A PAC-Bayesian Analysis of Graph Clustering and Pairwise Clustering
Seldin, Yevgeny
2010-01-01
We formulate weighted graph clustering as a prediction problem: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison of different approaches to graph clustering as well as comparison of graph clustering with other possible ways to model the graph. We adapt the PAC-Bayesian analysis of co-clustering (Seldin and Tishby, 2008; Seldin, 2009) to derive a PAC-Bayesian generalization bound for graph clustering. The bound shows that graph clustering should optimize a trade-off between empirical data fit and the mutual information that clusters preserve on the graph nodes. A similar trade-off derived from information-theoretic considerations was already shown to produce state-of-the-art results in practice (Slonim et al., 2005; Yom-Tov and Slonim, 2009). This paper supports the empirical evidence by providing a better theoretical foundation, suggesting formal generalization guarantees, and offering...
Xu, Zhiqiang
2017-02-16
Attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.
Detecting alternative graph clusterings.
Mandala, Supreet; Kumara, Soundar; Yao, Tao
2012-07-01
The problem of graph clustering or community detection has enjoyed a lot of attention in complex networks literature. A quality function, modularity, quantifies the strength of clustering and on maximization yields sensible partitions. However, in most real world networks, there are an exponentially large number of near-optimal partitions with some being very different from each other. Therefore, picking an optimal clustering among the alternatives does not provide complete information about network topology. To tackle this problem, we propose a graph perturbation scheme which can be used to identify an ensemble of near-optimal and diverse clusterings. We establish analytical properties of modularity function under the perturbation which ensures diversity. Our approach is algorithm independent and therefore can leverage any of the existing modularity maximizing algorithms. We numerically show that our methodology can systematically identify very different partitions on several existing data sets. The knowledge of diverse partitions sheds more light into the topological organization and helps gain a more complete understanding of the underlying complex network.
Energy Technology Data Exchange (ETDEWEB)
Winlaw, Manda [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); De Sterck, Hans [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoffrey [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-26
In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.
Hierarchical clustering for graph visualization
Clémençon, Stéphan; Rossi, Fabrice; Tran, Viet Chi
2012-01-01
This paper describes a graph visualization methodology based on hierarchical maximal modularity clustering, with interactive and significant coarsening and refining possibilities. An application of this method to HIV epidemic analysis in Cuba is outlined.
A new cluster algorithm for graphs
Dongen, S. van
1998-01-01
A new cluster algorithm for graphs called the emph{Markov Cluster algorithm ($MCL$ algorithm) is introduced. The graphs may be both weighted (with nonnegative weight) and directed. Let~$G$~be such a graph. The $MCL$ algorithm simulates flow in $G$ by first identifying $G$ in a canonical way with
Graph coarsening and clustering on the GPU
Fagginger Auer, B.O.; Bisseling, R.H.
2013-01-01
Agglomerative clustering is an effective greedy way to quickly generate graph clusterings of high modularity in a small amount of time. In an effort to use the power offered by multi-core CPU and GPU hardware to solve the clustering problem, we introduce a fine-grained sharedmemory parallel graph co
Malware Classification based on Call Graph Clustering
Kinable, Joris
2010-01-01
Each day, anti-virus companies receive tens of thousands samples of potentially harmful executables. Many of the malicious samples are variations of previously encountered malware, created by their authors to evade pattern-based detection. Dealing with these large amounts of data requires robust, automatic detection approaches. This paper studies malware classification based on call graph clustering. By representing malware samples as call graphs, it is possible to abstract certain variations away, and enable the detection of structural similarities between samples. The ability to cluster similar samples together will make more generic detection techniques possible, thereby targeting the commonalities of the samples within a cluster. To compare call graphs mutually, we compute pairwise graph similarity scores via graph matchings which approximately minimize the graph edit distance. Next, to facilitate the discovery of similar malware samples, we employ several clustering algorithms, including k-medoids and DB...
Graph Clustering with Density-Cut
Shao, Junming; Liu, Jinhu; Kramer, Stefan
2016-01-01
How can we find a good graph clustering of a real-world network, that allows insight into its underlying structure and also potential functions? In this paper, we introduce a new graph clustering algorithm Dcut from a density point of view. The basic idea is to envision the graph clustering as a density-cut problem, such that the vertices in the same cluster are densely connected and the vertices between clusters are sparsely connected. To identify meaningful clusters (communities) in a graph, a density-connected tree is first constructed in a local fashion. Owing to the density-connected tree, Dcut allows partitioning a graph into multiple densely tight-knit clusters directly. We demonstrate that our method has several attractive benefits: (a) Dcut provides an intuitive criterion to evaluate the goodness of a graph clustering in a more natural and precise way; (b) Built upon the density-connected tree, Dcut allows identifying the meaningful graph clusters of densely connected vertices efficiently; (c) The de...
Accelerating semantic graph databases on commodity clusters
Energy Technology Data Exchange (ETDEWEB)
Morari, Alessandro; Castellana, Vito G.; Haglin, David J.; Feo, John T.; Weaver, Jesse R.; Tumeo, Antonino; Villa, Oreste
2013-10-06
We are developing a full software system for accelerating semantic graph databases on commodity cluster that scales to hundreds of nodes while maintaining constant query throughput. Our framework comprises a SPARQL to C++ compiler, a library of parallel graph methods and a custom multithreaded runtime layer, which provides a Partitioned Global Address Space (PGAS) programming model with fork/join parallelism and automatic load balancing over a commodity clusters. We present preliminary results for the compiler and for the runtime.
Comments on Exchange Graphs in Cluster Algebras
Kim, Hyun Kyu
2016-01-01
An important problem in the theory of cluster algebras is to compute the fundamental group of the exchange graph. A non-trivial closed loop in the exchange graph, for example, generates a non-trivial identity for the classical and quantum dilogarithm functions. An interesting conjecture, partly motivated by dilogarithm functions, is that this fundamental group is generated by closed loops of mutations involving only two of the cluster variables. We present examples and counterexamples for this naive conjecture, and then formulate a better version of the conjecture for acyclic seeds.
Identify Implicit Communities by Graph Clustering
Institute of Scientific and Technical Information of China (English)
YANG Nan; MENG Xiaofeng
2006-01-01
How to find these communities is an important research work. Recently, community discovery are mainly categorized to HITS algorithm, bipartite cores algorithm and maximum flow/minimum cut framework. In this paper, we proposed a new method to extract communities. The MCL algorithm, which is short for the Markov Cluster Algorithm, a fast and scalable unsupervised cluster algorithm is used to extract communities. By putting mirror deleting procedure behind graph clustering, we decrease comparing cost considerably. After MCL and mirror deletion, we use community member select algorithm to produce the sets of community candidates. The experiment and results show the new method works effectively and properly.
A local search for a graph clustering problem
Navrotskaya, Anna; Il'ev, Victor
2016-10-01
In the clustering problems one has to partition a given set of objects (a data set) into some subsets (called clusters) taking into consideration only similarity of the objects. One of most visual formalizations of clustering is graph clustering, that is grouping the vertices of a graph into clusters taking into consideration the edge structure of the graph whose vertices are objects and edges represent similarities between the objects. In the graph k-clustering problem the number of clusters does not exceed k and the goal is to minimize the number of edges between clusters and the number of missing edges within clusters. This problem is NP-hard for any k ≥ 2. We propose a polynomial time (2k-1)-approximation algorithm for graph k-clustering. Then we apply a local search procedure to the feasible solution found by this algorithm and hold experimental research of obtained heuristics.
Bayesian Cosmic Web Reconstruction: BARCODE for Clusters
Bos, E. G. Patrick; van de Weygaert, Rien; Kitaura, Francisco; Cautun, Marius
2016-10-01
We describe the Bayesian \\barcode\\ formalism that has been designed towards the reconstruction of the Cosmic Web in a given volume on the basis of the sampled galaxy cluster distribution. Based on the realization that the massive compact clusters are responsible for the major share of the large scale tidal force field shaping the anisotropic and in particular filamentary features in the Cosmic Web. Given the nonlinearity of the constraints imposed by the cluster configurations, we resort to a state-of-the-art constrained reconstruction technique to find a proper statistically sampled realization of the original initial density and velocity field in the same cosmic region. Ultimately, the subsequent gravitational evolution of these initial conditions towards the implied Cosmic Web configuration can be followed on the basis of a proper analytical model or an N-body computer simulation. The BARCODE formalism includes an implicit treatment for redshift space distortions. This enables a direct reconstruction on the basis of observational data, without the need for a correction of redshift space artifacts. In this contribution we provide a general overview of the the Cosmic Web connection with clusters and a description of the Bayesian BARCODE formalism. We conclude with a presentation of its successful workings with respect to test runs based on a simulated large scale matter distribution, in physical space as well as in redshift space.
Hearing the clusters in a graph: A distributed algorithm
Sahai, Tuhin; Banaszuk, Andrzej
2009-01-01
We propose a novel distributed algorithm to decompose graphs or cluster data. The algorithm recovers the solution obtained from spectral clustering without need for expensive eigenvalue/ eigenvector computations. We demonstrate that by solving the wave equation on the graph, every node can assign itself to a cluster by performing a local fast Fourier transform. We prove the equivalence of our algorithm to spectral clustering, derive convergence rates and demonstrate it on examples.
Bayesian Cosmic Web Reconstruction: BARCODE for Clusters
Bos, E G Patrick; Kitaura, Francisco; Cautun, Marius
2016-01-01
We describe the Bayesian BARCODE formalism that has been designed towards the reconstruction of the Cosmic Web in a given volume on the basis of the sampled galaxy cluster distribution. Based on the realization that the massive compact clusters are responsible for the major share of the large scale tidal force field shaping the anisotropic and in particular filamentary features in the Cosmic Web. Given the nonlinearity of the constraints imposed by the cluster configurations, we resort to a state-of-the-art constrained reconstruction technique to find a proper statistically sampled realization of the original initial density and velocity field in the same cosmic region. Ultimately, the subsequent gravitational evolution of these initial conditions towards the implied Cosmic Web configuration can be followed on the basis of a proper analytical model or an N-body computer simulation. The BARCODE formalism includes an implicit treatment for redshift space distortions. This enables a direct reconstruction on the ...
Limited Random Walk Algorithm for Big Graph Data Clustering
Zhang, Honglei; Kiranyaz, Serkan; Gabbouj, Moncef
2016-01-01
Graph clustering is an important technique to understand the relationships between the vertices in a big graph. In this paper, we propose a novel random-walk-based graph clustering method. The proposed method restricts the reach of the walking agent using an inflation function and a normalization function. We analyze the behavior of the limited random walk procedure and propose a novel algorithm for both global and local graph clustering problems. Previous random-walk-based algorithms depend on the chosen fitness function to find the clusters around a seed vertex. The proposed algorithm tackles the problem in an entirely different manner. We use the limited random walk procedure to find attracting vertices in a graph and use them as features to cluster the vertices. According to the experimental results on the simulated graph data and the real-world big graph data, the proposed method is superior to the state-of-the-art methods in solving graph clustering problems. Since the proposed method uses the embarrass...
Graph-based clustering and data visualization algorithms
Vathy-Fogarassy, Ágnes
2013-01-01
This work presents a data visualization technique that combines graph-based topology representation and dimensionality reduction methods to visualize the intrinsic data structure in a low-dimensional vector space. The application of graphs in clustering and visualization has several advantages. A graph of important edges (where edges characterize relations and weights represent similarities or distances) provides a compact representation of the entire complex data set. This text describes clustering and visualization methods that are able to utilize information hidden in these graphs, based on
CRPCG—Clustering Routing Protocol based on Connected Graph
Directory of Open Access Journals (Sweden)
Feng Li
2011-05-01
Full Text Available In order to balance the load between cluster head, save the energy consumption of the inter-cluster routing, enhance reliability and flexibility of data transmission, the paper proposes a new clustering routing protocol based on connected graph (CRPCG. The protocol optimizes and innovates in three aspects: cluster head election, clusters formation and clusters routing. Eventually, a connected graph is constituted by the based station and all cluster heads, using the excellent algorithm of the graph theory, to guarantee the network connectivity and reliability, improve the link quality, balance node energy and prolong the network life cycle. The results of simulation show that, the protocol significantly prolong the network life cycle, balance the energy of network nodes, especially in the phase of inter-cluster data transmission, improving the reliability and efficiency of data transmission.
Bayesian Nonparametric Clustering for Positive Definite Matrices.
Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos
2016-05-01
Symmetric Positive Definite (SPD) matrices emerge as data descriptors in several applications of computer vision such as object tracking, texture recognition, and diffusion tensor imaging. Clustering these data matrices forms an integral part of these applications, for which soft-clustering algorithms (K-Means, expectation maximization, etc.) are generally used. As is well-known, these algorithms need the number of clusters to be specified, which is difficult when the dataset scales. To address this issue, we resort to the classical nonparametric Bayesian framework by modeling the data as a mixture model using the Dirichlet process (DP) prior. Since these matrices do not conform to the Euclidean geometry, rather belongs to a curved Riemannian manifold,existing DP models cannot be directly applied. Thus, in this paper, we propose a novel DP mixture model framework for SPD matrices. Using the log-determinant divergence as the underlying dissimilarity measure to compare these matrices, and further using the connection between this measure and the Wishart distribution, we derive a novel DPM model based on the Wishart-Inverse-Wishart conjugate pair. We apply this model to several applications in computer vision. Our experiments demonstrate that our model is scalable to the dataset size and at the same time achieves superior accuracy compared to several state-of-the-art parametric and nonparametric clustering algorithms.
Clustering with Multi-Layer Graphs: A Spectral Perspective
Dong, Xiaowen; Vandergheynst, Pierre; Nefedov, Nikolai
2011-01-01
Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this paper, we address the problem of combining different layers of the multi-layer graph for improved clustering of the vertices compared to using layers independently. We propose two novel methods, which are based on joint matrix factorization and graph regularization framework respectively, to efficiently combine the spectrum of the multiple graph layers, namely the eigenvectors of the graph Laplacian matrices. In each case, the resulting combination, which we call a "joint spectrum" of multiple graphs, is used for clustering the vertices. We evaluate our approaches by simulations with several real world social network datasets. Results demonstrate the superior or competitive performance of the proposed methods over state-of-the-art technique and common baseline methods, such a...
Bayesian Network Based Fault Prognosis via Bond Graph Modeling of High-Speed Railway Traction Device
Directory of Open Access Journals (Sweden)
Yunkai Wu
2015-01-01
component-level faults accurately for a high-speed railway traction system, a fault prognosis approach via Bayesian network and bond graph modeling techniques is proposed. The inherent structure of a railway traction system is represented by bond graph model, based on which a multilayer Bayesian network is developed for fault propagation analysis and fault prediction. For complete and incomplete data sets, two different parameter learning algorithms such as Bayesian estimation and expectation maximization (EM algorithm are adopted to determine the conditional probability table of the Bayesian network. The proposed prognosis approach using Pearl’s polytree propagation algorithm for joint probability reasoning can predict the failure probabilities of leaf nodes based on the current status of root nodes. Verification results in a high-speed railway traction simulation system can demonstrate the effectiveness of the proposed approach.
Graph partitions and cluster synchronization in networks of oscillators
Schaub, Michael T; Billeh, Yazan N; Delvenne, Jean-Charles; Lambiotte, Renaud; Barahona, Mauricio
2016-01-01
Synchronization over networks depends strongly on the structure of the coupling between the oscillators.When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable Partitions of the network graph and their associated quotient graphs. We exploit this graph-theoretical concept to study the phenomenon of cluster synchronization, in which different groups of nodes converge to distinct behaviors. We derive conditions and properties of networks in which such clustered behavior emerges, and show that the ensuing dynamics is the result of the localization of the eigenvectors of the associated graph Laplacians linked to the existence of invariant subspaces. The framework is applied to both linear and non-linear models, first for the standard case of networks with positive edges, before being generalized to the case of signed networks with both positive and negative interactions. We illustrate our results with examples of both signed and unsigned grap...
GraphAlignment: Bayesian pairwise alignment of biological networks
Directory of Open Access Journals (Sweden)
Kolář Michal
2012-11-01
Full Text Available Abstract Background With increased experimental availability and accuracy of bio-molecular networks, tools for their comparative and evolutionary analysis are needed. A key component for such studies is the alignment of networks. Results We introduce the Bioconductor package GraphAlignment for pairwise alignment of bio-molecular networks. The alignment incorporates information both from network vertices and network edges and is based on an explicit evolutionary model, allowing inference of all scoring parameters directly from empirical data. We compare the performance of our algorithm to an alternative algorithm, Græmlin 2.0. On simulated data, GraphAlignment outperforms Græmlin 2.0 in several benchmarks except for computational complexity. When there is little or no noise in the data, GraphAlignment is slower than Græmlin 2.0. It is faster than Græmlin 2.0 when processing noisy data containing spurious vertex associations. Its typical case complexity grows approximately as O(N2.6. On empirical bacterial protein-protein interaction networks (PIN and gene co-expression networks, GraphAlignment outperforms Græmlin 2.0 with respect to coverage and specificity, albeit by a small margin. On large eukaryotic PIN, Græmlin 2.0 outperforms GraphAlignment. Conclusions The GraphAlignment algorithm is robust to spurious vertex associations, correctly resolves paralogs, and shows very good performance in identification of homologous vertices defined by high vertex and/or interaction similarity. The simplicity and generality of GraphAlignment edge scoring makes the algorithm an appropriate choice for global alignment of networks.
A graph clustering method for community detection in complex networks
Zhou, HongFang; Li, Jin; Li, JunHuai; Zhang, FaCun; Cui, YingAn
2017-03-01
Information mining from complex networks by identifying communities is an important problem in a number of research fields, including the social sciences, biology, physics and medicine. First, two concepts are introduced, Attracting Degree and Recommending Degree. Second, a graph clustering method, referred to as AR-Cluster, is presented for detecting community structures in complex networks. Third, a novel collaborative similarity measure is adopted to calculate node similarities. In the AR-Cluster method, vertices are grouped together based on calculated similarity under a K-Medoids framework. Extensive experimental results on two real datasets show the effectiveness of AR-Cluster.
GPU Acceleration of Graph Matching, Clustering, and Partitioning
Fagginger Auer, B.O.
2013-01-01
We consider sequential algorithms for hypergraph partitioning and GPU (i.e., fine-grained shared-memory parallel) algorithms for graph partitioning and clustering. Our investigation into sequential hypergraph partitioning is concerned with the efficient construction of high-quality matchings for hyp
Trust from the past: Bayesian Personalized Ranking based Link Prediction in Knowledge Graphs
Energy Technology Data Exchange (ETDEWEB)
Zhang, Baichuan; Choudhury, Sutanay; Al-Hasan, Mohammad; Ning, Xia; Agarwal, Khushbu; Purohit, Sumit; Pesantez, Paola
2016-02-01
Estimating the confidence for a link is a critical task for Knowledge Graph construction. Link prediction, or predicting the likelihood of a link in a knowledge graph based on prior state is a key research direction within this area. We propose a Latent Feature Embedding based link recommendation model for prediction task and utilize Bayesian Personalized Ranking based optimization technique for learning models for each predicate. Experimental results on large-scale knowledge bases such as YAGO2 show that our approach achieves substantially higher performance than several state-of-art approaches. Furthermore, we also study the performance of the link prediction algorithm in terms of topological properties of the Knowledge Graph and present a linear regression model to reason about its expected level of accuracy.
Graph Laplacian for spectral clustering and seeded image segmentation
Wallace Correa de Oliveira Casaca
2014-01-01
Image segmentation is an essential tool to enhance the ability of computer systems to efficiently perform elementary cognitive tasks such as detection, recognition and tracking. In this thesis we concentrate on the investigation of two fundamental topics in the context of image segmentation: spectral clustering and seeded image segmentation. We introduce two new algorithms for those topics that, in summary, rely on Laplacian-based operators, spectral graph theory, and minimization of energy f...
Non-parametric Bayesian graph models reveal community structure in resting state fMRI
DEFF Research Database (Denmark)
Andersen, Kasper Winther; Madsen, Kristoffer H.; Siebner, Hartwig Roman
2014-01-01
Modeling of resting state functional magnetic resonance imaging (rs-fMRI) data using network models is of increasing interest. It is often desirable to group nodes into clusters to interpret the communication patterns between nodes. In this study we consider three different nonparametric Bayesian...
The Refinement Algorithm Consideration in Text Clustering Scheme Based on Multilevel Graph
Institute of Scientific and Technical Information of China (English)
CHEN Jian-bin; DONG Xiang-jun; SONG Han-tao
2004-01-01
To construct a high efficient text clustering algorithm, the multilevel graph model and the refinement algorithm used in the uncoarsening phase is discussed.The model is applied to text clustering.The performance of clustering algorithm has to be improved with the refinement algorithm application.The experiment result demonstrated that the multilevel graph text clustering algorithm is available.
Bayesian analysis for exponential random graph models using the adaptive exchange sampler
Jin, Ick Hoon
2013-01-01
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 existence of intractable normalizing constants. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the issue of intractable normalizing constants 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.
A Bayesian Analysis of the Ages of Four Open Clusters
Jeffery, Elizabeth J; van Dyk, David A; Stenning, David C; Robinson, Elliot; Stein, Nathan; Jefferys, W H
2016-01-01
In this paper we apply a Bayesian technique to determine the best fit of stellar evolution models to find the main sequence turn off age and other cluster parameters of four intermediate-age open clusters: NGC 2360, NGC 2477, NGC 2660, and NGC 3960. Our algorithm utilizes a Markov chain Monte Carlo technique to fit these various parameters, objectively finding the best-fit isochrone for each cluster. The result is a high-precision isochrone fit. We compare these results with the those of traditional "by-eye" isochrone fitting methods. By applying this Bayesian technique to NGC 2360, NGC 2477, NGC 2660, and NGC 3960, we determine the ages of these clusters to be 1.35 +/- 0.05, 1.02 +/- 0.02, 1.64 +/- 0.04, and 0.860 +/- 0.04 Gyr, respectively. The results of this paper continue our effort to determine cluster ages to higher precision than that offered by these traditional methods of isochrone fitting.
Application of Bayesian graphs to SN Ia data analysis and compression
Ma, Con; Bassett, Bruce A
2016-01-01
Bayesian graphical models are an efficient tool for modelling complex data and derive self-consistent expressions of the posterior distribution of model parameters. We apply Bayesian graphs to perform statistical analyses of Type Ia supernova (SN Ia) luminosity distance measurements from the Joint Light-curve Analysis (JLA) dataset (Betoule et al. 2014, arXiv:1401.4064). In contrast to the $\\chi^2$ approach used in previous studies, the Bayesian inference allows us to fully account for the standard-candle parameter dependence of the data covariance matrix. Comparing with $\\chi^2$ analysis results we find a systematic offset of the marginal model parameter bounds. We demonstrate that the bias is statistically significant in the case of the SN Ia standardization parameters with a maximal $6\\sigma$ shift of the SN light-curve colour correction. In addition, we find that the evidence for a host galaxy correction is now only $2.4\\sigma$. Systematic offsets on the cosmological parameters remain small, but may incre...
Application of Bayesian graphs to SN Ia data analysis and compression
Ma, Cong; Corasaniti, Pier-Stefano; Bassett, Bruce A.
2016-12-01
Bayesian graphical models are an efficient tool for modelling complex data and derive self-consistent expressions of the posterior distribution of model parameters. We apply Bayesian graphs to perform statistical analyses of Type Ia supernova (SN Ia) luminosity distance measurements from the joint light-curve analysis (JLA) data set. In contrast to the χ2 approach used in previous studies, the Bayesian inference allows us to fully account for the standard-candle parameter dependence of the data covariance matrix. Comparing with χ2 analysis results, we find a systematic offset of the marginal model parameter bounds. We demonstrate that the bias is statistically significant in the case of the SN Ia standardization parameters with a maximal 6σ shift of the SN light-curve colour correction. In addition, we find that the evidence for a host galaxy correction is now only 2.4σ. Systematic offsets on the cosmological parameters remain small, but may increase by combining constraints from complementary cosmological probes. The bias of the χ2 analysis is due to neglecting the parameter-dependent log-determinant of the data covariance, which gives more statistical weight to larger values of the standardization parameters. We find a similar effect on compressed distance modulus data. To this end, we implement a fully consistent compression method of the JLA data set that uses a Gaussian approximation of the posterior distribution for fast generation of compressed data. Overall, the results of our analysis emphasize the need for a fully consistent Bayesian statistical approach in the analysis of future large SN Ia data sets.
Application of Bayesian graphs to SN Ia data analysis and compression
Ma, Cong; Corasaniti, Pier-Stefano; Bassett, Bruce A.
2016-08-01
Bayesian graphical models are an efficient tool for modelling complex data and derive self-consistent expressions of the posterior distribution of model parameters. We apply Bayesian graphs to perform statistical analyses of Type Ia supernova (SN Ia) luminosity distance measurements from the Joint Light-curve Analysis (JLA) dataset (Betoule et al. 2014). In contrast to the χ2 approach used in previous studies, the Bayesian inference allows us to fully account for the standard-candle parameter dependence of the data covariance matrix. Comparing with χ2 analysis results we find a systematic offset of the marginal model parameter bounds. We demonstrate that the bias is statistically significant in the case of the SN Ia standardization parameters with a maximal 6σ shift of the SN light-curve colour correction. In addition, we find that the evidence for a host galaxy correction is now only 2.4σ. Systematic offsets on the cosmological parameters remain small, but may increase by combining constraints from complementary cosmological probes. The bias of the χ2 analysis is due to neglecting the parameter-dependent log-determinant of the data covariance, which gives more statistical weight to larger values of the standardization parameters. We find a similar effect on compressed distance modulus data. To this end we implement a fully consistent compression method of the JLA dataset that uses a Gaussian approximation of the posterior distribution for fast generation of compressed data. Overall, the results of our analysis emphasize the need for a fully consistent Bayesian statistical approach in the analysis of future large SN Ia datasets.
Clustered nested sampling: efficient Bayesian inference for cosmology
Shaw, R; Hobson, M P
2007-01-01
Bayesian model selection provides the cosmologist with an exacting tool to distinguish between competing models based purely on the data, via the Bayesian evidence. Previous methods to calculate this quantity either lacked general applicability or were computationally demanding. However, nested sampling (Skilling 2004), which was recently applied successfully to cosmology by Muhkerjee et al. 2006, overcomes both of these impediments. Their implementation restricts the parameter space sampled, and thus improves the efficiency, using a decreasing ellipsoidal bound in the $n$-dimensional parameter space centred on the maximum likelihood point. However, if the likelihood function contains any multi-modality, then the ellipse is prevented from constraining the sampling region efficiently. In this paper we introduce a method of clustered ellipsoidal nested sampling which can form multiple ellipses around each individual peak in the likelihood. In addition we have implemented a method for determining the expectation...
Approximating the Expansion Profile and Almost Optimal Local Graph Clustering
Gharan, Shayan Oveis
2012-01-01
Spectral partitioning is a simple, nearly-linear time, algorithm to find sparse cuts, and the Cheeger inequalities provide a worst-case guarantee for the quality of the approximation found by the algorithm. Local graph partitioning algorithms [ST08,ACL06,AP09] run in time that is nearly linear in the size of the output set, and their approximation guarantee is worse than the guarantee provided by the Cheeger inequalities by a polylogarithmic $\\log^{\\Omega(1)} n$ factor. It has been a long standing open problem to design a local graph clustering algorithm with an approximation guarantee close to the guarantee of the Cheeger inequalities and with a running time nearly linear in the size of the output. In this paper we solve this problem; we design an algorithm with the same guarantee (up to a constant factor) as the Cheeger inequality, that runs in time slightly super linear in the size of the output. This is the first sublinear (in the size of the input) time algorithm with almost the same guarantee as the Che...
Low-Complexity Bayesian Estimation of Cluster-Sparse Channels
Ballal, Tarig
2015-09-18
This paper addresses the problem of channel impulse response estimation for cluster-sparse channels under the Bayesian estimation framework. We develop a novel low-complexity minimum mean squared error (MMSE) estimator by exploiting the sparsity of the received signal profile and the structure of the measurement matrix. It is shown that due to the banded Toeplitz/circulant structure of the measurement matrix, a channel impulse response, such as underwater acoustic channel impulse responses, can be partitioned into a number of orthogonal or approximately orthogonal clusters. The orthogonal clusters, the sparsity of the channel impulse response and the structure of the measurement matrix, all combined, result in a computationally superior realization of the MMSE channel estimator. The MMSE estimator calculations boil down to simpler in-cluster calculations that can be reused in different clusters. The reduction in computational complexity allows for a more accurate implementation of the MMSE estimator. The proposed approach is tested using synthetic Gaussian channels, as well as simulated underwater acoustic channels. Symbol-error-rate performance and computation time confirm the superiority of the proposed method compared to selected benchmark methods in systems with preamble-based training signals transmitted over clustersparse channels.
Bayesian Analysis of Multiple Populations in Galactic Globular Clusters
Wagner-Kaiser, Rachel A.; Sarajedini, Ata; von Hippel, Ted; Stenning, David; Piotto, Giampaolo; Milone, Antonino; van Dyk, David A.; Robinson, Elliot; Stein, Nathan
2016-01-01
We use GO 13297 Cycle 21 Hubble Space Telescope (HST) observations and archival GO 10775 Cycle 14 HST ACS Treasury observations of Galactic Globular Clusters to find and characterize multiple stellar populations. Determining how globular clusters are able to create and retain enriched material to produce several generations of stars is key to understanding how these objects formed and how they have affected the structural, kinematic, and chemical evolution of the Milky Way. We employ a sophisticated Bayesian technique with an adaptive MCMC algorithm to simultaneously fit the age, distance, absorption, and metallicity for each cluster. At the same time, we also fit unique helium values to two distinct populations of the cluster and determine the relative proportions of those populations. Our unique numerical approach allows objective and precise analysis of these complicated clusters, providing posterior distribution functions for each parameter of interest. We use these results to gain a better understanding of multiple populations in these clusters and their role in the history of the Milky Way.Support for this work was provided by NASA through grant numbers HST-GO-10775 and HST-GO-13297 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555. This material is based upon work supported by the National Aeronautics and Space Administration under Grant NNX11AF34G issued through the Office of Space Science. This project was supported by the National Aeronautics & Space Administration through the University of Central Florida's NASA Florida Space Grant Consortium.
Wagner-Kaiser, R; Sarajedini, A; von Hippel, T; van Dyk, D A; Robinson, E; Stein, N; Jefferys, W H
2016-01-01
We use Cycle 21 Hubble Space Telescope (HST) observations and HST archival ACS Treasury observations of 30 Galactic Globular Clusters to characterize two distinct stellar populations. A sophisticated Bayesian technique is employed to simultaneously sample the joint posterior distribution of age, distance, and extinction for each cluster, as well as unique helium values for two populations within each cluster and the relative proportion of those populations. We find the helium differences among the two populations in the clusters fall in the range of ~0.04 to 0.11. Because adequate models varying in CNO are not presently available, we view these spreads as upper limits and present them with statistical rather than observational uncertainties. Evidence supports previous studies suggesting an increase in helium content concurrent with increasing mass of the cluster and also find that the proportion of the first population of stars increases with mass as well. Our results are examined in the context of proposed g...
Polanco, Xavier
2002-01-01
The proposal is to use clusters, graphs and networks as models in order to analyse the Web structure. Clusters, graphs and networks provide knowledge representation and organization. Clusters were generated by co-site analysis. The sample is a set of academic Web sites from the countries belonging to the European Union. These clusters are here revisited from the point of view of graph theory and social network analysis. This is a quantitative and structural analysis. In fact, the Internet is a computer network that connects people and organizations. Thus we may consider it to be a social network. The set of Web academic sites represents an empirical social network, and is viewed as a virtual community. The network structural properties are here analysed applying together cluster analysis, graph theory and social network analysis.
Wagner-Kaiser, R.; Stenning, D. C.; Sarajedini, A.; von Hippel, T.; van Dyk, D. A.; Robinson, E.; Stein, N.; Jefferys, W. H.
2016-12-01
We use Cycle 21 Hubble Space Telescope (HST) observations and HST archival ACS Treasury observations of 30 Galactic globular clusters to characterize two distinct stellar populations. A sophisticated Bayesian technique is employed to simultaneously sample the joint posterior distribution of age, distance, and extinction for each cluster, as well as unique helium values for two populations within each cluster and the relative proportion of those populations. We find the helium differences among the two populations in the clusters fall in the range of ˜0.04 to 0.11. Because adequate models varying in carbon, nitrogen, and oxygen are not presently available, we view these spreads as upper limits and present them with statistical rather than observational uncertainties. Evidence supports previous studies suggesting an increase in helium content concurrent with increasing mass of the cluster and we also find that the proportion of the first population of stars increases with mass as well. Our results are examined in the context of proposed globular cluster formation scenarios. Additionally, we leverage our Bayesian technique to shed light on the inconsistencies between the theoretical models and the observed data.
Bayesian nonparametric clustering in phylogenetics: modeling antigenic evolution in influenza.
Cybis, Gabriela B; Sinsheimer, Janet S; Bedford, Trevor; Rambaut, Andrew; Lemey, Philippe; Suchard, Marc A
2017-01-18
Influenza is responsible for up to 500,000 deaths every year, and antigenic variability represents much of its epidemiological burden. To visualize antigenic differences across many viral strains, antigenic cartography methods use multidimensional scaling on binding assay data to map influenza antigenicity onto a low-dimensional space. Analysis of such assay data ideally leads to natural clustering of influenza strains of similar antigenicity that correlate with sequence evolution. To understand the dynamics of these antigenic groups, we present a framework that jointly models genetic and antigenic evolution by combining multidimensional scaling of binding assay data, Bayesian phylogenetic machinery and nonparametric clustering methods. We propose a phylogenetic Chinese restaurant process that extends the current process to incorporate the phylogenetic dependency structure between strains in the modeling of antigenic clusters. With this method, we are able to use the genetic information to better understand the evolution of antigenicity throughout epidemics, as shown in applications of this model to H1N1 influenza. Copyright © 2017 John Wiley & Sons, Ltd.
Spectral clustering and biclustering learning large graphs and contingency tables
Bolla, Marianna
2013-01-01
Explores regular structures in graphs and contingency tables by spectral theory and statistical methods This book bridges the gap between graph theory and statistics by giving answers to the demanding questions which arise when statisticians are confronted with large weighted graphs or rectangular arrays. Classical and modern statistical methods applicable to biological, social, communication networks, or microarrays are presented together with the theoretical background and proofs. This book is suitable for a one-semester course for graduate students in data mining, mult
Advances in Bayesian Model Based Clustering Using Particle Learning
Energy Technology Data Exchange (ETDEWEB)
Merl, D M
2009-11-19
Recent work by Carvalho, Johannes, Lopes and Polson and Carvalho, Lopes, Polson and Taddy introduced a sequential Monte Carlo (SMC) alternative to traditional iterative Monte Carlo strategies (e.g. MCMC and EM) for Bayesian inference for a large class of dynamic models. The basis of SMC techniques involves representing the underlying inference problem as one of state space estimation, thus giving way to inference via particle filtering. The key insight of Carvalho et al was to construct the sequence of filtering distributions so as to make use of the posterior predictive distribution of the observable, a distribution usually only accessible in certain Bayesian settings. Access to this distribution allows a reversal of the usual propagate and resample steps characteristic of many SMC methods, thereby alleviating to a large extent many problems associated with particle degeneration. Furthermore, Carvalho et al point out that for many conjugate models the posterior distribution of the static variables can be parametrized in terms of [recursively defined] sufficient statistics of the previously observed data. For models where such sufficient statistics exist, particle learning as it is being called, is especially well suited for the analysis of streaming data do to the relative invariance of its algorithmic complexity with the number of data observations. Through a particle learning approach, a statistical model can be fit to data as the data is arriving, allowing at any instant during the observation process direct quantification of uncertainty surrounding underlying model parameters. Here we describe the use of a particle learning approach for fitting a standard Bayesian semiparametric mixture model as described in Carvalho, Lopes, Polson and Taddy. In Section 2 we briefly review the previously presented particle learning algorithm for the case of a Dirichlet process mixture of multivariate normals. In Section 3 we describe several novel extensions to the original
Model reduction of second-order network systems using graph clustering
Cheng, Xiaodong; Scherpen, Jacquelien M.A.; Kawano, Yu
2016-01-01
A general framework is proposed for structure-preserving model reduction of a second-order network system. The method is based on graph clustering, and a recursive algorithm is proposed to find an appropriate clustering. Behaviors of nodes are interpreted by transfer functions, and the similarities
Structuring heterogeneous biological information using fuzzy clustering of k-partite graphs
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Theis Fabian J
2010-10-01
Full Text Available Abstract Background Extensive and automated data integration in bioinformatics facilitates the construction of large, complex biological networks. However, the challenge lies in the interpretation of these networks. While most research focuses on the unipartite or bipartite case, we address the more general but common situation of k-partite graphs. These graphs contain k different node types and links are only allowed between nodes of different types. In order to reveal their structural organization and describe the contained information in a more coarse-grained fashion, we ask how to detect clusters within each node type. Results Since entities in biological networks regularly have more than one function and hence participate in more than one cluster, we developed a k-partite graph partitioning algorithm that allows for overlapping (fuzzy clusters. It determines for each node a degree of membership to each cluster. Moreover, the algorithm estimates a weighted k-partite graph that connects the extracted clusters. Our method is fast and efficient, mimicking the multiplicative update rules commonly employed in algorithms for non-negative matrix factorization. It facilitates the decomposition of networks on a chosen scale and therefore allows for analysis and interpretation of structures on various resolution levels. Applying our algorithm to a tripartite disease-gene-protein complex network, we were able to structure this graph on a large scale into clusters that are functionally correlated and biologically meaningful. Locally, smaller clusters enabled reclassification or annotation of the clusters' elements. We exemplified this for the transcription factor MECP2. Conclusions In order to cope with the overwhelming amount of information available from biomedical literature, we need to tackle the challenge of finding structures in large networks with nodes of multiple types. To this end, we presented a novel fuzzy k-partite graph partitioning
Co-clustering directed graphs to discover asymmetries and directional communities.
Rohe, Karl; Qin, Tai; Yu, Bin
2016-10-21
In directed graphs, relationships are asymmetric and these asymmetries contain essential structural information about the graph. Directed relationships lead to a new type of clustering that is not feasible in undirected graphs. We propose a spectral co-clustering algorithm called di-sim for asymmetry discovery and directional clustering. A Stochastic co-Blockmodel is introduced to show favorable properties of di-sim To account for the sparse and highly heterogeneous nature of directed networks, di-sim uses the regularized graph Laplacian and projects the rows of the eigenvector matrix onto the sphere. A nodewise asymmetry score and di-sim are used to analyze the clustering asymmetries in the networks of Enron emails, political blogs, and the Caenorhabditis elegans chemical connectome. In each example, a subset of nodes have clustering asymmetries; these nodes send edges to one cluster, but receive edges from another cluster. Such nodes yield insightful information (e.g., communication bottlenecks) about directed networks, but are missed if the analysis ignores edge direction.
A framework for graph-based synthesis, analysis, and visualization of HPC cluster job data.
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Mayo, Jackson R.; Kegelmeyer, W. Philip, Jr.; Wong, Matthew H.; Pebay, Philippe Pierre; Gentile, Ann C.; Thompson, David C.; Roe, Diana C.; De Sapio, Vincent; Brandt, James M.
2010-08-01
The monitoring and system analysis of high performance computing (HPC) clusters is of increasing importance to the HPC community. Analysis of HPC job data can be used to characterize system usage and diagnose and examine failure modes and their effects. This analysis is not straightforward, however, due to the complex relationships that exist between jobs. These relationships are based on a number of factors, including shared compute nodes between jobs, proximity of jobs in time, etc. Graph-based techniques represent an approach that is particularly well suited to this problem, and provide an effective technique for discovering important relationships in job queuing and execution data. The efficacy of these techniques is rooted in the use of a semantic graph as a knowledge representation tool. In a semantic graph job data, represented in a combination of numerical and textual forms, can be flexibly processed into edges, with corresponding weights, expressing relationships between jobs, nodes, users, and other relevant entities. This graph-based representation permits formal manipulation by a number of analysis algorithms. This report presents a methodology and software implementation that leverages semantic graph-based techniques for the system-level monitoring and analysis of HPC clusters based on job queuing and execution data. Ontology development and graph synthesis is discussed with respect to the domain of HPC job data. The framework developed automates the synthesis of graphs from a database of job information. It also provides a front end, enabling visualization of the synthesized graphs. Additionally, an analysis engine is incorporated that provides performance analysis, graph-based clustering, and failure prediction capabilities for HPC systems.
Network cluster detecting in associated bi-graph picture
He, Zhe; Xu, Rui-Jie; Wang, Bing-Hong; Ou-Yang, Zhong-Can
2014-01-01
We find that there is a close relationship between the associated bigraph and the clustering. the imbedding of the bigraph into some space can identify the clusters. Thus, we propose a new method for network cluster detecting through associated bigraph,of which the physical meaning is clear and the time complexity is acceptable. These characteristics help people to understand the structure and character of networks. We uncover the clusters on serval real networks in this paper as examples. The Zachary Network, which presents the structure of a karate club,can be partation into two clusters correctly by this method. And the Dolphin network is partitioned reasonably.
Clustering cliques for graph-based summarization of the biomedical research literature
DEFF Research Database (Denmark)
Zhang, Han; Fiszman, Marcelo; Shin, Dongwook
2013-01-01
Background: Graph-based notions are increasingly used in biomedical data mining and knowledge discovery tasks. In this paper, we present a clique-clustering method to automatically summarize graphs of semantic predications produced from PubMed citations (titles and abstracts).Results: Sem......Rep is used to extract semantic predications from the citations returned by a PubMed search. Cliques were identified from frequently occurring predications with highly connected arguments filtered by degree centrality. Themes contained in the summary were identified with a hierarchical clustering algorithm...
DEFF Research Database (Denmark)
Guillot, Gilles; Carpentier-Skandalis, Alexandra
2011-01-01
We study the accuracy of a Bayesian supervised method used to cluster individuals into genetically homogeneous groups on the basis of dominant or codominant molecular markers. We provide a formula relating an error criterion to the number of loci used and the number of clusters. This formula...
An effective trust-based recommendation method using a novel graph clustering algorithm
Moradi, Parham; Ahmadian, Sajad; Akhlaghian, Fardin
2015-10-01
Recommender systems are programs that aim to provide personalized recommendations to users for specific items (e.g. music, books) in online sharing communities or on e-commerce sites. Collaborative filtering methods are important and widely accepted types of recommender systems that generate recommendations based on the ratings of like-minded users. On the other hand, these systems confront several inherent issues such as data sparsity and cold start problems, caused by fewer ratings against the unknowns that need to be predicted. Incorporating trust information into the collaborative filtering systems is an attractive approach to resolve these problems. In this paper, we present a model-based collaborative filtering method by applying a novel graph clustering algorithm and also considering trust statements. In the proposed method first of all, the problem space is represented as a graph and then a sparsest subgraph finding algorithm is applied on the graph to find the initial cluster centers. Then, the proposed graph clustering algorithm is performed to obtain the appropriate users/items clusters. Finally, the identified clusters are used as a set of neighbors to recommend unseen items to the current active user. Experimental results based on three real-world datasets demonstrate that the proposed method outperforms several state-of-the-art recommender system methods.
Comparisons of Graph-structure Clustering Methods for Gene Expression Data
Institute of Scientific and Technical Information of China (English)
Zhuo FANG; Lei LIU; Jiong YANG; Qing-Ming LUO; Yi-Xue LI
2006-01-01
Although many numerical clustering algorithms have been applied to gene expression data analysis, the essential step is still biological interpretation by manual inspection. The correlation between genetic co-regulation and affiliation to a common biological process is what biologists expect. Here, we introduce some clustering algorithms that are based on graph structure constituted by biological knowledge. After applying a widely used dataset, we compared the result clusters of two of these algorithms in terms of the homogeneity of clusters and coherence of annotation and matching ratio. The results show that the clusters of knowledge-guided analysis are the kernel parts of the clusters of Gene Ontology (GO)-Cluster software, which contains the genes that are most expression correlative and most consistent with biological functions. Moreover, knowledge-guided analysis seems much more applicable than GO-Cluster in a larger dataset.
Directory of Open Access Journals (Sweden)
Guillaume Marrelec
Full Text Available The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC raises an important issue: some correction needs to be applied for the dimensionality of variables. In this work, we formulate the decision of merging dependent multivariate normal variables in an AHC procedure as a Bayesian model comparison. We found that the Bayesian formulation naturally shrinks the empirical covariance matrix towards a matrix set a priori (e.g., the identity, provides an automated stopping rule, and corrects for dimensionality using a term that scales up the measure as a function of the dimensionality of the variables. Also, the resulting log Bayes factor is asymptotically proportional to the plug-in estimate of mutual information, with an additive correction for dimensionality in agreement with the Bayesian information criterion. We investigated the behavior of these Bayesian alternatives (in exact and asymptotic forms to mutual information on simulated and real data. An encouraging result was first derived on simulations: the hierarchical clustering based on the log Bayes factor outperformed off-the-shelf clustering techniques as well as raw and normalized mutual information in terms of classification accuracy. On a toy example, we found that the Bayesian approaches led to results that were similar to those of mutual information clustering techniques, with the advantage of an automated thresholding. On real functional magnetic resonance imaging (fMRI datasets measuring brain activity, it identified clusters consistent with the established outcome of standard procedures. On this application, normalized mutual information had a highly atypical behavior, in the sense that it systematically favored very large clusters. These initial experiments suggest that the proposed Bayesian alternatives to mutual information are a useful new tool for hierarchical clustering.
GraphCrunch 2: Software tool for network modeling, alignment and clustering
Directory of Open Access Journals (Sweden)
Hayes Wayne
2011-01-01
Full Text Available Abstract Background Recent advancements in experimental biotechnology have produced large amounts of protein-protein interaction (PPI data. The topology of PPI networks is believed to have a strong link to their function. Hence, the abundance of PPI data for many organisms stimulates the development of computational techniques for the modeling, comparison, alignment, and clustering of networks. In addition, finding representative models for PPI networks will improve our understanding of the cell just as a model of gravity has helped us understand planetary motion. To decide if a model is representative, we need quantitative comparisons of model networks to real ones. However, exact network comparison is computationally intractable and therefore several heuristics have been used instead. Some of these heuristics are easily computable "network properties," such as the degree distribution, or the clustering coefficient. An important special case of network comparison is the network alignment problem. Analogous to sequence alignment, this problem asks to find the "best" mapping between regions in two networks. It is expected that network alignment might have as strong an impact on our understanding of biology as sequence alignment has had. Topology-based clustering of nodes in PPI networks is another example of an important network analysis problem that can uncover relationships between interaction patterns and phenotype. Results We introduce the GraphCrunch 2 software tool, which addresses these problems. It is a significant extension of GraphCrunch which implements the most popular random network models and compares them with the data networks with respect to many network properties. Also, GraphCrunch 2 implements the GRAph ALigner algorithm ("GRAAL" for purely topological network alignment. GRAAL can align any pair of networks and exposes large, dense, contiguous regions of topological and functional similarities far larger than any other
A Bayesian Approach Accounting for Stochastic Fluctuations in Stellar Cluster Properties
Fouesneau, M
2009-01-01
The integrated spectro-photometric properties of star clusters are subject to large cluster-to-cluster variations. They are distributed in non trivial ways around the average properties predicted by standard population synthesis models. This results from the stochastic mass distribution of the finite (small) number of luminous stars in each cluster, stars which may be either particularly blue or particularly red. The color distributions are broad and usually far from Gaussian, especially for young and intermediate age clusters, as found in interacting galaxies. When photometric measurements of clusters are used to estimate ages and masses in conjunction with standard models, biases are to be expected. We present a Bayesian approach that explicitly accounts for stochasticity when estimating ages and masses of star clusters that cannot be resolved into stars. Based on Monte-Carlo simulations, we are starting to explore the probability distributions of star cluster properties obtained given a set of multi-wavele...
Safner, T.; Miller, M.P.; McRae, B.H.; Fortin, M.-J.; Manel, S.
2011-01-01
Recently, techniques available for identifying clusters of individuals or boundaries between clusters using genetic data from natural populations have expanded rapidly. Consequently, there is a need to evaluate these different techniques. We used spatially-explicit simulation models to compare three spatial Bayesian clustering programs and two edge detection methods. Spatially-structured populations were simulated where a continuous population was subdivided by barriers. We evaluated the ability of each method to correctly identify boundary locations while varying: (i) time after divergence, (ii) strength of isolation by distance, (iii) level of genetic diversity, and (iv) amount of gene flow across barriers. To further evaluate the methods' effectiveness to detect genetic clusters in natural populations, we used previously published data on North American pumas and a European shrub. Our results show that with simulated and empirical data, the Bayesian spatial clustering algorithms outperformed direct edge detection methods. All methods incorrectly detected boundaries in the presence of strong patterns of isolation by distance. Based on this finding, we support the application of Bayesian spatial clustering algorithms for boundary detection in empirical datasets, with necessary tests for the influence of isolation by distance. ?? 2011 by the authors; licensee MDPI, Basel, Switzerland.
Bayesian model-based cluster analysis for predicting macrofaunal communities
Braak, ter C.J.F.; Hoijtink, H.; Akkermans, W.; Verdonschot, P.F.M.
2003-01-01
To predict macrofaunal community composition from environmental data a two-step approach is often followed: (1) the water samples are clustered into groups on the basis of the macrofauna data and (2) the groups are related to the environmental data, e.g. by discriminant analysis. For the cluster ana
Bayesian hierarchical clustering for studying cancer gene expression data with unknown statistics.
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Korsuk Sirinukunwattana
Full Text Available Clustering analysis is an important tool in studying gene expression data. The Bayesian hierarchical clustering (BHC algorithm can automatically infer the number of clusters and uses Bayesian model selection to improve clustering quality. In this paper, we present an extension of the BHC algorithm. Our Gaussian BHC (GBHC algorithm represents data as a mixture of Gaussian distributions. It uses normal-gamma distribution as a conjugate prior on the mean and precision of each of the Gaussian components. We tested GBHC over 11 cancer and 3 synthetic datasets. The results on cancer datasets show that in sample clustering, GBHC on average produces a clustering partition that is more concordant with the ground truth than those obtained from other commonly used algorithms. Furthermore, GBHC frequently infers the number of clusters that is often close to the ground truth. In gene clustering, GBHC also produces a clustering partition that is more biologically plausible than several other state-of-the-art methods. This suggests GBHC as an alternative tool for studying gene expression data. The implementation of GBHC is available at https://sites.google.com/site/gaussianbhc/
Combination of meta-analysis and graph clustering to identify prognostic markers of ESCC
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Hongyun Gao
2012-01-01
Full Text Available Esophageal squamous cell carcinoma (ESCC is one of the most malignant gastrointestinal cancers and occurs at a high frequency rate in China and other Asian countries. Recently, several molecular markers were identified for predicting ESCC. Notwithstanding, additional prognostic markers, with a clear understanding of their underlying roles, are still required. Through bioinformatics, a graph-clustering method by DPClus was used to detect co-expressed modules. The aim was to identify a set of discriminating genes that could be used for predicting ESCC through graph-clustering and GO-term analysis. The results showed that CXCL12, CYP2C9, TGM3, MAL, S100A9, EMP-1 and SPRR3 were highly associated with ESCC development. In our study, all their predicted roles were in line with previous reports, whereby the assumption that a combination of meta-analysis, graph-clustering and GO-term analysis is effective for both identifying differentially expressed genes, and reflecting on their functions in ESCC.
Combination of meta-analysis and graph clustering to identify prognostic markers of ESCC.
Gao, Hongyun; Wang, Lishan; Cui, Shitao; Wang, Mingsong
2012-04-01
Esophageal squamous cell carcinoma (ESCC) is one of the most malignant gastrointestinal cancers and occurs at a high frequency rate in China and other Asian countries. Recently, several molecular markers were identified for predicting ESCC. Notwithstanding, additional prognostic markers, with a clear understanding of their underlying roles, are still required. Through bioinformatics, a graph-clustering method by DPClus was used to detect co-expressed modules. The aim was to identify a set of discriminating genes that could be used for predicting ESCC through graph-clustering and GO-term analysis. The results showed that CXCL12, CYP2C9, TGM3, MAL, S100A9, EMP-1 and SPRR3 were highly associated with ESCC development. In our study, all their predicted roles were in line with previous reports, whereby the assumption that a combination of meta-analysis, graph-clustering and GO-term analysis is effective for both identifying differentially expressed genes, and reflecting on their functions in ESCC.
Individual organisms as units of analysis: Bayesian-clustering alternatives in population genetics.
Mank, Judith E; Avise, John C
2004-12-01
Population genetic analyses traditionally focus on the frequencies of alleles or genotypes in 'populations' that are delimited a priori. However, there are potential drawbacks of amalgamating genetic data into such composite attributes of assemblages of specimens: genetic information on individual specimens is lost or submerged as an inherent part of the analysis. A potential also exists for circular reasoning when a population's initial identification and subsequent genetic characterization are coupled. In principle, these problems are circumvented by some newer methods of population identification and individual assignment based on statistical clustering of specimen genotypes. Here we evaluate a recent method in this genre--Bayesian clustering--using four genotypic data sets involving different types of molecular markers in non-model organisms from nature. As expected, measures of population genetic structure (F(ST) and phiST) tended to be significantly greater in Bayesian a posteriori data treatments than in analyses where populations were delimited a priori. In the four biological contexts examined, which involved both geographic population structures and hybrid zones, Bayesian clustering was able to recover differentiated populations, and Bayesian assignments were able to identify likely population sources of specific individuals.
Peterson, Christine B; Stingo, Francesco C; Vannucci, Marina
2016-03-30
In this work, we develop a Bayesian approach to perform selection of predictors that are linked within a network. We achieve this by combining a sparse regression model relating the predictors to a response variable with a graphical model describing conditional dependencies among the predictors. The proposed method is well-suited for genomic applications because it allows the identification of pathways of functionally related genes or proteins that impact an outcome of interest. In contrast to previous approaches for network-guided variable selection, we infer the network among predictors using a Gaussian graphical model and do not assume that network information is available a priori. We demonstrate that our method outperforms existing methods in identifying network-structured predictors in simulation settings and illustrate our proposed model with an application to inference of proteins relevant to glioblastoma survival.
AGGLOMERATIVE CLUSTERING OF SOUND RECORD SPEECH SEGMENTS BASED ON BAYESIAN INFORMATION CRITERION
Directory of Open Access Journals (Sweden)
O. Yu. Kydashev
2013-01-01
Full Text Available This paper presents the detailed description of agglomerative clustering system implementation for speech segments based on Bayesian information criterion. Numerical experiment results with different acoustic features, as well as the full and diagonal covariance matrices application are given. The error rate DER equal to 6.4% for audio records of radio «Svoboda» was achieved by means of designed system.
A NOVEL TECHNIQUE TO IMPROVE PHOTOMETRY IN CONFUSED IMAGES USING GRAPHS AND BAYESIAN PRIORS
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Safarzadeh, Mohammadtaher [Department of Physics and Astronomy, Johns Hopkins University, 366 Bloomberg Center, 3400 North Charles Street, Baltimore, MD 21218 (United States); Ferguson, Henry C. [Space Telescope Science Institute, 3700 San Martin Boulevard, Baltimore, MD 21218 (United States); Lu, Yu [Kavli Institute for Particle Astrophysics and Cosmology, Stanford, CA 94309 (United States); Inami, Hanae [National Optical Astronomy Observatory, 950 North Cherry Avenue, Tucson, AZ 85719 (United States); Somerville, Rachel S., E-mail: mts@pha.jhu.edu [Department of Physics and Astronomy, Rutgers, The State University of New Jersey, 136 Frelinghuysen Road, Piscataway, NJ 08854 (United States)
2015-01-10
We present a new technique for overcoming confusion noise in deep far-infrared Herschel space telescope images making use of prior information from shorter λ < 2 μm wavelengths. For the deepest images obtained by Herschel, the flux limit due to source confusion is about a factor of three brighter than the flux limit due to instrumental noise and (smooth) sky background. We have investigated the possibility of de-confusing simulated Herschel PACS 160 μm images by using strong Bayesian priors on the positions and weak priors on the flux of sources. We find the blended sources and group them together and simultaneously fit their fluxes. We derive the posterior probability distribution function of fluxes subject to these priors through Monte Carlo Markov Chain (MCMC) sampling by fitting the image. Assuming we can predict the FIR flux of sources based on the ultraviolet-optical part of their SEDs to within an order of magnitude, the simulations show that we can obtain reliable fluxes and uncertainties at least a factor of three fainter than the confusion noise limit of 3σ {sub c} = 2.7 mJy in our simulated PACS-160 image. This technique could in principle be used to mitigate the effects of source confusion in any situation where one has prior information of positions and plausible fluxes of blended sources. For Herschel, application of this technique will improve our ability to constrain the dust content in normal galaxies at high redshift.
Constructing a graph of connections in clustering algorithm of complex objects
Directory of Open Access Journals (Sweden)
Татьяна Шатовская
2015-05-01
Full Text Available The article describes the results of modifying the algorithm Chameleon. Hierarchical multi-level algorithm consists of several phases: the construction of the count, coarsening, the separation and recovery. Each phase can be used various approaches and algorithms. The main aim of the work is to study the quality of the clustering of different sets of data using a set of algorithms combinations at different stages of the algorithm and improve the stage of construction by the optimization algorithm of k choice in the graph construction of k of nearest neighbors
Manual hierarchical clustering of regional geochemical data using a Bayesian finite mixture model
Ellefsen, Karl J.; Smith, David
2016-01-01
Interpretation of regional scale, multivariate geochemical data is aided by a statistical technique called “clustering.” We investigate a particular clustering procedure by applying it to geochemical data collected in the State of Colorado, United States of America. The clustering procedure partitions the field samples for the entire survey area into two clusters. The field samples in each cluster are partitioned again to create two subclusters, and so on. This manual procedure generates a hierarchy of clusters, and the different levels of the hierarchy show geochemical and geological processes occurring at different spatial scales. Although there are many different clustering methods, we use Bayesian finite mixture modeling with two probability distributions, which yields two clusters. The model parameters are estimated with Hamiltonian Monte Carlo sampling of the posterior probability density function, which usually has multiple modes. Each mode has its own set of model parameters; each set is checked to ensure that it is consistent both with the data and with independent geologic knowledge. The set of model parameters that is most consistent with the independent geologic knowledge is selected for detailed interpretation and partitioning of the field samples.
Bayesian Analysis and Characterization of Multiple Populations in Galactic Globular Clusters
Wagner-Kaiser, Rachel A.; Stenning, David; Sarajedini, Ata; von Hippel, Ted; van Dyk, David A.; Robinson, Elliot; Stein, Nathan; Jefferys, William H.; BASE-9, HST UVIS Globular Cluster Treasury Program
2017-01-01
Globular clusters have long been important tools to unlock the early history of galaxies. Thus, it is crucial we understand the formation and characteristics of the globular clusters (GCs) themselves. Historically, GCs were thought to be simple and largely homogeneous populations, formed via collapse of a single molecular cloud. However, this classical view has been overwhelmingly invalidated by recent work. It is now clear that the vast majority of globular clusters in our Galaxy host two or more chemically distinct populations of stars, with variations in helium and light elements at discrete abundance levels. No coherent story has arisen that is able to fully explain the formation of multiple populations in globular clusters nor the mechanisms that drive stochastic variations from cluster to cluster.We use Cycle 21 Hubble Space Telescope (HST) observations and HST archival ACS Treasury observations of 30 Galactic Globular Clusters to characterize two distinct stellar populations. A sophisticated Bayesian technique is employed to simultaneously sample the joint posterior distribution of age, distance, and extinction for each cluster, as well as unique helium values for two populations within each cluster and the relative proportion of those populations. We find the helium differences among the two populations in the clusters fall in the range of 0.04 to 0.11. Because adequate models varying in CNO are not presently available, we view these spreads as upper limits and present them with statistical rather than observational uncertainties. Evidence supports previous studies suggesting an increase in helium content concurrent with increasing mass of the cluster. We also find that the proportion of the first population of stars increases with mass. Our results are examined in the context of proposed globular cluster formation scenarios.
Rodríguez-Ramilo, Silvia T; Wang, Jinliang
2012-09-01
The inference of population genetic structures is essential in many research areas in population genetics, conservation biology and evolutionary biology. Recently, unsupervised Bayesian clustering algorithms have been developed to detect a hidden population structure from genotypic data, assuming among others that individuals taken from the population are unrelated. Under this assumption, markers in a sample taken from a subpopulation can be considered to be in Hardy-Weinberg and linkage equilibrium. However, close relatives might be sampled from the same subpopulation, and consequently, might cause Hardy-Weinberg and linkage disequilibrium and thus bias a population genetic structure analysis. In this study, we used simulated and real data to investigate the impact of close relatives in a sample on Bayesian population structure analysis. We also showed that, when close relatives were identified by a pedigree reconstruction approach and removed, the accuracy of a population genetic structure analysis can be greatly improved. The results indicate that unsupervised Bayesian clustering algorithms cannot be used blindly to detect genetic structure in a sample with closely related individuals. Rather, when closely related individuals are suspected to be frequent in a sample, these individuals should be first identified and removed before conducting a population structure analysis.
BayesHammer: Bayesian clustering for error correction in single-cell sequencing.
Nikolenko, Sergey I; Korobeynikov, Anton I; Alekseyev, Max A
2013-01-01
Error correction of sequenced reads remains a difficult task, especially in single-cell sequencing projects with extremely non-uniform coverage. While existing error correction tools designed for standard (multi-cell) sequencing data usually come up short in single-cell sequencing projects, algorithms actually used for single-cell error correction have been so far very simplistic.We introduce several novel algorithms based on Hamming graphs and Bayesian subclustering in our new error correction tool BAYESHAMMER. While BAYESHAMMER was designed for single-cell sequencing, we demonstrate that it also improves on existing error correction tools for multi-cell sequencing data while working much faster on real-life datasets. We benchmark BAYESHAMMER on both k-mer counts and actual assembly results with the SPADES genome assembler.
Directory of Open Access Journals (Sweden)
Wills Rachael A
2009-05-01
Full Text Available Abstract Background The problem of silent multiple comparisons is one of the most difficult statistical problems faced by scientists. It is a particular problem for investigating a one-off cancer cluster reported to a health department because any one of hundreds, or possibly thousands, of neighbourhoods, schools, or workplaces could have reported a cluster, which could have been for any one of several types of cancer or any one of several time periods. Methods This paper contrasts the frequentist approach with a Bayesian approach for dealing with silent multiple comparisons in the context of a one-off cluster reported to a health department. Two published cluster investigations were re-analysed using the Dunn-Sidak method to adjust frequentist p-values and confidence intervals for silent multiple comparisons. Bayesian methods were based on the Gamma distribution. Results Bayesian analysis with non-informative priors produced results similar to the frequentist analysis, and suggested that both clusters represented a statistical excess. In the frequentist framework, the statistical significance of both clusters was extremely sensitive to the number of silent multiple comparisons, which can only ever be a subjective "guesstimate". The Bayesian approach is also subjective: whether there is an apparent statistical excess depends on the specified prior. Conclusion In cluster investigations, the frequentist approach is just as subjective as the Bayesian approach, but the Bayesian approach is less ambitious in that it treats the analysis as a synthesis of data and personal judgements (possibly poor ones, rather than objective reality. Bayesian analysis is (arguably a useful tool to support complicated decision-making, because it makes the uncertainty associated with silent multiple comparisons explicit.
Stenning, D. C.; Wagner-Kaiser, R.; Robinson, E.; van Dyk, D. A.; von Hippel, T.; Sarajedini, A.; Stein, N.
2016-07-01
We develop a Bayesian model for globular clusters composed of multiple stellar populations, extending earlier statistical models for open clusters composed of simple (single) stellar populations. Specifically, we model globular clusters with two populations that differ in helium abundance. Our model assumes a hierarchical structuring of the parameters in which physical properties—age, metallicity, helium abundance, distance, absorption, and initial mass—are common to (i) the cluster as a whole or to (ii) individual populations within a cluster, or are unique to (iii) individual stars. An adaptive Markov chain Monte Carlo (MCMC) algorithm is devised for model fitting that greatly improves convergence relative to its precursor non-adaptive MCMC algorithm. Our model and computational tools are incorporated into an open-source software suite known as BASE-9. We use numerical studies to demonstrate that our method can recover parameters of two-population clusters, and also show how model misspecification can potentially be identified. As a proof of concept, we analyze the two stellar populations of globular cluster NGC 5272 using our model and methods. (BASE-9 is available from GitHub: https://github.com/argiopetech/base/releases).
Analysis of traffic accidents on rural highways using Latent Class Clustering and Bayesian Networks.
de Oña, Juan; López, Griselda; Mujalli, Randa; Calvo, Francisco J
2013-03-01
One of the principal objectives of traffic accident analyses is to identify key factors that affect the severity of an accident. However, with the presence of heterogeneity in the raw data used, the analysis of traffic accidents becomes difficult. In this paper, Latent Class Cluster (LCC) is used as a preliminary tool for segmentation of 3229 accidents on rural highways in Granada (Spain) between 2005 and 2008. Next, Bayesian Networks (BNs) are used to identify the main factors involved in accident severity for both, the entire database (EDB) and the clusters previously obtained by LCC. The results of these cluster-based analyses are compared with the results of a full-data analysis. The results show that the combined use of both techniques is very interesting as it reveals further information that would not have been obtained without prior segmentation of the data. BN inference is used to obtain the variables that best identify accidents with killed or seriously injured. Accident type and sight distance have been identify in all the cases analysed; other variables such as time, occupant involved or age are identified in EDB and only in one cluster; whereas variables vehicles involved, number of injuries, atmospheric factors, pavement markings and pavement width are identified only in one cluster.
Xu, Lizhen; Paterson, Andrew D; Xu, Wei
2017-04-01
Motivated by the multivariate nature of microbiome data with hierarchical taxonomic clusters, counts that are often skewed and zero inflated, and repeated measures, we propose a Bayesian latent variable methodology to jointly model multiple operational taxonomic units within a single taxonomic cluster. This novel method can incorporate both negative binomial and zero-inflated negative binomial responses, and can account for serial and familial correlations. We develop a Markov chain Monte Carlo algorithm that is built on a data augmentation scheme using Pólya-Gamma random variables. Hierarchical centering and parameter expansion techniques are also used to improve the convergence of the Markov chain. We evaluate the performance of our proposed method through extensive simulations. We also apply our method to a human microbiome study.
An empirical Bayesian analysis applied to the globular cluster pulsar population
Turk, P J
2013-01-01
We describe an empirical Bayesian approach to determine the most likely size of an astronomical population of sources of which only a small subset are observed above some limiting flux density threshold. The method is most naturally applied to astronomical source populations at a common distance (e.g.,stellar populations in globular clusters), and can be applied even to populations where a survey detects no objects. The model allows for the inclusion of physical parameters of the stellar population and the detection process. As an example, we apply this method to the current sample of radio pulsars in Galactic globular clusters. Using the sample of flux density limits on pulsar surveys in 94 globular clusters published by Boyles et al., we examine a large number of population models with different dependencies. We find that models which include the globular cluster two-body encounter rate, $\\Gamma$, are strongly favoured over models in which this is not a factor. The optimal model is one in which the mean num...
Godsey, Brian
2013-01-01
Inferring gene regulatory networks from expression data is difficult, but it is common and often useful. Most network problems are under-determined--there are more parameters than data points--and therefore data or parameter set reduction is often necessary. Correlation between variables in the model also contributes to confound network coefficient inference. In this paper, we present an algorithm that uses integrated, probabilistic clustering to ease the problems of under-determination and correlated variables within a fully Bayesian framework. Specifically, ours is a dynamic Bayesian network with integrated Gaussian mixture clustering, which we fit using variational Bayesian methods. We show, using public, simulated time-course data sets from the DREAM4 Challenge, that our algorithm outperforms non-clustering methods in many cases (7 out of 25) with fewer samples, rarely underperforming (1 out of 25), and often selects a non-clustering model if it better describes the data. Source code (GNU Octave) for BAyesian Clustering Over Networks (BACON) and sample data are available at: http://code.google.com/p/bacon-for-genetic-networks.
Nonparametric Bayesian Clustering of Structural Whole Brain Connectivity in Full Image Resolution
DEFF Research Database (Denmark)
Ambrosen, Karen Marie Sandø; Albers, Kristoffer Jon; Dyrby, Tim B.
2014-01-01
Diffusion magnetic resonance imaging enables measuring the structural connectivity of the human brain at a high spatial resolution. Local noisy connectivity estimates can be derived using tractography approaches and statistical models are necessary to quantify the brain’s salient structural...... organization. However, statistically modeling these massive structural connectivity datasets is a computational challenging task. We develop a high-performance inference procedure for the infinite relational model (a prominent non-parametric Bayesian model for clustering networks into structurally similar...... groups) that defines structural units at the resolution of statistical support. We apply the model to a network of structural brain connectivity in full image resolution with more than one hundred thousand regions (voxels in the gray-white matter boundary) and around one hundred million connections...
Gao, Xinbo; Li, Qi; Li, Jie
2003-09-01
Anchorperson shot detection is of significance for video shot semantic parsing and indexing clues extraction in content-based news video indexing and retrieval system. This paper presents a model-free anchorperson shot detection scheme based on the graph-theoretical clustering and fuzzy interference. First, a news video is segmented into video shots with any an effective video syntactic parsing algorithm. For each shot, one frame is extracted from the frame sequence as a representative key frame. Then the graph-theoretical clustering algorithm is performed on the key frames to identify the anchorperson frames. The anchorperson frames are further refined based on face detection and fuzzy interference with if-then rules. The proposed scheme achieves a precision of 98.40% and a recall of over 97.69% in the anchorperson shot detection experiment.
Generating Realistic Labelled, Weighted Random Graphs
Davis, Michael Charles; Liu, Weiru; Miller, Paul; Hunter, Ruth; Kee, Frank
2015-01-01
Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs) with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI) approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs). Our results allow us to draw conclusions about the contribution of vertex labels a...
Wagner-Kaiser, R; Robinson, E; von Hippel, T; Sarajedini, A; van Dyk, D A; Stein, N; Jefferys, W H
2016-01-01
We use Cycle 21 Hubble Space Telescope (HST) observations and HST archival ACS Treasury observations of Galactic Globular Clusters to find and characterize two stellar populations in NGC 5024 (M53), NGC 5272 (M3), and NGC 6352. For these three clusters, both single and double-population analyses are used to determine a best fit isochrone(s). We employ a sophisticated Bayesian analysis technique to simultaneously fit the cluster parameters (age, distance, absorption, and metallicity) that characterize each cluster. For the two-population analysis, unique population level helium values are also fit to each distinct population of the cluster and the relative proportions of the populations are determined. We find differences in helium ranging from $\\sim$0.05 to 0.11 for these three clusters. Model grids with solar $\\alpha$-element abundances ([$\\alpha$/Fe] =0.0) and enhanced $\\alpha$-elements ([$\\alpha$/Fe]=0.4) are adopted.
Bayesian investigation of isochrone consistency using the old open cluster NGC 188
Energy Technology Data Exchange (ETDEWEB)
Hills, Shane; Courteau, Stéphane [Department of Physics, Engineering Physics and Astronomy, Queen’s University, Kingston, ON K7L 3N6 Canada (Canada); Von Hippel, Ted [Department of Physical Sciences, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114 (United States); Geller, Aaron M., E-mail: shane.hills@queensu.ca, E-mail: courteau@astro.queensu.ca, E-mail: ted.vonhippel@erau.edu, E-mail: a-geller@northwestern.edu [Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208 (United States)
2015-03-01
This paper provides a detailed comparison of the differences in parameters derived for a star cluster from its color–magnitude diagrams (CMDs) depending on the filters and models used. We examine the consistency and reliability of fitting three widely used stellar evolution models to 15 combinations of optical and near-IR photometry for the old open cluster NGC 188. The optical filter response curves match those of theoretical systems and are thus not the source of fit inconsistencies. NGC 188 is ideally suited to this study thanks to a wide variety of high-quality photometry and available proper motions and radial velocities that enable us to remove non-cluster members and many binaries. Our Bayesian fitting technique yields inferred values of age, metallicity, distance modulus, and absorption as a function of the photometric band combinations and stellar models. We show that the historically favored three-band combinations of UBV and VRI can be meaningfully inconsistent with each other and with longer baseline data sets such as UBVRIJHK{sub S}. Differences among model sets can also be substantial. For instance, fitting Yi et al. (2001) and Dotter et al. (2008) models to UBVRIJHK{sub S} photometry for NGC 188 yields the following cluster parameters: age = (5.78 ± 0.03, 6.45 ± 0.04) Gyr, [Fe/H] = (+0.125 ± 0.003, −0.077 ± 0.003) dex, (m−M){sub V} = (11.441 ± 0.007, 11.525 ± 0.005) mag, and A{sub V} = (0.162 ± 0.003, 0.236 ± 0.003) mag, respectively. Within the formal fitting errors, these two fits are substantially and statistically different. Such differences among fits using different filters and models are a cautionary tale regarding our current ability to fit star cluster CMDs. Additional modeling of this kind, with more models and star clusters, and future Gaia parallaxes are critical for isolating and quantifying the most relevant uncertainties in stellar evolutionary models.
Eadie, Gwendolyn; Harris, William E.; Springford, Aaron; Widrow, Larry
2017-01-01
The mass and cumulative mass profile of the Milky Way's dark matter halo is a fundamental property of the Galaxy, and yet these quantities remain poorly constrained and span almost two orders of magnitude in the literature. There are a variety of methods to measure the mass of the Milky Way, and a common way to constrain the mass uses kinematic information of satellite objects (e.g. globular clusters) orbiting the Galaxy. One reason precise estimates of the mass and mass profile remain elusive is that the kinematic data of the globular clusters are incomplete; for some both line-of-sight and proper motion measurements are available (i.e. complete data), and for others there are only line-of-sight velocities (i.e. incomplete data). Furthermore, some proper motion measurements suffer from large measurement uncertainties, and these uncertainties can be difficult to take into account because they propagate in complicated ways. Past methods have dealt with incomplete data by using either only the line-of-sight measurements (and throwing away the proper motions), or only using the complete data. In either case, valuable information is not included in the analysis. During my PhD research, I have been developing a coherent hierarchical Bayesian method to estimate the mass and mass profile of the Galaxy that 1) includes both complete and incomplete kinematic data simultaneously in the analysis, and 2) includes measurement uncertainties in a meaningful way. In this presentation, I will introduce our approach in a way that is accessible and clear, and will also present our estimates of the Milky Way's total mass and mass profile using all available kinematic data from the globular cluster population of the Galaxy.
Qin, Zhaohui S; McCue, Lee Ann; Thompson, William; Mayerhofer, Linda; Lawrence, Charles E; Liu, Jun S
2003-04-01
The identification of co-regulated genes and their transcription-factor binding sites (TFBS) are key steps toward understanding transcription regulation. In addition to effective laboratory assays, various computational approaches for the detection of TFBS in promoter regions of coexpressed genes have been developed. The availability of complete genome sequences combined with the likelihood that transcription factors and their cognate sites are often conserved during evolution has led to the development of phylogenetic footprinting. The modus operandi of this technique is to search for conserved motifs upstream of orthologous genes from closely related species. The method can identify hundreds of TFBS without prior knowledge of co-regulation or coexpression. Because many of these predicted sites are likely to be bound by the same transcription factor, motifs with similar patterns can be put into clusters so as to infer the sets of co-regulated genes, that is, the regulons. This strategy utilizes only genome sequence information and is complementary to and confirmative of gene expression data generated by microarray experiments. However, the limited data available to characterize individual binding patterns, the variation in motif alignment, motif width, and base conservation, and the lack of knowledge of the number and sizes of regulons make this inference problem difficult. We have developed a Gibbs sampling-based Bayesian motif clustering (BMC) algorithm to address these challenges. Tests on simulated data sets show that BMC produces many fewer errors than hierarchical and K-means clustering methods. The application of BMC to hundreds of predicted gamma-proteobacterial motifs correctly identified many experimentally reported regulons, inferred the existence of previously unreported members of these regulons, and suggested novel regulons.
A novel Bayesian DNA motif comparison method for clustering and retrieval.
Directory of Open Access Journals (Sweden)
Naomi Habib
2008-02-01
Full Text Available Characterizing the DNA-binding specificities of transcription factors is a key problem in computational biology that has been addressed by multiple algorithms. These usually take as input sequences that are putatively bound by the same factor and output one or more DNA motifs. A common practice is to apply several such algorithms simultaneously to improve coverage at the price of redundancy. In interpreting such results, two tasks are crucial: clustering of redundant motifs, and attributing the motifs to transcription factors by retrieval of similar motifs from previously characterized motif libraries. Both tasks inherently involve motif comparison. Here we present a novel method for comparing and merging motifs, based on Bayesian probabilistic principles. This method takes into account both the similarity in positional nucleotide distributions of the two motifs and their dissimilarity to the background distribution. We demonstrate the use of the new comparison method as a basis for motif clustering and retrieval procedures, and compare it to several commonly used alternatives. Our results show that the new method outperforms other available methods in accuracy and sensitivity. We incorporated the resulting motif clustering and retrieval procedures in a large-scale automated pipeline for analyzing DNA motifs. This pipeline integrates the results of various DNA motif discovery algorithms and automatically merges redundant motifs from multiple training sets into a coherent annotated library of motifs. Application of this pipeline to recent genome-wide transcription factor location data in S. cerevisiae successfully identified DNA motifs in a manner that is as good as semi-automated analysis reported in the literature. Moreover, we show how this analysis elucidates the mechanisms of condition-specific preferences of transcription factors.
Review on Graph Clustering and Subgraph Similarity Based Analysis of Neurological Disorders
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Jaya Thomas
2016-06-01
Full Text Available How can complex relationships among molecular or clinico-pathological entities of neurological disorders be represented and analyzed? Graphs seem to be the current answer to the question no matter the type of information: molecular data, brain images or neural signals. We review a wide spectrum of graph representation and graph analysis methods and their application in the study of both the genomic level and the phenotypic level of the neurological disorder. We find numerous research works that create, process and analyze graphs formed from one or a few data types to gain an understanding of specific aspects of the neurological disorders. Furthermore, with the increasing number of data of various types becoming available for neurological disorders, we find that integrative analysis approaches that combine several types of data are being recognized as a way to gain a global understanding of the diseases. Although there are still not many integrative analyses of graphs due to the complexity in analysis, multi-layer graph analysis is a promising framework that can incorporate various data types. We describe and discuss the benefits of the multi-layer graph framework for studies of neurological disease.
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Ali Dashti
Full Text Available This paper presents an implementation of the brute-force exact k-Nearest Neighbor Graph (k-NNG construction for ultra-large high-dimensional data cloud. The proposed method uses Graphics Processing Units (GPUs and is scalable with multi-levels of parallelism (between nodes of a cluster, between different GPUs on a single node, and within a GPU. The method is applicable to homogeneous computing clusters with a varying number of nodes and GPUs per node. We achieve a 6-fold speedup in data processing as compared with an optimized method running on a cluster of CPUs and bring a hitherto impossible [Formula: see text]-NNG generation for a dataset of twenty million images with 15 k dimensionality into the realm of practical possibility.
Morton, Kenneth D., Jr.; Torrione, Peter A.; Collins, Leslie
2010-04-01
Time domain ground penetrating radar (GPR) has been shown to be a powerful sensing phenomenology for detecting buried objects such as landmines. Landmine detection with GPR data typically utilizes a feature-based pattern classification algorithm to discriminate buried landmines from other sub-surface objects. In high-fidelity GPR, the time-frequency characteristics of a landmine response should be indicative of the physical construction and material composition of the landmine and could therefore be useful for discrimination from other non-threatening sub-surface objects. In this research we propose modeling landmine time-domain responses with a nonparametric Bayesian time-series model and we perform clustering of these time-series models with a hierarchical nonparametric Bayesian model. Each time-series is modeled as a hidden Markov model (HMM) with autoregressive (AR) state densities. The proposed nonparametric Bayesian prior allows for automated learning of the number of states in the HMM as well as the AR order within each state density. This creates a flexible time-series model with complexity determined by the data. Furthermore, a hierarchical non-parametric Bayesian prior is used to group landmine responses with similar HMM model parameters, thus learning the number of distinct landmine response models within a data set. Model inference is accomplished using a fast variational mean field approximation that can be implemented for on-line learning.
Singh, Gurmeet; Nguyen, Thanh; Kressler, Bryan; Spincemaille, Pascal; Raj, Ashish; Zabih, Ramin; Wang, Yi
2006-01-01
High resolution 3D coronary artery MR angiography is time-consuming and can benefit from accelerated data acquisition provided by parallel imaging techniques without sacrificing spatial resolution. Currently, popular maximum likelihood based parallel imaging reconstruction techniques such as the SENSE algorithm offer this advantage at the cost of reduced signal-to-noise ratio (SNR). Maximum a posteriori (MAP) reconstruction techniques that incorporate globally smooth priors have been developed to recover this SNR loss, but they tend to blur sharp edges in the target image. The objective of this study is to demonstrate the feasibility of employing edge-preserving Markov random field priors in a MAP reconstruction framework, which can be solved efficiently using a graph cuts based optimization algorithm. The preliminary human study shows that our reconstruction provides significantly better SNR than the SENSE reconstruction performed by a commercially available scanner for navigator gated steady state free precession 3D coronary magnetic resonance angiography images (n = 4).
Clusters and Maps of Science Journals Based on Bi-connected Graphs in the Journal Citation Reports
Leydesdorff, Loet
2009-01-01
The aggregated journal-journal citation matrix derived from the Journal Citation Reports 2001 can be decomposed into a unique subject classification by using the graph-analytical algorithm of bi-connected components. This technique was recently incorporated in software tools for social network analysis. The matrix can be assessed in terms of its decomposability using articulation points which indicate overlap between the components. The articulation points of this set did not exhibit a next-order network of 'general science' journals. However, the clusters differ in size and in terms of the internal density of their relations. A full classification of the journals is provided in an Appendix. The clusters can also be extracted and mapped for the visualization.
What dot clusters and bar graphs reveal: subitizing is fast counting and subtraction.
Boles, David B; Phillips, Jeffrey B; Givens, Somer M
2007-08-01
In two studies, we found that dot enumeration tasks resulted in shallow-sloped response time (RT) functions for displays of 1-4 dots and steep-sloped functions for displays of 5-8 dots, replicating results implicating subitizing and counting processes for low and high ranges of dots, respectively. Extracting number from a specific type of bar graph within the same numerical range produced a shallow-sloped but scallop-shaped RT function. Factor analysis confirmed two independent subranges for dots, but all bar graph values defined a unitary factor. Significantly, factor scores and asymmetries both showed correlations of bar graph recognition to dot subitizing but not to dot counting, strongly suggesting that subitizing was used in both enumeration of low numbers of dots and bar graph recognition. According to these results, subitizing appears to be a nonverbal process operating flexibly in either additive or subtractive fashion on analog quantities having spatial extent, a conclusion consistent with a fast-counting model of subitizing but not with other models of the subitizing process.
Khanin, Alexander
2014-01-01
Cosmic rays (CRs) are protons and atomic nuclei that flow into our Solar system and reach the Earth with energies of up to ~10^21 eV. The sources of ultra-high energy cosmic rays (UHECRs) with E >~ 10^19 eV remain unknown, although there are theoretical reasons to think that at least some come from active galactic nuclei (AGNs). One way to assess the different hypotheses is by analysing the arrival directions of UHECRs, in particular their self-clustering. We have developed a fully Bayesian approach to analyzing the self-clustering of points on the sphere, which we apply to the UHECR arrival directions. The analysis is based on a multi-step approach that enables the application of Bayesian model comparison to cases with weak prior information. We have applied this approach to the 69 highest energy events recorded by the Pierre Auger Observatory (PAO), which is the largest current UHECR data set. We do not detect self-clustering, but simulations show that this is consistent with the AGN-sourced model for a dat...
Graph Based Models for Unsupervised High Dimensional Data Clustering and Network Analysis
2015-01-01
networks that people study are graphs, which consist of nodes (i.e., vertices) to represent the elementary units of a system and edges to represent pairwise...associated with eigenvalue zero. In fact, for Laplacian L, the eigenvalue zero has the exact algebraic multiplicity of k. In other words, L’s eigen... linear heat equation and thresholding. Because motion by mean curvature is a gradient flow of the TV semi-norm, the goal of the MBO scheme is to approxi
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J. Anitha
2015-06-01
Full Text Available Data mining has been a popular research area for more than a decade due to its vast spectrum of applications. However, the popularity and wide availability of data mining tools also raised concerns about the privacy of individuals. Thus, the burden of data privacy protection falls on the shoulder of the data holder and data disambiguation problem occurs in the data matrix, anonymized data becomes less secure. All of the existing privacy preservation clustering methods performs clustering based on single point of view, which is the origin, while the latter utilizes many different viewpoints, which are objects assumed to not be in the same cluster with the two objects being measured. To solve this all of above mentioned problems, this study presents a multiview point based clustering methods for anonymized data. Before that data disambiguation problem is solved by using Ramon-Gartner Subtree Graph Kernel (RGSGK, where the weight values are assigned and kernel value is determined for disambiguated data. Obtain privacy by anonymization, where the data is encrypted with secure key is obtained by the Ring-Based Fully Homomorphic Encryption (RBFHE. In order to group the anonymize data, in this study BAT clustering method is proposed based on multiview point based similarity measurement and the proposed method is called as MVBAT. However in this paper initially distance matrix is calculated and using which similarity matrix and dissimilarity matrix is formed. The experimental result of the proposed MVBAT Clustering algorithm is compared with conventional methods in terms of the F-Measure, running time, privacy loss and utility loss. RBFHE encryption results is also compared with existing methods in terms of the communication cost for UCI machine learning datasets such as adult dataset and house dataset.
Institute of Scientific and Technical Information of China (English)
Ping Yuan; Liang Qiao; Li Dai; Yan-Ping Wang; Guang-Xuan Zhou; Ying Han; Xiao-Xia Liu; Xun Zhang; Yi Cao; Juan Liang; Jun Zhu
2009-01-01
AIM:To investigate the spatial distribution patterns of anorectal atresia/stenosis in China.METHODS:Data were collected from the Chinese Birth Defects Monitoring Network (CBDMN),a hospitalbased congenital malformations registry system.All fetuses more than 28 wk of gestation and neonates up to 7 d of age in hospitals within the monitoring sites of the CBDMN were monitored from 2001 to 2005.Two-dimensional graph-theoretical clustering was used to divide monitoring sites of the CBDMN into different clusters according to the average incidences of anorectal atresia/stenosis in the different monitoring sites.RESULTS:The overall average incidence of anorectal atresia/stenosis in China was 3.17 per 10 000 from 2001 to 2005.The areas with the highest average incidences of anorectal atresia/stenosis were almost always focused in Eastern China.The monitoring sites were grouped into 6 clusters of areas.Cluster 1 comprised the monitoring sites in Heilongjiang Province,Jilin Province,and Liaoning Province;Cluster 2 was composed of those in Fujian Province,Guangdong Province,Hainan Province,Guangxi Zhuang Autonomous Region,south Hunan Province,and south Jiangxi Province;Cluster 3 consisted of those in Beijing Municipal City,Tianjin Municipal City,Hebei Province,Shandong Province,north Jiangsu Province,and north Anhui Province;Cluster 4 was made up of those in Zhejiang Province,Shanghai Municipal City,south Anhui Province,south Jiangsu Province,north Hunan Province,north Jiangxi Province,Hubei Province,Henan Province,Shanxi Province and Inner Mongolia Autonomous Region;Cluster 5 consisted of those in Ningxia Hui Autonomous Region,Gansu Province and Qinghai Province;and Cluster 6 included those in Shaanxi Province,Sichuan Province,Chongqing Municipal City,Yunnan Province,Guizhou Province,Xinjiang Uygur Autonomous Province and Tibet Autonomous Region.CONCLUSION:The findings in this research allow the display of the spatial distribution patterns of anorectal atresia/stenosis in
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Jing Chen
2015-06-01
Full Text Available This study takes the concept of food logistics distribution as the breakthrough point, by means of the aim of optimization of food logistics distribution routes and analysis of the optimization model of food logistics route, as well as the interpretation of the genetic algorithm, it discusses the optimization of food logistics distribution route based on genetic and cluster scheme algorithm.
Generating Realistic Labelled, Weighted Random Graphs
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Michael Charles Davis
2015-12-01
Full Text Available Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs. Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.
Shuai, Hong-Han; Yu, Philip S; Shen, Chih-Ya; Chen, Ming-Syan
2013-01-01
The importance of graph mining has been widely recognized thanks to a large variety of applications in many areas, while real datasets always play important roles to examine the solution quality and efficiency of a graph mining algorithm. Nevertheless, the size of a real dataset is usually fixed and constrained according to the available resources, such as the efforts to crawl an on-line social network. In this case, employing a synthetic graph generator is a possible way to generate a massive graph (e.g., billions nodes) for evaluating the scalability of an algorithm, and current popular statistical graph generators are properly designed to maintain statistical metrics such as total node degree, degree distribution, diameter, and clustering coefficient of the original social graphs. Nevertheless, in addition to the above metrics, recent studies on graph mining point out that graph frequent patterns are also important to provide useful implications for the corresponding social networking applications, but thi...
A Latent Variable Bayesian Approach to Spatial Clustering with Background Noise
Kayabol, K.
2011-01-01
We propose a finite mixture model for clustering of the spatial data patterns. The model is based on the spatial distances between the data locations in such a way that both the distances of the points to the cluster centers and the distances of a given point to its neighbors within a defined window
Bayesian History Reconstruction of Complex Human Gene Clusters on a Phylogeny
Vinař, Tomáš; Song, Giltae; Siepel, Adam
2009-01-01
Clusters of genes that have evolved by repeated segmental duplication present difficult challenges throughout genomic analysis, from sequence assembly to functional analysis. Improved understanding of these clusters is of utmost importance, since they have been shown to be the source of evolutionary innovation, and have been linked to multiple diseases, including HIV and a variety of cancers. Previously, Zhang et al. (2008) developed an algorithm for reconstructing parsimonious evolutionary histories of such gene clusters, using only human genomic sequence data. In this paper, we propose a probabilistic model for the evolution of gene clusters on a phylogeny, and an MCMC algorithm for reconstruction of duplication histories from genomic sequences in multiple species. Several projects are underway to obtain high quality BAC-based assemblies of duplicated clusters in multiple species, and we anticipate that our method will be useful in analyzing these valuable new data sets.
Graph-based unsupervised feature selection and multiview clustering for microarray data
Indian Academy of Sciences (India)
Tripti Swarnkar; Pabitra Mitra
2015-10-01
A challenge in bioinformatics is to analyse volumes of gene expression data generated through microarray experiments and obtain useful information. Consequently, most microarray studies demand complex data analysis to infer biologically meaningful information from such high-throughput data. Selection of informative genes is an important data analysis step to identify a set of genes which can further help in finding the biological information embedded in microarray data, and thus assists in diagnosis, prognosis and treatment of the disease. In this article we present an unsupervised feature selection technique which attempts to address the goal of explorative data analysis, unfolding the multi-faceted nature of data. It focuses on extracting multiple clustering views considering the diversity of each view from high-dimensional data. We evaluated our technique on benchmark data sets and the experimental results indicates the potential and effectiveness of the proposed model in comparison to the traditional single view clustering models, as well as other existing methods used in the literature for the studied datasets.
Clique graphs and overlapping communities
Evans, T. S.
2010-12-01
It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of communities or clusters is used to illustrate how a clique graph may be exploited. In particular a benchmark network is shown where clique graphs find the overlapping communities accurately while vertex partition methods fail.
Weighted cluster fusion algorithm based on graph%一种基于图论的加权聚类融合算法
Institute of Scientific and Technical Information of China (English)
谢岳山; 樊晓平; 廖志芳; 尹红练; 罗浩
2013-01-01
The results of the existing cluster fusion algorithms are usually not so good when they process the mixed attributes datas, the main reason is that the results of the algorithms are still dispersed. To solve this problem, this paper presented a new weighted cluster fusion algorithm based on graph theory. It first clustered the datasets and got cluster members, and then set weights to each data object with a proposed fusion function, and determined the relationship between the data-pair by setting weights to the edges between them, so it could get a weighted nearest neighbor graph. At last it did a last-clustering based on graph theory. Experiments show that the accuracy and stability of this cluster fusion algorithm is better than other clustering fusion algorithms.%现有聚类融合算法对混合属性数据进行处理的效果不佳,主要是融合后的结果仍存在一定的分散性.为解决这个问题,提出了一种基于图论的加权聚类融合算法,通过对数据集聚类得到聚类成员后,利用所设计的融合函数对各个数据对象赋予权重,同时通过设置各个数据对间边的权重来确定数据之间的关系,得到带权最近邻图,再用图论的方法进行聚类.实验表明,该算法的聚类精度和稳定性优于其他聚类融合算法.
Graph Embedding for Pattern Analysis
Ma, Yunqian
2013-01-01
Graph Embedding for Pattern Analysis covers theory methods, computation, and applications widely used in statistics, machine learning, image processing, and computer vision. This book presents the latest advances in graph embedding theories, such as nonlinear manifold graph, linearization method, graph based subspace analysis, L1 graph, hypergraph, undirected graph, and graph in vector spaces. Real-world applications of these theories are spanned broadly in dimensionality reduction, subspace learning, manifold learning, clustering, classification, and feature selection. A selective group of experts contribute to different chapters of this book which provides a comprehensive perspective of this field.
Novokmet, Natalija; Galov, Ana; Marjanović, Damir; Škaro, Vedrana; Projić, Petar; Lauc, Gordan; Primorac, Dragan; Rudan, Pavao
2015-01-01
The European Roma represent a transnational mosaic of minority population groups with different migration histories and contrasting experiences in their interactions with majority populations across the European continent. Although historical genetic contributions of European lineages to the Roma pool were investigated before, the extent of contemporary genetic admixture between Bayash Roma and non-Romani majority population remains elusive. The aim of this study was to assess the genetic structure of the Bayash Roma population from northwestern Croatia and the general Croatian population and to investigate the extent of admixture between them. A set of genetic data from two original studies (100 Bayash Roma from northwestern Croatia and 195 individuals from the general Croatian population) was analyzed by Bayesian clustering implemented in STRUCTURE software. By re-analyzing published data we intended to focus for the first time on genetic differentiation and structure and in doing so we clearly pointed to the importance of considering social phenomena in understanding genetic structuring. Our results demonstrated that two population clusters best explain the genetic structure, which is consistent with social exclusion of Roma and the demographic history of Bayash Roma who have settled in NW Croatia only about 150 years ago and mostly applied rules of endogamy. The presence of admixture was revealed, while the percentage of non-Croatian individuals in general Croatian population was approximately twofold higher than the percentage of non-Romani individuals in Roma population corroborating the presence of ethnomimicry in Roma.
Bayesian clustering of DNA sequences using Markov chains and a stochastic partition model.
Jääskinen, Väinö; Parkkinen, Ville; Cheng, Lu; Corander, Jukka
2014-02-01
In many biological applications it is necessary to cluster DNA sequences into groups that represent underlying organismal units, such as named species or genera. In metagenomics this grouping needs typically to be achieved on the basis of relatively short sequences which contain different types of errors, making the use of a statistical modeling approach desirable. Here we introduce a novel method for this purpose by developing a stochastic partition model that clusters Markov chains of a given order. The model is based on a Dirichlet process prior and we use conjugate priors for the Markov chain parameters which enables an analytical expression for comparing the marginal likelihoods of any two partitions. To find a good candidate for the posterior mode in the partition space, we use a hybrid computational approach which combines the EM-algorithm with a greedy search. This is demonstrated to be faster and yield highly accurate results compared to earlier suggested clustering methods for the metagenomics application. Our model is fairly generic and could also be used for clustering of other types of sequence data for which Markov chains provide a reasonable way to compress information, as illustrated by experiments on shotgun sequence type data from an Escherichia coli strain.
Directory of Open Access Journals (Sweden)
Mohammed Hussni O
2010-06-01
Full Text Available Abstract Background Cryptosporidium parvum is one of the most important biological contaminants in drinking water that produces life threatening infection in people with compromised immune systems. Dairy calves are thought to be the primary source of C. parvum contamination in watersheds. Understanding the spatial and temporal variation in the risk of C. parvum infection in dairy cattle is essential for designing cost-effective watershed management strategies to protect drinking water sources. Crude and Bayesian seasonal risk estimates for Cryptosporidium in dairy calves were used to investigate the spatio-temporal dynamics of C. parvum infection on dairy farms in the New York City watershed. Results Both global (Global Moran's I and specific (SaTScan cluster analysis methods revealed a significant (p C. parvum infection in all herds in the summer (p = 0.002, compared to the rest of the year. Bayesian estimates did not show significant spatial autocorrelation in any season. Conclusions Although we were not able to identify seasonal clusters using Bayesian approach, crude estimates highlighted both temporal and spatial clusters of C. parvum infection in dairy herds in a major watershed. We recommend that further studies focus on the factors that may lead to the presence of C. parvum clusters within the watershed, so that monitoring and prevention practices such as stream monitoring, riparian buffers, fencing and manure management can be prioritized and improved, to protect drinking water supplies and public health.
Directory of Open Access Journals (Sweden)
Arturo Medrano-Soto
2004-12-01
Full Text Available Based on mixture models, we present a Bayesian method (called BClass to classify biological entities (e.g. genes when variables of quite heterogeneous nature are analyzed. Various statistical distributions are used to model the continuous/categorical data commonly produced by genetic experiments and large-scale genomic projects. We calculate the posterior probability of each entry to belong to each element (group in the mixture. In this way, an original set of heterogeneous variables is transformed into a set of purely homogeneous characteristics represented by the probabilities of each entry to belong to the groups. The number of groups in the analysis is controlled dynamically by rendering the groups as 'alive' and 'dormant' depending upon the number of entities classified within them. Using standard Metropolis-Hastings and Gibbs sampling algorithms, we constructed a sampler to approximate posterior moments and grouping probabilities. Since this method does not require the definition of similarity measures, it is especially suitable for data mining and knowledge discovery in biological databases. We applied BClass to classify genes in RegulonDB, a database specialized in information about the transcriptional regulation of gene expression in the bacterium Escherichia coli. The classification obtained is consistent with current knowledge and allowed prediction of missing values for a number of genes. BClass is object-oriented and fully programmed in Lisp-Stat. The output grouping probabilities are analyzed and interpreted using graphical (dynamically linked plots and query-based approaches. We discuss the advantages of using Lisp-Stat as a programming language as well as the problems we faced when the data volume increased exponentially due to the ever-growing number of genomic projects.
Bayesian networks and food security - An introduction
Stein, A.
2004-01-01
This paper gives an introduction to Bayesian networks. Networks are defined and put into a Bayesian context. Directed acyclical graphs play a crucial role here. Two simple examples from food security are addressed. Possible uses of Bayesian networks for implementation and further use in decision sup
Regularity in Vague Intersection Graphs and Vague Line Graphs
Directory of Open Access Journals (Sweden)
Muhammad Akram
2014-01-01
Full Text Available Fuzzy graph theory is commonly used in computer science applications, particularly in database theory, data mining, neural networks, expert systems, cluster analysis, control theory, and image capturing. A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we introduce the notion of vague line graphs, and certain types of vague line graphs and present some of their properties. We also discuss an example application of vague digraphs.
Directory of Open Access Journals (Sweden)
Urbi Garay
2016-03-01
Full Text Available We define a dynamic and self-adjusting mixture of Gaussian Graphical Models to cluster financial returns, and provide a new method for extraction of nonparametric estimates of dynamic alphas (excess return and betas (to a choice set of explanatory factors in a multivariate setting. This approach, as well as the outputs, has a dynamic, nonstationary and nonparametric form, which circumvents the problem of model risk and parametric assumptions that the Kalman filter and other widely used approaches rely on. The by-product of clusters, used for shrinkage and information borrowing, can be of use to determine relationships around specific events. This approach exhibits a smaller Root Mean Squared Error than traditionally used benchmarks in financial settings, which we illustrate through simulation. As an illustration, we use hedge fund index data, and find that our estimated alphas are, on average, 0.13% per month higher (1.6% per year than alphas estimated through Ordinary Least Squares. The approach exhibits fast adaptation to abrupt changes in the parameters, as seen in our estimated alphas and betas, which exhibit high volatility, especially in periods which can be identified as times of stressful market events, a reflection of the dynamic positioning of hedge fund portfolio managers.
一种层次聚类的RDF图语义检索方法研究%Hierarchical clustering-based semantic retrieval of RDF graph
Institute of Scientific and Technical Information of China (English)
刘宁; 左凤华; 张俊
2012-01-01
The cun-ent research related RDF graph retrieve exists some problems, such as low efficiency of memory usage, low search efficiency and so on. This paper proposed a hierarchical clustering semantic retrieval model on RDF graph and the method based on the model to solve aforesaid problems. That extracting entities from RDF graph and hierarchical clustering by the guidance of the ontology library made the complex graph structure into a tree structure for efficient retrieval. Orientating target object which was one of nodes in the model in RDF conducted the semantic expansion queries. Retrieval efficiency increased because retrieval scope narrow down as construction of retrieval model and recall ratio increased by the semantic expansion queries.%针对当前信息资源描述框架(RDF)检索过程中存在的内存使用过大及检索效率低等问题,提出一个RDF图的层次聚类语义检索模型,设计并实现了相应的检索方法.首先从RDF图中抽取实体数据,在本体库的指导下,通过层次聚类,将复杂的图形结构转换为适合检索的树型结构；根据在树中查找到的目标对象,确定其在RDF图中的位置,进行语义扩充查询.检索模型的构建缩小了检索范围,从而提高了检索效率,其语义扩充查询还可以得到较好的查全率.
Learning Probabilistic Decision Graphs
DEFF Research Database (Denmark)
Jaeger, Manfred; Dalgaard, Jens; Silander, Tomi
2004-01-01
Probabilistic decision graphs (PDGs) are a representation language for probability distributions based on binary decision diagrams. PDGs can encode (context-specific) independence relations that cannot be captured in a Bayesian network structure, and can sometimes provide computationally more...... efficient representations than Bayesian networks. In this paper we present an algorithm for learning PDGs from data. First experiments show that the algorithm is capable of learning optimal PDG representations in some cases, and that the computational efficiency of PDG models learned from real-life data...
Higher-order graph wavelets and sparsity on circulant graphs
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.
Hendrix, William; Jenkins, John; Padmanabhan, Kanchana; Chakraborty, Arpan
2014-01-01
Practical Graph Mining with R presents a "do-it-yourself" approach to extracting interesting patterns from graph data. It covers many basic and advanced techniques for the identification of anomalous or frequently recurring patterns in a graph, the discovery of groups or clusters of nodes that share common patterns of attributes and relationships, the extraction of patterns that distinguish one category of graphs from another, and the use of those patterns to predict the category of new graphs. Hands-On Application of Graph Data Mining Each chapter in the book focuses on a graph mining task, such as link analysis, cluster analysis, and classification. Through applications using real data sets, the book demonstrates how computational techniques can help solve real-world problems. The applications covered include network intrusion detection, tumor cell diagnostics, face recognition, predictive toxicology, mining metabolic and protein-protein interaction networks, and community detection in social networks. De...
Institute of Scientific and Technical Information of China (English)
傅育熙
1998-01-01
The paper proposes reaction graphs as graphical representations of computational objects.A reaction graph is a directed graph with all its arrows and some of its nodes labeled.Computations are modled by graph rewriting of a simple nature.The basic rewriting rules embody the essence of both the communications among processes and cut-eliminations in proofs.Calculi of graphs are ideentified to give a formal and algebraic account of reaction graphs in the spirit of process algebra.With the help of the calculi,it is demonstrated that reaction graphs capture many interesting aspects of computations.
Current trends in Bayesian methodology with applications
Upadhyay, Satyanshu K; Dey, Dipak K; Loganathan, Appaia
2015-01-01
Collecting Bayesian material scattered throughout the literature, Current Trends in Bayesian Methodology with Applications examines the latest methodological and applied aspects of Bayesian statistics. The book covers biostatistics, econometrics, reliability and risk analysis, spatial statistics, image analysis, shape analysis, Bayesian computation, clustering, uncertainty assessment, high-energy astrophysics, neural networking, fuzzy information, objective Bayesian methodologies, empirical Bayes methods, small area estimation, and many more topics.Each chapter is self-contained and focuses on
Directory of Open Access Journals (Sweden)
Dolovich Lisa
2009-06-01
Full Text Available Abstract Background Cluster randomized trials (CRTs are increasingly used to assess the effectiveness of interventions to improve health outcomes or prevent diseases. However, the efficiency and consistency of using different analytical methods in the analysis of binary outcome have received little attention. We described and compared various statistical approaches in the analysis of CRTs using the Community Hypertension Assessment Trial (CHAT as an example. The CHAT study was a cluster randomized controlled trial aimed at investigating the effectiveness of pharmacy-based blood pressure clinics led by peer health educators, with feedback to family physicians (CHAT intervention against Usual Practice model (Control, on the monitoring and management of BP among older adults. Methods We compared three cluster-level and six individual-level statistical analysis methods in the analysis of binary outcomes from the CHAT study. The three cluster-level analysis methods were: i un-weighted linear regression, ii weighted linear regression, and iii random-effects meta-regression. The six individual level analysis methods were: i standard logistic regression, ii robust standard errors approach, iii generalized estimating equations, iv random-effects meta-analytic approach, v random-effects logistic regression, and vi Bayesian random-effects regression. We also investigated the robustness of the estimates after the adjustment for the cluster and individual level covariates. Results Among all the statistical methods assessed, the Bayesian random-effects logistic regression method yielded the widest 95% interval estimate for the odds ratio and consequently led to the most conservative conclusion. However, the results remained robust under all methods – showing sufficient evidence in support of the hypothesis of no effect for the CHAT intervention against Usual Practice control model for management of blood pressure among seniors in primary care. The
Sahasranand, K R
2010-01-01
Almost all known secret sharing schemes work on numbers. Such methods will have difficulty in sharing graphs since the number of graphs increases exponentially with the number of nodes. We propose a secret sharing scheme for graphs where we use graph intersection for reconstructing the secret which is hidden as a sub graph in the shares. Our method does not rely on heavy computational operations such as modular arithmetic or polynomial interpolation but makes use of very basic operations like assignment and checking for equality, and graph intersection can also be performed visually. In certain cases, the secret could be reconstructed using just pencil and paper by authorised parties but cannot be broken by an adversary even with unbounded computational power. The method achieves perfect secrecy for (2, n) scheme and requires far fewer operations compared to Shamir's algorithm. The proposed method could be used to share objects such as matrices, sets, plain text and even a heterogeneous collection of these. S...
Directory of Open Access Journals (Sweden)
Peixin Zhao
2014-01-01
Full Text Available This paper suggests a novel clustering method for analyzing the National Incident-Based Reporting System (NIBRS data, which include the determination of correlation of different crime types, the development of a likelihood index for crimes to occur in a jurisdiction, and the clustering of jurisdictions based on crime type. The method was tested by using the 2005 assault data from 121 jurisdictions in Virginia as a test case. The analyses of these data show that some different crime types are correlated and some different crime parameters are correlated with different crime types. The analyses also show that certain jurisdictions within Virginia share certain crime patterns. This information assists with constructing a pattern for a specific crime type and can be used to determine whether a jurisdiction may be more likely to see this type of crime occur in their area.
Zhao, Peixin; Darrah, Marjorie; Nolan, Jim; Zhang, Cun-Quan
2014-01-01
This paper suggests a novel clustering method for analyzing the National Incident-Based Reporting System (NIBRS) data, which include the determination of correlation of different crime types, the development of a likelihood index for crimes to occur in a jurisdiction, and the clustering of jurisdictions based on crime type. The method was tested by using the 2005 assault data from 121 jurisdictions in Virginia as a test case. The analyses of these data show that some different crime types are correlated and some different crime parameters are correlated with different crime types. The analyses also show that certain jurisdictions within Virginia share certain crime patterns. This information assists with constructing a pattern for a specific crime type and can be used to determine whether a jurisdiction may be more likely to see this type of crime occur in their area.
Li, Xueliang; Gutman, Ivan
2012-01-01
This book is about graph energy. The authors have included many of the important results on graph energy, such as the complete solution to the conjecture on maximal energy of unicyclic graphs, the Wagner-Heuberger's result on the energy of trees, the energy of random graphs or the approach to energy using singular values. It contains an extensive coverage of recent results and a gradual development of topics and the inclusion of complete proofs from most of the important recent results in the area. The latter fact makes it a valuable reference for researchers looking to get into the field of g
Directory of Open Access Journals (Sweden)
Susanne Altermann
Full Text Available The inclusion of molecular data is increasingly an integral part of studies assessing species boundaries. Analyses based on predefined groups may obscure patterns of differentiation, and population assignment tests provide an alternative for identifying population structure and barriers to gene flow. In this study, we apply population assignment tests implemented in the programs STRUCTURE and BAPS to single nucleotide polymorphisms from DNA sequence data generated for three previous studies of the lichenized fungal genus Letharia. Previous molecular work employing a gene genealogical approach circumscribed six species-level lineages within the genus, four putative lineages within the nominal taxon L. columbiana (Nutt. J.W. Thomson and two sorediate lineages. We show that Bayesian clustering implemented in the program STRUCTURE was generally able to recover the same six putative Letharia lineages. Population assignments were largely consistent across a range of scenarios, including: extensive amounts of missing data, the exclusion of SNPs from variable markers, and inferences based on SNPs from as few as three gene regions. While our study provided additional evidence corroborating the six candidate Letharia species, the equivalence of these genetic clusters with species-level lineages is uncertain due, in part, to limited phylogenetic signal. Furthermore, both the BAPS analysis and the ad hoc ΔK statistic from results of the STRUCTURE analysis suggest that population structure can possibly be captured with fewer genetic groups. Our findings also suggest that uneven sampling across taxa may be responsible for the contrasting inferences of population substructure. Our results consistently supported two distinct sorediate groups, 'L. lupina' and L. vulpina, and subtle morphological differences support this distinction. Similarly, the putative apotheciate species 'L. lucida' was also consistently supported as a distinct genetic cluster. However
DEFF Research Database (Denmark)
Vestergaard, Preben Dahl; Hartnell, Bert L.
2006-01-01
There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done, the gr...
Görke, Robert; Meyer-Bäse, Anke; Plant, Claudia; He, Huan; Emmett, Mark R.; Nilsson, Carol; Colman, Howard; Conrad, Charles A.
2011-06-01
Cancer stem cells (CSC) represent a very small percentage of the total tumor population however they pose a big challenge in treating cancer. Glycans play a key role in cancer therapeutics since overexpression of them depending on the glycan type can lead either to cell death or more invasive metastasis. Two major components, fetal bovine serum (FBS) and STAT3, are known to up- or down-regulate certain glycolipid or phospholipid compositions found in glioblastoma CSCs. The analysis and the understanding of the global interactional behavior of lipidomic networks remains a challenging task and can not be accomplished solely based on intuitive reasoning. The present contribution aims at applying graph clustering networks to analyze the functional aspects of certain activators or inhibitors at the molecular level in glioblastoma stem cells (GSCs). This research enhances our understanding of the differences in phenotype changes and determining the responses of glycans to certain treatments for the aggressive GSCs, and represents together with a quantitative phosphoproteomic study1 the most detailed systems biology study of GSCs differentiation known so far. Thus, these new paradigms are providing unique understanding of the mechanisms involved in GSC maintenance and tumorigenicity and are thus opening a new window to biomedical frontiers.
An Algorithm for Learning the Essential Graph
Noble, John M
2010-01-01
This article presents an algorithm for learning the essential graph of a Bayesian network. The basis of the algorithm is the Maximum Minimum Parents and Children algorithm developed by previous authors, with three substantial modifications. The MMPC algorithm is the first stage of the Maximum Minimum Hill Climbing algorithm for learning the directed acyclic graph of a Bayesian network, introduced by previous authors. The MMHC algorithm runs in two phases; firstly, the MMPC algorithm to locate the skeleton and secondly an edge orientation phase. The computationally expensive part is the edge orientation phase. The first modification introduced to the MMPC algorithm, which requires little additional computational cost, is to obtain the immoralities and hence the essential graph. This renders the edge orientation phase, the computationally expensive part, unnecessary, since the entire Markov structure that can be derived from data is present in the essential graph. Secondly, the MMPC algorithm can accept indepen...
2015-01-01
In this paper we develop a formal dynamic version of Chain Event Graphs (CEGs), a particularly expressive family of discrete graphical models. We demonstrate how this class links to semi-Markov models and provides a convenient generalization of the Dynamic Bayesian Network (DBN). In particular we develop a repeating time-slice Dynamic CEG providing a useful and simpler model in this family. We demonstrate how the Dynamic CEG’s graphical formulation exhibits asymmetric conditional independence...
Network reconstruction via graph blending
Estrada, Rolando
2016-05-01
Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.
Using Consensus Bayesian Network to Model the Reactive Oxygen Species Regulatory Pathway
Liangdong Hu; Limin Wang
2013-01-01
Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the bayesian network from microarray data directly. Although large numbers of bayesian network learning algorithms have been developed, when applying them to learn bayesian networks from microarray data, the accuracies are low due to that the databases they used to learn bayesian networks...
Trudeau, Richard J
1994-01-01
Preface1. Pure Mathematics Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. Graphs Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics The Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar Graphs Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions; Kuratowski's Theorem; Determining Whether a Graph is Planar or
Indian Academy of Sciences (India)
RAJAN SHRIVASTAVA; AVIJIT RAKSHIT; SUDHANSHU SHANKER; LOVEKESH VIG; PRADIPTA BANDYOPADHYAY
2016-09-01
The knowledge of degree of completeness of energy landscape search by stochastic algorithms is often lacking. A graph theory based method is used to investigate the completeness of search performed by Monte Carlo Temperature Basin Paving (MCTBP) algorithm for (H₂O)n, (n=6, 7, and 20). In the second part of the work, a combination of MCTBP and graph theory was used to devise a new algorithm for finding low energy structures of (H₂O)n, (n=21-25), where input structures for (H₂O)n comes from the graphs of (H₂O)n−1. The new algorithm can be a complementary tool to the MCTBP method.
DEFF Research Database (Denmark)
Seiller, Thomas
2016-01-01
Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should...... be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define...... "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite...
Energy Technology Data Exchange (ETDEWEB)
2016-06-01
GraphBench is a benchmark suite for graph pattern mining and graph analysis systems. The benchmark suite is a significant addition to conducting apples-apples comparison of graph analysis software (databases, in-memory tools, triple stores, etc.)
Graphs in Practical Situations
Institute of Scientific and Technical Information of China (English)
刘晓玫; 任心玥
2008-01-01
<正>Linear graphs are often used to depict conversion graphs and travel graphs. Example: The following graph shows the conversion between the Singapore dollar (S $) and the Malay- sian ringgit (RM) in 2000.
Reddy, A Satyanarayana
2011-01-01
A graph $X$ is said to be a pattern polynomial graph if its adjacency algebra is a coherent algebra. In this study we will find a necessary and sufficient condition for a graph to be a pattern polynomial graph. Some of the properties of the graphs which are polynomials in the pattern polynomial graph have been studied. We also identify known graph classes which are pattern polynomial graphs.
Warchalowski, Wiktor; Krawczyk, Malgorzata J.
2017-03-01
We found the Lindenmayer systems for line graphs built on selected fractals. We show that the fractal dimension of such obtained graphs in all analysed cases is the same as for their original graphs. Both for the original graphs and for their line graphs we identified classes of nodes which reflect symmetry of the graph.
Betweenness Centrality in Graphs
2014-01-01
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such ...
Lesaffre, Emmanuel
2012-01-01
The growth of biostatistics has been phenomenal in recent years and has been marked by considerable technical innovation in both methodology and computational practicality. One area that has experienced significant growth is Bayesian methods. The growing use of Bayesian methodology has taken place partly due to an increasing number of practitioners valuing the Bayesian paradigm as matching that of scientific discovery. In addition, computational advances have allowed for more complex models to be fitted routinely to realistic data sets. Through examples, exercises and a combination of introd
Clustering and Community Detection with Imbalanced Clusters
Aksoylar, Cem; Qian, Jing; Saligrama, Venkatesh
2016-01-01
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced cluster sizes since they tend to emphasize cut sizes over cut values. We propose a graph partitioning problem that seeks minimum cut partitions under minimum size constraints on partitions to de...
Gould, Ronald
2012-01-01
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S
Weinzierl, Stefan
2013-01-01
In these lectures I discuss Feynman graphs and the associated Feynman integrals. Of particular interest are the classes functions, which appear in the evaluation of Feynman integrals. The most prominent class of functions is given by multiple polylogarithms. The algebraic properties of multiple polylogarithms are reviewed in the second part of these lectures. The final part of these lectures is devoted to Feynman integrals, which cannot be expressed in terms of multiple polylogarithms. Methods from algebraic geometry provide tools to tackle these integrals.
Using consensus bayesian network to model the reactive oxygen species regulatory pathway.
Hu, Liangdong; Wang, Limin
2013-01-01
Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the bayesian network from microarray data directly. Although large numbers of bayesian network learning algorithms have been developed, when applying them to learn bayesian networks from microarray data, the accuracies are low due to that the databases they used to learn bayesian networks contain too few microarray data. In this paper, we propose a consensus bayesian network which is constructed by combining bayesian networks from relevant literatures and bayesian networks learned from microarray data. It would have a higher accuracy than the bayesian networks learned from one database. In the experiment, we validated the bayesian network combination algorithm on several classic machine learning databases and used the consensus bayesian network to model the Escherichia coli's ROS pathway.
新家, 健精
2013-01-01
© 2012 Springer Science+Business Media, LLC. All rights reserved. Article Outline: Glossary Definition of the Subject and Introduction The Bayesian Statistical Paradigm Three Examples Comparison with the Frequentist Statistical Paradigm Future Directions Bibliography
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan
2004-01-01
We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating...... and differentiating these circuits in time linear in their size. We report on experimental results showing the successful compilation, and efficient inference, on relational Bayesian networks whose {\\primula}--generated propositional instances have thousands of variables, and whose jointrees have clusters...
无尺度图k-中心点聚类算法在文本挖掘中的应用%Application of a Scale-Free Graph Clustering Algorithm in Text Mining
Institute of Scientific and Technical Information of China (English)
沈亚田; 沈夏炯; 马庆华
2009-01-01
The paper extracts the text features based on a method of word co-occurrence frequency,which is related to the semantics of document.We also introduce the theory of scale-free network,and cluster the documents with a scale-free graph clustering algorithm. The average and deviation methods of misclassification(MI) show the experimental results.%本文基于词的同现频率的方法对文本的特征进行提取,涉及了文档的语义.同时,引入了无尺度网络的理论,用无尺度图聚类算法对文本进行聚类.最后,我们使用错误分类度(MI)的均值和离差方法显示实验的结果.
Bayesian Networks: Aspects of Approximate Inference
Bolt, J.H.
2008-01-01
A Bayesian network can be used to model consisely the probabilistic knowledge with respect to a given problem domain. Such a network consists of an acyclic directed graph in which the nodes represent stochastic variables, supplemented with probabilities indicating the strength of the influences betw
Merris, Russell
2001-01-01
A lively invitation to the flavor, elegance, and power of graph theoryThis mathematically rigorous introduction is tempered and enlivened by numerous illustrations, revealing examples, seductive applications, and historical references. An award-winning teacher, Russ Merris has crafted a book designed to attract and engage through its spirited exposition, a rich assortment of well-chosen exercises, and a selection of topics that emphasizes the kinds of things that can be manipulated, counted, and pictured. Intended neither to be a comprehensive overview nor an encyclopedic reference, th
Diestel, Reinhard
2012-01-01
HauptbeschreibungThis standard textbook of modern graph theory, now in its fourth edition, combinesthe authority of a classic with the engaging freshness of style that is the hallmarkof active mathematics. It covers the core material of the subject with concise yetreliably complete proofs, while offering glimpses of more advanced methodsin each field by one or two deeper results, again with proofs given in full detail.The book can be used as a reliable text for an introductory course, as a graduatetext, and for self-study. Rezension"Deep, clear, wonderful. This is a serious book about the
Graphs in machine learning: an introduction
Latouche, Pierre
2015-01-01
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper, we give an introduction to some methods relying on graphs for learning. This includes both unsupervised and supervised methods. Unsupervised learning algorithms usually aim at visualising graphs in latent spaces and/or clustering the nodes. Both focus on extracting knowledge from graph topologies. While most existing techniques are only applicable to static graphs, where edges do not evolve through time, recent developments have shown that they could be extended to deal with evolving networks. In a supervised context, one generally aims at inferring labels or numerical values attached to nodes using both the graph and, when they are available, node characteristics. Balancing the two sources of information can be challenging, especially as they can disagree locally or globall...
Parallel Graph Partitioning for Complex Networks
Meyerhenke, Henning; Schulz, Christian
2014-01-01
Processing large complex networks like social networks or web graphs has recently attracted considerable interest. In order to do this in parallel, we need to partition them into pieces of about equal size. Unfortunately, previous parallel graph partitioners originally developed for more regular mesh-like networks do not work well for these networks. This paper addresses this problem by parallelizing and adapting the label propagation technique originally developed for graph clustering. By introducing size constraints, label propagation becomes applicable for both the coarsening and the refinement phase of multilevel graph partitioning. We obtain very high quality by applying a highly parallel evolutionary algorithm to the coarsened graph. The resulting system is both more scalable and achieves higher quality than state-of-the-art systems like ParMetis or PT-Scotch. For large complex networks the performance differences are very big. For example, our algorithm can partition a web graph with 3.3 billion edges ...
Understanding Graphs & Charts.
Cleary, John J.; Gravely, Mary Liles
Developed by educators from the Emily Griffith Opportunity School, this teacher's guide was developed for a 4-hour workshop to teach employees how to read the charts and graphs they need in the workplace. The unit covers four types of graphs: pictographs, bar graphs, line graphs, and circle graphs. The guide is divided into four sections: reading…
Spectral bounds for percolation on directed and undirected graphs
Hamilton, Kathleen E
2015-01-01
We give several algebraic bounds for percolation on directed and undirected graphs: proliferation of strongly-connected clusters, proliferation of in- and out-clusters, and the transition associated with the number of giant components.
DEFF Research Database (Denmark)
Mørup, Morten; Schmidt, Mikkel N
2012-01-01
Many networks of scientific interest naturally decompose into clusters or communities with comparatively fewer external than internal links; however, current Bayesian models of network communities do not exert this intuitive notion of communities. We formulate a nonparametric Bayesian model...... consistent with ground truth, and on real networks, it outperforms existing approaches in predicting missing links. This suggests that community structure is an important structural property of networks that should be explicitly modeled....... for community detection consistent with an intuitive definition of communities and present a Markov chain Monte Carlo procedure for inferring the community structure. A Matlab toolbox with the proposed inference procedure is available for download. On synthetic and real networks, our model detects communities...
Spanning Tree Based Attribute Clustering
DEFF Research Database (Denmark)
Zeng, Yifeng; Jorge, Cordero Hernandez
2009-01-01
inconsistent edges from a maximum spanning tree by starting appropriate initial modes, therefore generating stable clusters. It discovers sound clusters through simple graph operations and achieves significant computational savings. We compare the Star Discovery algorithm against earlier attribute clustering...
Preserving Differential Privacy in Degree-Correlation based Graph Generation.
Wang, Yue; Wu, Xintao
2013-08-01
Enabling accurate analysis of social network data while preserving differential privacy has been challenging since graph features such as cluster coefficient often have high sensitivity, which is different from traditional aggregate functions (e.g., count and sum) on tabular data. In this paper, we study the problem of enforcing edge differential privacy in graph generation. The idea is to enforce differential privacy on graph model parameters learned from the original network and then generate the graphs for releasing using the graph model with the private parameters. In particular, we develop a differential privacy preserving graph generator based on the dK-graph generation model. We first derive from the original graph various parameters (i.e., degree correlations) used in the dK-graph model, then enforce edge differential privacy on the learned parameters, and finally use the dK-graph model with the perturbed parameters to generate graphs. For the 2K-graph model, we enforce the edge differential privacy by calibrating noise based on the smooth sensitivity, rather than the global sensitivity. By doing this, we achieve the strict differential privacy guarantee with smaller magnitude noise. We conduct experiments on four real networks and compare the performance of our private dK-graph models with the stochastic Kronecker graph generation model in terms of utility and privacy tradeoff. Empirical evaluations show the developed private dK-graph generation models significantly outperform the approach based on the stochastic Kronecker generation model.
Bernardo, Jose M
2000-01-01
This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critica
Blundell, Charles; Heller, Katherine A
2012-01-01
Hierarchical structure is ubiquitous in data across many domains. There are many hier- archical clustering methods, frequently used by domain experts, which strive to discover this structure. However, most of these meth- ods limit discoverable hierarchies to those with binary branching structure. This lim- itation, while computationally convenient, is often undesirable. In this paper we ex- plore a Bayesian hierarchical clustering algo- rithm that can produce trees with arbitrary branching structure at each node, known as rose trees. We interpret these trees as mixtures over partitions of a data set, and use a computationally efficient, greedy ag- glomerative algorithm to find the rose trees which have high marginal likelihood given the data. Lastly, we perform experiments which demonstrate that rose trees are better models of data than the typical binary trees returned by other hierarchical clustering algorithms.
Tan, Yong
2013-01-01
In this paper, author uses set theory to construct a logic model of abstract figure from binary relation. Based on the uniform quantified structure, author gives two logic system for graph traversal and graph coloring respectively, moreover shows a new method of cutting graph. Around this model, there are six algorithms in this paper including exact graph traversal, Algebra calculation of natural number, graph partition and graph coloring.
Understanding the Scalability of Bayesian Network Inference Using Clique Tree Growth Curves
Mengshoel, Ole J.
2010-01-01
One of the main approaches to performing computation in Bayesian networks (BNs) is clique tree clustering and propagation. The clique tree approach consists of propagation in a clique tree compiled from a Bayesian network, and while it was introduced in the 1980s, there is still a lack of understanding of how clique tree computation time depends on variations in BN size and structure. In this article, we improve this understanding by developing an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN s non-root nodes to the number of root nodes, and (ii) the expected number of moral edges in their moral graphs. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for the total size of each set. For the special case of bipartite BNs, there are two sets and two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, where random bipartite BNs generated using the BPART algorithm are studied, we systematically increase the out-degree of the root nodes in bipartite Bayesian networks, by increasing the number of leaf nodes. Surprisingly, root clique growth is well-approximated by Gompertz growth curves, an S-shaped family of curves that has previously been used to describe growth processes in biology, medicine, and neuroscience. We believe that this research improves the understanding of the scaling behavior of clique tree clustering for a certain class of Bayesian networks; presents an aid for trade-off studies of clique tree clustering using growth curves; and ultimately provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms.
Institute of Scientific and Technical Information of China (English)
李志敏; 郝盼超; 黄鸿; 黄文
2016-01-01
针对图的半监督聚类算法(Semi-Supervised Graph-Based Clustering, SSGC)中出现的对先验信息利用不充分、不足以应对数据异构、计算耗时大等问题，本文提出一种基于半监督复合核的图聚类算法，并应用于高光谱图像。该算法首先通过引入半监督学习方法对径向基函数(Radial Basis Function, RBF)进行了改进，以充分利用少量的标记样本和无标记样本；其次将 RBF 核与光谱角核进行融合，构造复合核权重矩阵。在权重矩阵的构造过程中， K-近邻方法的引入也简化了计算过程。在Indian Pine和Botswana高光谱数据集上的实验结果表明，相对于SSGC算法，本文算法不仅实现了更高的分类正确率，其总体分类精度提升1%∼4%，而且有效提升了运算速度。%A semi-supervised graph-based clustering method is presented with composite kernel for the hyperspectral images, mainly to solve the problems existed in an algorithm called Semi-Supervised Graph-Based Clustering (SSGC) and improve its performance. As for the realization, it firstly reforms the Radial Basis Function (RBF) by adopting semi-supervised approach, to exploit the wealth of unlabeled samples in the image. Then, it incorporates the spectral angle kernel with RBF kernel, and constructs a composite kernel. At last, the use of K-Nearest Neighbor (KNN) method while constructing the weight matrix has greatly simplified the calculation. Experimental result in Indian Pine and Botswana hyperspectral data demonstrates that this algorithm can not only get higher classification accuracy (1%∼4% higher than SSGC, 10%∼20% higher than K-means and Fuzzy C-Means (FCM), but effectively improve operation speed compared with SSGC.
Pattern vectors from algebraic graph theory.
Wilson, Richard C; Hancock, Edwin R; Luo, Bin
2005-07-01
Graph structures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low-dimensional space using a number of alternative strategies, including principal components analysis (PCA), multidimensional scaling (MDS), and locality preserving projection (LPP). Experimentally, we demonstrate that the embeddings result in well-defined graph clusters. Our experiments with the spectral representation involve both synthetic and real-world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real-world experiments show that the method can be used to locate clusters of graphs.
Graph measures and network robustness
Ellens, W
2013-01-01
Network robustness research aims at finding a measure to quantify network robustness. Once such a measure has been established, we will be able to compare networks, to improve existing networks and to design new networks that are able to continue to perform well when it is subject to failures or attacks. In this paper we survey a large amount of robustness measures on simple, undirected and unweighted graphs, in order to offer a tool for network administrators to evaluate and improve the robustness of their network. The measures discussed in this paper are based on the concepts of connectivity (including reliability polynomials), distance, betweenness and clustering. Some other measures are notions from spectral graph theory, more precisely, they are functions of the Laplacian eigenvalues. In addition to surveying these graph measures, the paper also contains a discussion of their functionality as a measure for topological network robustness.
Villalba, Jesús
2015-01-01
In this document we are going to derive the equations needed to implement a Variational Bayes estimation of the parameters of the simplified probabilistic linear discriminant analysis (SPLDA) model. This can be used to adapt SPLDA from one database to another with few development data or to implement the fully Bayesian recipe. Our approach is similar to Bishop's VB PPCA.
DEFF Research Database (Denmark)
Dashab, Golam Reza; Kadri, Naveen Kumar; Mahdi Shariati, Mohammad;
2012-01-01
) Mixed model analysis (MMA), 2) Random haplotype model (RHM), 3) Genealogy-based mixed model (GENMIX), and 4) Bayesian variable selection (BVS). The data consisted of phenotypes of 2000 animals from 20 sire families and were genotyped with 9990 SNPs on five chromosomes. Results: Out of the eight...
Graph spectral analysis of protein interaction network evolution
Thorne, Thomas; Stumpf, Michael P. H.
2012-01-01
We present an analysis of protein interaction network data via the comparison of models of network evolution to the observed data. We take a Bayesian approach and perform posterior density estimation using an approximate Bayesian computation with sequential Monte Carlo method. Our approach allows us to perform model selection over a selection of potential network growth models. The methodology we apply uses a distance defined in terms of graph spectra which captures the network data more natu...
Interactive Graph Layout of a Million Nodes
Directory of Open Access Journals (Sweden)
Peng Mi
2016-12-01
Full Text Available Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph topology. This algorithm can interactively layout graphs with millions of nodes, and support real-time interaction to explore alternative graph layouts. Users can directly manipulate the layout of vertices in a force-directed fashion. The complexity of traditional repulsive force computation is reduced by approximating calculations based on the hierarchical structure of multi-level clustered graphs. We evaluate the algorithm performance, and demonstrate human-in-the-loop layout in two sensemaking case studies. Moreover, we summarize lessons learned for designing interactive large graph layout algorithms on the GPU.
Evolutionary Games of Multiplayer Cooperation on Graphs.
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.
Lawes, Jonathan F.
2013-01-01
Graphing polar curves typically involves a combination of three traditional techniques, all of which can be time-consuming and tedious. However, an alternative method--graphing the polar function on a rectangular plane--simplifies graphing, increases student understanding of the polar coordinate system, and reinforces graphing techniques learned…
2014-01-01
© 2015 Elsevier B.V. Motivated by recent extensive studies on Wenger graphs, we introduce a new infinite class of bipartite graphs of a similar type, called linearized Wenger graphs. The spectrum, diameter and girth of these linearized Wenger graphs are determined.
Line graphs as social networks
Krawczyk, Malgorzata; Mańka-Krasoń, Anna; Kułakowski, Krzysztof
2010-01-01
The line graphs are clustered and assortative. They share these topological features with some social networks. We argue that this similarity reveals the cliquey character of the social networks. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8 x 10^6 people. In particular, sharp maxima of the observed data of the degree dependence of the clustering coefficient C(k) are associated with cliques in the social network.
Probability and interference based social network clustering technology%基于概率与推断的社交网络聚类技术研究
Institute of Scientific and Technical Information of China (English)
宋传超; 王庚
2013-01-01
本文将位置敏感哈希算法(LSH)应用于图聚类,提出了概率化的图聚类法(PGC).利用LSH技术比较图中各结点邻居集的相似度,并结合贝叶斯统计推断进行验证,在线性时间内找到图中最紧密的、非精确聚类.测试结果表明,随着图尺寸的增大PGC扩展性更强,在现实世界数据集上PGC比PageRank Cluster聚类速度快约1倍,是一种有效的解决方案.%We apply Locality Sensitive Hashing (LSH) to graph clustering, and then present a new clustering technology, Probabilistic Graph Cluster (PGC). We also compare the similarity of the neighbor set of every node in a graph, and verify it with Bayesian statistic inference to find the most compact and inexact clustering in linear time. Experimental results show that PGC is more scalable with the enlargement of a graph and that the clustering speed of PGC is twice faster than that of PageRank Cluster in real data sets, PGC is therefore an effective and alternative solution.
Hedlund, Jonas
2014-01-01
This paper introduces private sender information into a sender-receiver game of Bayesian persuasion with monotonic sender preferences. I derive properties of increasing differences related to the precision of signals and use these to fully characterize the set of equilibria robust to the intuitive criterion. In particular, all such equilibria are either separating, i.e., the sender's choice of signal reveals his private information to the receiver, or fully disclosing, i.e., the outcome of th...
Kirstein, Roland
2005-01-01
This paper presents a modification of the inspection game: The ?Bayesian Monitoring? model rests on the assumption that judges are interested in enforcing compliant behavior and making correct decisions. They may base their judgements on an informative but imperfect signal which can be generated costlessly. In the original inspection game, monitoring is costly and generates a perfectly informative signal. While the inspection game has only one mixed strategy equilibrium, three Perfect Bayesia...
Estrada, Ernesto
2015-01-01
A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square \\left[0,1\\right]^{2}. The topological properties, such as connectivity, average degree, average path length and clustering, of the random rectangular graphs (RRGs) generated by this model are then studied as a function of the rectangle sides lengths a and b=1/a, and the radius r used to connect the nodes. When a=1 we recover the RGG, and when a\\rightarrow\\infty the very elongated rectangle generated resembles a one-dimensional RGG. We provided computational and analytical evidence that the topological properties of the RRG differ significantly from those of the RGG. The connectivity of the RRG depends not only on the number of nodes as in the case of the RGG, but also on the side length of the rectangle. As the rectangle is more elongated the critical radius for connectivity increases following first a power-law an...
Directory of Open Access Journals (Sweden)
Brudey Karine
2008-04-01
Full Text Available Abstract Background French Guiana has the highest tuberculosis (TB burden among all French departments, with a strong increase in the TB incidence over the last few years. It is now uncertain how best to explain this incidence. The objective of this study was to compare three different methods evaluating the extent of recent TB transmission in French Guiana. Methods We conducted a population-based molecular epidemiology study of tuberculosis in French Guiana based on culture-positive TB strains (1996 to 2003, n = 344 to define molecular relatedness between isolates, i.e. potential transmission events. Phylogenetic relationships were inferred by comparing two methods: a "cluster-graph" method based on spoligotyping results, and a minimum spanning tree method based on both spoligotyping and variable number of tandem DNA repeats (VNTR. Furthermore, three indices attempting to reflect the extent of recent TB transmission (RTIn, RTIn-1 and TMI were compared. Results Molecular analyses showed a total amount of 120 different spoligotyping patterns and 273 clinical isolates (79.4% that were grouped in 49 clusters. The comparison of spoligotypes from French Guiana with an international spoligotype database (SpolDB4 showed that the majority of isolates belonged to major clades of M. tuberculosis (Haarlem, 22.6%; Latin American-Mediterranean, 23.3%; and T, 32.6%. Indices designed to quantify transmission of tuberculosis gave the following values: RTIn = 0.794, RTIn-1 = 0.651, and TMI = 0.146. Conclusion Our data showed a high number of Mycobacterium tuberculosis clusters, suggesting a high level of recent TB transmission, nonetheless an estimation of transmission rate taking into account cluster size and mutation rate of genetic markers showed a low ongoing transmission rate (14.6%. Our results indicate an endemic mode of TB transmission in French Guiana, with both resurgence of old spatially restricted genotypes, and a significant importation of new TB
Applications of Graph Theory in Computer Science
Directory of Open Access Journals (Sweden)
U. Sekar
2013-11-01
Full Text Available The field of mathematics plays vital role in various fields. One of the important areas in mathematics is graph theory which is used in structural models. This structural arrangements of various objects or technologies lead to new inventions and modifications in the existing environment for enhancement in those fields. The field graph theory started its journey from the problem of Konigsberg Bridge in 1735. This paper gives an overview of the applications of graph theory in heterogeneous fields to some extent but mainly focuses on the computer science applications that uses graph theoretical concepts. Various papers based on graph theory have been studied related to scheduling concepts, computer science applications and an overview has been presented here.Graph theoretical ideas are highly utilized by computer science applications. Especially in research areas of computer science such data mining, image segmentation, clustering, image capturing, networking etc., For example a data structure can be designed in the form of tree which in turn utilized vertices and edges. Similarly modeling of network topologies can be done using graph concepts. In the same way the most important concept of graph coloring is utilized in resource allocation, scheduling. Also, paths, walks and circuits in graph theory are used in tremendous applications say traveling salesman problem, database design concepts, resource networking. This leads to the development of new algorithms and new theorems that can be used in tremendous applications. First section gives the historical background of graph theory and some applications in scheduling. Second section emphasizes how graph theory is utilized in various computer applications.
Generative Graph Prototypes from Information Theory.
Han, Lin; Wilson, Richard C; Hancock, Edwin R
2015-10-01
In this paper we present a method for constructing a generative prototype for a set of graphs by adopting a minimum description length approach. The method is posed in terms of learning a generative supergraph model from which the new samples can be obtained by an appropriate sampling mechanism. We commence by constructing a probability distribution for the occurrence of nodes and edges over the supergraph. We encode the complexity of the supergraph using an approximate Von Neumann entropy. A variant of the EM algorithm is developed to minimize the description length criterion in which the structure of the supergraph and the node correspondences between the sample graphs and the supergraph are treated as missing data. To generate new graphs, we assume that the nodes and edges of graphs arise under independent Bernoulli distributions and sample new graphs according to their node and edge occurrence probabilities. Empirical evaluations on real-world databases demonstrate the practical utility of the proposed algorithm and show the effectiveness of the generative model for the tasks of graph classification, graph clustering and generating new sample graphs.
Bapat, Ravindra B
2014-01-01
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...
Bessiere, Pierre; Ahuactzin, Juan Manuel; Mekhnacha, Kamel
2013-01-01
Probability as an Alternative to Boolean LogicWhile logic is the mathematical foundation of rational reasoning and the fundamental principle of computing, it is restricted to problems where information is both complete and certain. However, many real-world problems, from financial investments to email filtering, are incomplete or uncertain in nature. Probability theory and Bayesian computing together provide an alternative framework to deal with incomplete and uncertain data. Decision-Making Tools and Methods for Incomplete and Uncertain DataEmphasizing probability as an alternative to Boolean
Spectral recognition of graphs
Directory of Open Access Journals (Sweden)
Cvetković Dragoš
2012-01-01
Full Text Available At some time, in the childhood of spectral graph theory, it was conjectured that non-isomorphic graphs have different spectra, i.e. that graphs are characterized by their spectra. Very quickly this conjecture was refuted and numerous examples and families of non-isomorphic graphs with the same spectrum (cospectral graphs were found. Still some graphs are characterized by their spectra and several mathematical papers are devoted to this topic. In applications to computer sciences, spectral graph theory is considered as very strong. The benefit of using graph spectra in treating graphs is that eigenvalues and eigenvectors of several graph matrices can be quickly computed. Spectral graph parameters contain a lot of information on the graph structure (both global and local including some information on graph parameters that, in general, are computed by exponential algorithms. Moreover, in some applications in data mining, graph spectra are used to encode graphs themselves. The Euclidean distance between the eigenvalue sequences of two graphs on the same number of vertices is called the spectral distance of graphs. Some other spectral distances (also based on various graph matrices have been considered as well. Two graphs are considered as similar if their spectral distance is small. If two graphs are at zero distance, they are cospectral. In this sense, cospectral graphs are similar. Other spectrally based measures of similarity between networks (not necessarily having the same number of vertices have been used in Internet topology analysis, and in other areas. The notion of spectral distance enables the design of various meta-heuristic (e.g., tabu search, variable neighbourhood search algorithms for constructing graphs with a given spectrum (spectral graph reconstruction. Several spectrally based pattern recognition problems appear in many areas (e.g., image segmentation in computer vision, alignment of protein-protein interaction networks in bio
Directory of Open Access Journals (Sweden)
C. Dalfo
2015-10-01
Full Text Available We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors.
BS P模型下基于边聚簇的大图划分与迭代处理%Edge Cluster Based Large Graph Partitioning and Iterative Processing in BSP
Institute of Scientific and Technical Information of China (English)
冷芳玲; 刘金鹏; 王志刚; 陈昌宁; 鲍玉斌; 于戈; 邓超
2015-01-01
近年来随着互联网的普及和相关技术的日益成熟，大规模图数据处理成为新的研究热点。由于传统的如Hadoop等通用云平台不适合迭代式地处理图数据，研究人员基于BSP模型提出了新的处理方案，如Pregel ，Hama ，Giraph等。然而，图处理算法需要按照图的拓扑结构频繁交换中间计算结果而导致巨大的通信开销，这严重地影响了基于BSP模型的系统的处理性能。首先从降低消息通信的角度分析当前主流BSP系统的处理方案，然后提出了一种基于边聚簇的垂直混合划分策略（EC‐VHP），并建立代价收益模型分析其消息通信优化的效果。在EC‐V H P的基础上，提出了一个点‐边计算模型，并设计了简单Hash索引和多队列并行顺序索引机制，进一步提高消息通信的处理效率。最后，在真实数据集和模拟数据集上的大量实验，验证了EC‐V H P策略和索引机制的正确性和有效性。%With the development of Internet and the gradual maturity of related techniques in recent years ,the processing of large graphs has become a new hot research topic .Since it is not appropriate for traditional cloud computing platforms to process graph data iteratively , such as Hadoop , researchers have proposed some solutions based on the BSP model ,such as Pregel ,Hama and Giraph . However ,since graph algorithms need to frequently exchange intermediate results in accordance with the graph's topological structure , the tremendous communication overhead impacts the processing performance of systems based on the BSP model greatly .In this paper ,we first analyze the solutions proposed by the well‐known BSP‐based systems in reducing communication overhead , and then propose a graph partition strategy named edge cluster based vertically hybrid partitioning (EC‐VHP) , building a cost benefit model to study its effectiveness to the communication overhead .Then based on EC
Pancyclic and bipancyclic graphs
George, John C; Wallis, W D
2016-01-01
This book is focused on pancyclic and bipancyclic graphs and is geared toward researchers and graduate students in graph theory. Readers should be familiar with the basic concepts of graph theory, the definitions of a graph and of a cycle. Pancyclic graphs contain cycles of all possible lengths from three up to the number of vertices in the graph. Bipartite graphs contain only cycles of even lengths, a bipancyclic graph is defined to be a bipartite graph with cycles of every even size from 4 vertices up to the number of vertices in the graph. Cutting edge research and fundamental results on pancyclic and bipartite graphs from a wide range of journal articles and conference proceedings are composed in this book to create a standalone presentation. The following questions are highlighted through the book: - What is the smallest possible number of edges in a pancyclic graph with v vertices? - When do pancyclic graphs exist with exactly one cycle of every possible length? - What is the smallest possible number of...
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark
2006-01-01
We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference...... by evaluating and differentiating these circuits in time linear in their size. We report on experimental results showing successful compilation and efficient inference on relational Bayesian networks, whose PRIMULA--generated propositional instances have thousands of variables, and whose jointrees have clusters...
Continuous Time Group Discovery in Dynamic Graphs
Energy Technology Data Exchange (ETDEWEB)
Miller, K; Eliassi-Rad, T
2010-11-04
With the rise in availability and importance of graphs and networks, it has become increasingly important to have good models to describe their behavior. While much work has focused on modeling static graphs, we focus on group discovery in dynamic graphs. We adapt a dynamic extension of Latent Dirichlet Allocation to this task and demonstrate good performance on two datasets. Modeling relational data has become increasingly important in recent years. Much work has focused on static graphs - that is fixed graphs at a single point in time. Here we focus on the problem of modeling dynamic (i.e. time-evolving) graphs. We propose a scalable Bayesian approach for community discovery in dynamic graphs. Our approach is based on extensions of Latent Dirichlet Allocation (LDA). LDA is a latent variable model for topic modeling in text corpora. It was extended to deal with topic changes in discrete time and later in continuous time. These models were referred to as the discrete Dynamic Topic Model (dDTM) and the continuous Dynamic Topic Model (cDTM), respectively. When adapting these models to graphs, we take our inspiration from LDA-G and SSN-LDA, applications of LDA to static graphs that have been shown to effectively factor out community structure to explain link patterns in graphs. In this paper, we demonstrate how to adapt and apply the cDTM to the task of finding communities in dynamic networks. We use link prediction to measure the quality of the discovered community structure and apply it to two different relational datasets - DBLP author-keyword and CAIDA autonomous systems relationships. We also discuss a parallel implementation of this approach using Hadoop. In Section 2, we review LDA and LDA-G. In Section 3, we review the cDTM and introduce cDTMG, its adaptation to modeling dynamic graphs. We discuss inference for the cDTM-G and details of our parallel implementation in Section 4 and present its performance on two datasets in Section 5 before concluding in
On molecular graph comparison.
Melo, Jenny A; Daza, Edgar
2011-06-01
Since the last half of the nineteenth century, molecular graphs have been present in several branches of chemistry. When used for molecular structure representation, they have been compared after mapping the corresponding graphs into mathematical objects. However, direct molecular comparison of molecular graphs is a research field less explored. The goal of this mini-review is to show some distance and similarity coefficients which were proposed to directly compare molecular graphs or which could be useful to do so.
Evolutionary Graph Drawing Algorithms
Institute of Scientific and Technical Information of China (English)
Huang Jing-wei; Wei Wen-fang
2003-01-01
In this paper, graph drawing algorithms based on genetic algorithms are designed for general undirected graphs and directed graphs. As being shown, graph drawing algorithms designed by genetic algorithms have the following advantages: the frames of the algorithms are unified, the method is simple, different algorithms may be attained by designing different objective functions, therefore enhance the reuse of the algorithms. Also, aesthetics or constrains may be added to satisfy different requirements.
Network evolution driven by dynamics applied to graph coloring
Institute of Scientific and Technical Information of China (English)
Wu Jian-She; Li Li-Guang; Wang Xiao-Hua; Yu Xin; Jiao Li-Cheng
2013-01-01
An evolutionary network driven by dynamics is studied and applied to the graph coloring problem.From an initial structure,both the topology and the coupling weights evolve according to the dynamics.On the other hand,the dynamics of the network are determined by the topology and the coupling weights,so an interesting structure-dynamics co-evolutionary scheme appears.By providing two evolutionary strategies,a network described by the complement of a graph will evolve into several clusters of nodes according to their dynamics.The nodes in each cluster can be assigned the same color and nodes in different clusters assigned different colors.In this way,a co-evolution phenomenon is applied to the graph coloring problem.The proposed scheme is tested on several benchmark graphs for graph coloring.
Graphing Inequalities, Connecting Meaning
Switzer, J. Matt
2014-01-01
Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…
Loukas, A.
2015-01-01
We have recently seen a surge of research focusing on the processing of graph data. The emerging field of signal processing on graphs focuses on the extension of classical discrete signal processing techniques to the graph setting. Arguably, the greatest breakthrough of the field has been the extens
Ellens, W.; Spieksma, F.M.; Mieghem, P. van; Jamakovic, A.; Kooij, R.E.
2011-01-01
This paper studies an interesting graph measure that we call the effective graph resistance. The notion of effective graph resistance is derived from the field of electric circuit analysis where it is defined as the accumulated effective resistance between all pairs of vertices. The objective of the
Directory of Open Access Journals (Sweden)
Charles Suffel
1982-01-01
Full Text Available A graph is subeulerian if it is spanned by an eulerian supergraph. Boesch, Suffel and Tindell have characterized the class of subeulerian graphs and determined the minimum number of additional lines required to make a subeulerian graph eulerian.
Bayesian Methods for Radiation Detection and Dosimetry
Groer, Peter G
2002-01-01
We performed work in three areas: radiation detection, external and internal radiation dosimetry. In radiation detection we developed Bayesian techniques to estimate the net activity of high and low activity radioactive samples. These techniques have the advantage that the remaining uncertainty about the net activity is described by probability densities. Graphs of the densities show the uncertainty in pictorial form. Figure 1 below demonstrates this point. We applied stochastic processes for a method to obtain Bayesian estimates of 222Rn-daughter products from observed counting rates. In external radiation dosimetry we studied and developed Bayesian methods to estimate radiation doses to an individual with radiation induced chromosome aberrations. We analyzed chromosome aberrations after exposure to gammas and neutrons and developed a method for dose-estimation after criticality accidents. The research in internal radiation dosimetry focused on parameter estimation for compartmental models from observed comp...
Learning Bayesian Networks from Data by Particle Swarm Optimization
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Learning Bayesian network is an NP-hard problem. When the number of variables is large, the process of searching optimal network structure could be very time consuming and tends to return a structure which is local optimal. The particle swarm optimization (PSO) was introduced to the problem of learning Bayesian networks and a novel structure learning algorithm using PSO was proposed. To search in directed acyclic graphs spaces efficiently, a discrete PSO algorithm especially for structure learning was proposed based on the characteristics of Bayesian networks. The results of experiments show that our PSO based algorithm is fast for convergence and can obtain better structures compared with genetic algorithm based algorithms.
Line graphs as social networks
Krawczyk, M. J.; Muchnik, L.; Mańka-Krasoń, A.; Kułakowski, K.
2011-07-01
It was demonstrated recently that the line graphs are clustered and assortative. These topological features are known to characterize some social networks [M.E.J. Newman, Y. Park, Why social networks are different from other types of networks, Phys. Rev. E 68 (2003) 036122]; it was argued that this similarity reveals their cliquey character. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8×10 6 people.
Yoder, Sharon K.
This book discusses four kinds of graphs that are taught in mathematics at the middle school level: pictographs, bar graphs, line graphs, and circle graphs. The chapters on each of these types of graphs contain information such as starting, scaling, drawing, labeling, and finishing the graphs using "LogoWriter." The final chapter of the book…
Energy Technology Data Exchange (ETDEWEB)
D' Azevedo, Ed F [ORNL; Imam, Neena [ORNL
2015-01-01
This document describes the effort to implement the Graph 500 benchmark using OpenSHMEM based on the MPI-2 one-side version. The Graph 500 benchmark performs a breadth-first search in parallel on a large randomly generated undirected graph and can be implemented using basic MPI-1 and MPI-2 one-sided communication. Graph 500 requires atomic bit-wise operations on unsigned long integers but neither atomic bit-wise operations nor OpenSHMEM for unsigned long are available in OpenSHEM. Such needed bit-wise atomic operations and support for unsigned long are implemented using atomic condition swap (CSWAP) on signed long integers. Preliminary results on comparing the OpenSHMEM and MPI-2 one-sided implementations on a Silicon Graphics Incorporated (SGI) cluster and the Cray XK7 are presented.
Gross, Jonathan L
2003-01-01
The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approaches as well as ""pure"" graph theory. They then carefully edited the compilation to produce a unified, authoritative work ideal for ready reference.Designed and edited with non-experts in mind, the Handbook of Graph Theory makes information easy to fi
Spectral Clustering with Imbalanced Data
Qian, Jing; Saligrama, Venkatesh
2013-01-01
Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data since they tend to emphasize cut sizes over cut values. We propose a graph partitioning problem that seeks minimum cut partitions under minimum size constraints on partitions to deal with imbalanced data. Our approach parameterizes a family of graphs, by ada...
Approximation methods for efficient learning of Bayesian networks
Riggelsen, C
2008-01-01
This publication offers and investigates efficient Monte Carlo simulation methods in order to realize a Bayesian approach to approximate learning of Bayesian networks from both complete and incomplete data. For large amounts of incomplete data when Monte Carlo methods are inefficient, approximations are implemented, such that learning remains feasible, albeit non-Bayesian. The topics discussed are: basic concepts about probabilities, graph theory and conditional independence; Bayesian network learning from data; Monte Carlo simulation techniques; and, the concept of incomplete data. In order to provide a coherent treatment of matters, thereby helping the reader to gain a thorough understanding of the whole concept of learning Bayesian networks from (in)complete data, this publication combines in a clarifying way all the issues presented in the papers with previously unpublished work.
Caetano, Tiberio S; Cheng, Li; Le, Quoc V; Smola, Alex J
2008-01-01
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the `labels' are ma...
Harrison, JM; Robbins, JM; 10.1098/rspa.2010.0254
2011-01-01
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph, concentrating on the simplest case of abelian statistics for two particles. In spite of the fact that graphs are locally one-dimensional, anyon statistics emerge in a generalized form. A given graph may support a family of independent anyon phases associated with topologically inequivalent exchange processes. In addition, for sufficiently complex graphs, there appear new discrete-valued phases. Our analysis is simplified by considering combinatorial rather than metric graphs -- equivalently, a many-particle tight-binding model. The results demonstrate that graphs provide an arena in which to study new manifestations of quantum statistics. Possible applications include topological quantum computing, topological insulators, the fractional quantum Hall effect, superconductivity and molec...
Simplicial complexes of graphs
Jonsson, Jakob
2008-01-01
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
GoFFish: A Sub-Graph Centric Framework for Large-Scale Graph Analytics1
Energy Technology Data Exchange (ETDEWEB)
Simmhan, Yogesh; Kumbhare, Alok; Wickramaarachchi, Charith; Nagarkar, Soonil; Ravi, Santosh; Raghavendra, Cauligi; Prasanna, Viktor
2014-08-25
Large scale graph processing is a major research area for Big Data exploration. Vertex centric programming models like Pregel are gaining traction due to their simple abstraction that allows for scalable execution on distributed systems naturally. However, there are limitations to this approach which cause vertex centric algorithms to under-perform due to poor compute to communication overhead ratio and slow convergence of iterative superstep. In this paper we introduce GoFFish a scalable sub-graph centric framework co-designed with a distributed persistent graph storage for large scale graph analytics on commodity clusters. We introduce a sub-graph centric programming abstraction that combines the scalability of a vertex centric approach with the flexibility of shared memory sub-graph computation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation.
DEFF Research Database (Denmark)
Böcker, S.; Baumbach, Jan
2013-01-01
. The problem has been the inspiration for numerous algorithms in bioinformatics, aiming at clustering entities such as genes, proteins, phenotypes, or patients. In this paper, we review exact and heuristic methods that have been proposed for the Cluster Editing problem, and also applications......The Cluster Editing problem asks to transform a graph into a disjoint union of cliques using a minimum number of edge modifications. Although the problem has been proven NP-complete several times, it has nevertheless attracted much research both from the theoretical and the applied side...
Introduction to Bayesian statistics
Bolstad, William M
2017-01-01
There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this Third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian staistics. The author continues to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inferenfe cfor discrete random variables, bionomial proprotion, Poisson, normal mean, and simple linear regression. In addition, newly-developing topics in the field are presented in four new chapters: Bayesian inference with unknown mean and variance; Bayesian inference for Multivariate Normal mean vector; Bayesian inference for Multiple Linear RegressionModel; and Computati...
基于图聚集算法的寄存器传输级ALU工艺映射算法%Graph Clustering Algorithm for RT Level ALU Technology Mapping
Institute of Scientific and Technical Information of China (English)
周海峰; 林争辉; 曹炜
2002-01-01
Register-transfer level mapping (RTLM) algorithm for technology mapping at RT level is presented,which supports current design methodologies using high-level design and design reuse.The mapping rules implement a source ALU using target ALU.The source ALUs and the target ALUs are all represented by the general ALUs and the mapping rules are applied in the algorithm.The mapping rules are described in a table fashion.The graph-clustering algorithm is a branch and bound algorithm based on the graph formulation of the mapping algorithm.The mapping algorithm suits well mapping of regularly structured data-path.Comparisons are made between the experimental results generated by 1-greedy algorithm and graphclustering algorithm,showing the feasibility of presented algorithm.%给出了寄存器传输级工艺映射(RTLM)算法,该方法支持使用高层次综合和设计再利用的现代VLSI设计方法学,允许复杂的RT级组件,尤其是算术逻辑单元(ALU)在设计中重用.首先提出了ALU的工艺映射问题,给出了源组件和目标组件以及标准组件的定义,在此基础上通过表格的方式给出映射规则的描述.映射算法套用一定的映射规则用目标ALU组件来实现源ALU组件.采用一种基于分支估界法的图聚集算法,用该算法不仅可以产生面积最优的,而且还可以产生延时最优的设计.针对不同库的实验结果证明该算法对于规则结构的数据通路特别有效.
面向个性化推荐的两层混合图模型%Hybrid Graph Model with Two Layers for Personalized Recommendation
Institute of Scientific and Technical Information of China (English)
张少中; 陈德人
2009-01-01
A hybrid graph model for personalized recom-mendation,which is based on small world network and Bayesian network,is presented.The hybrid graph model has two-layers.The bottom level means user's layer and the upper one means merchandise's layer.The user's layer is an undirected arcs graph,which describes the relation of the user's nodes by small world network.The undirected arcs inside the connected nodes of user's layer mean the similarity of the preference of users.These arcs are weighted by relational strength.The weight represents node's similarity or link's strength and intensity.Nodes in the same group are more similar to each other or more strongly connected.Users in a produce to others.It is connected by directed links,which means an implicated definition among merchandises,a user that purchase certain merchandise also tends to purchase another.The properties and content of merchandise can be used to show the similarity of the merchandise.The relations between user's layer and merchandise's layer are connected by directed links.The start nede of the directed links is a user node in user's layer belonging to some node group,which is gained by small world network.The end node of links is the node of some merchandise of the merchandise's layer.The directed links between the user's layer and the merchandise's layer are connected based on trade information of users.The strength of the relation between users and merchandises can be denoted by the probability parameter.The probability parameter shows a possibility of some users selecting for some merchandises. Firstly,algorithms for users clustering and for analysis of new user interest are presented to construct a hybrid graph model.Two important characteristic parameters,which are in small-world network,are introduced.These are characteristic path length and clustering coefficient.New user interest analysis is to judge which clustering group is the best match by calculating the distance of the new user node to
Bayesian artificial intelligence
Korb, Kevin B
2003-01-01
As the power of Bayesian techniques has become more fully realized, the field of artificial intelligence has embraced Bayesian methodology and integrated it to the point where an introduction to Bayesian techniques is now a core course in many computer science programs. Unlike other books on the subject, Bayesian Artificial Intelligence keeps mathematical detail to a minimum and covers a broad range of topics. The authors integrate all of Bayesian net technology and learning Bayesian net technology and apply them both to knowledge engineering. They emphasize understanding and intuition but also provide the algorithms and technical background needed for applications. Software, exercises, and solutions are available on the authors' website.
Bayesian artificial intelligence
Korb, Kevin B
2010-01-01
Updated and expanded, Bayesian Artificial Intelligence, Second Edition provides a practical and accessible introduction to the main concepts, foundation, and applications of Bayesian networks. It focuses on both the causal discovery of networks and Bayesian inference procedures. Adopting a causal interpretation of Bayesian networks, the authors discuss the use of Bayesian networks for causal modeling. They also draw on their own applied research to illustrate various applications of the technology.New to the Second EditionNew chapter on Bayesian network classifiersNew section on object-oriente
Topological structure of dictionary graphs
Fukś, Henryk; Krzemiński, Mark
2009-09-01
We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers—that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 103 and 104. A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.
Arrighi, Pablo
2012-01-01
We generalize the theory of Cellular Automata to arbitrary, time-varying graphs. In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that information can only ever be transmitted at a bounded speed, with respect to the distance given by the graph. The notion of translation-invariance is also generalized. The definition we provide for these `causal graph dynamics' is simple and axiomatic. The theorems we provide also show that it is robust. For instance, causal graph dynamics are stable under composition and under restriction to radius one. In the finite case some fundamental facts of Cellular Automata theory carry through: causal graph dynamics admit a characterization as continuous functions and they are stable under inversion. The provided examples suggest a wide range of applications of this mathematical object, from complex systems science to theoretical physics. Keywords: Dynamical networks, Boolean network...
Dosen, K
2011-01-01
Plural (or multiple-conclusion) cuts are inferences made by applying a structural rule introduced by Gentzen for his sequent formulation of classical logic. As singular (single-conclusion) cuts yield trees, which underlie ordinary natural deduction derivations, so plural cuts yield graphs of a more complicated kind, related to trees, which this paper defines. Besides the inductive definition of these oriented graphs, which is based on sequent systems, a non-inductive, graph-theoretical, combinatorial, definition is given, and to reach that other definition is the main goal of the paper. As trees underlie multicategories, so the graphs of plural cuts underlie polycategories. The graphs of plural cuts are interesting in particular when the plural cuts are appropriate for sequent systems without the structural rule of permutation, and the main body of the paper deals with that matter. It gives a combinatorial characterization of the planarity of the graphs involved.
Fujie, Futaba
2014-01-01
Covering Walks in Graphs is aimed at researchers and graduate students in the graph theory community and provides a comprehensive treatment on measures of two well studied graphical properties, namely Hamiltonicity and traversability in graphs. This text looks into the famous Kӧnigsberg Bridge Problem, the Chinese Postman Problem, the Icosian Game and the Traveling Salesman Problem as well as well-known mathematicians who were involved in these problems. The concepts of different spanning walks with examples and present classical results on Hamiltonian numbers and upper Hamiltonian numbers of graphs are described; in some cases, the authors provide proofs of these results to illustrate the beauty and complexity of this area of research. Two new concepts of traceable numbers of graphs and traceable numbers of vertices of a graph which were inspired by and closely related to Hamiltonian numbers are introduced. Results are illustrated on these two concepts and the relationship between traceable concepts and...
Velasco, Pedro Pablo Perez
2008-01-01
This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely algebraic approach does not exist up to now. A Chomsky (or string) grammar is, roughly speaking, a precise description of a formal language (which in essence is a set of strings). On a more discrete mathematical style, it can be said that graph grammars -- Matrix Graph Grammars in particular -- study dynamics of graphs. Ideally, this algebraization would enforce our understanding of grammars in general, providing new analysis techniques and generalizations of concepts, problems and results known so far.
Buczyńska, Weronika
2010-01-01
We define toric projective model of a trivalent graph as a generalization of a binary symmetric model of a trivalent phylogenetic tree. Generators of the projective coordinate ring of the models of graphs with one cycle are explicitly described. The models of graphs with the same topological invariants are deformation equivalent and share the same Hilbert function. We also provide an algorithm to compute the Hilbert function.
Chartrand, Gary
1984-01-01
Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap
Macroscopic Models of Clique Tree Growth for Bayesian Networks
National Aeronautics and Space Administration — In clique tree clustering, inference consists of propagation in a clique tree compiled from a Bayesian network. In this paper, we develop an analytical approach to...
Institute of Scientific and Technical Information of China (English)
Ping WANG; Jiong Sheng LI
2005-01-01
Let G be a finite simple graph with adjacency matrix A, and let P(A) be the convex closure of the set of all permutation matrices commuting with A. G is said to be compact if every doubly stochastic matrix which commutes with A is in P(A). In this paper, we characterize 3-regular compact graphs and prove that if G is a connected regular compact graph, G - v is also compact, and give a family of almost regular compact connected graphs.
Creating more effective graphs
Robbins, Naomi B
2012-01-01
A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr
Gelfand, I M; Shnol, E E
2002-01-01
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu
Bradford, Robert; Chmutov, Sergei
2011-01-01
We introduce an additional structure on ribbon graphs, arrow structure. We extend the Bollob\\'as-Riordan polynomial to ribbon graph with this structure. The extended polynomial satisfies the contraction-deletion relations and naturally behaves with respect to the partial duality of ribbon graphs. We construct an arrow ribbon graph from a virtual link whose extended Bollob\\'as-Riordan polynomial specializes to the arrow polynomial of the virtual link recently introduced by H.Dye and L.Kauffman. This result generalizes the classical Thistlethwaite theorem to the arrow polynomial of virtual links.
DEFF Research Database (Denmark)
Thomassen, Carsten
2014-01-01
We prove a general result on graph factors modulo k . A special case says that, for each natural number k , every (12k−7)-edge-connected graph with an even number of vertices contains a spanning subgraph in which each vertex has degree congruent to k modulo 2k.......We prove a general result on graph factors modulo k . A special case says that, for each natural number k , every (12k−7)-edge-connected graph with an even number of vertices contains a spanning subgraph in which each vertex has degree congruent to k modulo 2k....
Energy Technology Data Exchange (ETDEWEB)
Lothian, Josh [ORNL; Powers, Sarah S [ORNL; Sullivan, Blair D [ORNL; Baker, Matthew B [ORNL; Schrock, Jonathan [ORNL; Poole, Stephen W [ORNL
2013-12-01
The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of dierent application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.
Framings for graph hypersurfaces
Brown, Francis
2013-01-01
We present a method for computing the framing on the cohomology of graph hypersurfaces defined by the Feynman differential form. This answers a question of Bloch, Esnault and Kreimer in the affirmative for an infinite class of graphs for which the framings are Tate motives. Applying this method to the modular graphs of Brown and Schnetz, we find that the Feynman differential form is not of Tate type in general. This finally disproves a folklore conjecture stating that the periods of Feynman integrals of primitive graphs in phi^4 theory factorise through a category of mixed Tate motives.
Bayesian networks in educational assessment
Almond, Russell G; Steinberg, Linda S; Yan, Duanli; Williamson, David M
2015-01-01
Bayesian inference networks, a synthesis of statistics and expert systems, have advanced reasoning under uncertainty in medicine, business, and social sciences. This innovative volume is the first comprehensive treatment exploring how they can be applied to design and analyze innovative educational assessments. Part I develops Bayes nets’ foundations in assessment, statistics, and graph theory, and works through the real-time updating algorithm. Part II addresses parametric forms for use with assessment, model-checking techniques, and estimation with the EM algorithm and Markov chain Monte Carlo (MCMC). A unique feature is the volume’s grounding in Evidence-Centered Design (ECD) framework for assessment design. This “design forward” approach enables designers to take full advantage of Bayes nets’ modularity and ability to model complex evidentiary relationships that arise from performance in interactive, technology-rich assessments such as simulations. Part III describes ECD, situates Bayes nets as ...
Applied Bayesian Hierarchical Methods
Congdon, Peter D
2010-01-01
Bayesian methods facilitate the analysis of complex models and data structures. Emphasizing data applications, alternative modeling specifications, and computer implementation, this book provides a practical overview of methods for Bayesian analysis of hierarchical models.
How mutation affects evolutionary games on graphs.
Allen, Benjamin; Traulsen, Arne; Tarnita, Corina E; Nowak, Martin A
2012-04-21
Evolutionary dynamics are affected by population structure, mutation rates and update rules. Spatial or network structure facilitates the clustering of strategies, which represents a mechanism for the evolution of cooperation. Mutation dilutes this effect. Here we analyze how mutation influences evolutionary clustering on graphs. We introduce new mathematical methods to evolutionary game theory, specifically the analysis of coalescing random walks via generating functions. These techniques allow us to derive exact identity-by-descent (IBD) probabilities, which characterize spatial assortment on lattices and Cayley trees. From these IBD probabilities we obtain exact conditions for the evolution of cooperation and other game strategies, showing the dual effects of graph topology and mutation rate. High mutation rates diminish the clustering of cooperators, hindering their evolutionary success. Our model can represent either genetic evolution with mutation, or social imitation processes with random strategy exploration.
Gelman, Andrew; Stern, Hal S; Dunson, David B; Vehtari, Aki; Rubin, Donald B
2013-01-01
FUNDAMENTALS OF BAYESIAN INFERENCEProbability and InferenceSingle-Parameter Models Introduction to Multiparameter Models Asymptotics and Connections to Non-Bayesian ApproachesHierarchical ModelsFUNDAMENTALS OF BAYESIAN DATA ANALYSISModel Checking Evaluating, Comparing, and Expanding ModelsModeling Accounting for Data Collection Decision AnalysisADVANCED COMPUTATION Introduction to Bayesian Computation Basics of Markov Chain Simulation Computationally Efficient Markov Chain Simulation Modal and Distributional ApproximationsREGRESSION MODELS Introduction to Regression Models Hierarchical Linear
Learning Bayesian Networks from Correlated Data
Bae, Harold; Monti, Stefano; Montano, Monty; Steinberg, Martin H.; Perls, Thomas T.; Sebastiani, Paola
2016-05-01
Bayesian networks are probabilistic models that represent complex distributions in a modular way and have become very popular in many fields. There are many methods to build Bayesian networks from a random sample of independent and identically distributed observations. However, many observational studies are designed using some form of clustered sampling that introduces correlations between observations within the same cluster and ignoring this correlation typically inflates the rate of false positive associations. We describe a novel parameterization of Bayesian networks that uses random effects to model the correlation within sample units and can be used for structure and parameter learning from correlated data without inflating the Type I error rate. We compare different learning metrics using simulations and illustrate the method in two real examples: an analysis of genetic and non-genetic factors associated with human longevity from a family-based study, and an example of risk factors for complications of sickle cell anemia from a longitudinal study with repeated measures.
Learning Bayesian Networks from Correlated Data.
Bae, Harold; Monti, Stefano; Montano, Monty; Steinberg, Martin H; Perls, Thomas T; Sebastiani, Paola
2016-05-05
Bayesian networks are probabilistic models that represent complex distributions in a modular way and have become very popular in many fields. There are many methods to build Bayesian networks from a random sample of independent and identically distributed observations. However, many observational studies are designed using some form of clustered sampling that introduces correlations between observations within the same cluster and ignoring this correlation typically inflates the rate of false positive associations. We describe a novel parameterization of Bayesian networks that uses random effects to model the correlation within sample units and can be used for structure and parameter learning from correlated data without inflating the Type I error rate. We compare different learning metrics using simulations and illustrate the method in two real examples: an analysis of genetic and non-genetic factors associated with human longevity from a family-based study, and an example of risk factors for complications of sickle cell anemia from a longitudinal study with repeated measures.
Institute of Scientific and Technical Information of China (English)
曹晓龙; 宋威; 梁久祯
2011-01-01
As for the problems that the input query are usually ambiguous and concise in the current information retrieval, this paper presents a personalized query recommendation method based on the TF IQF model and graph clustering. It provides query recommendation for a giving query, helps the users to amend query and retrieves the information needed. Simultaneously, it will achieve the goal of providing personalized query suggestions by capturing different user preferences. The experimental results show that the method gives personalized query suggestions, provides the potential resources that the user is interested in and obtains high precision which improves the quality of personalized retrieval systems.%针对信息检索领域存在的用词歧义和检索词简短的问题,本文提出了一种基于TF-IQF模型和图聚类的个性化查询建议方法.对于用户的查询请求,提供查询建议,帮助用户进行查询修正,进而检索到其所需的信息；同时通过获取不同用户的查询偏好,以达到个性化查询推荐的目的.实验结果表明,该方法能够给出个性化的查询建议,为用户提供潜在感兴趣的资源,具有较高的准确率.
Clique percolation in random graphs
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 clique percolation in Erdős-Rényi 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.
Directory of Open Access Journals (Sweden)
A. Assari
2016-01-01
Full Text Available In this paper, a graph is assigned to any probability measure on the σ-algebra of Borel sets of a topological space. Using this construction, it is proved that given any number n (finite or infinite there exists a nonregular graph such that its clique, chromatic, and dominating number equals n.
Kim, Suh-Ryung; Park, Boram; Sano, Yoshio
2011-01-01
The competition graph of a digraph $D$ is a (simple undirected) graph which has the same vertex set as $D$ and has an edge between $x$ and $y$ if and only if there exists a vertex $v$ in $D$ such that $(x,v)$ and $(y,v)$ are arcs of $D$. For any graph $G$, $G$ together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number $k(G)$ of $G$ is the smallest number of such isolated vertices. In general, it is hard to compute the competition number $k(G)$ for a graph $G$ and it has been one of the important research problems in the study of competition graphs. Opsut~[1982] suggested that the edge clique cover number $\\theta_E(G)$ should be closely related to $k(G)$ by showing $\\theta_E(G)-|V(G)|+2 \\leq k(G) \\leq \\theta_E(G)$. In this note, we study on these inequalities. We first show that for any positive integer $m$ satisfying $2 \\leq m \\leq |V(G)|$, there is a graph $G$ satisfying $k(G)=\\theta_E(G)-|V(G)|+m$ and characterize a graph $G$ satisfying $k(G)=\\...
Belkhechine, Houmem; Elayech, Mohamed Baka
2010-01-01
Given a (directed) graph G=(V,A), a subset X of V is an interval of G provided that for any a, b\\in X and x\\in V-X, (a,x)\\in A if and only if (b,x)\\in A and (x,a)\\in A if and only if (x,b)\\in A. For example, \\emptyset, \\{x\\} (x \\in V) and V are intervals of G, called trivial intervals. A graph, all the intervals of which are trivial, is indecomposable; otherwise, it is decomposable. A vertex x of an indecomposable graph is critical if G-x is decomposable. In 1993, J.H. Schmerl and W.T. Trotter characterized the indecomposable graphs, all the vertices of which are critical, called critical graphs. In this article, we characterize the indecomposable graphs which admit a single non critical vertex, that we call (-1)-critical graphs.} This gives an answer to a question asked by Y. Boudabbous and P. Ille in a recent article studying the critical vertices in an indecomposable graph.
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems i
Husfeldt, Thore
2015-01-01
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available techniques and is organized by algorithmic paradigm.
Moment graphs and representations
DEFF Research Database (Denmark)
Jantzen, Jens Carsten
2012-01-01
Moment graphs and sheaves on moment graphs are basically combinatorial objects that have be used to describe equivariant intersectiion cohomology. In these lectures we are going to show that they can be used to provide a direct link from this cohomology to the representation theory of simple Lie...
DEFF Research Database (Denmark)
Husfeldt, Thore
2015-01-01
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...
Graphs: Associated Markov Chains
2012-01-01
In this research paper, weighted / unweighted, directed / undirected graphs are associated with interesting Discrete Time Markov Chains (DTMCs) as well as Continuous Time Markov Chains (CTMCs). The equilibrium / transient behaviour of such Markov chains is studied. Also entropy dynamics (Shannon entropy) of certain structured Markov chains is investigated. Finally certain structured graphs and the associated Markov chains are studied.
Mol, de Maarten; Rensink, Arend; Hunt, James J.
2012-01-01
This paper introduces an approach for adding graph transformation-based functionality to existing JAVA programs. The approach relies on a set of annotations to identify the intended graph structure, as well as on user methods to manipulate that structure, within the user’s own JAVA class declaration
Caetano, Tibério S; McAuley, Julian J; Cheng, Li; Le, Quoc V; Smola, Alex J
2009-06-01
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the 'labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.
Rensink, Arend; Distefano, Dino
2005-01-01
Graphs may be used as representations of system states in operational semantics and model checking; in the latter context, they are being investigated as an alternative to bit vectors. The corresponding transitions are obtained as derivations from graph production rules. In this paper we propose an
Rensink, Arend; Distefano, Dino; Mukhopadhyay, S.; Roychoudhury, A.; Yang, Z.
2006-01-01
Graphs may be used as representations of system states in operational semantics and model checking; in the latter context, they are being investigated as an alternative to bit vectors. The corresponding transitions are obtained as derivations from graph production rules. In this paper we propose an
Generalized connectivity of graphs
Li, Xueliang
2016-01-01
Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Learning Local Components to Understand Large Bayesian Networks
DEFF Research Database (Denmark)
Zeng, Yifeng; Xiang, Yanping; Cordero, Jorge
2009-01-01
Bayesian networks are known for providing an intuitive and compact representation of probabilistic information and allowing the creation of models over a large and complex domain. Bayesian learning and reasoning are nontrivial for a large Bayesian network. In parallel, it is a tough job for users...... (domain experts) to extract accurate information from a large Bayesian network due to dimensional difficulty. We define a formulation of local components and propose a clustering algorithm to learn such local components given complete data. The algorithm groups together most inter-relevant attributes...... in a domain. We evaluate its performance on three benchmark Bayesian networks and provide results in support. We further show that the learned components may represent local knowledge more precisely in comparison to the full Bayesian networks when working with a small amount of data....
Likelihood-based inference for clustered line transect data
DEFF Research Database (Denmark)
Waagepetersen, Rasmus Plenge; Schweder, Tore
is implemented using Markov Chain Monte Carlo methods to obtain efficient estimates of spatial clustering parameters. Uncertainty is addressed using parametric bootstrap or by consideration of posterior distributions in a Bayesian setting. Maximum likelihood estimation and Bayesian inference is compared...
Application of Graph Coloring to Biological Networks
Khor, Susan
2009-01-01
We explore the application of graph coloring to biological networks, specifically protein-protein interaction (PPI) networks. First, we find that given similar conditions (i.e. number of nodes, number of links, degree distribution and clustering), fewer colors are needed to color disassortative (high degree nodes tend to connect to low degree nodes and vice versa) than assortative networks. Fewer colors create fewer independent sets which in turn imply higher concurrency potential for a network. Since PPI networks tend to be disassortative, we suggest that in addition to functional specificity and stability proposed previously by Maslov and Sneppen (Science 296, 2002), the disassortative nature of PPI networks may promote the ability of cells to perform multiple, crucial and functionally diverse tasks concurrently. Second, since graph coloring is closely related to the presence of cliques in a graph, the significance of node coloring information to the problem of identifying protein complexes, i.e. dense subg...
Scale-invariant geometric random graphs
Xie, Zheng
2015-01-01
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 an influence zone that depends on node position in space and time, capturing the heterogeneity and increased specialization found in growing networks. Through calculations and numerical simulations we explore the consequences of scale-invariance for geometric 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 behaviour. Moreover, we show how these properties provide a good fit to those of empirically observed web graphs.
Bayesian inference for Hawkes processes
DEFF Research Database (Denmark)
Rasmussen, Jakob Gulddahl
2013-01-01
The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....
Bayesian inference for Hawkes processes
DEFF Research Database (Denmark)
Rasmussen, Jakob Gulddahl
The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....
Bidimensionality and Geometric Graphs
Fomin, Fedor V; Saurabh, Saket
2011-01-01
In this paper we use several of the key ideas from Bidimensionality to give a new generic approach to design EPTASs and subexponential time parameterized algorithms for problems on classes of graphs which are not minor closed, but instead exhibit a geometric structure. In particular we present EPTASs and subexponential time parameterized algorithms for Feedback Vertex Set, Vertex Cover, Connected Vertex Cover, Diamond Hitting Set, on map graphs and unit disk graphs, and for Cycle Packing and Minimum-Vertex Feedback Edge Set on unit disk graphs. Our results are based on the recent decomposition theorems proved by Fomin et al [SODA 2011], and our algorithms work directly on the input graph. Thus it is not necessary to compute the geometric representations of the input graph. To the best of our knowledge, these results are previously unknown, with the exception of the EPTAS and a subexponential time parameterized algorithm on unit disk graphs for Vertex Cover, which were obtained by Marx [ESA 2005] and Alber and...
Directory of Open Access Journals (Sweden)
Niedzialomski Amanda
2016-11-01
Full Text Available For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u − f(v| ≥ k + 1 − d(u, v. We consider k-radio labelings of G when k = diam(G. In this setting, f is injective; if f is also surjective onto {1, 2, . . . , |V (G|}, then f is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio graceful Hamming graphs. The main result shows that the Cartesian product of t copies of a complete graph is radio graceful for certain t. Graphs of this form provide infinitely many examples of radio graceful graphs of arbitrary diameter. We also show that these graphs are not radio graceful for large t.
Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?
Öçal, Mehmet Fatih
2017-01-01
Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students' learning during graphing functions. However, the display of graphs of functions that students sketched by hand may…
Bollobas, Bela
2004-01-01
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A
Yoshinaga, Masahiko
2015-01-01
Finite graphs that have a common chromatic polynomial have the same number of regular $n$-colorings. A natural question is whether there exists a natural bijection between regular $n$-colorings. We address this question using a functorial formulation. Let $G$ be a simple graph. Then for each set $X$ we can associate a set of $X$-colorings. This defines a functor, "chromatic functor" from the category of sets with injections to itself. The first main result verifies that two finite graphs dete...
The Interval Graph Completion Problem on Split Graphs
Institute of Scientific and Technical Information of China (English)
ZHANG Zhen-kun; YU Min
2015-01-01
The interval graph completion problem on a graph G is to find an added edge set F such that G+F is an interval supergraph with the smallest possible number of edges. The problem has important applications to numerical algebra, V LSI-layout and algorithm graph theory etc; And it has been known to be N P-complete on general graphs. Some classes of special graphs have been investigated in the literatures. In this paper the interval graph completion problem on split graphs is investigated.
GraphState - a tool for graph identification and labelling
Batkovich, D; Kompaniets, M; Novikov, S
2014-01-01
We present python libraries for Feynman graphs manipulation. The key feature of these libraries is usage of generalization of graph representation offered by B. G. Nickel et al. In this approach graph is represented in some unique 'canonical' form that depends only on its combinatorial type. The uniqueness of graph representation gives an efficient way for isomorphism finding, searching for subgraphs and other graph manipulation tasks. Though offered libraries were originally designed for Feynman graphs, they might be useful for more general graph problems.
Graph Operations on Clique-Width Bounded Graphs
Gurski, Frank
2007-01-01
Clique-width is a well-known graph parameter. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded clique-width. The same holds for NLC-width. In this paper we study the behavior of clique-width and NLC-width under various graph operations and graph transformations. We give upper and lower bounds for the clique-width and NLC-width of the modified graphs in terms of the clique-width and NLC-width of the involved graphs.
Algorithms and Complexity Results for Exact Bayesian Structure Learning
Ordyniak, Sebastian
2012-01-01
Bayesian structure learning is the NP-hard problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact Bayesian structure learning under graph theoretic restrictions on the super-structure. The super-structure (a concept introduced by Perrier, Imoto, and Miyano, JMLR 2008) is an undirected graph that contains as subgraphs the skeletons of solution networks. Our results apply to several variants of score-based Bayesian structure learning where the score of a network decomposes into local scores of its nodes. Results: We show that exact Bayesian structure learning can be carried out in non-uniform polynomial time if the super-structure has bounded treewidth and in linear time if in addition the super-structure has bounded maximum degree. We complement this with a number of hardness results. We show that both restrictions (treewidth and degree) are essential and cannot be dropped without loosing uniform ...
Alspach, BR
1985-01-01
This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.
The Least Eigenvalue of Graphs
Institute of Scientific and Technical Information of China (English)
Guidong YU; Yizheng FAN; Yi WANG
2012-01-01
In this paper we investigate the least eigenvalue of a graph whose complement is connected,and present a lower bound for the least eigenvalue of such graph.We also characterize the unique graph whose least eigenvalue attains the second minimum among all graphs of fixed order.
A Semantic Graph Query Language
Energy Technology Data Exchange (ETDEWEB)
Kaplan, I L
2006-10-16
Semantic graphs can be used to organize large amounts of information from a number of sources into one unified structure. A semantic query language provides a foundation for extracting information from the semantic graph. The graph query language described here provides a simple, powerful method for querying semantic graphs.
Categorical constructions in graph theory
Directory of Open Access Journals (Sweden)
Richard T. Bumby
1986-01-01
Full Text Available This paper presents some graph-theoretic questions from the viewpoint of the portion of category theory which has become common knowledge. In particular, the reader is encouraged to consider whether there is only one natural category of graphs and how theories of directed graphs and undirected graphs are related.
Local Interaction on Random Graphs
Directory of Open Access Journals (Sweden)
Hans Haller
2010-08-01
Full Text Available We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph cannot change over time.
Cluster Algebras and the Positive Grassmannian
Paulos, Miguel F
2014-01-01
Plabic graphs are intimately connected to the positroid stratification of the positive Grassmannian. The duals to these graphs are quivers, and it is possible to associate to them cluster algebras. For the top-cell graph of $Gr_{+}(k,n)$, this cluster algebra is the homogeneous coordinate ring of the corresponding positroid variety. We prove that the same statement holds for plabic graphs describing lower dimensional cells. In this way we obtain a map from the positroid strata onto cluster subalgebras of $Gr_{+}(k,n)$. We explore some of the consequences of this map for tree-level scattering amplitudes in $\\mathcal N=4$ super Yang-Mills theory.
Solsolitons associated with graphs
Lafuente, Ramiro A
2010-01-01
We show how to associate with each graph with a certain property (positivity) a family of simply connected solvable Lie groups endowed with left-invariant Riemannian metrics that are Ricci solitons (called solsolitons). We classify them up to isometry, obtaining families depending on many parameters of explicit examples of Ricci solitons. A classification of graphs with up to 3 coherent components according to positivity is also given.
Quantifying Uncertainty in Brain Network Measures using Bayesian Connectomics
Directory of Open Access Journals (Sweden)
Ronald Johannes Janssen
2014-10-01
Full Text Available The wiring diagram of the human brain can be described in terms of graph measures that characterize structural regularities. These measures require an estimate of whole-brain structural connectivity for which one may resort to deterministic or thresholded probabilistic streamlining procedures. While these procedures have provided important insights about the characteristics of human brain networks, they ultimately rely on unwarranted assumptions such as those of noise-free data or the use of an arbitrary threshold. Therefore, resulting structural connectivity estimates as well as derived graph measures fail to fully take into account the inherent uncertainty in the structural estimate.In this paper, we illustrate an easy way of obtaining posterior distributions over graph metrics using Bayesian inference. It is shown that this posterior distribution can be used to quantify uncertainty about graph-theoretical measures at the single subject level, thereby providing a more nuanced view of the graph-theoretical properties of human brain connectivity. We refer to this model-based approach to connectivity analysis as Bayesian connectomics.
Arrighi, Pablo
2016-01-01
Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded speed, with respect to the distance given by the graph. Suppose, moreover, that the graph itself is subject to the evolution, and may be driven to be in a quantum superposition of graphs---in accordance to the superposition principle. We show that these unitary causal operators must decompose as a finite-depth circuit of local unitary gates. This unifies a result on Quantum Cellular Automata with another on Reversible Causal Graph Dynamics. Along the way we formalize a notion of causality which is valid in the context of quantum superpositions of time-varying graphs, and has a number of good properties. Keywords: Quantum Lattice Gas Automata, Block-representation, Curtis-Hedlund-Lyndon, No-signalling, Localizability, Quantum Gravity, Quantum Graphity, Causal Dynamical Triangula...
Commuting projections on graphs
Energy Technology Data Exchange (ETDEWEB)
Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Zikatanov, Ludmil T. [Pennsylvania State Univ., University Park, PA (United States). Dept. of Mathematics
2013-02-19
For a given (connected) graph, we consider vector spaces of (discrete) functions defined on its vertices and its edges. These two spaces are related by a discrete gradient operator, Grad and its adjoint, ₋Div, referred to as (negative) discrete divergence. We also consider a coarse graph obtained by aggregation of vertices of the original one. Then a coarse vertex space is identified with the subspace of piecewise constant functions over the aggregates. We consider the ℓ_{2}-projection Q_{H} onto the space of these piecewise constants. In the present paper, our main result is the construction of a projection π _{H} from the original edge-space onto a properly constructed coarse edge-space associated with the edges of the coarse graph. The projections π _{H} and Q_{H} commute with the discrete divergence operator, i.e., we have div π _{H} = Q_{H} div. The respective pair of coarse edge-space and coarse vertexspace offer the potential to construct two-level, and by recursion, multilevel methods for the mixed formulation of the graph Laplacian which utilizes the discrete divergence operator. The performance of one two-level method with overlapping Schwarz smoothing and correction based on the constructed coarse spaces for solving such mixed graph Laplacian systems is illustrated on a number of graph examples.
Bollobás, Béla
1998-01-01
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...
Barnes, J.; Dekel, A.; Efstathiou, G.; Frenk, C. S.
1985-01-01
The cluster correlation function xi sub c(r) is compared with the particle correlation function, xi(r) in cosmological N-body simulations with a wide range of initial conditions. The experiments include scale-free initial conditions, pancake models with a coherence length in the initial density field, and hybrid models. Three N-body techniques and two cluster-finding algorithms are used. In scale-free models with white noise initial conditions, xi sub c and xi are essentially identical. In scale-free models with more power on large scales, it is found that the amplitude of xi sub c increases with cluster richness; in this case the clusters give a biased estimate of the particle correlations. In the pancake and hybrid models (with n = 0 or 1), xi sub c is steeper than xi, but the cluster correlation length exceeds that of the points by less than a factor of 2, independent of cluster richness. Thus the high amplitude of xi sub c found in studies of rich clusters of galaxies is inconsistent with white noise and pancake models and may indicate a primordial fluctuation spectrum with substantial power on large scales.
Energy Technology Data Exchange (ETDEWEB)
Barnes, J.; Dekel, A.; Efstathiou, G.; Frenk, C.S.
1985-08-01
The cluster correlation function xi sub c(r) is compared with the particle correlation function, xi(r) in cosmological N-body simulations with a wide range of initial conditions. The experiments include scale-free initial conditions, pancake models with a coherence length in the initial density field, and hybrid models. Three N-body techniques and two cluster-finding algorithms are used. In scale-free models with white noise initial conditions, xi sub c and xi are essentially identical. In scale-free models with more power on large scales, it is found that the amplitude of xi sub c increases with cluster richness; in this case the clusters give a biased estimate of the particle correlations. In the pancake and hybrid models (with n = 0 or 1), xi sub c is steeper than xi, but the cluster correlation length exceeds that of the points by less than a factor of 2, independent of cluster richness. Thus the high amplitude of xi sub c found in studies of rich clusters of galaxies is inconsistent with white noise and pancake models and may indicate a primordial fluctuation spectrum with substantial power on large scales. 30 references.
Bayesian Games with Intentions
Directory of Open Access Journals (Sweden)
Adam Bjorndahl
2016-06-01
Full Text Available We show that standard Bayesian games cannot represent the full spectrum of belief-dependent preferences. However, by introducing a fundamental distinction between intended and actual strategies, we remove this limitation. We define Bayesian games with intentions, generalizing both Bayesian games and psychological games, and prove that Nash equilibria in psychological games correspond to a special class of equilibria as defined in our setting.
Cascades on clique-based graphs
Hackett, Adam
2013-01-01
We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly-clustered random graphs introduced in [J. P. Gleeson, Phys. Rev. E 80, 036107 (2009)]. A condition for the existence of global cascades is also derived. Applications of this approach include analyses of percolation, and Watts's model. We show how our techniques can be used to study the effects of in-group bias in cascades on social networks.
Bayesian statistics an introduction
Lee, Peter M
2012-01-01
Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee’s book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques. This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as wel
Understanding Computational Bayesian Statistics
Bolstad, William M
2011-01-01
A hands-on introduction to computational statistics from a Bayesian point of view Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective, Understanding Computational Bayesian Statistics successfully guides readers through this new, cutting-edge approach. With its hands-on treatment of the topic, the book shows how samples can be drawn from the posterior distribution when the formula giving its shape is all that is known, and how Bayesian inferences can be based on these samples from the posterior. These ideas are illustrated on common statistic
Thinking Graphically: Connecting Vision and Cognition during Graph Comprehension
2008-01-01
described. Keywords: Graph Comprehension, Diagrammatic Reasoning, Eye Tracking Ratwani, Trafton, & Boehm-Davis: Thinking Graphically 3...visual clusters found from eye tracking should relate to the number of verbal clusters in the verbal data. Second, after forming visual clusters...by a single unique letter or number positioned in the center of the county to allow for more accurate eye tracking . Each county differed in size, the
The STAPL Parallel Graph Library
Harshvardhan,
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.
Quantitative graph theory mathematical foundations and applications
Dehmer, Matthias
2014-01-01
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat
Application of Bayesian Network Learning Methods to Land Resource Evaluation
Institute of Scientific and Technical Information of China (English)
HUANG Jiejun; HE Xiaorong; WAN Youchuan
2006-01-01
Bayesian network has a powerful ability for reasoning and semantic representation, which combined with qualitative analysis and quantitative analysis, with prior knowledge and observed data, and provides an effective way to deal with prediction, classification and clustering. Firstly, this paper presented an overview of Bayesian network and its characteristics, and discussed how to learn a Bayesian network structure from given data, and then constructed a Bayesian network model for land resource evaluation with expert knowledge and the dataset. The experimental results based on the test dataset are that evaluation accuracy is 87.5%, and Kappa index is 0.826. All these prove the method is feasible and efficient, and indicate that Bayesian network is a promising approach for land resource evaluation.
Directory of Open Access Journals (Sweden)
Vassilis Giakoumakis
1997-12-01
Full Text Available We study the P 4-tidy graphs, a new class defined by Rusu [30] in order to illustrate the notion of P 4-domination in perfect graphs. This class strictly contains the P 4-extendible graphs and the P 4-lite graphs defined by Jamison & Olariu in [19] and [23] and we show that the P 4-tidy graphs and P 4-lite graphs are closely related. Note that the class of P 4-lite graphs is a class of brittle graphs strictly containing the P 4-sparse graphs defined by Hoang in [14]. McConnel & Spinrad [2] and independently Cournier & Habib [5] have shown that the modular decomposition tree of any graph is computable in linear time. For recognizing in linear time P 4-tidy graphs, we apply a method introduced by Giakoumakis in [9] and Giakoumakis & Fouquet in [6] using modular decomposition of graphs and we propose linear algorithms for optimization problems on such graphs, as clique number, stability number, chromatic number and scattering number. We show that the Hamiltonian Path Problem is linear for this class of graphs. Our study unifies and generalizes previous results of Jamison & Olariu ([18], [21], [22], Hochstattler & Schindler[16], Jung [25] and Hochstattler & Tinhofer [15].
Yuan, Ying; MacKinnon, David P.
2009-01-01
In this article, we propose Bayesian analysis of mediation effects. Compared with conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian…
SOMBI: Bayesian identification of parameter relations in unstructured cosmological data
Frank, Philipp; Enßlin, Torsten A
2016-01-01
This work describes the implementation and application of a correlation determination method based on Self Organizing Maps and Bayesian Inference (SOMBI). SOMBI aims to automatically identify relations between different observed parameters in unstructured cosmological or astrophysical surveys by automatically identifying data clusters in high-dimensional datasets via the Self Organizing Map neural network algorithm. Parameter relations are then revealed by means of a Bayesian inference within respective identified data clusters. Specifically such relations are assumed to be parametrized as a polynomial of unknown order. The Bayesian approach results in a posterior probability distribution function for respective polynomial coefficients. To decide which polynomial order suffices to describe correlation structures in data, we include a method for model selection, the Bayesian Information Criterion, to the analysis. The performance of the SOMBI algorithm is tested with mock data. As illustration we also provide ...
von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo
2014-06-01
Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.
Partial Order MCMC for Structure Discovery in Bayesian Networks
Niinimaki, Teppo; Koivisto, Mikko
2012-01-01
We present a new Markov chain Monte Carlo method for estimating posterior probabilities of structural features in Bayesian networks. The method draws samples from the posterior distribution of partial orders on the nodes; for each sampled partial order, the conditional probabilities of interest are computed exactly. We give both analytical and empirical results that suggest the superiority of the new method compared to previous methods, which sample either directed acyclic graphs or linear orders on the nodes.
Feynman motives of banana graphs
Aluffi, Paolo
2008-01-01
We consider the infinite family of Feynman graphs known as the ``banana graphs'' and compute explicitly the classes of the corresponding graph hypersurfaces in the Grothendieck ring of varieties as well as their Chern--Schwartz--MacPherson classes, using the classical Cremona transformation and the dual graph, and a blowup formula for characteristic classes. We outline the interesting similarities between these operations and we give formulae for cones obtained by simple operations on graphs. We formulate a positivity conjecture for characteristic classes of graph hypersurfaces and discuss briefly the effect of passing to noncommutative spacetime.
Graph theory and interconnection networks
Hsu, Lih-Hsing
2008-01-01
The advancement of large scale integrated circuit technology has enabled the construction of complex interconnection networks. Graph theory provides a fundamental tool for designing and analyzing such networks. Graph Theory and Interconnection Networks provides a thorough understanding of these interrelated topics. After a brief introduction to graph terminology, the book presents well-known interconnection networks as examples of graphs, followed by in-depth coverage of Hamiltonian graphs. Different types of problems illustrate the wide range of available methods for solving such problems. The text also explores recent progress on the diagnosability of graphs under various models.
Iacovacci, Jacopo
2015-01-01
Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network science. In this work we introduce and study the concept of visibility graph motifs, smaller substructures that appear with characteristic frequencies. We develop a theory to compute in an exact way the motif profiles associated to general classes of deterministic and stochastic dynamics. We find that this simple property is indeed a highly informative and computationally efficient feature capable to distinguish among different dynamics and robust against noise contamination. We finally confirm that it can be used in practice to perform unsupervised learning, by extracting motif profiles from experimental heart-rate series and being able, accordingly, to disentangle meditative from other relaxation states. Applications of this general theory include the automatic classification a...
White, AT
1985-01-01
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.
Bordenave, Charles; Salez, Justin
2011-01-01
We prove that the local weak convergence of a sequence of graphs is enough to guarantee the convergence of their normalized matching numbers. The limiting quantity is described by a local recursion defined on the weak limit of the graph sequence. However, this recursion may admit several solutions, implying non-trivial long-range dependencies between the edges of a largest matching. We overcome this lack of correlation decay by introducing a perturbative parameter called the temperature, which we let progressively go to zero. When the local weak limit is a unimodular Galton-Watson tree, the recursion simplifies into a distributional equation, resulting into an explicit formula that considerably extends the well-known one by Karp and Sipser for Erd\\"os-R\\'enyi random graphs.
Subdominant pseudoultrametric on graphs
Energy Technology Data Exchange (ETDEWEB)
Dovgoshei, A A; Petrov, E A [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)
2013-08-31
Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.
Hyperbolicity in Median Graphs
Indian Academy of Sciences (India)
José M Sigarreta
2013-11-01
If is a geodesic metric space and $x_1,x_2,x_3\\in X$, a geodesic triangle $T=\\{x_1,x_2,x_3\\}$ is the union of the three geodesics $[x_1 x_2],[x_2 x_3]$ and $[x_3 x_1]$ in . The space is -hyperbolic (in the Gromov sense) if any side of is contained in a -neighborhood of the union of the two other sides, for every geodesic triangle in . If is hyperbolic, we denote by () the sharp hyperbolicity constant of , i.e.,$(X)=\\inf\\{≥ 0: X \\quad\\text{is}\\quad -\\text{hyperbolic}\\}$. In this paper we study the hyperbolicity of median graphs and we also obtain some results about general hyperbolic graphs. In particular, we prove that a median graph is hyperbolic if and only if its bigons are thin.
SOME RESULTS ON CIRCULAR PERFECT GRAPHS AND PERFECT GRAPHS
Institute of Scientific and Technical Information of China (English)
XU Baogang
2005-01-01
An r-circular coloring of a graph G is a map f from V(G) to the set of open unit intervals of an Euclidean circle of length r,such that f(u) ∩ f(v) = φ whenever uv ∈ E(G).Circular perfect graphs are defined analogously to perfect graphs by means of two parameters,the circular chromatic number and the circular clique number.In this paper,we study the properties of circular perfect graphs.We give (1) a necessary condition for a graph to be circular perfect,(2) some circular critical imperfect graphs,and (3) a characterization of graphs with the property that each of their induced subgraphs has circular clique number the same as its clique number,and then the two conjectures that are equivalent to the perfect graph conjecture.
Graph-based knowledge representation computational foundations of conceptual graphs
Chein, Michel; Chein, Michel
2008-01-01
In addressing the question of how far it is possible to go in knowledge representation and reasoning through graphs, the authors cover basic conceptual graphs, computational aspects, and kernel extensions. The basic mathematical notions are summarized.
Kisku, Dakshina Ranjan; Sing, Jamuna Kanta
2010-01-01
This paper presents a feature level fusion approach which uses the improved K-medoids clustering algorithm and isomorphic graph for face and palmprint biometrics. Partitioning around medoids (PAM) algorithm is used to partition the set of n invariant feature points of the face and palmprint images into k clusters. By partitioning the face and palmprint images with scale invariant features SIFT points, a number of clusters is formed on both the images. Then on each cluster, an isomorphic graph is drawn. In the next step, the most probable pair of graphs is searched using iterative relaxation algorithm from all possible isomorphic graphs for a pair of corresponding face and palmprint images. Finally, graphs are fused by pairing the isomorphic graphs into augmented groups in terms of addition of invariant SIFT points and in terms of combining pair of keypoint descriptors by concatenation rule. Experimental results obtained from the extensive evaluation show that the proposed feature level fusion with the improve...
Konstruksi Bayesian Network Dengan Algoritma Bayesian Association Rule Mining Network
Octavian
2015-01-01
Beberapa tahun terakhir, Bayesian Network telah menjadi konsep yang populer digunakan dalam berbagai bidang kehidupan seperti dalam pengambilan sebuah keputusan dan menentukan peluang suatu kejadian dapat terjadi. Sayangnya, pengkonstruksian struktur dari Bayesian Network itu sendiri bukanlah hal yang sederhana. Oleh sebab itu, penelitian ini mencoba memperkenalkan algoritma Bayesian Association Rule Mining Network untuk memudahkan kita dalam mengkonstruksi Bayesian Network berdasarkan data ...
Cheung, King Sing
2014-01-01
Petri nets are a formal and theoretically rich model for the modelling and analysis of systems. A subclass of Petri nets, augmented marked graphs possess a structure that is especially desirable for the modelling and analysis of systems with concurrent processes and shared resources.This monograph consists of three parts: Part I provides the conceptual background for readers who have no prior knowledge on Petri nets; Part II elaborates the theory of augmented marked graphs; finally, Part III discusses the application to system integration. The book is suitable as a first self-contained volume
Stevanovic, Dragan
2015-01-01
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the
Institute of Scientific and Technical Information of China (English)
ZHANG Guoqiang; CHEN Yixiang
2001-01-01
This paper provides a concrete and simple introduction to two pillars of domain theory: (1) solving recursive domain equations, and (2) universal and saturated domains. Our exposition combines Larsen and Winskel's idea on solving domain equations using information systems with Girard's idea of stable domain theory in the form of coherence spaces, or graphs.Detailed constructions are given for universal and even homogeneous objects in two categories of graphs: one representing binary complete, prime algebraic domains with complete primes covering the bottom; the other representing ω-algebraic, prime algebraic lattices. The backand-forth argument in model theory helps to enlighten the constructions.
Distributed Evolutionary Graph Partitioning
Sanders, Peter
2011-01-01
We present a novel distributed evolutionary algorithm, KaFFPaE, to solve the Graph Partitioning Problem, which makes use of KaFFPa (Karlsruhe Fast Flow Partitioner). The use of our multilevel graph partitioner KaFFPa provides new effective crossover and mutation operators. By combining these with a scalable communication protocol we obtain a system that is able to improve the best known partitioning results for many inputs in a very short amount of time. For example, in Walshaw's well known benchmark tables we are able to improve or recompute 76% of entries for the tables with 1%, 3% and 5% imbalance.
Handbook of graph grammars and computing by graph transformation
Engels, G; Kreowski, H J; Rozenberg, G
1999-01-01
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran
Market Segmentation Using Bayesian Model Based Clustering
Van Hattum, P.
2009-01-01
This dissertation deals with two basic problems in marketing, that are market segmentation, which is the grouping of persons who share common aspects, and market targeting, which is focusing your marketing efforts on one or more attractive market segments. For the grouping of persons who share commo
Directory of Open Access Journals (Sweden)
Engels Rajangam
2016-02-01
Full Text Available —Reasoning is the fundamental capability which requires knowledge. Various graph models have proven to be very valuable in knowledge representation and reasoning. Recently, explosive data generation and accumulation capabilities have paved way for Big Data and Data Intensive Systems. Knowledge Representation and Reasoning with large and growing data is extremely challenging but crucial for businesses to predict trends and support decision making. Any contemporary, reasonably complex knowledge based system will have to consider this onslaught of data, to use appropriate and sufficient reasoning for semantic processing of information by machines. This paper surveys graph based knowledge representation and reasoning, various graph models such as Conceptual Graphs, Concept Graphs, Semantic Networks, Inference Graphs and Causal Bayesian Networks used for representation and reasoning, common and recent research uses of these graph models, typically in Big Data environment, and the near future needs and challenges for graph based KRR in computing systems. Observations are presented in a table, highlighting suitability of the surveyed graph models for contemporary scenarios.
A COMPOUND POISSON MODEL FOR LEARNING DISCRETE BAYESIAN NETWORKS
Institute of Scientific and Technical Information of China (English)
Abdelaziz GHRIBI; Afif MASMOUDI
2013-01-01
We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks.
Model Diagnostics for Bayesian Networks
Sinharay, Sandip
2006-01-01
Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…
Nemirovsky, Ricardo; Tierney, Cornelia; Wright, Tracy
1998-01-01
Analyzed two children's use of a computer-based motion detector to make sense of symbolic expressions (Cartesian graphs). Found three themes: (1) tool perspectives, efforts to understand graphical responses to body motion; (2) fusion, emergent ways of talking and behaving that merge symbols and referents; and (3) graphical spaces, when changing…
Coloring geographical threshold graphs
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Percus, Allon [Los Alamos National Laboratory; Muller, Tobias [EINDHOVEN UNIV. OF TECH
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.
Institute of Scientific and Technical Information of China (English)
Wenjun Xiao
2002-01-01
Wu, Lakshmivarahan and Dhall[5] recently described a deterministic, distributed routing scheme for some special classes of metacyclic graphs. However they have no proof of correctness that the scheme is a shortest path routing algorithm. In the note we give a suboptimal, deterministic routing algorithm.
Pitts Bannister, Vanessa R.; Jamar, Idorenyin; Mutegi, Jomo W.
2007-01-01
In this article, the learning progress of one fifth-grade student is examined with regard to the development of her graph interpretation skills as she participated in the Junior Science Institute (JSI), a two-week, science intensive summer camp in which participants engaged in microbiology research and application. By showcasing the student's…
Neural networks and graph theory
Institute of Scientific and Technical Information of China (English)
许进; 保铮
2002-01-01
The relationships between artificial neural networks and graph theory are considered in detail. The applications of artificial neural networks to many difficult problems of graph theory, especially NP-complete problems, and the applications of graph theory to artificial neural networks are discussed. For example graph theory is used to study the pattern classification problem on the discrete type feedforward neural networks, and the stability analysis of feedback artificial neural networks etc.
Temporal Representation in Semantic Graphs
Energy Technology Data Exchange (ETDEWEB)
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.
Institute of Scientific and Technical Information of China (English)
李浩; 刘群
1989-01-01
Because of the widespread applications of tree and treee graph in computer science,we are interested in studying the reee graph.M.Farber,B.Richter and H.Shang in [1] showed that the graph τ2(G)is 2-edge-connected as |V(G)）≥3，at the same time,we will show the best lower bounds about vertex number and minimum degree of graph τ2(G）.
Spectral Graph Theory Analysis of Software-Defined Networks to Improve Performance and Security
2015-09-01
theory , spectral graph theory and closed-loop control are provided in Chapter II. The dual-basis and its role in defining the state of the network...finding is a significant research area within graph theory . Its applications range from finding groups within social networks [35] to finding clusters...GRAPH THEORY ANALYSIS OF SOFTWARE-DEFINED NETWORKS TO IMPROVE PERFORMANCE AND SECURITY by Thomas C. Parker September 2015 Dissertation Co
An Analytical Study of Computation and Communication Tradeoffs in Distributed Graph
Directory of Open Access Journals (Sweden)
Amirreza Abdolrashidi
2015-12-01
Full Text Available Distributed vertex-centric graph processing systems such as Pregel, Giraph and GPS have acquired significant popularity in recent years. Although the manner in which graph data is partitioned and placed on the computational nodes has considerable impact on the performance of the vertex-centric graph processing cluster, there are very few comprehensive studies on this topic. Towards enhancing our understanding of this important factor, in this paper, we propose a novel model for analyzing the performance of such clusters. Using three graph algorithms as case studies, we also characterize the inherent tradeoff between the computational load distribution and the communication overheads of a BSP cluster. This paper also reports a detailed experimental study investigating the performance of commonly-used graph partitioning mechanisms with respect to their computational load distribution characteristics and the associated communication overheads.
Asteroidal Quadruples in non Rooted Path Graphs
Directory of Open Access Journals (Sweden)
Gutierrez Marisa
2015-11-01
Full Text Available A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted path graph is the intersection graph of a family of directed subpaths of a rooted tree. Rooted path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted path graphs. For this purpose, we are studying in this paper directed path graphs that are non rooted path graphs. We prove that such graphs always contain an asteroidal quadruple.
Submanifolds Weakly Associated with Graphs
Indian Academy of Sciences (India)
A Carriazo; L M Fernández; A Rodríguez-Hidalgo
2009-06-01
We establish an interesting link between differential geometry and graph theory by defining submanifolds weakly associated with graphs. We prove that, in a local sense, every submanifold satisfies such an association, and other general results. Finally, we study submanifolds associated with graphs either in low dimensions or belonging to some special families.
Mining and Indexing Graph Databases
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.…
Hopkins, Brian
2004-01-01
The interconnected world of actors and movies is a familiar, rich example for graph theory. This paper gives the history of the "Kevin Bacon Game" and makes extensive use of a Web site to analyze the underlying graph. The main content is the classroom development of the weighted average to determine the best choice of "center" for the graph. The…
Skurnick, Ronald; Davi, Charles; Skurnick, Mia
2005-01-01
Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…
Text analysis for knowledge graphs
Popping, Roel
2007-01-01
The concept of knowledge graphs is introduced as a method to represent the state of the art in a specific scientific discipline. Next the text analysis part in the construction of such graphs is considered. Here the 'translation' from text to graph takes place. The method that is used here is compar
Hitting times, commute distances and the spectral gap for large random geometric graphs
von Luxburg, Ulrike; Hein, Matthias
2010-01-01
The commute distance between two vertices in a graph is the expected time it takes a random walk to travel from the first to the second vertex and back. According to folklore opinion, it has the property that vertices in the same cluster of the graph are close to each other while vertices in different clusters are far from each other. We study the behavior of the commute distance and hitting times on random geometric graphs ($\\epsilon$-graphs, $k$-nearest neighbor graphs and Gaussian similarity graphs). It turns out that as the size of the graph increases, the suitably rescaled hitting times and commute distances can be approximated by extremely simple expressions. However, these expressions no longer take into account the cluster structure of the graph, which leads to a completely meaningless distance function. Consequently, the use of the commute distance for machine learning purposes is discouraged for large graphs and in high dimensions. Our paper also makes several important technical contributions such ...
Bayesian Lensing Shear Measurement
Bernstein, Gary M
2013-01-01
We derive an estimator of weak gravitational lensing shear from background galaxy images that avoids noise-induced biases through a rigorous Bayesian treatment of the measurement. The Bayesian formalism requires a prior describing the (noiseless) distribution of the target galaxy population over some parameter space; this prior can be constructed from low-noise images of a subsample of the target population, attainable from long integrations of a fraction of the survey field. We find two ways to combine this exact treatment of noise with rigorous treatment of the effects of the instrumental point-spread function and sampling. The Bayesian model fitting (BMF) method assigns a likelihood of the pixel data to galaxy models (e.g. Sersic ellipses), and requires the unlensed distribution of galaxies over the model parameters as a prior. The Bayesian Fourier domain (BFD) method compresses galaxies to a small set of weighted moments calculated after PSF correction in Fourier space. It requires the unlensed distributi...
Fox, G.J.A.; Berg, van den S.M.; Veldkamp, B.P.; Irwing, P.; Booth, T.; Hughes, D.
2015-01-01
In educational and psychological studies, psychometric methods are involved in the measurement of constructs, and in constructing and validating measurement instruments. Assessment results are typically used to measure student proficiency levels and test characteristics. Recently, Bayesian item resp
Noncausal Bayesian Vector Autoregression
DEFF Research Database (Denmark)
Lanne, Markku; Luoto, Jani
We propose a Bayesian inferential procedure for the noncausal vector autoregressive (VAR) model that is capable of capturing nonlinearities and incorporating effects of missing variables. In particular, we devise a fast and reliable posterior simulator that yields the predictive distribution...
Granade, Christopher; Cory, D G
2015-01-01
In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of- the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we solve all three problems. First, we use modern statistical methods, as pioneered by Husz\\'ar and Houlsby and by Ferrie, to make Bayesian tomography numerically tractable. Our approach allows for practical computation of Bayesian point and region estimators for quantum states and channels. Second, we propose the first informative priors on quantum states and channels. Finally, we develop a method that allows online tracking of time-dependent states and estimates the drift and diffusion processes affecting a state. We provide source code and animated visual examples for our methods.
Characterizing path graphs by forbidden induced subgraphs
Lévêque, Benjamin; Preissmann, Myriam
2008-01-01
A graph is a path graph if it is the intersection graph of a family of subpaths of a tree. In 1970, Renz asked for a characterizaton of path graph by forbidden induced subgraphs. Here we answer this question by listing all graphs that are not path graphs and are minimal with this property.
Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver
Livne, Oren E
2011-01-01
Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic partial differential equations discretized on unstructured grids with finite elements. A Lean Algebraic Multigrid (LAMG) solver of the linear system Ax=b is presented, where A is a graph Laplacian. LAMG's run time and storage are linear in the number of graph edges. LAMG consists of a setup phase, in which a sequence of increasingly-coarser Laplacian systems is constructed, and an iterative solve phase using multigrid cycles. General graphs pose algorithmic challenges not encountered in traditional applications of algebraic multigrid. LAMG combines a lean piecewise-constant interpolation, judicious node aggregation based on a new node proximity definition, and an energy correction of the coarse-level systems. This results in fast convergence and substantial overhead and memory s...
Bayesian Inference in Queueing Networks
Sutton, Charles
2010-01-01
Modern Web services, such as those at Google, Yahoo!, and Amazon, handle billions of requests per day on clusters of thousands of computers. Because these services operate under strict performance requirements, a statistical understanding of their performance is of great practical interest. Such services are modeled by networks of queues, where one queue models each of the individual computers in the system. A key challenge is that the data is incomplete, because recording detailed information about every request to a heavily used system can require unacceptable overhead. In this paper we develop a Bayesian perspective on queueing models in which the arrival and departure times that are not observed are treated as latent variables. Underlying this viewpoint is the observation that a queueing model defines a deterministic transformation between the data and a set of independent variables called the service times. With this viewpoint in hand, we sample from the posterior distribution over missing data and model...
Entropy and Graph Based Modelling of Document Coherence using Discourse Entities
DEFF Research Database (Denmark)
Petersen, Casper; Lioma, Christina; Simonsen, Jakob Grue
2015-01-01
] that represents text as a graph of discourse entities, linked by different relations, such as their distance or adjacency in text. We use several graph topology metrics to approximate different aspects of the discourse flow that can indicate coherence, such as the average clustering or betweenness of discourse...
Harary, Frank
2015-01-01
Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc
Boxicity of Circular Arc Graphs
Bhowmick, Diptendu; Chandran, L. Sunil
2008-01-01
A $k$-dimensional box is the cartesian product $R_1 \\times R_2 \\times ... \\times R_k$ where each $R_i$ is a closed interval on the real line. The {\\it boxicity} of a graph $G$, denoted as $box(G)$, is the minimum integer $k$ such that $G$ can be represented as the intersection graph of a collection of $k$-dimensional boxes: that is two vertices are adjacent if and only if their corresponding boxes intersect. A circular arc graph is a graph that can be represented as the intersection graph of ...
Spectral fluctuations of quantum graphs
Energy Technology Data Exchange (ETDEWEB)
Pluhař, Z. [Faculty of Mathematics and Physics, Charles University, 180 00 Praha 8 (Czech Republic); Weidenmüller, H. A. [Max-Planck-Institut für Kernphysik, 69029 Heidelberg (Germany)
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.
Dynamic Representations of Sparse Graphs
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Fagerberg, Rolf
1999-01-01
We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....
Bayesian Estimation and Inference Using Stochastic Electronics.
Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M; Hamilton, Tara J; Tapson, Jonathan; van Schaik, André
2016-01-01
In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.
Resolvability in Circulant Graphs
Institute of Scientific and Technical Information of China (English)
Muhammad SALMAN; Imran JAVAID; Muhammad Anwar CHAUDHRY
2012-01-01
A set W of the vertices of a connected graph G is called a resolving set for G if for every two distinct vertices u,v ∈ V(G) there is a vertex w ∈ W such that d(u,w) ≠ d(v,w).A resolving set of minimum cardinality is called a metric basis for G and the number of vertices in a metric basis is called the metric dimension of G,denoted by dim(G).For a vertex u of G and a subset S of V(G),the distance between u and S is the number mins∈s d(u,s).A k-partition H ={S1,S2,...,Sk} of V(G) is called a resolving partition if for every two distinct vertices u,v ∈ V(G) there is a set Si in Π such that d(u,Si) ≠ d(v,Si).The minimum k for which there is a resolving k-partition of V(G) is called the partition dimension of G,denoted by pd(G).The circulant graph is a graph with vertex set Zn,an additive group ofintegers modulo n,and two vertices labeled i and j adjacent if and only if i - j (mod n) ∈ C,where C C Zn has the property that C =-C and 0(∈) C.The circulant graph is denoted by Xn,△ where A =|C|.In this paper,we study the metric dimension of a family of circulant graphs Xn,3 with connection set C ={1,-n/2,n - 1} and prove that dim(Xn,3) is independent of choice of n by showing that 3 for all n =0 (mod 4),dim(X,n,3) ={ 4 for all n =2 (mod 4).We also study the partition dimension of a family of circulant graphs Xn,4 with connection set C ={±1,±2} and prove that pd(Xn,4) is independent of choice of n and show that pd(X5,4) =5 and 3 forall odd n≥9,pd(Xn,4) ={ 4 for all even n ≥ 6 and n =7.
Conditional coloring of some parameterized graphs
Reddy, P Venkata Subba
2010-01-01
For integers k>0 and r>0, a conditional (k,r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex v of degree d(v) in G is adjacent to vertices with at least min{r,d(v)} different colors. The smallest integer k for which a graph G has a conditional (k,r)-coloring is called the rth order conditional chromatic number, denoted by $\\chi_r(G)$. For different values of r we obtain $\\chi_r(G)$ of certain parameterized graphs viz., Windmill graph, line graph of Windmill graph, middle graph of Friendship graph, middle graph of a cycle, line graph of Friendship graph, middle graph of complete k-partite graph and middle graph of a bipartite graph.
Bond percolation on isoradial graphs
Grimmett, Geoffrey
2012-01-01
In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star-triangle transformation, by transporting the box-crossing property across the family of isoradial graphs. As a consequence, we obtain the universality of these models at the critical point, in the sense that the one-arm and 2j-alternating-arm critical exponents (and therefore also the connectivity and volume exponents) are constant across the family of such percolation processes. The isoradial graphs in question are those that satisfy certain weak conditions on their embedding and on their track system. This class of graphs includes, for example, isoradial embeddings of periodic graphs, and graphs derived from rhombic Penrose tilings.
Identities between Modular Graph Forms
D'Hoker, Eric
2016-01-01
This paper investigates the relations between modular graph forms, which are generalizations of the modular graph functions that were introduced in earlier papers motivated by the structure of the low energy expansion of genus-one Type II superstring amplitudes. These modular graph forms are multiple sums associated with decorated Feynman graphs on the world-sheet torus. The action of standard differential operators on these modular graph forms admits an algebraic representation on the decorations. First order differential operators are used to map general non-holomorphic modular graph functions to holomorphic modular forms. This map is used to provide proofs of the identities between modular graph functions for weight less than six conjectured in earlier work, by mapping these identities to relations between holomorphic modular forms which are proven by holomorphic methods. The map is further used to exhibit the structure of identities at arbitrary weight.
Valiant Transform of Forney Graphs
Al-Bashabsheh, Ali
2010-01-01
The introduction of Forney graphs, or normal graphs, and the duality result therein [1] is a landmark in the theory of codes on graphs and in graph-based iterative decoding. A generic modeling framework for codes and systems, Forney graphs have since found various applications. It is unfortunate however that the development of the theory and application of Forney graphs to date has been restricted to the context of linear (and group) codes and systems, and the primary tool of Forney graphs is the duality result introduced in [1]. In a rather distant area of computer science, Valiant has recently presented a powerful family of new algorithms, which he calls holographic algorithms [2]. Using holographic algorithms, Valiant provides polynomial-time solutions to families of problems previously unknown to be tractable. At the heart of Valiant's holographic algorithms is the notion of "holographic reduction", which is the engine used in holographic algorithms to reduce from one problem to another. Recognizing the c...
Hierarchy of Modular Graph Identities
D'Hoker, Eric
2016-01-01
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analy...
Bayesian network learning for natural hazard assessments
Vogel, Kristin
2016-04-01
Even though quite different in occurrence and consequences, from a modelling perspective many natural hazards share similar properties and challenges. Their complex nature as well as lacking knowledge about their driving forces and potential effects make their analysis demanding. On top of the uncertainty about the modelling framework, inaccurate or incomplete event observations and the intrinsic randomness of the natural phenomenon add up to different interacting layers of uncertainty, which require a careful handling. Thus, for reliable natural hazard assessments it is crucial not only to capture and quantify involved uncertainties, but also to express and communicate uncertainties in an intuitive way. Decision-makers, who often find it difficult to deal with uncertainties, might otherwise return to familiar (mostly deterministic) proceedings. In the scope of the DFG research training group „NatRiskChange" we apply the probabilistic framework of Bayesian networks for diverse natural hazard and vulnerability studies. The great potential of Bayesian networks was already shown in previous natural hazard assessments. Treating each model component as random variable, Bayesian networks aim at capturing the joint distribution of all considered variables. Hence, each conditional distribution of interest (e.g. the effect of precautionary measures on damage reduction) can be inferred. The (in-)dependencies between the considered variables can be learned purely data driven or be given by experts. Even a combination of both is possible. By translating the (in-)dependences into a graph structure, Bayesian networks provide direct insights into the workings of the system and allow to learn about the underlying processes. Besides numerous studies on the topic, learning Bayesian networks from real-world data remains challenging. In previous studies, e.g. on earthquake induced ground motion and flood damage assessments, we tackled the problems arising with continuous variables
Exponential random graph models
Fronczak, Agata
2012-01-01
Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power. An excellent basic discussion of exponential random graphs addressed to social science students and researchers is given in [Anderson et al., 1999][Robins et al., 2007]. This essay is intentionally designed to be more theoretical in comparison with the well-known primers just mentioned. Given the interdisciplinary character of the new emerging science of complex networks, the essay aims to give a contribution upon which network scientists and practitioners, who represent different research areas, could build a common area of understanding.
Normal Order: Combinatorial Graphs
Solomon, A I; Blasiak, P; Horzela, A; Penson, K A; Solomon, Allan I.; Duchamp, Gerard; Blasiak, Pawel; Horzela, Andrzej; Penson, Karol A.
2004-01-01
A conventional context for supersymmetric problems arises when we consider systems containing both boson and fermion operators. In this note we consider the normal ordering problem for a string of such operators. In the general case, upon which we touch briefly, this problem leads to combinatorial numbers, the so-called Rook numbers. Since we assume that the two species, bosons and fermions, commute, we subsequently restrict ourselves to consideration of a single species, single-mode boson monomials. This problem leads to elegant generalisations of well-known combinatorial numbers, specifically Bell and Stirling numbers. We explicitly give the generating functions for some classes of these numbers. In this note we concentrate on the combinatorial graph approach, showing how some important classical results of graph theory lead to transparent representations of the combinatorial numbers associated with the boson normal ordering problem.
Jordan, Jonathan
2011-01-01
We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random element, and there are three parameters, $\\alpha$, $\\beta$ and $\\gamma$, which are the probabilities of edges appearing between different types of vertices. We show that as the probabilities associated with the model vary there are a number of phase transitions, in particular concerning the degree sequence. If $(1+\\alpha)(1+\\gamma)1$ then the degree of a typical vertex grows to infinity, and the proportion of vertices having any fixed degree $d$ tends to zero. We also give some results on the number of edges and on the spectral gap.
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
2010-12-02
evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in
Lawson, Andrew B
2002-01-01
Research has generated a number of advances in methods for spatial cluster modelling in recent years, particularly in the area of Bayesian cluster modelling. Along with these advances has come an explosion of interest in the potential applications of this work, especially in epidemiology and genome research. In one integrated volume, this book reviews the state-of-the-art in spatial clustering and spatial cluster modelling, bringing together research and applications previously scattered throughout the literature. It begins with an overview of the field, then presents a series of chapters that illuminate the nature and purpose of cluster modelling within different application areas, including astrophysics, epidemiology, ecology, and imaging. The focus then shifts to methods, with discussions on point and object process modelling, perfect sampling of cluster processes, partitioning in space and space-time, spatial and spatio-temporal process modelling, nonparametric methods for clustering, and spatio-temporal ...
The phylogeny graphs of doubly partial orders
Park, Boram
2011-01-01
The competition graph of a doubly partial order is known to be an interval graph. The CCE graph and the niche graph of a doubly partial order are also known to be interval graphs if the graphs do not contain a cycle of length four and three as an induced subgraph, respectively. Phylogeny graphs are variant of competition graphs. The phylogeny graph $P(D)$ of a digraph $D$ is the (simple undirected) graph defined by $V(P(D)):=V(D)$ and $E(P(D)):=\\{xy \\mid N^+_D(x) \\cap N^+_D(y) \
Kinetic Stable Delaunay Graphs
Agarwal, Pankaj K; Guibas, Leonidas J; Kaplan, Haim; Koltun, Vladlen; Rubin, Natan; Sharir, Micha
2011-01-01
We consider the problem of maintaining the Euclidean Delaunay triangulation $\\DT$ of a set $P$ of $n$ moving points in the plane, along algebraic trajectories of constant description complexity. Since the best known upper bound on the number of topological changes in the full $\\DT$ is nearly cubic, we seek to maintain a suitable portion of it that is less volatile yet retains many useful properties. We introduce the notion of a stable Delaunay graph, which is a dynamic subgraph of the Delaunay triangulation. The stable Delaunay graph (a) is easy to define, (b) experiences only a nearly quadratic number of discrete changes, (c) is robust under small changes of the norm, and (d) possesses certain useful properties. The stable Delaunay graph ($\\SDG$ in short) is defined in terms of a parameter $\\alpha>0$, and consists of Delaunay edges $pq$ for which the angles at which $p$ and $q$ see their Voronoi edge $e_{pq}$ are at least $\\alpha$. We show that (i) $\\SDG$ always contains at least roughly one third of the Del...
Zhou, Feng; de la Torre, Fernando
2015-11-19
Graph matching (GM) is a fundamental problem in computer science, and it plays a central role to solve correspondence problems in computer vision. GM problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem (QAP). Although widely used, solving the correspondence problem through GM has two main limitations: (1) the QAP is NP-hard and difficult to approximate; (2) GM algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems. To address aforementioned problems, this paper proposes factorized graph matching (FGM). FGM factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges. Four are the benefits that follow from this factorization: (1) There is no need to compute the costly (in space and time) pairwise affinity matrix; (2) The factorization allows the use of a path-following optimization algorithm, that leads to improved optimization strategies and matching performance; (3) Given the factorization, it becomes straight-forward to incorporate geometric transformations (rigid and non-rigid) to the GM problem. (4) Using a matrix formulation for the GM problem and the factorization, it is easy to reveal commonalities and differences between different GM methods. The factorization also provides a clean connection with other matching algorithms such as iterative closest point; Experimental results on synthetic and real databases illustrate how FGM outperforms state-of-the-art algorithms for GM. The code is available at http://humansensing.cs.cmu.edu/fgm.
Exploratory Visualization of Graphs Based on Community Structure
Liu, Yujie
2013-01-01
Communities, also called clusters or modules, are groups of nodes which probably share common properties and/or play similar roles within a graph. They widely exist in real networks such as biological, social, and information networks. Allowing users to interactively browse and explore the community structure, which is essential for understanding…
Mizan: Optimizing Graph Mining in Large Parallel Systems
Kalnis, Panos
2012-03-01
Extracting information from graphs, from nding shortest paths to complex graph mining, is essential for many ap- plications. Due to the shear size of modern graphs (e.g., social networks), processing must be done on large paral- lel computing infrastructures (e.g., the cloud). Earlier ap- proaches relied on the MapReduce framework, which was proved inadequate for graph algorithms. More recently, the message passing model (e.g., Pregel) has emerged. Although the Pregel model has many advantages, it is agnostic to the graph properties and the architecture of the underlying com- puting infrastructure, leading to suboptimal performance. In this paper, we propose Mizan, a layer between the users\\' code and the computing infrastructure. Mizan considers the structure of the input graph and the architecture of the in- frastructure in order to: (i) decide whether it is bene cial to generate a near-optimal partitioning of the graph in a pre- processing step, and (ii) choose between typical point-to- point message passing and a novel approach that puts com- puting nodes in a virtual overlay ring. We deployed Mizan on a small local Linux cluster, on the cloud (256 virtual machines in Amazon EC2), and on an IBM Blue Gene/P supercomputer (1024 CPUs). We show that Mizan executes common algorithms on very large graphs 1-2 orders of mag- nitude faster than MapReduce-based implementations and up to one order of magnitude faster than implementations relying on Pregel-like hash-based graph partitioning.
Graph theoretical model of a sensorimotor connectome in zebrafish.
Directory of Open Access Journals (Sweden)
Michael Stobb
Full Text Available Mapping the detailed connectivity patterns (connectomes of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome.
Duality in Geometric Graphs: Vector Graphs, Kirchhoff Graphs and Maxwell Reciprocal Figures
Directory of Open Access Journals (Sweden)
Tyler Reese
2016-02-01
Full Text Available We compare two mathematical theories that address duality between cycles and vertex-cuts of graphs in geometric settings. First, we propose a rigorous definition of a new type of graph, vector graphs. The special case of R2-vector graphs matches the intuitive notion of drawing graphs with edges taken as vectors. This leads to a discussion of Kirchhoff graphs, as originally presented by Fehribach, which can be defined independent of any matrix relations. In particular, we present simple cases in which vector graphs are guaranteed to be Kirchhoff or non-Kirchhoff. Next, we review Maxwell’s method of drawing reciprocal figures as he presented in 1864, using modern mathematical language. We then demonstrate cases in which R2-vector graphs defined from Maxwell reciprocals are “dual” Kirchhoff graphs. Given an example in which Maxwell’s theories are not sufficient to define vector graphs, we begin to explore other methods of developing dual Kirchhoff graphs.
Modelling of JET diagnostics using Bayesian Graphical Models
Energy Technology Data Exchange (ETDEWEB)
Svensson, J. [IPP Greifswald, Greifswald (Germany); Ford, O. [Imperial College, London (United Kingdom); McDonald, D.; Hole, M.; Nessi, G. von; Meakins, A.; Brix, M.; Thomsen, H.; Werner, A.; Sirinelli, A.
2011-07-01
The mapping between physics parameters (such as densities, currents, flows, temperatures etc) defining the plasma 'state' under a given model and the raw observations of each plasma diagnostic will 1) depend on the particular physics model used, 2) is inherently probabilistic, from uncertainties on both observations and instrumental aspects of the mapping, such as calibrations, instrument functions etc. A flexible and principled way of modelling such interconnected probabilistic systems is through so called Bayesian graphical models. Being an amalgam between graph theory and probability theory, Bayesian graphical models can simulate the complex interconnections between physics models and diagnostic observations from multiple heterogeneous diagnostic systems, making it relatively easy to optimally combine the observations from multiple diagnostics for joint inference on parameters of the underlying physics model, which in itself can be represented as part of the graph. At JET about 10 diagnostic systems have to date been modelled in this way, and has lead to a number of new results, including: the reconstruction of the flux surface topology and q-profiles without any specific equilibrium assumption, using information from a number of different diagnostic systems; profile inversions taking into account the uncertainties in the flux surface positions and a substantial increase in accuracy of JET electron density and temperature profiles, including improved pedestal resolution, through the joint analysis of three diagnostic systems. It is believed that the Bayesian graph approach could potentially be utilised for very large sets of diagnostics, providing a generic data analysis framework for nuclear fusion experiments, that would be able to optimally utilize the information from multiple diagnostics simultaneously, and where the explicit graph representation of the connections to underlying physics models could be used for sophisticated model testing. This
Wagstaff, Kiri L.
2012-03-01
matrices—cases in which only pairwise information is known. The list of algorithms covered in this chapter is representative of those most commonly in use, but it is by no means comprehensive. There is an extensive collection of existing books on clustering that provide additional background and depth. Three early books that remain useful today are Anderberg’s Cluster Analysis for Applications [3], Hartigan’s Clustering Algorithms [25], and Gordon’s Classification [22]. The latter covers basics on similarity measures, partitioning and hierarchical algorithms, fuzzy clustering, overlapping clustering, conceptual clustering, validations methods, and visualization or data reduction techniques such as principal components analysis (PCA),multidimensional scaling, and self-organizing maps. More recently, Jain et al. provided a useful and informative survey [27] of a variety of different clustering algorithms, including those mentioned here as well as fuzzy, graph-theoretic, and evolutionary clustering. Everitt’s Cluster Analysis [19] provides a modern overview of algorithms, similarity measures, and evaluation methods.
Graphs cospectral with a friendship graph or its complement
Directory of Open Access Journals (Sweden)
Alireza Abdollahi
2013-12-01
Full Text Available Let $n$ be any positive integer and let $F_n$ be the friendship (or Dutch windmill graph with $2n+1$ vertices and $3n$ edges. Here we study graphs with the same adjacency spectrum as the $F_n$. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let $G$ be a graph cospectral with $F_n$. Here we prove that if $G$ has no cycle of length $4$ or $5$, then $Gcong F_n$. Moreover if $G$ is connected and planar then $Gcong F_n$.All but one of connected components of $G$ are isomorphic to $K_2$.The complement $overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues, that is, if $overline{F_n}$ is cospectral with a graph $H$, then $Hcong overline{F_n}$.
Cascades on clique-based graphs
Hackett, Adam; Gleeson, James P.
2013-06-01
We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly clustered random graphs introduced by Gleeson [J. P. Gleeson, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.80.036107 80, 036107 (2009)]. A condition for the existence of global cascades is also derived. Applications of this approach include analyses of percolation, and Watts's model. We show how our techniques can be used to study the effects of in-group bias in cascades on social networks.
An Algebraic Representation of Graphs and Applications to Graph Enumeration
Directory of Open Access Journals (Sweden)
Ângela Mestre
2013-01-01
Full Text Available We give a recursion formula to generate all the equivalence classes of connected graphs with coefficients given by the inverses of the orders of their groups of automorphisms. We use an algebraic graph representation to apply the result to the enumeration of connected graphs, all of whose biconnected components have the same number of vertices and edges. The proof uses Abel’s binomial theorem and generalizes Dziobek’s induction proof of Cayley’s formula.
Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs
DEFF Research Database (Denmark)
Bensmail, Julien; Renault, Gabriel
2016-01-01
An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪⋯∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently co...
Spectral Radius of Hamiltonian Planar Graphs and Outerplanar Graphs
Institute of Scientific and Technical Information of China (English)
周建; 林翠琴; 胡冠章
2001-01-01
The spectral radius is an important parameter of a graph related to networks. A method forestimating the spectral radius of each spanning subgraph is used to prove that the spectral radius of aHamiltonian planar graph of order n ≥ 4 is less than or equal toand the spectral radius of theouterplanar graph of order n ≥ 6 is less than or equal to, which are improvements overprevious results. A direction for further study is then suggested.``
Evaluation of Graph Pattern Matching Workloads in Graph Analysis Systems
Energy Technology Data Exchange (ETDEWEB)
Hong, Seokyong [North Carolina State University (NCSU), Raleigh; Lee, Sangkeun (Matt) [ORNL; Lim, Seung-Hwan [ORNL; Sukumar, Sreenivas Rangan [ORNL; Vatsavai, Raju [North Carolina State University (NCSU), Raleigh
2016-01-01
Graph analysis has emerged as a powerful method for data scientists to represent, integrate, query, and explore heterogeneous data sources. As a result, graph data management and mining became a popular area of research, and led to the development of plethora of systems in recent years. Unfortunately, the number of emerging graph analysis systems and the wide range of applications, coupled with a lack of apples-to-apples comparisons, make it difficult to understand the trade-offs between different systems and the graph operations for which they are designed. A fair comparison of these systems is a challenging task for the following reasons: multiple data models, non-standardized serialization formats, various query interfaces to users, and diverse environments they operate in. To address these key challenges, in this paper we present a new benchmark suite by extending the Lehigh University Benchmark (LUBM) to cover the most common capabilities of various graph analysis systems. We provide the design process of the benchmark, which generalizes the workflow for data scientists to conduct the desired graph analysis on different graph analysis systems. Equipped with this extended benchmark suite, we present performance comparison for nine subgraph pattern retrieval operations over six graph analysis systems, namely NetworkX, Neo4j, Jena, Titan, GraphX, and uRiKA. Through the proposed benchmark suite, this study reveals both quantitative and qualitative findings in (1) implications in loading data into each system; (2) challenges in describing graph patterns for each query interface; and (3) different sensitivity of each system to query selectivity. We envision that this study will pave the road for: (i) data scientists to select the suitable graph analysis systems, and (ii) data management system designers to advance graph analysis systems.
Data clustering algorithms and applications
Aggarwal, Charu C
2013-01-01
Research on the problem of clustering tends to be fragmented across the pattern recognition, database, data mining, and machine learning communities. Addressing this problem in a unified way, Data Clustering: Algorithms and Applications provides complete coverage of the entire area of clustering, from basic methods to more refined and complex data clustering approaches. It pays special attention to recent issues in graphs, social networks, and other domains.The book focuses on three primary aspects of data clustering: Methods, describing key techniques commonly used for clustering, such as fea
Bayesian Face Sketch Synthesis.
Wang, Nannan; Gao, Xinbo; Sun, Leiyu; Li, Jie
2017-03-01
Exemplar-based face sketch synthesis has been widely applied to both digital entertainment and law enforcement. In this paper, we propose a Bayesian framework for face sketch synthesis, which provides a systematic interpretation for understanding the common properties and intrinsic difference in different methods from the perspective of probabilistic graphical models. The proposed Bayesian framework consists of two parts: the neighbor selection model and the weight computation model. Within the proposed framework, we further propose a Bayesian face sketch synthesis method. The essential rationale behind the proposed Bayesian method is that we take the spatial neighboring constraint between adjacent image patches into consideration for both aforementioned models, while the state-of-the-art methods neglect the constraint either in the neighbor selection model or in the weight computation model. Extensive experiments on the Chinese University of Hong Kong face sketch database demonstrate that the proposed Bayesian method could achieve superior performance compared with the state-of-the-art methods in terms of both subjective perceptions and objective evaluations.
Studying the corona product of graphs under some graph invariants
Directory of Open Access Journals (Sweden)
M. Tavakoli
2014-09-01
Full Text Available The corona product $Gcirc H$ of two graphs $G$ and $H$ is obtained by taking one copy of $G$ and $|V(G|$ copies of $H$; and by joining each vertex of the $i$-th copy of $H$ to the $i$-th vertex of $G$, where $1 leq i leq |V(G|$. In this paper, exact formulas for the eccentric distance sum and the edge revised Szeged indices of the corona product of graphs are presented. We also study the conditions under which the corona product of graphs produces a median graph.
Graph Coarsening for Path Finding in Cybersecurity Graphs
Energy Technology Data Exchange (ETDEWEB)
Hogan, Emilie A.; Johnson, John R.; Halappanavar, Mahantesh
2013-01-01
n the pass-the-hash attack, hackers repeatedly steal password hashes and move through a computer network with the goal of reaching a computer with high level administrative privileges. In this paper we apply graph coarsening in network graphs for the purpose of detecting hackers using this attack or assessing the risk level of the network's current state. We repeatedly take graph minors, which preserve the existence of paths in the graph, and take powers of the adjacency matrix to count the paths. This allows us to detect the existence of paths as well as find paths that have high risk of being used by adversaries.
Statistical mechanics on isoradial graphs
Boutillier, Cédric
2010-01-01
Isoradial graphs are a natural generalization of regular graphs which give, for many models of statistical mechanics, the right framework for studying models at criticality. In this survey paper, we first explain how isoradial graphs naturally arise in two approaches used by physicists: transfer matrices and conformal field theory. This leads us to the fact that isoradial graphs provide a natural setting for discrete complex analysis, to which we dedicate one section. Then, we give an overview of explicit results obtained for different models of statistical mechanics defined on such graphs: the critical dimer model when the underlying graph is bipartite, the 2-dimensional critical Ising model, random walk and spanning trees and the q-state Potts model.
A Review on Large Scale Graph Processing Using Big Data Based Parallel Programming Models
Directory of Open Access Journals (Sweden)
Anuraj Mohan
2017-02-01
Full Text Available Processing big graphs has become an increasingly essential activity in various fields like engineering, business intelligence and computer science. Social networks and search engines usually generate large graphs which demands sophisticated techniques for social network analysis and web structure mining. Latest trends in graph processing tend towards using Big Data platforms for parallel graph analytics. MapReduce has emerged as a Big Data based programming model for the processing of massively large datasets. Apache Giraph, an open source implementation of Google Pregel which is based on Bulk Synchronous Parallel Model (BSP is used for graph analytics in social networks like Facebook. This proposed work is to investigate the algorithmic effects of the MapReduce and BSP model on graph problems. The triangle counting problem in graphs is considered as a benchmark and evaluations are made on the basis of time of computation on the same cluster, scalability in relation to graph and cluster size, resource utilization and the structure of the graph.
Bayesian least squares deconvolution
Asensio Ramos, A.; Petit, P.
2015-11-01
Aims: We develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods: We consider LSD under the Bayesian framework and we introduce a flexible Gaussian process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results: We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
Hybrid Batch Bayesian Optimization
Azimi, Javad; Fern, Xiaoli
2012-01-01
Bayesian Optimization aims at optimizing an unknown non-convex/concave function that is costly to evaluate. We are interested in application scenarios where concurrent function evaluations are possible. Under such a setting, BO could choose to either sequentially evaluate the function, one input at a time and wait for the output of the function before making the next selection, or evaluate the function at a batch of multiple inputs at once. These two different settings are commonly referred to as the sequential and batch settings of Bayesian Optimization. In general, the sequential setting leads to better optimization performance as each function evaluation is selected with more information, whereas the batch setting has an advantage in terms of the total experimental time (the number of iterations). In this work, our goal is to combine the strength of both settings. Specifically, we systematically analyze Bayesian optimization using Gaussian process as the posterior estimator and provide a hybrid algorithm t...
Bayesian least squares deconvolution
Ramos, A Asensio
2015-01-01
Aims. To develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods. We consider LSD under the Bayesian framework and we introduce a flexible Gaussian Process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results. We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
Bayesian Exploratory Factor Analysis
DEFF Research Database (Denmark)
Conti, Gabriella; Frühwirth-Schnatter, Sylvia; Heckman, James J.;
2014-01-01
This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corr......This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor......, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study confirms the validity of the approach. The method is used to produce interpretable low dimensional aggregates...
Center, Julian L.; Knuth, Kevin H.
2011-03-01
Visual odometry refers to tracking the motion of a body using an onboard vision system. Practical visual odometry systems combine the complementary accuracy characteristics of vision and inertial measurement units. The Mars Exploration Rovers, Spirit and Opportunity, used this type of visual odometry. The visual odometry algorithms in Spirit and Opportunity were based on Bayesian methods, but a number of simplifying approximations were needed to deal with onboard computer limitations. Furthermore, the allowable motion of the rover had to be severely limited so that computations could keep up. Recent advances in computer technology make it feasible to implement a fully Bayesian approach to visual odometry. This approach combines dense stereo vision, dense optical flow, and inertial measurements. As with all true Bayesian methods, it also determines error bars for all estimates. This approach also offers the possibility of using Micro-Electro Mechanical Systems (MEMS) inertial components, which are more economical, weigh less, and consume less power than conventional inertial components.
Dettlaff, Magda; Yero, Ismael G
2012-01-01
The bondage number $b(G)$ of a nonempty graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than the domination number of $G$. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some Cartesian product, strong product or direct product of two paths.
Dettlaff, Magda; Lemanska, Magdalena; Yero, Ismael G.
2012-01-01
The bondage number $b(G)$ of a nonempty graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than the domination number of $G$. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.
Probabilistic Inferences in Bayesian Networks
Ding, Jianguo
2010-01-01
This chapter summarizes the popular inferences methods in Bayesian networks. The results demonstrates that the evidence can propagated across the Bayesian networks by any links, whatever it is forward or backward or intercausal style. The belief updating of Bayesian networks can be obtained by various available inference techniques. Theoretically, exact inferences in Bayesian networks is feasible and manageable. However, the computing and inference is NP-hard. That means, in applications, in ...
Yap, Hian-Poh
1996-01-01
This book provides an up-to-date and rapid introduction to an important and currently active topic in graph theory. The author leads the reader to the forefront of research in this area. Complete and easily readable proofs of all the main theorems, together with numerous examples, exercises and open problems are given. The book is suitable for use as a textbook or as seminar material for advanced undergraduate and graduate students. The references are comprehensive and so it will also be useful for researchers as a handbook.
Graphs Theory and Applications
Fournier, Jean-Claude
2008-01-01
This book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings and the timetabling problem, matchings and the optimal assignment problem, and Hamiltonian cycles and the traveling salesman problem, to name but a few. Exercises at various levels are given at the end of each chapter, and a final chapter presents a few general problems with hints for solutions, thus providing the reader with the opportunity to test and refine their knowledge on the
DEFF Research Database (Denmark)
Kucharik, Marcel; Hofacker, Ivo; Stadler, Peter
2014-01-01
Motivation RNA folding is a complicated kinetic process. The minimum free energy structure provides only a static view of the most stable conformational state of the system. It is insufficient to give detailed insights into the dynamic behavior of RNAs. A sufficiently sophisticated analysis...... of the folding free energy landscape, however, can provide the relevant information. Results We introduce the basin hopping graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect...
Zeps, Dainis
2009-01-01
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces. Further, we define multiplication of these objects, that coincides with the multiplication of permutations. We consider closed under multiplication classes of combinatorial maps that consist of closed classes of combinatorial maps with fixed edges where each such class is defined by a knot. One class among them is special, containing selfconjugate maps.
Burleigh, Scott C.
2011-01-01
Contact Graph Routing (CGR) is a dynamic routing system that computes routes through a time-varying topology of scheduled communication contacts in a network based on the DTN (Delay-Tolerant Networking) architecture. It is designed to enable dynamic selection of data transmission routes in a space network based on DTN. This dynamic responsiveness in route computation should be significantly more effective and less expensive than static routing, increasing total data return while at the same time reducing mission operations cost and risk. The basic strategy of CGR is to take advantage of the fact that, since flight mission communication operations are planned in detail, the communication routes between any pair of bundle agents in a population of nodes that have all been informed of one another's plans can be inferred from those plans rather than discovered via dialogue (which is impractical over long one-way-light-time space links). Messages that convey this planning information are used to construct contact graphs (time-varying models of network connectivity) from which CGR automatically computes efficient routes for bundles. Automatic route selection increases the flexibility and resilience of the space network, simplifying cross-support and reducing mission management costs. Note that there are no routing tables in Contact Graph Routing. The best route for a bundle destined for a given node may routinely be different from the best route for a different bundle destined for the same node, depending on bundle priority, bundle expiration time, and changes in the current lengths of transmission queues for neighboring nodes; routes must be computed individually for each bundle, from the Bundle Protocol agent's current network connectivity model for the bundle s destination node (the contact graph). Clearly this places a premium on optimizing the implementation of the route computation algorithm. The scalability of CGR to very large networks remains a research topic
Endomorphisms of graph algebras
DEFF Research Database (Denmark)
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D...... that the restriction to the diagonal MASA of an automorphism which globally preserves both D_E and the core AF-subalgebra eventually commutes with the corresponding one-sided shift. Secondly, we exhibit several properties of proper endomorphisms, investigate invertibility of localized endomorphisms both on C...
Intuitionistic Fuzzy Graphs with Categorical Properties
Directory of Open Access Journals (Sweden)
Hossein Rashmanlou
2015-09-01
Full Text Available The main purpose of this paper is to show the rationality of some operations, defined or to be defined, on intuitionistic fuzzy graphs. Firstly, three kinds of new product operations (called direct product, lexicographic product, and strong product are defined in intuitionistic fuzzy graphs, and some important notions on intuitionistic fuzzy graphs are demonstrated by characterizing these notions and their level counterparts graphs such as intuitionistic fuzzy complete graph, cartesian product of intuitionistic fuzzy graphs, composition of intuitionistic fuzzy graphs, union of intuitionistic fuzzy graphs, and join of intuitionistic fuzzy graphs. As a result, a kind of representations of intuitionistic fuzzy graphs and intuitionistic fuzzy complete graphs are given. Next, categorical goodness of intuitionistic fuzzy graphs is illustrated by proving that the category of intuitionistic fuzzy graphs and homomorphisms between them is isomorphic-closed, complete, and co-complete.
Bayesian multiple target tracking
Streit, Roy L
2013-01-01
This second edition has undergone substantial revision from the 1999 first edition, recognizing that a lot has changed in the multiple target tracking field. One of the most dramatic changes is in the widespread use of particle filters to implement nonlinear, non-Gaussian Bayesian trackers. This book views multiple target tracking as a Bayesian inference problem. Within this framework it develops the theory of single target tracking, multiple target tracking, and likelihood ratio detection and tracking. In addition to providing a detailed description of a basic particle filter that implements
Edge Ideals of Weighted Graphs
Paulsen, Chelsey
2012-01-01
We study weighted graphs and their "edge ideals" which are ideals in polynomial rings that are defined in terms of the graphs. We provide combinatorial descriptions of m-irreducible decompositions for the edge ideal of a weighted graph in terms of the combinatorics of "weighted vertex covers". We use these, for instance, to say when these ideals are m-unmixed. We explicitly describe which weighted cycles and trees are unmixed and which ones are Cohen-Macaulay, and we prove that all weighted complete graphs are Cohen-Macaulay.
Nested Dynamic Condition Response Graphs
DEFF Research Database (Denmark)
Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs
2012-01-01
We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner...... Exformatics, a danish provider of case and workflow management systems. We formalize the semantics by giving first a map from Nested to (flat) DCR Graphs with milestones, and then extending the previously given mapping from DCR Graphs to Buchi-automata to include the milestone relation....
Partitions of generalized split graphs
Shklarsky, Oren
2012-01-01
We discuss matrix partition problems for graphs that admit a partition into k independent sets and ` cliques. We show that when k + ` 6 2, any matrix M has finitely many (k; `) minimal obstructions and hence all of these problems are polynomial time solvable. We provide upper bounds for the size of any (k; `) minimal obstruction when k = ` = 1 (split graphs), when k = 2; ` = 0 (bipartite graphs), and when k = 0; ` = 2 (co-bipartite graphs). When k = ` = 1, we construct an exponential size spl...
A Modal-Logic Based Graph Abstraction
Bauer, J.; Boneva, I.B.; Kurban, M.E.; Rensink, A.; Ehrig, H.; Heckel, R.; Rozenberg, G.; Taentzer, G.
2008-01-01
Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract graphs
Double-Critical Graphs and Complete Minors
DEFF Research Database (Denmark)
Kawarabayashi, Ken-ichi; Pedersen, Anders Sune; Toft, Bjarne
2010-01-01
A connected $k$-chromatic graph $G$ is double-critical if for all edges $uv$ of $G$ the graph $G - u - v$ is $(k-2)$-colourable. The only known double-critical $k$-chromatic graph is the complete $k$-graph $K_k$. The conjecture that there are no other double-critical graphs is a special case...
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
Said Broumi; Mohamed Talea; Assia Bakali; Florentin Smarandache
2016-01-01
In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.
Wang, Suijie
2010-01-01
In this paper, we give a Laplacian characterization of the product of the complete graphs $K_m$ with trees, unicyclic graphs, and bicyclic graphs. More precisely, let $G$ be a connected graph with at most two independent cycles. If $G$ is neither $C_{6}$ nor $\\Theta_{3,2,5}$ and determined by its Laplacain spectrum, then the product $G\\times K_{m}$ is also a graph determined by its Laplacian spectrum. In addition, we find the cosepctral graphs of $C_{6}\\times K_{m}$ and $\\Theta_{3,2,5}\\times K_{m}$, where the case $m=1$ is shown in Figure \\ref{F1} and \\ref{F2}.
Identification of Functional Clusters in the Striatum Using Infinite Relational Modeling
DEFF Research Database (Denmark)
Andersen, Kasper Winther; Madsen, Kristoffer Hougaard; Siebner, Hartwig
2011-01-01
In this paper we investigate how the Infinite Relational Model can be used to infer functional groupings of the human striatum using resting state fMRI data from 30 healthy subjects. The Infinite Relational Model is a non-parametric Bayesian method for infering community structure in complex...... and non-links in the graphs as missing. We find that the model is performing well above chance for all subjects....... networks. We visualize the solution found by performing evidence accumulation clustering on the maximum a posterior solutions found in 100 runs of the sampling scheme. The striatal groupings found are symmetric between hemispheres indicating that the model is able to group voxels across hemispheres, which...
Energy Technology Data Exchange (ETDEWEB)
Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
Bayesian methods for hackers probabilistic programming and Bayesian inference
Davidson-Pilon, Cameron
2016-01-01
Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples a...
Cross over of recurrence networks to random graphs and random geometric graphs
Jacob, Rinku; Harikrishnan, K. P.; Misra, R.; Ambika, G.
2017-02-01
Recurrence networks are complex networks constructed from the time series of chaotic dynamical systems where the connection between two nodes is limited by the recurrence threshold. This condition makes the topology of every recurrence network unique with the degree distribution determined by the probability density variations of the representative attractor from which it is constructed. Here we numerically investigate the properties of recurrence networks from standard low-dimensional chaotic attractors using some basic network measures and show how the recurrence networks are different from random and scale-free networks. In particular, we show that all recurrence networks can cross over to random geometric graphs by adding sufficient amount of noise to the time series and into the classical random graphs by increasing the range of interaction to the system size. We also highlight the effectiveness of a combined plot of characteristic path length and clustering coefficient in capturing the small changes in the network characteristics.
Cross over of recurrence networks to random graphs and random geometric graphs
Indian Academy of Sciences (India)
RINKU JACOB; K P HARIKRISHNAN; R MISRA; G AMBIKA
2017-02-01
Recurrence networks are complex networks constructed from the time series of chaotic dynamical systems where the connection between two nodes is limited by the recurrence threshold. This condition makes the topology of every recurrence network unique with the degree distribution determined by the probability densityvariations of the representative attractor from which it is constructed. Here we numerically investigate the properties of recurrence networks from standard low-dimensional chaotic attractors using some basic network measuresand show how the recurrence networks are different from random and scale-free networks. In particular, we show that all recurrence networks can cross over to random geometric graphs by adding sufficient amount of noise tothe time series and into the classical random graphs by increasing the range of interaction to the system size. We also highlight the effectiveness of a combined plot of characteristic path length and clustering coefficient in capturing the small changes in the network characteristics.
Bayesian Discovery of Linear Acyclic Causal Models
Hoyer, Patrik O
2012-01-01
Methods for automated discovery of causal relationships from non-interventional data have received much attention recently. A widely used and well understood model family is given by linear acyclic causal models (recursive structural equation models). For Gaussian data both constraint-based methods (Spirtes et al., 1993; Pearl, 2000) (which output a single equivalence class) and Bayesian score-based methods (Geiger and Heckerman, 1994) (which assign relative scores to the equivalence classes) are available. On the contrary, all current methods able to utilize non-Gaussianity in the data (Shimizu et al., 2006; Hoyer et al., 2008) always return only a single graph or a single equivalence class, and so are fundamentally unable to express the degree of certainty attached to that output. In this paper we develop a Bayesian score-based approach able to take advantage of non-Gaussianity when estimating linear acyclic causal models, and we empirically demonstrate that, at least on very modest size networks, its accur...
Measure Transformer Semantics for Bayesian Machine Learning
Borgström, Johannes; Gordon, Andrew D.; Greenberg, Michael; Margetson, James; van Gael, Jurgen
The Bayesian approach to machine learning amounts to inferring posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables. There is a trend in machine learning towards expressing Bayesian models as probabilistic programs. As a foundation for this kind of programming, we propose a core functional calculus with primitives for sampling prior distributions and observing variables. We define combinators for measure transformers, based on theorems in measure theory, and use these to give a rigorous semantics to our core calculus. The original features of our semantics include its support for discrete, continuous, and hybrid measures, and, in particular, for observations of zero-probability events. We compile our core language to a small imperative language that has a straightforward semantics via factor graphs, data structures that enable many efficient inference algorithms. We use an existing inference engine for efficient approximate inference of posterior marginal distributions, treating thousands of observations per second for large instances of realistic models.
Corona graphs as a model of small-world networks
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.
Quantization of gauge fields, graph polynomials and graph homology
Energy Technology Data Exchange (ETDEWEB)
Kreimer, Dirk, E-mail: kreimer@physik.hu-berlin.de [Humboldt University, 10099 Berlin (Germany); Sars, Matthias [Humboldt University, 10099 Berlin (Germany); Suijlekom, Walter D. van [Radboud University Nijmegen, 6525 AJ Nijmegen (Netherlands)
2013-09-15
We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials. The transition to the full gauge theory amplitude is obtained by the use of a third, new, graph polynomial, the corolla polynomial. This implies effectively a covariant quantization without ghosts, where all the relevant signs of the ghost sector are incorporated in a double complex furnished by the corolla polynomial–we call it cycle homology–and by graph homology. -- Highlights: •We derive gauge theory Feynman from scalar field theory with 3-valent vertices. •We clarify the role of graph homology and cycle homology. •We use parametric renormalization and the new corolla polynomial.
DEFF Research Database (Denmark)
Jensen, Finn Verner; Nielsen, Thomas Dyhre
2016-01-01
and edges. The nodes represent variables, which may be either discrete or continuous. An edge between two nodes A and B indicates a direct influence between the state of A and the state of B, which in some domains can also be interpreted as a causal relation. The wide-spread use of Bayesian networks...
DEFF Research Database (Denmark)
Antoniou, Constantinos; Harrison, Glenn W.; Lau, Morten I.;
2015-01-01
A large literature suggests that many individuals do not apply Bayes’ Rule when making decisions that depend on them correctly pooling prior information and sample data. We replicate and extend a classic experimental study of Bayesian updating from psychology, employing the methods of experimental...
Clustering by hypergraphs and dimensionality of cluster systems
Albeverio, S
2012-01-01
In the present paper we discuss the clustering procedure in the case where instead of a single metric we have a family of metrics. In this case we can obtain a partially ordered graph of clusters which is not necessarily a tree. We discuss a structure of a hypergraph above this graph. We propose two definitions of dimension for hyperedges of this hypergraph and show that for the multidimensional p-adic case both dimensions are reduced to the number of p-adic parameters. We discuss the application of the hypergraph clustering procedure to the construction of phylogenetic graphs in biology. In this case the dimension of a hyperedge will describe the number of sources of genetic diversity.
Graph Transformation and AI Planning
Edelkamp, S.; Rensink, A.; Edelkamp, S.; Frank, J.
2007-01-01
This document provides insight to the similarities and differences of Graph Transformation and AI Planning, two rising research fields with different publication organs and tools. While graph transformation systems can be used as a graphical knowledge engineering front-end for designing planning pr
2005-06-01
intuitive results on a variety of synthetic and real-world datasets. Here, we will verify their scalability. Figure 5.9 shows results on a “ caveman ...show timing results on a “ caveman ” graph with 3 caves. The plot shows wall-clock time vs. the number of edges E in the graph, for both SPLIT (dashed
Paley Graphs and Their Generalizations
Elsawy, Ahmed Noubi
2012-01-01
To construct a Paley graph, we fix a finite field and consider its elements as vertices of the Paley graph. Two vertices are connected by an edge if their difference is a square in the field. We will study some important properties of the Paley graphs. In particular, we will show that the Paley graphs are connected, symmetric, and self-complementary. Also we will show that the Paley graph of order q is (q-1)/2 -regular, and every two adjacent vertices have (q-5)/4 common neighbors, and every two non-adjacent vertices have q-1/4 common neighbors, which means that the Paley graphs are strongly regular with parameters(q,q-1/2,q-5/4, q-1/4). Paley graphs are generalized by many mathematicians. In the first section of Chapter 3 we will see three examples of these generalizations and some of their basic properties. In the second section of Chapter 3 we will define a new generalization of the Paley graphs, in which pairs of elements of a finite field are connected by an edge if and only if there difference belongs t...
Graph Representation of Projective Resolutions
Institute of Scientific and Technical Information of China (English)
Hong Bo SHI
2011-01-01
We generalize the concept - dimension tree and the related results for monomial algebras to a more general case - relations algebras Λ by bringing Gr(o)bner basis into play. More precisely,graph to be called the minimal resolution graph for M. Algorithms for computing such diagraphs and applications as well will be presented.
Quantum Markov fields on graphs
2009-01-01
We introduce generalized quantum Markov states and generalized d-Markov chains which extend the notion quantum Markov chains on spin systems to that on $C^*$-algebras defined by general graphs. As examples of generalized d-Markov chains, we construct the entangled Markov fields on tree graphs. The concrete examples of generalized d-Markov chains on Cayley trees are also investigated.
Open Graphs and Monoidal Theories
Dixon, Lucas
2010-01-01
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of these diagrams is that edges need not be connected to vertices at both ends, and these unconnected ends can be interpreted as the inputs and outputs of a diagram. In this paper, we give a concrete construction for string diagrams using a special kind of typed graph called an open-graph. While the category of open-graphs is not itself adhesive, we introduce the notion of a selective adhesive functor, and show that such a functor embeds the category of open-graphs into the ambient adhesive category of typed graphs. Using this functor, the category of open-graphs inherits "enough adhesivity" from the category of typed graphs to perform double-pushout (DPO) graph rewriting. A salient feature of our theory is that it ensures rewrite systems are "type-safe" in the sense that rewriting respects the inputs and outputs. This formalism lets u...
Subgraph Enumeration in Massive Graphs
DEFF Research Database (Denmark)
Silvestri, Francesco
bound also applies with high probability. Our algorithm is I/O optimal, in the worst-case, when the sample graph belongs to the Alon class, which includes cliques, cycles and every graph with a perfect matching: indeed, we show that any algorithm enumerating $T$ instances must always use $\\BOM...
A Collection of Features for Semantic Graphs
Energy Technology Data Exchange (ETDEWEB)
Eliassi-Rad, T; Fodor, I K; Gallagher, B
2007-05-02
Semantic graphs are commonly used to represent data from one or more data sources. Such graphs extend traditional graphs by imposing types on both nodes and links. This type information defines permissible links among specified nodes and can be represented as a graph commonly referred to as an ontology or schema graph. Figure 1 depicts an ontology graph for data from National Association of Securities Dealers. Each node type and link type may also have a list of attributes. To capture the increased complexity of semantic graphs, concepts derived for standard graphs have to be extended. This document explains briefly features commonly used to characterize graphs, and their extensions to semantic graphs. This document is divided into two sections. Section 2 contains the feature descriptions for static graphs. Section 3 extends the features for semantic graphs that vary over time.
Planar graphs theory and algorithms
Nishizeki, T
1988-01-01
Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.
Quantum walks on general graphs
Kendon, V
2003-01-01
A scheme for a discrete time quantum walk on a general graph of N vertices with undirected edges is given, and compared with the continuous time quantum walk on a general graph introduced by Farhi and Gutmann [PRA 58 915 (1998)]. Both walks are contrasted with the examples of quantum walks in the literature treating graphs of fixed, small (< log N) degree. This illustrates the way in which extra information about the graph allows more efficient algorithms to be designed. To obtain a quantum speed up over classical for comparable resources it is necessary to code the position space of the quantum walk into a qubit register (or equivalent). The role of the oracle is also discussed and an efficient gate sequence is presented for implementing a discrete quantum walk given one copy of a quantum state encoding the adjacency matrix of the graph.
Parallel Graph Transformation based on Merged Approach
Directory of Open Access Journals (Sweden)
Asmaa Aouat
2013-01-01
Full Text Available Graph transformation is one of the key concepts in graph grammar. In order to accelerate the graph transformation, the concept of parallel graph transformation has been proposed by different tools such as AGG tool. The theory of parallel graph transformation used by AGG just allows clarifying the concepts of conflict and dependency between the transformation rules. This work proposes an approach of parallel graph transformations which enables dependent transformation rules to be executed in parallel.
Girth 5 graphs from relative difference sets
DEFF Research Database (Denmark)
Jørgensen, Leif Kjær
2005-01-01
We consider the problem of construction of graphs with given degree $k$ and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed ...... by Royle, four of the known cages including the Hoffman-Singleton graph, some graphs constructed by Exoo and some new smallest known graphs....
Girth 5 graphs from relative difference sets
DEFF Research Database (Denmark)
Jørgensen, Leif Kjær
We consider the problem of construction of graphs with given degree and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by G....... Royle, four of the known cages including the Hoffman-Singleton graph, some graphs constructed by G. Exoo and some new smallest known graphs. k...
On characterizing terrain visibility graphs
Directory of Open Access Journals (Sweden)
William Evans
2015-06-01
Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.
Periodic 2-graphs arising from subshifts
Pask, David; Weaver, Natasha
2009-01-01
Higher-rank graphs were introduced by Kumjian and Pask to provide models for higher-rank Cuntz-Krieger algebras. In a previous paper, we constructed 2-graphs whose path spaces are rank-two subshifts of finite type, and showed that this construction yields aperiodic 2-graphs whose $C^*$-algebras are simple and are not ordinary graph algebras. Here we show that the construction also gives a family of periodic 2-graphs which we call \\emph{domino graphs}. We investigate the combinatorial structure of domino graphs, finding interesting points of contact with the existing combinatorial literature, and prove a structure theorem for the $C^*$-algebras of domino graphs.
Algorithms for Planar Graphs and Graphs in Metric Spaces
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
of magnitude faster than the corresponding algorithms for general graphs. The first and main part of this thesis focuses on the development of efficient planar graph algorithms. The most important contributions include a faster single-source shortest path algorithm, a distance oracle with subquadratic...... preprocessing time, an O(n log n) time algorithm for the replacement paths problem, and a min st-cut oracle with nearlinear preprocessing time. We also give improved time bounds for computing various graph invariants such as diameter and girth. In the second part, we consider stretch factor problems...
Extended Bayesian Information Criteria for Gaussian Graphical Models
Foygel, Rina
2010-01-01
Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization objectives for algorithms searching through sets of graphs or for selection of tuning parameters of other methods such as the graphical lasso, which is a likelihood penalization technique. In this paper we establish the consistency of an extended Bayesian information criterion for Gaussian graphical models in a scenario where both the number of variables p and the sample size n grow. Compared to earlier work on the regression case, our treatment allows for growth in the number of non-zero parameters in the true model, which is necessary in order to cover connected graphs. We demonstrate the performance of this criterion on simulated data when used in conjunction with the graphical lasso, and verify that the criterion indeed performs better than either cross-validation or the ordi...
Semantic graphs and associative memories.
Pomi, Andrés; Mizraji, Eduardo
2004-12-01
Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.
Design Pattern Mining Using Graph Matching
Institute of Scientific and Technical Information of China (English)
LI Qing-hua; ZHANG Zhi-xiang; BEN Ke-rong
2004-01-01
The identification of design pattern instances is important for program understanding and software maintenance. Aiming at the mining of design patterns in existing systems, this paper proposes a sub-graph isomorphism approach to discover several design patterns in a legacy system at a time. The attributed relational graph is used to describe design patterns and legacy systems. The sub-graph isomorphism approach consists of decomposition and composition process. During the decomposition process, graphs corresponding to the design patterns are decomposed into sub-graphs, some of which are graphs corresponding to the elemental design patterns. The composition process tries to get sub-graph isomorphism of the matched graph if sub-graph isomorphism of each sub-graph is obtained. Due to the common structures between design patterns, the proposed approach can reduce the matching times of entities and relations. Compared with the existing methods, the proposed algorithm is not linearly dependent on the number of design pattern graphs.
Probability and Bayesian statistics
1987-01-01
This book contains selected and refereed contributions to the "Inter national Symposium on Probability and Bayesian Statistics" which was orga nized to celebrate the 80th birthday of Professor Bruno de Finetti at his birthplace Innsbruck in Austria. Since Professor de Finetti died in 1985 the symposium was dedicated to the memory of Bruno de Finetti and took place at Igls near Innsbruck from 23 to 26 September 1986. Some of the pa pers are published especially by the relationship to Bruno de Finetti's scientific work. The evolution of stochastics shows growing importance of probability as coherent assessment of numerical values as degrees of believe in certain events. This is the basis for Bayesian inference in the sense of modern statistics. The contributions in this volume cover a broad spectrum ranging from foundations of probability across psychological aspects of formulating sub jective probability statements, abstract measure theoretical considerations, contributions to theoretical statistics an...
Complex Network Community Detection Based on Core Graph Incremental Clustering%基于核心图增量聚类的复杂网络划分算法
Institute of Scientific and Technical Information of China (English)
张新猛; 蒋盛益
2013-01-01
借鉴基于聚类的无监督入侵检测算法(Clustering-based method for the unsupervised intrusion detection,CBUID)聚类原理,提出一种基于核心图增量聚类的社区划分算法(Clustering-based method for community detection,CBCD).本文提出一种社区构建方法,给出节点与社区相似度的计算公式.首先,对由少量高度数节点组成的核心网络采用现有算法进行核心社区划分,然后,采用增量方式依据节点与社区相似度,将剩余节点划分到核心社区中.算法复杂度主要依赖于网络规模、边的数量及划分的社区个数,具有线性复杂度.通过在几个典型真实网络数据集上测试,所提算法能够有效地进行社区划分.%This paper references the principle of clustering in clustering-based method for the unsupervised intrusion detection algorithm (CBUID),and proposes a clustering-based method for community detection (CBCD).We propose a method of community summary building,and give the formula of the similarity between node and community.First,it detects communities on the core network composed of a small amount of high-degree core nodes,then partitions the remaining nodes into core community according to the similarity between the node and community incrementally.Its running time mainly depends on the network size,the number of edges and the number of communities,and our algorithm has essentially a linear time complexity.Applications on several common real networks demonstrate that this method is very effective at community detection of networks.
Bayesian Independent Component Analysis
DEFF Research Database (Denmark)
Winther, Ole; Petersen, Kaare Brandt
2007-01-01
In this paper we present an empirical Bayesian framework for independent component analysis. The framework provides estimates of the sources, the mixing matrix and the noise parameters, and is flexible with respect to choice of source prior and the number of sources and sensors. Inside the engine...... in a Matlab toolbox, is demonstrated for non-negative decompositions and compared with non-negative matrix factorization....
Acyclic edge colorings of planar graphs and series parallel graphs
Institute of Scientific and Technical Information of China (English)
HOU JianFeng; WU JianLiang; LIU GuiZhen; LIU Bin
2009-01-01
A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G.The acyclic edge chromatic number of G,denoted by a'(G),is the least number of colors in an acyclic edge coloring of G.Alon et al.conjectured that a'(G) ≤△(G) +2 for any graphs.For planar graphs G with girth g(G),we prove that a'(G) ≤ max{2△(G)-2,△(G) +22} if g(G) ≥3,a'(G)≤△(G)+2if g(G) ≥ 5,a'(G) ≤△(G)+1 if g(G) ≥ 7,and a'(G)=△(G) if g(G) ≥ 16 and △(G) ≥ 3.For series-parallel graphs G,we have a'(G) ≤ △(G) +1.
Bipartite graphs as models of population structures in evolutionary multiplayer games.
Directory of Open Access Journals (Sweden)
Jorge Peña
Full Text Available By combining evolutionary game theory and graph theory, "games on graphs" study the evolutionary dynamics of frequency-dependent selection in population structures modeled as geographical or social networks. Networks are usually represented by means of unipartite graphs, and social interactions by two-person games such as the famous prisoner's dilemma. Unipartite graphs have also been used for modeling interactions going beyond pairwise interactions. In this paper, we argue that bipartite graphs are a better alternative to unipartite graphs for describing population structures in evolutionary multiplayer games. To illustrate this point, we make use of bipartite graphs to investigate, by means of computer simulations, the evolution of cooperation under the conventional and the distributed N-person prisoner's dilemma. We show that several implicit assumptions arising from the standard approach based on unipartite graphs (such as the definition of replacement neighborhoods, the intertwining of individual and group diversity, and the large overlap of interaction neighborhoods can have a large impact on the resulting evolutionary dynamics. Our work provides a clear example of the importance of construction procedures in games on graphs, of the suitability of bigraphs and hypergraphs for computational modeling, and of the importance of concepts from social network analysis such as centrality, centralization and bipartite clustering for the understanding of dynamical processes occurring on networked population structures.
Multigraph: Reusable Interactive Data Graphs
Phillips, M. B.
2010-12-01
There are surprisingly few good software tools available for presenting time series data on the internet. The most common practice is to use a desktop program such as Excel or Matlab to save a graph as an image which can be included in a web page like any other image. This disconnects the graph from the data in a way that makes updating a graph with new data a cumbersome manual process, and it limits the user to one particular view of the data. The Multigraph project defines an XML format for describing interactive data graphs, and software tools for creating and rendering those graphs in web pages and other internet connected applications. Viewing a Multigraph graph is extremely simple and intuitive, and requires no instructions; the user can pan and zoom by clicking and dragging, in a familiar "Google Maps" kind of way. Creating a new graph for inclusion in a web page involves writing a simple XML configuration file. Multigraph can read data in a variety of formats, and can display data from a web service, allowing users to "surf" through large data sets, downloading only those the parts of the data that are needed for display. The Multigraph XML format, or "MUGL" for short, provides a concise description of the visual properties of a graph, such as axes, plot styles, data sources, labels, etc, as well as interactivity properties such as how and whether the user can pan or zoom along each axis. Multigraph reads a file in this format, draws the described graph, and allows the user to interact with it. Multigraph software currently includes a Flash application for embedding graphs in web pages, a Flex component for embedding graphs in larger Flex/Flash applications, and a plugin for creating graphs in the WordPress content management system. Plans for the future include a Java version for desktop viewing and editing, a command line version for batch and server side rendering, and possibly Android and iPhone versions. Multigraph is currently in use on several web
Chordal Graphs are Fully Orientable
Lai, Hsin-Hao
2012-01-01
Suppose that D is an acyclic orientation of a graph G. An arc of D is called dependent if its reversal creates a directed cycle. Let m and M denote the minimum and the maximum of the number of dependent arcs over all acyclic orientations of G. We call G fully orientable if G has an acyclic orientation with exactly d dependent arcs for every d satisfying m <= d <= M. A graph G is called chordal if every cycle in G of length at least four has a chord. We show that all chordal graphs are fully orientable.
On Dominator Colorings in Graphs
Indian Academy of Sciences (India)
S Arumugam; Jay Bagga; K Raja Chandrasekar
2012-11-01
A dominator coloring of a graph is a proper coloring of in which every vertex dominates every vertex of at least one color class. The minimum number of colors required for a dominator coloring of is called the dominator chromatic number of and is denoted by $ d(G)$. In this paper we present several results on graphs with $ d(G)=(G)$ and $ d(G)=(G)$ where $(G)$ and $(G)$ denote respectively the chromatic number and the domination number of a graph . We also prove that if $(G)$ is the Mycielskian of , then $ d(G)+1≤ d((G))≤ d(G)+2$.
Cubature formulas on combinatorial graphs
Pesenson, Isaac Z
2011-01-01
Many contemporary applications, for example, cataloging of galaxies, document analysis, face recognition, learning theory, image processing, operate with a large amount of data which is often represented as a graph embedded into a high dimensional Euclidean space. The variety of problems arising in contemporary data processing requires development on graphs such topics of the classical harmonic analysis as Shannon sampling, splines, wavelets, cubature formulas. The goal of the paper is to establish cubature formulas on finite combinatorial graphs. The results have direct applications to problems that arise in connection with data filtering, data denoising and data dimension reduction.
Recursive processing of cyclic graphs.
Bianchini, Monica; Gori, Marco; Sarti, Lorenzo; Scarselli, Franco
2006-01-01
Recursive neural networks are a powerful tool for processing structured data. According to the recursive learning paradigm, the input information consists of directed positional acyclic graphs (DPAGs). In fact, recursive networks are fed following the partial order defined by the links of the graph. Unfortunately, the hypothesis of processing DPAGs is sometimes too restrictive, being the nature of some real-world problems intrinsically cyclic. In this paper, a methodology is proposed, which allows us to process any cyclic directed graph. Therefore, the computational power of recursive networks is definitely established, also clarifying the underlying limitations of the model.
Symmetry properties of subdivision graphs
Daneshkhah, Ashraf; Devillers, Alice; Praeger, Cheryl E.
2010-01-01
The subdivision graph $S(\\Sigma)$ of a graph $\\Sigma$ is obtained from $\\Sigma$ by `adding a vertex' in the middle of every edge of $\\Si$. Various symmetry properties of $\\S(\\Sigma)$ are studied. We prove that, for a connected graph $\\Sigma$, $S(\\Sigma)$ is locally $s$-arc transitive if and only if $\\Sigma$ is $\\lceil\\frac{s+1}{2}\\rceil$-arc transitive. The diameter of $S(\\Sigma)$ is $2d+\\delta$, where $\\Sigma$ has diameter $d$ and $0\\leqslant \\delta\\leqslant 2$, and local $s$-distance transi...
Bayesian theory and applications
Dellaportas, Petros; Polson, Nicholas G; Stephens, David A
2013-01-01
The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances in virtually all areas of applied and theoretical Bayesian statistics. This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field. The book has a unique format. There is an explanatory chapter devoted to each conceptual advance followed by journal-style chapters that provide applications or further advances on the concept. Thus, the volume is both a textbook and a compendium of papers covering a vast range of topics. It is appropriate for a well-informed novice interested in understanding the basic approach, methods and recent applications. Because of its advanced chapters and recent work, it is also appropriate for a more mature reader interested in recent applications and devel...
Modularity of tree-like and random regular graphs
McDiarmid, Colin
2016-01-01
Clustering algorithms for large networks typically use the modularity score to compare which partitions better represent modular structure in the data. Given a network, the modularity of a partition of the vertex set is a number in [0, 1) which measures the extent to which edge density is higher within parts than between parts; and the modularity of the network is the maximum modularity of any partition. We show that random cubic graphs usually have modularity in the interval (0.666, 0.804); and random r-regular graphs for large r usually have modularity ${\\Theta}(1/\\sqrt{r})$. Our results can give thresholds for the statistical significance of clustering found in large regular networks. The modularity of cycles and low degree trees is known to be asymptotically 1. We extend these results to all graphs whose product of treewidth and maximum degree is much less than the number of edges. This shows for example that random planar graphs typically have modularity close to 1.
Scale-free Graphs for General Aviation Flight Schedules
Alexandov, Natalia M. (Technical Monitor); Kincaid, Rex K.
2003-01-01
In the late 1990s a number of researchers noticed that networks in biology, sociology, and telecommunications exhibited similar characteristics unlike standard random networks. In particular, they found that the cummulative degree distributions of these graphs followed a power law rather than a binomial distribution and that their clustering coefficients tended to a nonzero constant as the number of nodes, n, became large rather than O(1/n). Moreover, these networks shared an important property with traditional random graphs as n becomes large the average shortest path length scales with log n. This latter property has been coined the small-world property. When taken together these three properties small-world, power law, and constant clustering coefficient describe what are now most commonly referred to as scale-free networks. Since 1997 at least six books and over 400 articles have been written about scale-free networks. In this manuscript an overview of the salient characteristics of scale-free networks. Computational experience will be provided for two mechanisms that grow (dynamic) scale-free graphs. Additional computational experience will be given for constructing (static) scale-free graphs via a tabu search optimization approach. Finally, a discussion of potential applications to general aviation networks is given.
Local dependence in random graph models: characterization, properties and statistical inference.
Schweinberger, Michael; Handcock, Mark S
2015-06-01
Dependent phenomena, such as relational, spatial and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-defined sense are dependent. In contrast with spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighbourhood structure in the sense that it is unknown which units are close and thus dependent. Owing to the challenge of characterizing local dependence and constructing random graph models with local dependence, many conventional exponential family random graph models induce strong dependence and are not amenable to statistical inference. We take first steps to characterize local dependence in random graph models, inspired by the notion of finite neighbourhoods in spatial statistics and M-dependence in time series, and we show that local dependence endows random graph models with desirable properties which make them amenable to statistical inference. We show that random graph models with local dependence satisfy a natural domain consistency condition which every model should satisfy, but conventional exponential family random graph models do not satisfy. In addition, we establish a central limit theorem for random graph models with local dependence, which suggests that random graph models with local dependence are amenable to statistical inference. We discuss how random graph models with local dependence can be constructed by exploiting either observed or unobserved neighbourhood structure. In the absence of observed neighbourhood structure, we take a Bayesian view and express the uncertainty about the neighbourhood structure by specifying a prior on a set of suitable neighbourhood structures. We present simulation results and applications to two real world networks with 'ground truth'.
BASE-9: Bayesian Analysis for Stellar Evolution with nine variables
Robinson, Elliot; von Hippel, Ted; Stein, Nathan; Stenning, David; Wagner-Kaiser, Rachel; Si, Shijing; van Dyk, David
2016-08-01
The BASE-9 (Bayesian Analysis for Stellar Evolution with nine variables) software suite recovers star cluster and stellar parameters from photometry and is useful for analyzing single-age, single-metallicity star clusters, binaries, or single stars, and for simulating such systems. BASE-9 uses a Markov chain Monte Carlo (MCMC) technique along with brute force numerical integration to estimate the posterior probability distribution for the age, metallicity, helium abundance, distance modulus, line-of-sight absorption, and parameters of the initial-final mass relation (IFMR) for a cluster, and for the primary mass, secondary mass (if a binary), and cluster probability for every potential cluster member. The MCMC technique is used for the cluster quantities (the first six items listed above) and numerical integration is used for the stellar quantities (the last three items in the above list).
Bayesian Analysis of Multiple Populations I: Statistical and Computational Methods
Stenning, D C; Robinson, E; van Dyk, D A; von Hippel, T; Sarajedini, A; Stein, N
2016-01-01
We develop a Bayesian model for globular clusters composed of multiple stellar populations, extending earlier statistical models for open clusters composed of simple (single) stellar populations (vanDyk et al. 2009, Stein et al. 2013). Specifically, we model globular clusters with two populations that differ in helium abundance. Our model assumes a hierarchical structuring of the parameters in which physical properties---age, metallicity, helium abundance, distance, absorption, and initial mass---are common to (i) the cluster as a whole or to (ii) individual populations within a cluster, or are unique to (iii) individual stars. An adaptive Markov chain Monte Carlo (MCMC) algorithm is devised for model fitting that greatly improves convergence relative to its precursor non-adaptive MCMC algorithm. Our model and computational tools are incorporated into an open-source software suite known as BASE-9. We use numerical studies to demonstrate that our method can recover parameters of two-population clusters, and al...
Content-Agnostic Malware Detection in Heterogeneous Malicious Distribution Graph
Alabdulmohsin, Ibrahim
2016-10-26
Malware detection has been widely studied by analysing either file dropping relationships or characteristics of the file distribution network. This paper, for the first time, studies a global heterogeneous malware delivery graph fusing file dropping relationship and the topology of the file distribution network. The integration offers a unique ability of structuring the end-to-end distribution relationship. However, it brings large heterogeneous graphs to analysis. In our study, an average daily generated graph has more than 4 million edges and 2.7 million nodes that differ in type, such as IPs, URLs, and files. We propose a novel Bayesian label propagation model to unify the multi-source information, including content-agnostic features of different node types and topological information of the heterogeneous network. Our approach does not need to examine the source codes nor inspect the dynamic behaviours of a binary. Instead, it estimates the maliciousness of a given file through a semi-supervised label propagation procedure, which has a linear time complexity w.r.t. the number of nodes and edges. The evaluation on 567 million real-world download events validates that our proposed approach efficiently detects malware with a high accuracy. © 2016 Copyright held by the owner/author(s).
Open Graphs and Computational Reasoning
Directory of Open Access Journals (Sweden)
Lucas Dixon
2010-06-01
Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.
Algorithms for Comparing Pedigree Graphs
Kirkpatrick, Bonnie; Finucane, Hilary; Jiang, Haitao; Zhu, Binhai; Karp, Richard M
2010-01-01
Pedigree graphs, which represent family relationships, are often constructed by collecting data from genealogical records to determine which pairs of people are parent and child. This process is expensive, and small mistakes in data collection--for example, one missing parent-child relationship--can cause large differences in the pedigree graphs created. In this paper, we introduce a simple pedigree definition based on a different type of data which is potentially easier to collect. This alternative characterization of a pedigree that describes a pedigree as a list of the descendants of each individual, rather than a list of parent-child relationships. We then introduce an algorithm that generates the pedigree graph from this list of descendants. We also consider the problem of comparing two pedigree graphs, which could be useful to evaluate the differences between pedigrees constructed via different methods. Specifically, this could be useful to evaluate pedigree reconstruction methods. We define the edit di...
Connectivity threshold for Bluetooth graphs
Broutin, Nicolas; Fraiman, Nicolas; Lugosi, Gábor
2011-01-01
We study the connectivity properties of random Bluetooth graphs that model certain "ad hoc" wireless networks. The graphs are obtained as "irrigation subgraphs" of the well-known random geometric graph model. There are two parameters that control the model: the radius $r$ that determines the "visible neighbors" of each node and the number of edges $c$ that each node is allowed to send to these. The randomness comes from the underlying distribution of data points in space and from the choices of each vertex. We prove that no connectivity can take place with high probability for a range of parameters $r, c$ and completely characterize the connectivity threshold (in $c$) for values of $r$ close the critical value for connectivity in the underlying random geometric graph.
Tree decompositions and social graphs
Adcock, Aaron B; Mahoney, Michael W
2014-01-01
Recent work has established that large informatics graphs such as social and information networks have non-trivial tree-like structure when viewed at moderate size scales. Here, we present results from the first detailed empirical evaluation of the use of tree decomposition (TD) heuristics for structure identification and extraction in social graphs. Although TDs have historically been used in structural graph theory and scientific computing, we show that---even with existing TD heuristics developed for those very different areas---TD methods can identify interesting structure in a wide range of realistic informatics graphs. Among other things, we show that TD methods can identify structures that correlate strongly with the core-periphery structure of realistic networks, even when using simple greedy heuristics; we show that the peripheral bags of these TDs correlate well with low-conductance communities (when they exist) found using local spectral computations; and we show that several types of large-scale "...
Baillie, C F; Kownacki, J P
1994-01-01
The Ising model on ``thin'' graphs (standard Feynman diagrams) displays several interesting properties. For ferromagnetic couplings there is a mean field phase transition at the corresponding Bethe lattice transition point. For antiferromagnetic couplings the replica trick gives some evidence for a spin glass phase. In this paper we investigate both the ferromagnetic and antiferromagnetic models with the aid of simulations. We confirm the Bethe lattice values of the critical points for the ferromagnetic model on \\phi^3 and \\phi^4 graphs and examine the putative spin glass phase in the antiferromagnetic model by looking at the overlap between replicas in a quenched ensemble of graphs. We also compare the Ising results with those for higher state Potts models and Ising models on ``fat'' graphs, such as those used in 2D gravity simulations.
Rank of Stably Dissipative Graphs
Duarte, Pedro
2011-01-01
For the class of stably dissipative Lotka-Volterra systems we prove that the rank of its defining matrix, which is the dimension of the associated invariant foliation, is completely determined by the system's graph.
Chordal Graphs and Semidefinite Optimization
DEFF Research Database (Denmark)
Vandenberghe, Lieven; Andersen, Martin Skovgaard
2015-01-01
in combinatorial optimization, linear algebra, statistics, signal processing, machine learning, and nonlinear optimization. This survey covers the theory and applications of chordal graphs, with an emphasis on algorithms developed in the literature on sparse Cholesky factorization. These algorithms are formulated......Chordal graphs play a central role in techniques for exploiting sparsity in large semidefinite optimization problems and in related con-vex optimization problems involving sparse positive semidefinite matrices. Chordal graph properties are also fundamental to several classical results...... as recursions on elimination trees, supernodal elimination trees, or clique trees associated with the graph. The best known example is the multifrontal Cholesky factorization algorithm, but similar algorithms can be formulated for a variety of related problems, including the computation of the partial inverse...
Exploration of Periodically Varying Graphs
Flocchini, Paola; Santoro, Nicola
2009-01-01
We study the computability and complexity of the exploration problem in a class of highly dynamic graphs: periodically varying (PV) graphs, where the edges exist only at some (unknown) times defined by the periodic movements of carriers. These graphs naturally model highly dynamic infrastructure-less networks such as public transports with fixed timetables, low earth orbiting (LEO) satellite systems, security guards' tours, etc. We establish necessary conditions for the problem to be solved. We also derive lower bounds on the amount of time required in general, as well as for the PV graphs defined by restricted classes of carriers movements: simple routes, and circular routes. We then prove that the limitations on computability and complexity we have established are indeed tight. In fact we prove that all necessary conditions are also sufficient and all lower bounds on costs are tight. We do so constructively presenting two worst case optimal solution algorithms, one for anonymous systems, and one for those w...
Digital Line Graph - Large Scale
U.S. Geological Survey, Department of the Interior — Digital line graph (DLG) data are digital representations of cartographic information. DLGs of map features are converted to digital form from maps and related...
Total Restrained Bondage in Graphs
Institute of Scientific and Technical Information of China (English)
Nader JAFARI RAD; Roslan HASNI; Joanna RACZEK; Lutz VOLKMANN
2013-01-01
A subset S of vertices of a graph G with no isolated vertex is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V(G)-S is also adjacent to a vertex in V(G)-S.The total restrained domination number of G is the minimum cardinality of a total restrained dominating set of G.In this paper we initiate the study of total restrained bondage in graphs.The total restrained bondage number in a graph G with no isolated vertex,is the minimum cardinality of a subset of edges E such that G-E has no isolated vertex and the total restrained domination number of G-E is greater than the total restrained domination number of G.We obtain several properties,exact values and bounds for the total restrained bondage number of a graph.
Special Issue on Graph Algorithms
2013-01-01
This special issue of Algorithms is devoted to the design and analysis of algorithms for solving combinatorial problems of a theoretical or practical nature involving graphs, with a focus on computational complexity.
Graph Model Based Indoor Tracking
DEFF Research Database (Denmark)
Jensen, Christian Søndergaard; Lu, Hua; Yang, Bin
2009-01-01
The tracking of the locations of moving objects in large indoor spaces is important, as it enables a range of applications related to, e.g., security and indoor navigation and guidance. This paper presents a graph model based approach to indoor tracking that offers a uniform data management...... infrastructure for different symbolic positioning technologies, e.g., Bluetooth and RFID. More specifically, the paper proposes a model of indoor space that comprises a base graph and mappings that represent the topology of indoor space at different levels. The resulting model can be used for one or several...... indoor positioning technologies. Focusing on RFID-based positioning, an RFID specific reader deployment graph model is built from the base graph model. This model is then used in several algorithms for constructing and refining trajectories from raw RFID readings. Empirical studies with implementations...
Graphs whose complement and square are isomorphic
DEFF Research Database (Denmark)
Milanic, M.; Pedersen, Anders Sune; Pellicer, D.;
2014-01-01
We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square...
Generalized wreath products of graphs and groups
Donno, Alfredo
2013-01-01
Inspired by the definition of generalized wreath product of permutation groups, we define the generalized wreath product of graphs, containing the classical Cartesian and wreath product of graphs as particular cases. We prove that the generalized wreath product of Cayley graphs of finite groups is the Cayley graph of the generalized wreath product of the corresponding groups.
Hard graphs for the maximum clique problem
Hoede, Cornelis
1988-01-01
The maximum clique problem is one of the NP-complete problems. There are graphs for which a reduction technique exists that transforms the problem for these graphs into one for graphs with specific properties in polynomial time. The resulting graphs do not grow exponentially in order and number. Gra
Some Graphs Containing Unique Hamiltonian Cycles
Lynch, Mark A. M.
2002-01-01
In this paper, two classes of graphs of arbitrary order are described which contain unique Hamiltonian cycles. All the graphs have mean vertex degree greater than one quarter the order of the graph. The Hamiltonian cycles are detailed, their uniqueness proved and simple rules for the construction of the adjacency matrix of the graphs are given.…
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
CUDA Enabled Graph Subset Examiner
Energy Technology Data Exchange (ETDEWEB)
2016-12-22
Finding Godsil-McKay switching sets in graphs is one way to demonstrate that a specific graph is not determined by its spectrum--the eigenvalues of its adjacency matrix. An important area of active research in pure mathematics is determining which graphs are determined by their spectra, i.e. when the spectrum of the adjacency matrix uniquely determines the underlying graph. We are interested in exploring the spectra of graphs in the Johnson scheme and specifically seek to determine which of these graphs are determined by their spectra. Given a graph G, a Godsil-McKay switching set is an induced subgraph H on 2k vertices with the following properties: I) H is regular, ii) every vertex in G/H is adjacent to either 0, k, or 2k vertices of H, and iii) at least one vertex in G/H is adjacent to k vertices in H. The software package examines each subset of a user specified size to determine whether or not it satisfies those 3 conditions. The software makes use of the massive parallel processing power of CUDA enabled GPUs. It also exploits the vertex transitivity of graphs in the Johnson scheme by reasoning that if G has a Godsil-McKay switching set, then it has a switching set which includes vertex 1. While the code (in its current state) is tuned to this specific problem, the method of examining each induced subgraph of G can be easily re-written to check for any user specified conditions on the subgraphs and can therefore be used much more broadly.
Fundamental cycles and graph embeddings
Institute of Scientific and Technical Information of China (English)
2009-01-01
In this paper, we investigate fundamental cycles in a graph G and their relations with graph embeddings. We show that a graph G may be embedded in an orientable surface with genus at least g if and only if for any spanning tree T , there exists a sequence of fundamental cycles C1, C2, . . . , C2g with C2i-1 ∩ C2i≠ф for 1≤ i ≤g. In particular, among β(G) fundamental cycles of any spanning tree T of a graph G, there are exactly 2γM (G) cycles C1, C2, . . . , C2γM (G) such that C2i-1 ∩ C2i≠ф for 1 ≤i≤γM (G), where β(G) and γM (G) are the Betti number and the maximum genus of G, respectively. This implies that it is possible to construct an orientable embedding with large genus of a graph G from an arbitrary spanning tree T (which may have very large number of odd components in G\\E(T )). This is different from the earlier work of Xuong and Liu, where spanning trees with small odd components are needed. In fact, this makes a common generalization of Xuong, Liu and Fu et al. Furthermore, we show that (1) this result is useful for locating the maximum genus of a graph having a specific edge-cut. Some known results for embedded graphs are also concluded; (2) the maximum genus problem may be reduced to the maximum matching problem. Based on this result and the algorithm of Micali-Vazirani, we present a new efficient algorithm to determine the maximum genus of a graph in O((β(G)) 25 ) steps. Our method is straight and quite different from the algorithm of Furst, Gross and McGeoch which depends on a result of Giles where matroid parity method is needed.
Localized endomorphisms of graph algebras
Conti, Roberto; Szymanski, Wojciech
2011-01-01
Endomorphisms of graph C*-algebras are investigated. A combinatorial approach to analysis of permutative endomorphisms is developed. Then invertibility criteria for localized endomorphisms are given. Furthermore, proper endomorphisms which restrict to automorphisms of the canonical diagonal MASA are analyzed. The Weyl group and the restricted Weyl group of a graph C*-algebra are introduced and investigated. Criteria of outerness for automorphisms in the restricted Weyl group are found.
A new algorithm for extracting a small representative subgraph from a very large graph
Sethu, Harish
2012-01-01
Many real-world networks are prohibitively large for data retrieval, storage and analysis of all of its nodes and links. Understanding the structure and dynamics of these networks entails creating a smaller representative sample of the full graph while preserving its relevant topological properties. In this report, we show that graph sampling algorithms currently proposed in the literature are not able to preserve network properties even with sample sizes containing as many as 20% of the nodes from the original graph. We present a new sampling algorithm, called Tiny Sample Extractor, with a new goal of a sample size smaller than 5% of the original graph while preserving two key properties of a network, the degree distribution and its clustering co-efficient. Our approach is based on a new empirical method of estimating measurement biases in crawling algorithms and compensating for them accordingly. We present a detailed comparison of best known graph sampling algorithms, focusing in particular on how the prop...
The Rank of Integral Circulant Graphs
Institute of Scientific and Technical Information of China (English)
ZHOU Hou-qing
2014-01-01
A graph is called an integral graph if it has an integral spectrum i.e., all eigen-values are integers. A graph is called circulant graph if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. The rank of a graph is defined to be the rank of its adjacency matrix. This importance of the rank, due to applications in physics, chemistry and combinatorics. In this paper, using Ramanujan sums, we study the rank of integral circulant graphs and gave some simple computational formulas for the rank and provide an example which shows the formula is sharp.
Cycle-maximal triangle-free graphs
DEFF Research Database (Denmark)
Durocher, Stephane; Gunderson, David S.; Li, Pak Ching
2015-01-01
Abstract We conjecture that the balanced complete bipartite graph K ⌊ n / 2 ⌋ , ⌈ n / 2 ⌉ contains more cycles than any other n -vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds...... on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and use the bounds to show that among regular graphs, the conjecture holds. We also consider graphs that are close to being regular, with the minimum and maximum degrees differing...
Color Energy Of A Unitary Cayley Graph
Directory of Open Access Journals (Sweden)
Adiga Chandrashekar
2014-11-01
Full Text Available Let G be a vertex colored graph. The minimum number χ(G of colors needed for coloring of a graph G is called the chromatic number. Recently, Adiga et al. [1] have introduced the concept of color energy of a graph Ec(G and computed the color energy of few families of graphs with χ(G colors. In this paper we derive explicit formulas for the color energies of the unitary Cayley graph Xn, the complement of the colored unitary Cayley graph (Xnc and some gcd-graphs.
Directory of Open Access Journals (Sweden)
Nilanjan De
2014-01-01
Full Text Available The connective eccentric index of a graph is a topological index involving degrees and eccentricities of vertices of the graph. In this paper, we have studied the connective eccentric index for double graph and double cover. Also we give the connective eccentric index for some graph operations such as joins, symmetric difference, disjunction, and splice of graphs.
Information Spreading in Dynamic Graphs
Clementi, Andrea; Trevisan, Luca
2011-01-01
We present a general approach to study the flooding time (a measure of how fast information spreads) in dynamic graphs (graphs whose topology changes with time according to a random process). We consider arbitrary converging Markovian dynamic graph process, that is, processes in which the topology of the graph at time $t$ depends only on its topology at time $t-1$ and which have a unique stationary distribution. The most well studied models of dynamic graphs are all Markovian and converging. Under general conditions, we bound the flooding time in terms of the mixing time of the dynamic graph process. We recover, as special cases of our result, bounds on the flooding time for the \\emph{random trip} model and the \\emph{random path} models; previous analysis techniques provided bounds only in restricted settings for such models. Our result also provides the first bound for the \\emph{random waypoint} model (which is tight for certain ranges of parameters) whose analysis had been an important open question.
Weak Total Resolvability In Graphs
Directory of Open Access Journals (Sweden)
Casel Katrin
2016-02-01
Full Text Available A vertex v ∈ V (G is said to distinguish two vertices x, y ∈ V (G of a graph G if the distance from v to x is di erent from the distance from v to y. A set W ⊆ V (G is a total resolving set for a graph G if for every pair of vertices x, y ∈ V (G, there exists some vertex w ∈ W − {x, y} which distinguishes x and y, while W is a weak total resolving set if for every x ∈ V (G−W and y ∈ W, there exists some w ∈ W −{y} which distinguishes x and y. A weak total resolving set of minimum cardinality is called a weak total metric basis of G and its cardinality the weak total metric dimension of G. Our main contributions are the following ones: (a Graphs with small and large weak total metric bases are characterised. (b We explore the (tight relation to independent 2-domination. (c We introduce a new graph parameter, called weak total adjacency dimension and present results that are analogous to those presented for weak total dimension. (d For trees, we derive a characterisation of the weak total (adjacency metric dimension. Also, exact figures for our parameters are presented for (generalised fans and wheels. (e We show that for Cartesian product graphs, the weak total (adjacency metric dimension is usually pretty small. (f The weak total (adjacency dimension is studied for lexicographic products of graphs.
On P-transitive graphs and applications
Directory of Open Access Journals (Sweden)
Giacomo Lenzi
2011-06-01
Full Text Available We introduce a new class of graphs which we call P-transitive graphs, lying between transitive and 3-transitive graphs. First we show that the analogue of de Jongh-Sambin Theorem is false for wellfounded P-transitive graphs; then we show that the mu-calculus fixpoint hierarchy is infinite for P-transitive graphs. Both results contrast with the case of transitive graphs. We give also an undecidability result for an enriched mu-calculus on P-transitive graphs. Finally, we consider a polynomial time reduction from the model checking problem on arbitrary graphs to the model checking problem on P-transitive graphs. All these results carry over to 3-transitive graphs.
Employing Power Graph Analysis to Facilitate Modeling Molecular Interaction Networks
Directory of Open Access Journals (Sweden)
Momchil Nenov
2015-04-01
Full Text Available Mathematical modeling is used to explore and understand complex systems ranging from weather patterns to social networks to gene-expression regulatory mechanisms. There is an upper limit to the amount of details that can be reflected in a model imposed by finite computational resources. Thus, there are methods to reduce the complexity of the modeled system to its most significant parameters. We discuss the suitability of clustering techniques, in particular Power Graph Analysis as an intermediate step of modeling.
The Clique Problem in Ray Intersection Graphs
Cabello, Sergio; Langerman, Stefan
2011-01-01
Ray intersection graphs are intersection graphs of rays, or halflines, in the plane. We show that any planar graph has an even subdivision whose complement is a ray intersection graph. The construction can be done in polynomial time and implies that finding a maximum clique in a segment intersection graph is NP-hard. This solves a 21-year old open problem posed by Kratochv\\'il and Ne\\v{s}et\\v{r}il.
Directory of Open Access Journals (Sweden)
Ullas Thomas
2015-07-01
Full Text Available This paper contains certain properties of set-magic graphs and obtained the set-magic number of certain classes of graphs. All spanning super graphs of a set-magic graph always set-magic and all cycles and Hamiltonian graphs are set-magic. Also set-magic number of any cycle of size 2n is always greater than n.
Ahmed, Faraz; Jin, Rong; Liu, Alex X.
2013-01-01
Online social networks are being increasingly used for analyzing various societal phenomena such as epidemiology, information dissemination, marketing and sentiment flow. Popular analysis techniques such as clustering and influential node analysis, require the computation of eigenvectors of the real graph's adjacency matrix. Recent de-anonymization attacks on Netflix and AOL datasets show that an open access to such graphs pose privacy threats. Among the various privacy preserving models, Dif...
DEFF Research Database (Denmark)
Hartelius, Karsten; Carstensen, Jens Michael
2003-01-01
A method for locating distorted grid structures in images is presented. The method is based on the theories of template matching and Bayesian image restoration. The grid is modeled as a deformable template. Prior knowledge of the grid is described through a Markov random field (MRF) model which...... nodes and the arc prior models variations in row and column spacing across the grid. Grid matching is done by placing an initial rough grid over the image and applying an ensemble annealing scheme to maximize the posterior distribution of the grid. The method can be applied to noisy images with missing...
Congdon, Peter
2014-01-01
This book provides an accessible approach to Bayesian computing and data analysis, with an emphasis on the interpretation of real data sets. Following in the tradition of the successful first edition, this book aims to make a wide range of statistical modeling applications accessible using tested code that can be readily adapted to the reader's own applications. The second edition has been thoroughly reworked and updated to take account of advances in the field. A new set of worked examples is included. The novel aspect of the first edition was the coverage of statistical modeling using WinBU
Bayesian nonparametric data analysis
Müller, Peter; Jara, Alejandro; Hanson, Tim
2015-01-01
This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in on-line software pages.
GraphMeta: Managing HPC Rich Metadata in Graphs
Energy Technology Data Exchange (ETDEWEB)
Dai, Dong; Chen, Yong; Carns, Philip; Jenkins, John; Zhang, Wei; Ross, Robert
2016-01-01
High-performance computing (HPC) systems face increasingly critical metadata management challenges, especially in the approaching exascale era. These challenges arise not only from exploding metadata volumes, but also from increasingly diverse metadata, which contains data provenance and arbitrary user-defined attributes in addition to traditional POSIX metadata. This ‘rich’ metadata is becoming critical to supporting advanced data management functionality such as data auditing and validation. In our prior work, we identified a graph-based model as a promising solution to uniformly manage HPC rich metadata due to its flexibility and generality. However, at the same time, graph-based HPC rich metadata anagement also introduces significant challenges to the underlying infrastructure. In this study, we first identify the challenges on the underlying infrastructure to support scalable, high-performance rich metadata management. Based on that, we introduce GraphMeta, a graphbased engine designed for this use case. It achieves performance scalability by introducing a new graph partitioning algorithm and a write-optimal storage engine. We evaluate GraphMeta under both synthetic and real HPC metadata workloads, compare it with other approaches, and demonstrate its advantages in terms of efficiency and usability for rich metadata management in HPC systems.
Private Graphs - Access Rights on Graphs for Seamless Navigation
Dorner, W.; Hau, F.; Pagany, R.
2016-06-01
After the success of GNSS (Global Navigational Satellite Systems) and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS - Real Time Locating Services (e.g. WIFI) and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites), but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.
Roman domination in Cartesian product graphs and strong product graphs
Yero, Ismael G
2011-01-01
A set $S$ of vertices of a graph $G$ is a dominating set for $G$ if every vertex outside of $S$ is adjacent to at least one vertex belonging to $S$. The minimum cardinality of a dominating set for $G$ is called the domination number of $G$. A map $f : V \\rightarrow \\{0, 1, 2\\}$ is a Roman dominating function on a graph $G$ if for every vertex $v$ with $f(v) = 0$, there exists a vertex $u$, adjacent to $v$, such that $f(u) = 2$. The weight of a Roman dominating function is given by $f(V) =\\sum_{u\\in V}f(u)$. The minimum weight of a Roman dominating function on $G$ is called the Roman domination number of $G$. In this article we study the Roman domination number of Cartesian product graphs and strong product graphs. More precisely, we study the relationships between the Roman domination number of product graphs and the (Roman) domination number of the factors.
Complexity of Cocktail Party Graph and Crown Graph
Directory of Open Access Journals (Sweden)
S. N. Daoud
2012-01-01
Full Text Available Problem statement: The number of spanning trees τ(G in graphs (networks was an important invariant. Approach: Using the properties of the Chebyshev polynomials of the second kind and the linear algebra techniques to evaluate the associated determinants. Results: The complexity, number of spanning trees, of the cocktail party graph on 2n vertices, given in detail in the text was proved. Also the complexity of the crown graph on 2n vertices was shown to had the value nn-2 (n-1 (n-2n-1. Conclusion: The number of spanning trees τ(G in graphs (networks is an important invariant. The evaluation of this number and analyzing its behavior is not only interesting from a mathematical (computational perspective, but also, it is an important measure of reliability of a network and designing electrical circuits. Some computationally hard problems such as the travelling salesman problem can be solved approximately by using spanning trees. Due to the high dependence of the network design and reliability on the graph theory we introduced the above important theorems and lemmas and their proofs.
Subvoxel accurate graph search using non-Euclidean graph space.
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Michael D Abràmoff
Full Text Available Graph search is attractive for the quantitative analysis of volumetric medical images, and especially for layered tissues, because it allows globally optimal solutions in low-order polynomial time. However, because nodes of graphs typically encode evenly distributed voxels of the volume with arcs connecting orthogonally sampled voxels in Euclidean space, segmentation cannot achieve greater precision than a single unit, i.e. the distance between two adjoining nodes, and partial volume effects are ignored. We generalize the graph to non-Euclidean space by allowing non-equidistant spacing between nodes, so that subvoxel accurate segmentation is achievable. Because the number of nodes and edges in the graph remains the same, running time and memory use are similar, while all the advantages of graph search, including global optimality and computational efficiency, are retained. A deformation field calculated from the volume data adaptively changes regional node density so that node density varies with the inverse of the expected cost. We validated our approach using optical coherence tomography (OCT images of the retina and 3-D MR of the arterial wall, and achieved statistically significant increased accuracy. Our approach allows improved accuracy in volume data acquired with the same hardware, and also, preserved accuracy with lower resolution, more cost-effective, image acquisition equipment. The method is not limited to any specific imaging modality and readily extensible to higher dimensions.
PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION
Directory of Open Access Journals (Sweden)
W. Dorner
2016-06-01
Full Text Available After the success of GNSS (Global Navigational Satellite Systems and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS – Real Time Locating Services (e.g. WIFI and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites, but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.
Classification using Bayesian neural nets
J.C. Bioch (Cor); O. van der Meer; R. Potharst (Rob)
1995-01-01
textabstractRecently, Bayesian methods have been proposed for neural networks to solve regression and classification problems. These methods claim to overcome some difficulties encountered in the standard approach such as overfitting. However, an implementation of the full Bayesian approach to neura
Bayesian Intersubjectivity and Quantum Theory
Pérez-Suárez, Marcos; Santos, David J.
2005-02-01
Two of the major approaches to probability, namely, frequentism and (subjectivistic) Bayesian theory, are discussed, together with the replacement of frequentist objectivity for Bayesian intersubjectivity. This discussion is then expanded to Quantum Theory, as quantum states and operations can be seen as structural elements of a subjective nature.
Bayesian Approach for Inconsistent Information.
Stein, M; Beer, M; Kreinovich, V
2013-10-01
In engineering situations, we usually have a large amount of prior knowledge that needs to be taken into account when processing data. Traditionally, the Bayesian approach is used to process data in the presence of prior knowledge. Sometimes, when we apply the traditional Bayesian techniques to engineering data, we get inconsistencies between the data and prior knowledge. These inconsistencies are usually caused by the fact that in the traditional approach, we assume that we know the exact sample values, that the prior distribution is exactly known, etc. In reality, the data is imprecise due to measurement errors, the prior knowledge is only approximately known, etc. So, a natural way to deal with the seemingly inconsistent information is to take this imprecision into account in the Bayesian approach - e.g., by using fuzzy techniques. In this paper, we describe several possible scenarios for fuzzifying the Bayesian approach. Particular attention is paid to the interaction between the estimated imprecise parameters. In this paper, to implement the corresponding fuzzy versions of the Bayesian formulas, we use straightforward computations of the related expression - which makes our computations reasonably time-consuming. Computations in the traditional (non-fuzzy) Bayesian approach are much faster - because they use algorithmically efficient reformulations of the Bayesian formulas. We expect that similar reformulations of the fuzzy Bayesian formulas will also drastically decrease the computation time and thus, enhance the practical use of the proposed methods.
Inference in hybrid Bayesian networks
DEFF Research Database (Denmark)
Lanseth, Helge; Nielsen, Thomas Dyhre; Rumí, Rafael
2009-01-01
Since the 1980s, Bayesian Networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability-techniques (like fault trees...... decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability....
Searching chemical space with the Bayesian Idea Generator.
van Hoorn, Willem P; Bell, Andrew S
2009-10-01
The Pfizer Global Virtual Library (PGVL) is defined as a set compounds that could be synthesized using validated protocols and monomers. However, it is too large (10(12) compounds) to search by brute-force methods for close analogues of a given input structure. In this paper the Bayesian Idea Generator is described which is based on a novel application of Bayesian statistics to narrow down the search space to a prioritized set of existing library arrays (the default is 16). For each of these libraries the 6 closest neighbors are retrieved from the existing compound file, resulting in a screenable hypothesis of 96 compounds. Using the Bayesian models for library space, the Pfizer file of singleton compounds has been mapped to library space and is optionally searched as well. The method is >99% accurate in retrieving known library provenance from an independent test set. The compounds retrieved strike a balance between similarity and diversity resulting in frequent scaffold hops. Four examples of how the Bayesian Idea Generator has been successfully used in drug discovery are provided. The methodology of the Bayesian Idea Generator can be used for any collection of compounds containing distinct clusters, and an example using compound vendor catalogues has been included.
Bayesian Inference on Gravitational Waves
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Asad Ali
2015-12-01
Full Text Available The Bayesian approach is increasingly becoming popular among the astrophysics data analysis communities. However, the Pakistan statistics communities are unaware of this fertile interaction between the two disciplines. Bayesian methods have been in use to address astronomical problems since the very birth of the Bayes probability in eighteenth century. Today the Bayesian methods for the detection and parameter estimation of gravitational waves have solid theoretical grounds with a strong promise for the realistic applications. This article aims to introduce the Pakistan statistics communities to the applications of Bayesian Monte Carlo methods in the analysis of gravitational wave data with an overview of the Bayesian signal detection and estimation methods and demonstration by a couple of simplified examples.
Graph-based interpretation of the Molecular Interstellar Medium Segmentation
Colombo, Dario; Ginsburg, Adam; Duarte-Cabral, Ana; Hughes, Annie
2015-01-01
We present a generalization of the Giant Molecular Cloud (GMC) identification problem based on cluster analysis. The method we designed, SCIMES (Spectral Clustering for Interstellar Molecular Emission Segmentation) considers the dendrogram of emission in the broader framework of graph theory and utilizes spectral clustering to find discrete regions with similar emission properties. For Galactic molecular cloud structures, we show that the characteristic volume and/or integrated CO luminosity are useful criteria to define the clustering, yielding emission structures that closely reproduce "by-eye" identification results. SCIMES performs best on well-resolved, high-resolution data, making it complementary to other available algorithms. Using 12CO(1-0) data for the Orion-Monoceros complex, we demonstrate that SCIMES provides robust results against changes of the dendrogram-construction parameters, noise realizations and degraded resolution. By comparing SCIMES with other cloud decomposition approaches, we show t...
Kirchoff Index of Graphs and some Graph Operations
Indian Academy of Sciences (India)
A Nikseresht; Z Sepasdar; M H Shirdareh-Haghighi
2014-08-01
Let be a rooted tree, a connected graph, $x,y\\in V(G)$ be fixed and $G_i$’s be $|V(T)|$ disjoint copies of with $x_i$ and $y_i$ denoting the corresponding copies of and in $G_i$, respectively. We define the -repetition of to be the graph obtained by joining $y_i$ to $x_j$ for each $i\\in V(T)$ and each child of . In this paper, we compute the Kirchhoff index of the -repetition of in terms of parameters of and . Also we study how $Kf(G)$ behaves under some graph operations such as joining vertices or subdividing edges.
Approximate Bayesian computation.
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Mikael Sunnåker
Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.
The monadic second-order logic of graphs XVI : Canonical graph
decompositions
Courcelle, Bruno
2005-01-01
This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more general result covering canonical graph decompositions like the modular decomposition and the Tutte decomposition of 2-connected graphs into 3-connected components. As an application, we prove that the set of graphs having the same cycle matroid as a given 2-connected graph can be defined from this graph by Monadic Se...
A structural analysis of the A5/1 state transition graph
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Andreas Beckmann
2012-10-01
Full Text Available We describe efficient algorithms to analyze the cycle structure of the graph induced by the state transition function of the A5/1 stream cipher used in GSM mobile phones and report on the results of the implementation. The analysis is performed in five steps utilizing HPC clusters, GPGPU and external memory computation. A great reduction of this huge state transition graph of 2^64 nodes is achieved by focusing on special nodes in the first step and removing leaf nodes that can be detected with limited effort in the second step. This step does not break the overall structure of the graph and keeps at least one node on every cycle. In the third step the nodes of the reduced graph are connected by weighted edges. Since the number of nodes is still huge an efficient bitslice approach is presented that is implemented with NVIDIA's CUDA framework and executed on several GPUs concurrently. An external memory algorithm based on the STXXL library and its parallel pipelining feature further reduces the graph in the fourth step. The result is a graph containing only cycles that can be further analyzed in internal memory to count the number and size of the cycles. This full analysis which previously would take months can now be completed within a few days and allows to present structural results for the full graph for the first time. The structure of the A5/1 graph deviates notably from the theoretical results for random mappings.
Graph theoretic metrics for spectral imagery with application to change detection
Albano, James A.; Messinger, David W.; Schlamm, Ariel; Basener, William
2011-06-01
Many spectral algorithms that are routinely applied to spectral imagery are based on the following models: statistical, linear mixture, and linear subspace. As a result, assumptions are made about the underlying distribution of the data such as multivariate normality or other geometric restrictions. Here we present a graph based model for spectral data that avoids these restrictive assumptions and apply graph based metrics to quantify certain aspects of the resulting graph. The construction of the spectral graph begins by connecting each pixel to its k-nearest neighbors with an undirected weighted edge. The weight of each edge corresponds to the spectral Euclidean distance between the adjacent pixels. The number of nearest neighbors, k, is chosen such that the graph is connected i.e., there is a path from each pixel xi to every other. This requirement ensures the existence of inter-cluster connections which will prove vital for our application to change detection. Once the graph is constructed, we calculate a metric called the Normalized Edge Volume (NEV) that describes the internal structural volume based on the vertex connectivity and weighted edges of the graph. Finally, we demonstrate a graph based change detection method that applies this metric.
On $k$-connectivity and minimum vertex degree in random $s$-intersection graphs
Zhao, Jun; Gligor, Virgil
2014-01-01
Random s-intersection graphs have recently received much interest [1-9]. In a random s-intersection graph, each vertex is assigned to a set of items in some manner, and two vertices have an edge in between if and only if they share at least s items. In particular, in a uniform random s-intersection graph, each vertex independently selects the same number of items uniformly at random from a common item pool, while in a binomial random s-intersection graph, each item in some item pool is independently attached to each vertex with the same probability. These two graph models have numerous applications; e.g., using uniform random s-intersection graph for cryptanalysis [14,15], and to model secure wireless sensor networks [8-10] and online social networks [11,12], and using a binomial random s-intersection graph for clustering analysis [17], classification [18] and the design of integrated circuits [34]. For binomial/uniform random s-intersection graphs, we present results related to k-connectivity and minimum ver...
Time-dependence of graph theory metrics in functional connectivity analysis.
Chiang, Sharon; Cassese, Alberto; Guindani, Michele; Vannucci, Marina; Yeh, Hsiang J; Haneef, Zulfi; Stern, John M
2016-01-15
Brain graphs provide a useful way to computationally model the network structure of the connectome, and this has led to increasing interest in the use of graph theory to quantitate and investigate the topological characteristics of the healthy brain and brain disorders on the network level. The majority of graph theory investigations of functional connectivity have relied on the assumption of temporal stationarity. However, recent evidence increasingly suggests that functional connectivity fluctuates over the length of the scan. In this study, we investigate the stationarity of brain network topology using a Bayesian hidden Markov model (HMM) approach that estimates the dynamic structure of graph theoretical measures of whole-brain functional connectivity. In addition to extracting the stationary distribution and transition probabilities of commonly employed graph theory measures, we propose two estimators of temporal stationarity: the S-index and N-index. These indexes can be used to quantify different aspects of the temporal stationarity of graph theory measures. We apply the method and proposed estimators to resting-state functional MRI data from healthy controls and patients with temporal lobe epilepsy. Our analysis shows that several graph theory measures, including small-world index, global integration measures, and betweenness centrality, may exhibit greater stationarity over time and therefore be more robust. Additionally, we demonstrate that accounting for subject-level differences in the level of temporal stationarity of network topology may increase discriminatory power in discriminating between disease states. Our results confirm and extend findings from other studies regarding the dynamic nature of functional connectivity, and suggest that using statistical models which explicitly account for the dynamic nature of functional connectivity in graph theory analyses may improve the sensitivity of investigations and consistency across investigations.
Single-subject grey matter graphs in Alzheimer's disease.
Tijms, Betty M; Möller, Christiane; Vrenken, Hugo; Wink, Alle Meije; de Haan, Willem; van der Flier, Wiesje M; Stam, Cornelis J; Scheltens, Philip; Barkhof, Frederik
2013-01-01
Coordinated patterns of cortical morphology have been described as structural graphs and previous research has demonstrated that properties of such graphs are altered in Alzheimer's disease (AD). However, it remains unknown how these alterations are related to cognitive deficits in individuals, as such graphs are restricted to group-level analysis. In the present study we investigated this question in single-subject grey matter networks. This new method extracts large-scale structural graphs where nodes represent small cortical regions that are connected by edges when they show statistical similarity. Using this method, unweighted and undirected networks were extracted from T1 weighted structural magnetic resonance imaging scans of 38 AD patients (19 female, average age 72±4 years) and 38 controls (19 females, average age 72±4 years). Group comparisons of standard graph properties were performed after correcting for grey matter volumetric measurements and were correlated to scores of general cognitive functioning. AD networks were characterised by a more random topology as indicated by a decreased small world coefficient (p = 3.53×10(-5)), decreased normalized clustering coefficient (p = 7.25×10(-6)) and decreased normalized path length (p = 1.91×10(-7)). Reduced normalized path length explained significantly (p = 0.004) more variance in measurements of general cognitive decline (32%) in comparison to volumetric measurements (9%). Altered path length of the parahippocampal gyrus, hippocampus, fusiform gyrus and precuneus showed the strongest relationship with cognitive decline. The present results suggest that single-subject grey matter graphs provide a concise quantification of cortical structure that has clinical value, which might be of particular importance for disease prognosis. These findings contribute to a better understanding of structural alterations and cognitive dysfunction in AD.
Cluster networks and Bruhat-Tits buildings
Kozyrev, S. V.
2014-08-01
We consider a clustering procedure in the case where a family of metrics is used instead of a fixed metric. In this case, a classification network (a directed acyclic graph with nondirected cycles) is obtained instead of a classification tree. We discuss the relation to Bruhat-Tits buildings and introduce the notion of the dimension of a general cluster network.
The competition numbers of ternary Hamming graphs
Park, Boram
2010-01-01
The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x,v) and (y,v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of important research problems in the study of competition graphs to characterize a graph by its competition number. In this paper, we give the exact values of the competition numbers of ternary Hamming graphs.