analysis of singular systems using orthogonal functions the use of orthogonal functions to analyze singular systems is investigated it is shown that the differential algebraic system equation may be converted to an algebraic generalized lyapunov equation that can be solved for the coefficients of x t in terms of the orthogonal basis functions this generalized lyapunov equation may be considered as a discrete equation on the slow subspace of the system and as a continuous equation on its fast subspace necessary and sufficient conditions for the existence of a unique solution are given in terms of the relative spectrum of the system a generalized bartels stewart algorithm based on the qz algorithm is presented for its efficient solution relations are drawn with the invariant subspaces of the system

community detection algorithms a comparative analysis uncovering the community structure exhibited by real networks is a crucial step toward an understanding of complex systems that goes beyond the local organization of their constituents many algorithms have been proposed so far but none of them has been subjected to strict tests to evaluate their performance most of the sporadic tests performed so far involved small networks with known community structure and or artificial graphs with a simplified structure which is very uncommon in real systems here we test several methods against a recently introduced class of benchmark graphs with heterogeneous distributions of degree and community size the methods are also tested against the benchmark by girvan and newman proc natl acad sci u s a 99 7821 2002 and on random graphs as a result of our analysis three recent algorithms introduced by rosvall and bergstrom proc natl acad sci u s a 104 7327 2007 proc natl acad sci u s a 105 1118 2008 blondel et al j stat mech theory exp 2008 p10008 and ronhovde and nussinov phys rev e 80 016109 2009 have an excellent performance with the additional advantage of low computational complexity which enables one to analyze large systems

model comparison of coordinate free multivariate skewed distributions with an application to stochastic frontiers we consider classes of multivariate distributions which can model skewness and are closed under orthogonal transformations we review two classes of such distributions proposed in the literature and focus our attention on a particular yet quite flexible subclass of one of these classes members of this subclass are defined by affine transformations of univariate skewed distributions that ensure the existence of a set of coordinate axes along which there is independence and the marginals are known analytically the choice of an appropriate m dimensional skewed distribution is then restricted to the simpler problem of choosing m univariate skewed distributions we introduce a bayesian model comparison setup for selection of these univariate skewed distributions the analysis does not rely on the existence of moments allowing for any tail behaviour and uses equivalent priors on the common characteristics of the different models finally we apply this framework to multi output stochastic frontiers using data from dutch dairy farms

a constructive representation of univariate skewed distributions we introduce a general perspective on the introduction of skewness into symmetric distributions through inverse probability integral transformations we provide a constructive representation of skewed distributions where the skewing mechanism and the original symmetric distributions are specified separately we study the effects of the skewing mechanism on e g modality tail behavior and the amount of skewness generated the representation is used to introduce novel classes of skewed distributions where we induce certain prespecified characteristics through particular choices of the skewing mechanism finally we use a bayesian linear regression framework to compare the new classes with some existing distributions in the context of two empirical examples

the multivariate skew normal distribution summary the paper extends earlier work on the so called skew normal distribution a family of distributions including the normal but with an extra parameter to regulate skewness the present work introduces a multivariate parametric family such that the marginal densities are scalar skew normal and studies its properties with special emphasis on the bivariate case

statistical mechanics of community detection starting from a general ansatz we show how community detection can be interpreted as finding the ground state of an infinite range spin glass our approach applies to weighted and directed networks alike it contains the ad hoc introduced quality function from j reichardt and s bornholdt phys rev lett 93 218701 2004 and the modularity q as defined by newman and girvan phys rev e 69 026113 2004 as special cases the community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices we elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study further we show how hierarchies and overlap in the community structure can be detected computationally efficient local update rules for optimization procedures to find the ground state are given we show how the ansatz may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension finally we give expectation values for the modularity of random graphs which can be used in the assessment of statistical significance of community structure

complex network based time series analysis abstract recent works show that complex network theory may be a powerful tool in time series analysis we propose in this paper a reliable procedure for constructing complex networks from the correlation matrix of a time series an original stock time series the corresponding return series and its amplitude series are considered the degree distribution of the original series can be well fitted with a power law while that of the return series can be well fitted with a gaussian function the degree distribution of the amplitude series contains two asymmetric gaussian branches reconstruction of networks from time series is a common problem in diverse research the proposed strategy may be a reasonable solution to this problem

the intrinsic bayes factor for model selection and prediction abstract in the bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions it is typically not possible to utilize standard noninformative or default prior distributions this has led bayesians to use conventional proper prior distributions or crude approximations to bayes factors in this article we introduce a new criterion called the intrinsic bayes factor which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual bayes factors the criterion can be used for nested or nonnested models and for multiple model comparison and prediction from another perspective the development suggests a general definition of a reference prior for model comparison

time series clustering via community detection in networks in this paper we propose a technique for time series clustering using community detection in complex networks firstly we present a method to transform a set of time series into a network using different distance functions where each time series is represented by a vertex and the most similar ones are connected then we apply community detection algorithms to identify groups of strongly connected vertices called a community and consequently identify time series clusters still in this paper we make a comprehensive analysis on the influence of various combinations of time series distance functions network generation methods and community detection techniques on clustering results experimental study shows that the proposed network based approach achieves better results than various classic or up to date clustering techniques under consideration statistical tests confirm that the proposed method outperforms some classic clustering algorithms such as k medoids diana median linkage and centroid linkage in various data sets interestingly the proposed method can effectively detect shape patterns presented in time series due to the topological structure of the underlying network constructed in the clustering process at the same time other techniques fail to identify such patterns moreover the proposed method is robust enough to group time series presenting similar pattern but with time shifts and or amplitude variations in summary the main point of the proposed method is the transformation of time series from time space domain to topological domain therefore we hope that our approach contributes not only for time series clustering but also for general time series analysis tasks

benchmark graphs for testing community detection algorithms community structure is one of the most important features of real networks and reveals the internal organization of the nodes many algorithms have been proposed but the crucial issue of testing i e the question of how good an algorithm is with respect to others is still open standard tests include the analysis of simple artificial graphs with a built in community structure that the algorithm has to recover however the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks here we introduce a class of benchmark graphs that account for the heterogeneity in the distributions of node degrees and of community sizes we use this benchmark to test two popular methods of community detection modularity optimization and potts model clustering the results show that the benchmark poses a much more severe test to algorithms than standard benchmarks revealing limits that may not be apparent at a first analysis

global renyi index of the distance matrix abstract in previous studies the heterogeneity of complex networks has been extensively studied in our study the heterogeneity of distance matrices is studied based on the renyi index of networks we define a new metric and name it global renyi index g r i and prove several properties in particular the g r i value of the distance matrix corresponding to the evenly distributed point set in the euclidean space is zero some model data were used to clarify the geometric meanings of g r i and then we studied the g r i value of financial data the results show that the g r i value in the real market changes drastically and is significantly different from the g r i value of the model generated data these results suggest that the proposed concept g r i is meaningful to the study distance matrix and provides a new perspective based on the network

a bayesian analysis of multiple output production frontiers in this paper we develop bayesian tools for estimating multi output production frontiers in applications where only input and output data are available firm specific inefficiency is measured relative to such frontiers our work has important differences from the existing literature which either assumes a classical econometric perspective with restrictive functional form assumptions or a non stochastic approach which directly estimates the output distance function bayesian inference is implemented using a markov chain monte carlo algorithm a banking application shows the ease and practicality of our approach

a stabilization criterion for matrix pencils under bilinear transformation abstract in the literature the dual matrix pencils sf g and f s g are identified with the homogeneous pencil sf s g in the present paper for a given a homogeneous pencil which is unstable in the sense that it has roots in the closed right half plane a bilinear transformation is determined such that the new homogeneous bilinear equivalent matrix pencil is stable the notion of bilinear equivalence is introduced and a stabilization criterion of a homogeneous matrix pencil is finally derived

riemannian manifold learning recently manifold learning has been widely exploited in pattern recognition data analysis and machine learning this paper presents a novel framework called riemannian manifold learning rml based on the assumption that the input high dimensional data lie on an intrinsically low dimensional riemannian manifold the main idea is to formulate the dimensionality reduction problem as a classical problem in riemannian geometry that is how to construct coordinate charts for a given riemannian manifold we implement the riemannian normal coordinate chart which has been the most widely used in riemannian geometry for a set of unorganized data points first two input parameters the neighborhood size k and the intrinsic dimension d are estimated based on an efficient simplicial reconstruction of the underlying manifold then the normal coordinates are computed to map the input high dimensional data into a low dimensional space experiments on synthetic data as well as real world images demonstrate that our algorithm can learn intrinsic geometric structures of the data preserve radial geodesic distances and yield regular embeddings

evolution of worldwide stock markets correlation structure and correlation based graphs we investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period january 1996 to july 2009 we discover that the correlation among market indices presents both a fast and a slow dynamics the slow dynamics reflects the development and consolidation of globalization the fast dynamics is associated with critical events that originate in a specific country or region of the world and rapidly affect the global system we provide evidence that the short term time scale of correlation among market indices is less than 3 trading months about 60 trading days the average values of the nondiagonal elements of the correlation matrix correlation based graphs and the spectral properties of the largest eigenvalues and eigenvectors of the correlation matrix are carrying information about the fast and slow dynamics of the correlation of market indices we introduce a measure of mutual information based on link co occurrence in networks in order to detect the fast dynamics of successive changes of correlation based graphs in a quantitative way

constructing a homogeneous lti descriptor system with desired properties using perturbation theory in the literature regarding linear systems and mathematical control theory several different techniques have been developed for obtaining the solution of homogeneous linear time invariant lti descriptor differential systems in this article applying the complex weierstrass canonical form we investigate the conditions under which a descriptor system with a specific structure and desired properties is being constructed using perturbation theory our approach is very general and as an example a stable homogeneous lti descriptor system is designed thus a proportional and derivative controller can be used such as the case where a family of perturbed pencils is defined and the solutions of the initial and the relative perturbed systems are close with respect to a frobenius distance a step algorithm and an illustrative example are also presented to illustrate the results of this article

hessian eigenmaps locally linear embedding techniques for high dimensional data we describe a method for recovering the underlying parametrization of scattered data m i lying on a manifold m embedded in high dimensional euclidean space the method hessian based locally linear embedding derives from a conceptual framework of local isometry in which the manifold m viewed as a riemannian submanifold of the ambient euclidean space r n is locally isometric to an open connected subset of euclidean space r d because does not have to be convex this framework is able to handle a significantly wider class of situations than the original isomap algorithm the theoretical framework revolves around a quadratic form h f m h f m f dm defined on functions f m r here hf denotes the hessian of f and h f averages the frobenius norm of the hessian over m to define the hessian we use orthogonal coordinates on the tangent planes of m the key observation is that if m truly is locally isometric to an open connected subset of r d then h f has a d 1 dimensional null space consisting of the constant functions and a d dimensional space of functions spanned by the original isometric coordinates hence the isometric coordinates can be recovered up to a linear isometry our method may be viewed as a modification of locally linear embedding and our theoretical framework as a modification of the laplacian eigenmaps framework where we substitute a quadratic form based on the hessian in place of one based on the laplacian

local resolution limit free potts model for community detection we report on an exceptionally accurate spin glass type potts model for community detection with a simple algorithm we find that our approach is at least as accurate as the best currently available algorithms and robust to the effects of noise it is also competitive with the best currently available algorithms in terms of speed and size of solvable systems we find that the computational demand often exhibits superlinear scaling o l 1 3 where l is the number of edges in the system and we have applied the algorithm to synthetic systems as large as 40 ifmmode times else texttimes fi 10 6 nodes and over 1 ifmmode times else texttimes fi 10 9 edges a previous stumbling block encountered by popular community detection methods is the so called resolution limit being a local measure of community structure our potts model is free from this resolution limit effect and it further remains a local measure on weighted and directed graphs we also address the mitigation of resolution limit effects for two other popular potts models

on bayesian modeling of fat tails and skewness abstract we consider a bayesian analysis of linear regression models that can account for skewed error distributions with fat tails the latter two features are often observed characteristics of empirical datasets and we formally incorporate them in the inferential process a general procedure for introducing skewness into symmetric distributions is first proposed even though this allows for a great deal of flexibility in distributional shape tail behavior is not affected applying this skewness procedure to a student t distribution we generate a skewed student distribution which displays both flexible tails and possible skewness each entirely controlled by a separate scalar parameter the linear regression model with a skewed student error term is the main focus of the article we first characterize existence of the posterior distribution and its moments using standard improper priors and allowing for inference on skewness and tail parameters for posterior inference with this model we suggest

stochastic frontier models a bayesian perspective abstract a bayesian approach to estimation prediction and model comparison in composed error production models is presented a broad range of distributions on the inefficiency term define the contending models which can either be treated separately or pooled posterior results are derived for the individual efficiences as well as for the parameters and the differences with the usual sampling theory approach are highlighted the required numerical integrations are handled by monte carlo methods with importance sampling and an empirical example illustrates the procedures

approximate bayesian inference with the weighted likelihood bootstrap we introduce the weighted likelihood bootstrap wlb as a way to simulate approximately from a posterior distribution this method is often easy to implement requiring only an algorithm for calculating the maximum likelihood estimator such as iteratively reweighted least squares in the generic weighting scheme the wlb is first order correct under quite general conditions inaccuracies can be removed by using the wlb as a source of samples in the sampling importance resampling sir algorithm which also allows incorporation of particular prior information the sir adjusted wlb can be a competitive alternative to other integration methods in certain models asymptotic expansions elucidate the second order properties of the wlb which is a generalization of rubin s bayesian bootstrap the calculation of approximate bayes factors for model comparison is also considered we note that given a sample simulated from the posterior distribution the required marginal likelihood may be simulation consistently estimated by the harmonic mean of the associated likelihood values a modification of this estimator that avoids instability is also noted these methods provide simple ways of calculating approximate bayes factors and posterior model probabilities for a very wide class of models

finding community structure in very large networks the discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community but most methods proposed so far are unsuitable for very large networks because of their computational cost here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms its running time on a network with n vertices and m edges is o md phantom rule 0 2em 0ex mathrm log phantom rule 0 2em 0ex n where d is the depth of the dendrogram describing the community structure many real world networks are sparse and hierarchical with m ensuremath sim n and d ensuremath sim mathrm log phantom rule 0 2em 0ex n in which case our algorithm runs in essentially linear time o n phantom rule 0 2em 0ex mathrm log 2 phantom rule 0 2em 0ex n as an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on line retailer items in the network being linked if they are frequently purchased by the same buyer the network has more than 400 000 vertices and 2 ifmmode times else texttimes fi 10 6 edges we show that our algorithm can extract meaningful communities from this network revealing large scale patterns present in the purchasing habits of customers

benchmark priors for bayesian model averaging in contrast to a posterior analysis given a particular sampling model posterior model probabilities in the context of model uncertainty are typically rather sensitive to the speciflcation of the prior in particular difiuse priors on model speciflc parameters can lead to quite unexpected consequences here we focus on the practically relevant situation where we need to entertain a large number of sampling models and we have or wish to use little or no subjective prior information we aim at providing an automatic or benchmark prior structure that can be used in such cases we focus on the normal linear regression model with uncertainty in the choice of re gressors we propose a partly noninformative prior structure related to a natural conjugate g prior speciflcation where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter g0j the consequences of difierent choices for g0j are examined we investigate theoretical properties such as consistency of the implied bayesian procedure links with classical information criteria are provided in addition we examine the flnite sample implications of several choices of g0j in a simulation study the use of the mc 3 algorithm of madigan and york 1995 combined with e cient coding in fortran makes it feasible to conduct large simulations in addition to posterior criteria we shall also compare the predictive performance of difierent priors a classic exam ple concerning the economics of crime will also be provided and contrasted with results in the literature the main flndings of the paper will lead us to propose a benchmark prior speciflcation in a linear regression context with model uncertainty

fractional bayes factors for model comparison bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves however there are difficulties with this approach when prior information about the parameters of the various models is weak partial bayes factors offer a resoiution of the problem by setting aside part of the data as a training sampie the training sampie is used to obtain an initiai informative posterior distribution of the parameters in each model model comparison is then based on a bayes factor calculated from the remaining data properties of partial bayes factors are discussed particularly in the context of weak prior information and they are found to have advantages over other proposed methods of model comparison a new variant of the partial bayes factor the fractional bayes factor is advocated on grounds of consistency simplicity robustness and coherence

models prior information and bayesian analysis abstract formulation of models for observations and prior densities for their parameters is an important activity in many sciences in the present paper after a discussion of this area of activity entropy based methods are employed to derive many central econometric and statistical models and noninformative and informative prior densities for their parameters in an explicit reproducible manner examples are provided to illustrate the general procedures in particular maxent is employed to produce linear and nonlinear regression and autoregression models hierarchical models time varying parameter models etc then maximal data information prior mdip densities for hyperparameters common parameters in different likelihood functions multinomial parameters etc are derived also the mdip approach is utilized to produce prior odds for alternative hypotheses or models

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

constructing financial network based on pmfg and threshold method abstract based on planar maximally filtered graph p m f g and threshold method we introduced a correlation based network named p m f g based threshold network p t n we studied the community structure of p t n and applied i s o m a p algorithm to represent p t n in low dimensional euclidean space the results show that the community corresponds well to the cluster in the euclidean space further we studied the dynamics of the community structure and constructed the normalized mutual information n m i matrix based on the real data in the market we found that the volatility of the market can lead to dramatic changes in the community structure and the structure is more stable during the financial crisis

on the relation of the drazin inverse and matrix pencil theory methods for the study of generalized linear systems in control theory the methodology of the drazin inverse and matrix pencil theory methods for generalized regular systems are extensively used thus in this paper a relation between the drazin inverse and the weierstrass form of a regular pencil is derived and fully investigated

bayesian analysis of systems of seemingly unrelated regression equations under a recursive extended natural conjugate prior density abstract a recursive extended natural conjugate prior density is proposed for systems of seemingly unrelated regression equations compared to other classes of extended natural conjugate prior densities it offers the advantage that analytical expressions are available for the prior covariance matrix of the regression coefficients the posterior analysis combines analytical and numerical techniques numerical integration is based on monte carlo importance sampling an application to a system of four wage equations for eec countries serves to evaluate different techniques discussed in the paper

evolution of correlation structure of industrial indices of u s equity markets we investigate the dynamics of correlations present between pairs of industry indices of u s stocks traded in u s markets by studying correlation based networks and spectral properties of the correlation matrix the study is performed by using 49 industry index time series computed by k french and e fama during the time period from july 1969 to december 2011 which spans more than 40 years we show that the correlation between industry indices presents both a fast and a slow dynamics the slow dynamics has a time scale longer than 5 years showing that a different degree of diversification of the investment is possible in different periods of time moreover we also detect a fast dynamics associated with exogenous or endogenous events the fast time scale we use is a monthly time scale and the evaluation time period is a 3 month time period by investigating the correlation dynamics monthly we are able to detect two examples of fast variations in the first and second eigenvalue of the correlation matrix the first occurs during the dot com bubble from march 1999 to april 2001 and the second occurs during the period of highest impact of the subprime crisis from august 2008 to august 2009

social significance of community structure statistical view community structure analysis is a powerful tool for social networks that can simplify their topological and functional analysis considerably however since community detection methods have random factors and real social networks obtained from complex systems always contain error edges evaluating the significance of a partitioned community structure is an urgent and important question in this paper integrating the specific characteristics of real society we present a framework to analyze the significance of a social community the dynamics of social interactions are modeled by identifying social leaders and corresponding hierarchical structures instead of a direct comparison with the average outcome of a random model we compute the similarity of a given node with the leader by the number of common neighbors to determine the membership vector an efficient community detection algorithm is proposed based on the position of the nodes and their corresponding leaders then using a log likelihood score the tightness of the community can be derived based on the distribution of community tightness we establish a connection between p value theory and network analysis and then we obtain a significance measure of statistical form finally the framework is applied to both benchmark networks and real social networks experimental results show that our work can be used in many fields such as determining the optimal number of communities analyzing the social significance of a given community comparing the performance among various algorithms etc