the graph. This measure depends on the abundance of indirect paths between a peptide and a disease, rather than solely on the strength of the shortest path connecting them. We provide real-world examples, showing how the method successfully retrieves known pathophysiological Mode of Action and finds new ones by meaningfully selecting and aggregating contributions from known bio-molecular interactions. Applications of this methodology are presented, and prove the efficacy of the method for selecting drugs as treatment options for rare diseases. PMID:24416311

  2. Modeling the Relationships between Test-Taking Strategies and Test Performance on a Graph-Writing Task: Implications for EAP

    ERIC Educational Resources Information Center

    Yang, Hui-Chun

    2012-01-01

    With the increasing use of integrated tasks in assessing writing, more and more research studies have been conducted to examine the construct validity of such tasks. Previous studies have largely focused on reading-writing tasks, while relatively little is known about graph-writing tasks. This study examines second language (L2) writers'…

  3. Fast Kalman Filter for Random Walk Forecast model

    NASA Astrophysics Data System (ADS)

    Saibaba, A.; Kitanidis, P. K.

    2013-12-01

    Kalman filtering is a fundamental tool in statistical time series analysis to understand the dynamics of large systems for which limited, noisy observations are available. However, standard implementations of the Kalman filter are prohibitive because they require O(N^2) in memory and O(N^3) in computational cost, where N is the dimension of the state variable. In this work, we focus our attention on the Random walk forecast model which assumes the state transition matrix to be the identity matrix. This model is frequently adopted when the data is acquired at a timescale that is faster than the dynamics of the state variables and there is considerable uncertainty as to the physics governing the state evolution. We derive an efficient representation for the a priori and a posteriori estimate covariance matrices as a weighted sum of two contributions - the process noise covariance matrix and a low rank term which contains eigenvectors from a generalized eigenvalue problem, which combines information from the noise covariance matrix and the data. We describe an efficient algorithm to update the weights of the above terms and the computation of eigenmodes of the generalized eigenvalue problem (GEP). The resulting algorithm for the Kalman filter with Random walk forecast model scales as O(N) or O(N log N), both in memory and computational cost. This opens up the possibility of real-time adaptive experimental design and optimal control in systems of much larger dimension than was previously feasible. For a small number of measurements (~ 300 - 400), this procedure can be made numerically exact. However, as the number of measurements increase, for several choices of measurement operators and noise covariance matrices, the spectrum of the (GEP) decays rapidly and we are justified in only retaining the dominant eigenmodes. We discuss tradeoffs between accuracy and computational cost. The resulting algorithms are applied to an example application from ray-based travel time

  4. Percolation on correlated random networks

    NASA Astrophysics Data System (ADS)

    Agliari, E.; Cioli, C.; Guadagnini, E.

    2011-09-01

    We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model, and, by performing percolation processes, we get information about topology and resilience properties of the networks themselves. Given the weighted nature of the graphs, different kinds of bond percolation can be studied: stochastic (deleting links randomly) and deterministic (deleting links based on rank weights), each mimicking a different physical process. The evolution of the network is accordingly different, as evidenced by the behavior of the largest component size and of the distribution of cluster sizes. In particular, we can derive that weak ties are crucial in order to maintain the graph connected and that, when they are the most prone to failure, the giant component typically shrinks without abruptly breaking apart; these results have been recently evidenced in several kinds of social networks.

  5. Understanding earthquake source processes with spatial random field models

    NASA Astrophysics Data System (ADS)

    Song, S.

    2011-12-01

    Earthquake rupture is a complex mechanical process that can be formulated as a dynamically running shear crack on a frictional interface embedded in an elastic continuum. This type of dynamic description of earthquake rupture is often preferred among researchers because they believe the kinematic description is likely to miss physical constraints introduced by dynamic approaches and to lead to arbitrary and nonphysical kinematic fault motions. However, dynamic rupture modeling, although they produce physically consistent models, often uses arbitrary input parameters, e.g., stress and fracture energy, partially because they are more difficult to constrain with data compared to kinematic ones. I propose to describe earthquake rupture as a stochastic model with a set of random variables (e.g., random field) that represent the spatial distribution of kinematic source parameters such as slip, rupture velocity, slip duration and velocity. This is a kinematic description of earthquake rupture in the sense that a model is formulated with kinematic parameters, but since the model can be constrained by both rupture dynamics and data, it may have both physical and observational constraints inside. The stochastic model is formulated by quantifying the 1-point and 2-point statistics of the kinematic parameters. 1-point statistics define a marginal probability density function for a certain source parameter at a given point on a fault. For example, a probability distribution for earthquake slip at a given point can control a possible range of values taken by earthquake slip and their likelihood. In the same way, we can control the existence of supershear rupture with a 1-point variability of the rupture velocity. Two point statistics, i.e. auto- and cross-coherence between source parameters, control the heterogeneity of each source parameter and their coupling, respectively. Several interesting features of earthquake rupture have been found by investigating cross

  6. Graph500 in OpenSHMEM

    SciTech Connect

    D'Azevedo, Ed F; Imam, Neena

    2015-01-01

    This document describes the effort to implement the Graph 500 benchmark using OpenSHMEM based on the MPI-2 one-side version. The Graph 500 benchmark performs a breadth-first search in parallel on a large randomly generated undirected graph and can be implemented using basic MPI-1 and MPI-2 one-sided communication. Graph 500 requires atomic bit-wise operations on unsigned long integers but neither atomic bit-wise operations nor OpenSHMEM for unsigned long are available in OpenSHEM. Such needed bit-wise atomic operations and support for unsigned long are implemented using atomic condition swap (CSWAP) on signed long integers. Preliminary results on comparing the OpenSHMEM and MPI-2 one-sided implementations on a Silicon Graphics Incorporated (SGI) cluster and the Cray XK7 are presented.

  7. Hedonic travel cost and random utility models of recreation

    SciTech Connect

    Pendleton, L.; Mendelsohn, R.; Davis, E.W.

    1998-07-09

    Micro-economic theory began as an attempt to describe, predict and value the demand and supply of consumption goods. Quality was largely ignored at first, but economists have started to address quality within the theory of demand and specifically the question of site quality, which is an important component of land management. This paper demonstrates that hedonic and random utility models emanate from the same utility theoretical foundation, although they make different estimation assumptions. Using a theoretically consistent comparison, both approaches are applied to examine the quality of wilderness areas in the Southeastern US. Data were collected on 4778 visits to 46 trails in 20 different forest areas near the Smoky Mountains. Visitor data came from permits and an independent survey. The authors limited the data set to visitors from within 300 miles of the North Carolina and Tennessee border in order to focus the analysis on single purpose trips. When consistently applied, both models lead to results with similar signs but different magnitudes. Because the two models are equally valid, recreation studies should continue to use both models to value site quality. Further, practitioners should be careful not to make simplifying a priori assumptions which limit the effectiveness of both techniques.

  8. Spin-glass phase transitions and minimum energy of the random feedback vertex set problem.

    PubMed

    Qin, Shao-Meng; Zeng, Ying; Zhou, Hai-Jun

    2016-08-01

    A feedback vertex set (FVS) of an undirected graph contains vertices from every cycle of this graph. Constructing a FVS of sufficiently small cardinality is very difficult in the worst cases, but for random graphs this problem can be efficiently solved by converting it into an appropriate spin-glass model [H.-J. Zhou, Eur. Phys. J. B 86, 455 (2013)EPJBFY1434-602810.1140/epjb/e2013-40690-1]. In the present work we study the spin-glass phase transitions and the minimum energy density of the random FVS problem by the first-step replica-symmetry-breaking (1RSB) mean-field theory. For both regular random graphs and Erdös-Rényi graphs, we determine the inverse temperature β_{l} at which the replica-symmetric mean-field theory loses its local stability, the inverse temperature β_{d} of the dynamical (clustering) phase transition, and the inverse temperature β_{s} of the static (condensation) phase transition. These critical inverse temperatures all change with the mean vertex degree in a nonmonotonic way, and β_{d} is distinct from β_{s} for regular random graphs of vertex degrees K>60, while β_{d} are identical to β_{s} for Erdös-Rényi graphs at least up to mean vertex degree c=512. We then derive the zero-temperature limit of the 1RSB theory and use it to compute the minimum FVS cardinality. PMID:27627285

  9. [Critical of the additive model of the randomized controlled trial].

    PubMed

    Boussageon, Rémy; Gueyffier, François; Bejan-Angoulvant, Theodora; Felden-Dominiak, Géraldine

    2008-01-01

    Randomized, double-blind, placebo-controlled clinical trials are currently the best way to demonstrate the clinical effectiveness of drugs. Its methodology relies on the method of difference (John Stuart Mill), through which the observed difference between two groups (drug vs placebo) can be attributed to the pharmacological effect of the drug being tested. However, this additive model can be questioned in the event of statistical interactions between the pharmacological and the placebo effects. Evidence in different domains has shown that the placebo effect can influence the effect of the active principle. This article evaluates the methodological, clinical and epistemological consequences of this phenomenon. Topics treated include extrapolating results, accounting for heterogeneous results, demonstrating the existence of several factors in the placebo effect, the necessity to take these factors into account for given symptoms or pathologies, as well as the problem of the "specific" effect. PMID:18387273

  10. Efficient Ab initio Modeling of Random Multicomponent Alloys

    NASA Astrophysics Data System (ADS)

    Jiang, Chao; Uberuaga, Blas P.

    2016-03-01

    We present in this Letter a novel small set of ordered structures (SSOS) method that allows extremely efficient ab initio modeling of random multicomponent alloys. Using inverse II-III spinel oxides and equiatomic quinary bcc (so-called high entropy) alloys as examples, we demonstrate that a SSOS can achieve the same accuracy as a large supercell or a well-converged cluster expansion, but with significantly reduced computational cost. In particular, because of this efficiency, a large number of quinary alloy compositions can be quickly screened, leading to the identification of several new possible high-entropy alloy chemistries. The SSOS method developed here can be broadly useful for the rapid computational design of multicomponent materials, especially those with a large number of alloying elements, a challenging problem for other approaches.

  11. Local random potentials of high differentiability to model the Landscape

    SciTech Connect

    Battefeld, T.; Modi, C.

    2015-03-09

    We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class C{sup k}, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble (other ensembles might be chosen if desired). Potentials in such higher differentiability classes (k≥2) are required/desirable to model string theoretical landscapes, for instance to compute cosmological perturbations (e.g., k=2 for the power-spectrum) or to search for minima (e.g., suitable de Sitter vacua for our universe). Since potentials are created locally, numerical studies become feasible even if the dimension of field space is large (D∼100). In addition to the theoretical prescription, we provide some numerical examples to highlight properties of such potentials; concrete cosmological applications will be discussed in companion publications.

  12. Local random potentials of high differentiability to model the Landscape

    NASA Astrophysics Data System (ADS)

    Battefeld, T.; Modi, C.

    2015-03-01

    We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class Ck, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble (other ensembles might be chosen if desired). Potentials in such higher differentiability classes (k>= 2) are required/desirable to model string theoretical landscapes, for instance to compute cosmological perturbations (e.g., k=2 for the power-spectrum) or to search for minima (e.g., suitable de Sitter vacua for our universe). Since potentials are created locally, numerical studies become feasible even if the dimension of field space is large (0D~ 10). In addition to the theoretical prescription, we provide some numerical examples to highlight properties of such potentials; concrete cosmological applications will be discussed in companion publications.

  13. Continuum random-phase approximation for relativistic point coupling models

    SciTech Connect

    Daoutidis, J.; Ring, P.

    2009-08-15

    Continuum relativistic random-phase approximation (CRPA) is used to investigate collective excitation phenomena in several spherical nuclei along the periodic table. We start from relativistic mean-field calculations based on a covariant density functional with density-dependent zero-range forces. From the same functional an effective interaction is obtained as the second derivative with respect to the density. This interaction is used in relativistic CRPA calculations for the investigation of isoscalar monopole, isovector dipole, and isoscalar quadrupole resonances of spherical nuclei. In particular we study the low-lying E1 strength in the vicinity of the neutron evaporation threshold. The properties of the resonances, such as centroid energies and strengths distributions are compared with results of discrete RPA calculations for the same model as well as with experimental data.

  14. Efficient Ab initio Modeling of Random Multicomponent Alloys.

    PubMed

    Jiang, Chao; Uberuaga, Blas P

    2016-03-11

    We present in this Letter a novel small set of ordered structures (SSOS) method that allows extremely efficient ab initio modeling of random multicomponent alloys. Using inverse II-III spinel oxides and equiatomic quinary bcc (so-called high entropy) alloys as examples, we demonstrate that a SSOS can achieve the same accuracy as a large supercell or a well-converged cluster expansion, but with significantly reduced computational cost. In particular, because of this efficiency, a large number of quinary alloy compositions can be quickly screened, leading to the identification of several new possible high-entropy alloy chemistries. The SSOS method developed here can be broadly useful for the rapid computational design of multicomponent materials, especially those with a large number of alloying elements, a challenging problem for other approaches. PMID:27015491

  15. Generative Graph Prototypes from Information Theory.

    PubMed

    Han, Lin; Wilson, Richard C; Hancock, Edwin R

    2015-10-01

    In this paper we present a method for constructing a generative prototype for a set of graphs by adopting a minimum description length approach. The method is posed in terms of learning a generative supergraph model from which the new samples can be obtained by an appropriate sampling mechanism. We commence by constructing a probability distribution for the occurrence of nodes and edges over the supergraph. We encode the complexity of the supergraph using an approximate Von Neumann entropy. A variant of the EM algorithm is developed to minimize the description length criterion in which the structure of the supergraph and the node correspondences between the sample graphs and the supergraph are treated as missing data. To generate new graphs, we assume that the nodes and edges of graphs arise under independent Bernoulli distributions and sample new graphs according to their node and edge occurrence probabilities. Empirical evaluations on real-world databases demonstrate the practical utility of the proposed algorithm and show the effectiveness of the generative model for the tasks of graph classification, graph clustering and generating new sample graphs. PMID:26340255

  16. Measuring Graph Comprehension, Critique, and Construction in Science

    ERIC Educational Resources Information Center

    Lai, Kevin; Cabrera, Julio; Vitale, Jonathan M.; Madhok, Jacquie; Tinker, Robert; Linn, Marcia C.

    2016-01-01

    Interpreting and creating graphs plays a critical role in scientific practice. The K-12 Next Generation Science Standards call for students to use graphs for scientific modeling, reasoning, and communication. To measure progress on this dimension, we need valid and reliable measures of graph understanding in science. In this research, we designed…

  17. Evolution in random fitness landscapes: the infinite sites model

    NASA Astrophysics Data System (ADS)

    Park, Su-Chan; Krug, Joachim

    2008-04-01

    We consider the evolution of an asexually reproducing population in an uncorrelated random fitness landscape in the limit of infinite genome size, which implies that each mutation generates a new fitness value drawn from a probability distribution g(w). This is the finite population version of Kingman's house of cards model (Kingman 1978 J. Appl. Probab. 15 1). In contrast to Kingman's work, the focus here is on unbounded distributions g(w) which lead to an indefinite growth of the population fitness. The model is solved analytically in the limit of infinite population size N \\to \\infty and simulated numerically for finite N. When the genome-wide mutation probability U is small, the long-time behavior of the model reduces to a point process of fixation events, which is referred to as a diluted record process (DRP). The DRP is similar to the standard record process except that a new record candidate (a number that exceeds all previous entries in the sequence) is accepted only with a certain probability that depends on the values of the current record and the candidate. We develop a systematic analytic approximation scheme for the DRP. At finite U the fitness frequency distribution of the population decomposes into a stationary part due to mutations and a traveling wave component due to selection, which is shown to imply a reduction of the mean fitness by a factor of 1-U compared to the U \\to 0 limit.

  18. Modeling X Chromosome Data Using Random Forests: Conquering Sex Bias.

    PubMed

    Winham, Stacey J; Jenkins, Gregory D; Biernacka, Joanna M

    2016-02-01

    Machine learning methods, including Random Forests (RF), are increasingly used for genetic data analysis. However, the standard RF algorithm does not correctly model the effects of X chromosome single nucleotide polymorphisms (SNPs), leading to biased estimates of variable importance. We propose extensions of RF to correctly model X SNPs, including a stratified approach and an approach based on the process of X chromosome inactivation. We applied the new and standard RF approaches to case-control alcohol dependence data from the Study of Addiction: Genes and Environment (SAGE), and compared the performance of the alternative approaches via a simulation study. Standard RF applied to a case-control study of alcohol dependence yielded inflated variable importance estimates for X SNPs, even when sex was included as a variable, but the results of the new RF methods were consistent with univariate regression-based approaches that correctly model X chromosome data. Simulations showed that the new RF methods eliminate the bias in standard RF variable importance for X SNPs when sex is associated with the trait, and are able to detect causal autosomal and X SNPs. Even in the absence of sex effects, the new extensions perform similarly to standard RF. Thus, we provide a powerful multimarker approach for genetic analysis that accommodates X chromosome data in an unbiased way. This method is implemented in the freely available R package "snpRF" (http://www.cran.r-project.org/web/packages/snpRF/). PMID:26639183

  19. Topologies on directed graphs

    NASA Technical Reports Server (NTRS)

    Lieberman, R. N.

    1972-01-01

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

  20. Graph Generator Survey

    SciTech Connect

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

    2013-12-01

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

  1. mpiGraph

    Energy Science and Technology Software Center (ESTSC)

    2007-05-22

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

  2. mpiGraph

    SciTech Connect

    Moody, Adam

    2007-05-22

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

  3. Multi-A Graph Patrolling and Partitioning

    NASA Astrophysics Data System (ADS)

    Elor, Y.; Bruckstein, A. M.

    2012-12-01

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

  4. Object-oriented Markov random model for classification of high resolution satellite imagery based on wavelet transform

    NASA Astrophysics Data System (ADS)

    Hong, Liang; Liu, Cun; Yang, Kun; Deng, Ming

    2013-07-01

    The high resolution satellite imagery (HRSI) have higher spatial resolution and less spectrum number, so there are some "object with different spectra, different objects with same spectrum" phenomena. The objective of this paper is to utilize the extracted features of high resolution satellite imagery (HRSI) obtained by the wavelet transform(WT) for segmentation. WT provides the spatial and spectral characteristics of a pixel along with its neighbors. The object-oriented Markov random Model in the wavelet domain is proposed in order to segment high resolution satellite imagery (HRSI). The proposed method is made up of three blocks: (1) WT-based feature extrcation.the aim of extraction of feature using WT for original spectral bands is to exploit the spatial and frequency information of the pixels; (2) over-segmentation object generation. Mean-Shift algorithm is employed to obtain over-segmentation objects; (3) classification based on Object-oriented Markov Random Model. Firstly the object adjacent graph (OAG) can be constructed on the over-segmentation objects. Secondly MRF model is easily defined on the OAG, in which WT-based feature of pixels are modeled in the feature field model and the neighbor system, potential cliques and energy functions of OAG are exploited in the labeling model. Experiments are conducted on one HRSI dataset-QuickBird images. We evaluate and compare the proposed approach with the well-known commercial software eCognition(object-based analysis approach) and Maximum Likelihood(ML) based pixels. Experimental results show that the proposed the method in this paper obviously outperforms the other methods.

  5. Time series, correlation matrices and random matrix models

    SciTech Connect

    Vinayak; Seligman, Thomas H.

    2014-01-08

    In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null hypothesis or a minimum information hypothesis for the description of a quantum system or subsystem. In the former case various forms of correlation matrices of time series associated with the classical observables of some system. The fact that such series are necessarily finite, inevitably introduces noise and this finite time influence lead to a random or stochastic component in these time series. By consequence random correlation matrices have a random component, and corresponding ensembles are used. In the latter we use random matrices to describe high temperature environment or uncontrolled perturbations, ensembles of differing chaotic systems etc. The common theme of the lectures is thus the importance of random matrix theory in a wide range of fields in and around physics.

  6. Wealth condensation in a multiplicative random asset exchange model

    NASA Astrophysics Data System (ADS)

    Moukarzel, C. F.; Gonçalves, S.; Iglesias, J. R.; Rodríguez-Achach, M.; Huerta-Quintanilla, R.

    2007-04-01

    Random Asset Exchange (RAE) models, despite a number of simplifying assumptions, serve the purpose of establishing direct relationships between microscopic exchange mechanisms and observed economical data. In this work a conservative multiplicative RAE model is discussed in which, at each timestep, two agents “bet” for a fraction f of the poorest agent's wealth. When the poorest agent wins the bet with probability p, we show that, in a well defined region of the (p,f) phase space, there is wealth condensation. This means that all wealth ends up owned by only one agent, in the long run. We derive the condensation conditions analytically by two different procedures, and find results in accordance with previous numerical estimates. In the non-condensed phase, the equilibrium wealth distribution is a power law for small wealths. The associated exponent is derived analytically and it is found that it tends to -1 on the condensation interface. I turns out that wealth condensation happens also for values of p much larger than 0.5, that is under microscopic exchange rules that, apparently, favor the poor. We argue that the observed “rich get richer” effect is enhanced by the multiplicative character of the dynamics.

  7. A Unified Approach to Power Calculation and Sample Size Determination for Random Regression Models

    ERIC Educational Resources Information Center

    Shieh, Gwowen

    2007-01-01

    The underlying statistical models for multiple regression analysis are typically attributed to two types of modeling: fixed and random. The procedures for calculating power and sample size under the fixed regression models are well known. However, the literature on random regression models is limited and has been confined to the case of all…

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

    SciTech Connect

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

    2015-01-01

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

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

    DOE PAGESBeta

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

    2015-01-01

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

  10. A Graph Search Heuristic for Shortest Distance Paths

    SciTech Connect

    Chow, E

    2005-03-24

    This paper presents a heuristic for guiding A* search for finding the shortest distance path between two vertices in a connected, undirected, and explicitly stored graph. The heuristic requires a small amount of data to be stored at each vertex. The heuristic has application to quickly detecting relationships between two vertices in a large information or knowledge network. We compare the performance of this heuristic with breadth-first search on graphs with various topological properties. The results show that one or more orders of magnitude improvement in the number of vertices expanded is possible for large graphs, including Poisson random graphs.

  11. Communication Graph Generator for Parallel Programs

    Energy Science and Technology Software Center (ESTSC)

    2014-04-08

    Graphator is a collection of relatively simple sequential programs that generate communication graphs/matrices for commonly occurring patterns in parallel programs. Currently, there is support for five communication patterns: two-dimensional 4-point stencil, four-dimensional 8-point stencil, all-to-alls over sub-communicators, random near-neighbor communication, and near-neighbor communication.

  12. Expert interpretation of bar and line graphs: the role of graphicacy in reducing the effect of graph format

    PubMed Central

    Peebles, David; Ali, Nadia

    2015-01-01

    The distinction between informational and computational equivalence of representations, first articulated by Larkin and Simon (1987) has been a fundamental principle in the analysis of diagrammatic reasoning which has been supported empirically on numerous occasions. We present an experiment that investigates this principle in relation to the performance of expert graph users of 2 × 2 “interaction” bar and line graphs. The study sought to determine whether expert interpretation is affected by graph format in the same way that novice interpretations are. The findings revealed that, unlike novices—and contrary to the assumptions of several graph comprehension models—experts' performance was the same for both graph formats, with their interpretation of bar graphs being no worse than that for line graphs. We discuss the implications of the study for guidelines for presenting such data and for models of expert graph comprehension. PMID:26579052

  13. Graph Theory and the High School Student.

    ERIC Educational Resources Information Center

    Chartrand, Gary; Wall, Curtiss E.

    1980-01-01

    Graph theory is presented as a tool to instruct high school mathematics students. A variety of real world problems can be modeled which help students recognize the importance and difficulty of applying mathematics. (MP)

  14. Continuous Time Group Discovery in Dynamic Graphs

    SciTech Connect

    Miller, K; Eliassi-Rad, T

    2010-11-04

    With the rise in availability and importance of graphs and networks, it has become increasingly important to have good models to describe their behavior. While much work has focused on modeling static graphs, we focus on group discovery in dynamic graphs. We adapt a dynamic extension of Latent Dirichlet Allocation to this task and demonstrate good performance on two datasets. Modeling relational data has become increasingly important in recent years. Much work has focused on static graphs - that is fixed graphs at a single point in time. Here we focus on the problem of modeling dynamic (i.e. time-evolving) graphs. We propose a scalable Bayesian approach for community discovery in dynamic graphs. Our approach is based on extensions of Latent Dirichlet Allocation (LDA). LDA is a latent variable model for topic modeling in text corpora. It was extended to deal with topic changes in discrete time and later in continuous time. These models were referred to as the discrete Dynamic Topic Model (dDTM) and the continuous Dynamic Topic Model (cDTM), respectively. When adapting these models to graphs, we take our inspiration from LDA-G and SSN-LDA, applications of LDA to static graphs that have been shown to effectively factor out community structure to explain link patterns in graphs. In this paper, we demonstrate how to adapt and apply the cDTM to the task of finding communities in dynamic networks. We use link prediction to measure the quality of the discovered community structure and apply it to two different relational datasets - DBLP author-keyword and CAIDA autonomous systems relationships. We also discuss a parallel implementation of this approach using Hadoop. In Section 2, we review LDA and LDA-G. In Section 3, we review the cDTM and introduce cDTMG, its adaptation to modeling dynamic graphs. We discuss inference for the cDTM-G and details of our parallel implementation in Section 4 and present its performance on two datasets in Section 5 before concluding in

  15. Making "Photo" Graphs

    ERIC Educational Resources Information Center

    Doto, Julianne; Golbeck, Susan

    2007-01-01

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

  16. Reflections on "The Graph"

    ERIC Educational Resources Information Center

    Petrosino, Anthony

    2012-01-01

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

  17. Exploring Graphs: WYSIWYG.

    ERIC Educational Resources Information Center

    Johnson, Millie

    1997-01-01

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

  18. Walking Out Graphs

    ERIC Educational Resources Information Center

    Shen, Ji

    2009-01-01

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

  19. Real World Graph Connectivity

    ERIC Educational Resources Information Center

    Lind, Joy; Narayan, Darren

    2009-01-01

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

  20. Graphing Electric Potential.

    ERIC Educational Resources Information Center

    De Jong, Marvin L.

    1993-01-01

    Describes the powerful graphing ability of computer algebra systems (CAS) to create three-dimensional graphs or surface graphics of electric potentials. Provides equations along with examples of the printouts. Lists the programs Mathematica, Maple, Derive, Theorist, MathCad, and MATLAB as promising CAS systems. (MVL)