Science.gov

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. 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

  2. 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.

  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. 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.

  7. 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.

  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

    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.

  14. 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.

  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. 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

  3. 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

  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

    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

  1. Evolutionary Games of Multiplayer Cooperation on Graphs

    PubMed Central

    Arranz, Jordi; Traulsen, Arne

    2016-01-01

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

  2. 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. 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.

  9. 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.

  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. 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…

  18. 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

  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. 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…

  11. 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.

  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. 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

  4. 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

  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. 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.

  1. 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

  2. Quantum walks on quotient graphs

    SciTech Connect

    Krovi, Hari; Brun, Todd A.

    2007-06-15

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

  3. 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. 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

  5. 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.

  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. 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.

  19. 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

  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. 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.

  2. 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

  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

    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.

  6. 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

  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. 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.

  10. 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