structural properties of the synchronized cluster on complex networks we investigate how the largest synchronized connected component lscc is formed and evolves to achieve a global synchronization on complex networks using kuramoto model in this study we use two different networks erdosi renyi network and barabasi albert network from the finite size scaling analysis we find that the scaling exponents for the percolation order parameter and mean cluster size on both networks agree with the mean field percolation theory beta gamma 1 we also find that the finite size scaling exponent nu also agrees with the mean field percolation result nu 3 moreover we also show that the cluster size distributions are identical with the mean field percolation distribution on both networks combining with the analysis for the merging clusters we directly show that the lscc on both networks evolves by merging clusters of various sizes

stability and stabilization of switched linear time invariant systems with saddle points and switching delays this paper addresses global asymptotic stability gas and stabilization issues of switched linear time invariant lti systems with saddle points and time varying switching delays firstly two criteria of gas are proposed for such switched systems with all subsystems sharing a common unique saddle point under arbitrary periodic quasi periodic switching paths psp qsp secondly by using our stability results we design global asymptotic stabilizing controls gasc periodic quasi periodic stabilizing switching paths pssp qssp and an algorithm of gasc and pssp qssp for the switched systems finally we present a numerical example of a switching multi agent system to illustrate the effectiveness and practicality of our new results

cluster synchrony in systems of coupled phase oscillators with higher order coupling we study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher order modes dominate the coupling between oscillators for the first time we develop a complete analytic description of the dynamics in the limit of a large number of oscillators and use it to quantify the degree of cluster synchrony cluster asymmetry and switching we use a variation of the recent dimensionality reduction technique of ott and antonsen chaos 18 037113 2008 and find an analytic description of the degree of cluster synchrony valid on a globally attracting manifold shaped by this manifold there is an infinite family of steady state distributions of oscillators resulting in a high degree of multistability in the cluster asymmetry we also show how through external forcing the degree of asymmetry can be controlled and suggest that systems displaying cluster synchrony can be used to encode and store data

the role of degree weighted couplings in the synchronous onset of kuramoto oscillator networks abstract this paper investigates the role of asymmetrical degree dependent weighted couplings in synchronization of a network of kuramoto oscillators where the conditions of coupling criticality for the onset of phase synchronization in degree weighted complex networks are arrived at the numerical simulations visualize that for networks having power law or exponential degree distributions asymmetrical degree weighted couplings with increasing weighting exponent increases the critical coupling to achieve the onset of phase synchronization in the networks

a multiple imputation approach to cox regression with interval censored data we propose a general semiparametric method based on multiple imputation for cox regression with interval censored data the method consists of iterating the following two steps first from finite interval censored but not right censored data exact failure times are imputed using tanner and wei s poor man s or asymptotic normal data augmentation scheme based on the current estimates of the regression coefficient and the baseline survival curve second a standard statistical procedure for right censored data such as the cox partial likelihood method is applied to imputed data to update the estimates through simulation we demonstrate that the resulting estimate of the regression coefficient and its associated standard error provide a promising alternative to the nonparametric maximum likelihood estimate our proposal is easily implemented by taking advantage of existing computer programs for right censored data

inference with imputed conditional means abstract in this article we present analytic techniques for inference from a dataset in which missing values have been replaced by predictive means derived from an imputation model the derivations are based on asymptotic expansions of point estimators and their associated variance estimators and the resulting formulas can be thought of as first order approximations to standard multiple imputation procedures with an infinite number of imputations for the missing values our method where applicable may require substantially less computational effort than creating and managing a multiply imputed database moreover the resulting inferences can be more precise than those derived from multiple imputation because they do not rely on simulation our techniques use components of the standard complete data analysis along with two summary measures from the fitted imputation model if the imputation and analysis phases are carried out by the same person or organization then the method provides a quick assessm

multiple imputation when records used for imputation are not used or disseminated for analysis summary when some of the records used to estimate the imputation models in multiple imputation are not used or available for analysis the usual multiple imputation variance estimator has positive bias we present an alternative approach that enables unbiased estimation of variances and hence calibrated inferences in such contexts first using all records the imputer samples m values of the parameters of the imputation model second for each parameter draw the imputer simulates the missing values for all records n times from these mn completed datasets the imputer can analyse or disseminate the appropriate subset of records we develop methods for interval estima tion and significance testing for this approach methods are presented in the context of multiple imputation for measurement error

input to state stabilization of switched nonlinear systems this note derives some sufficient conditions to ensure that the whole switched nonlinear system is input to state stabilizable iss when each mode is iss both cases that the switchings of system modes coincide exactly and that they do not coincide with those of the corresponding controllers are considered for the latter a model based identification scheme is used to identify the system modes the proposed scheme can overcome the finite escape time that may happen in this case

analysis of cluster explosive synchronization in complex networks correlations between intrinsic dynamics and local topology have become a new trend in the study of synchronization in complex networks in this paper we investigate the influence of topology on the dynamics of networks made up of second order kuramoto oscillators in particular based on mean field calculations we provide a detailed investigation of cluster explosive synchronization ces phys rev lett 110 218701 2013 in scale free networks as a function of several topological properties moreover we investigate the robustness of discontinuous transitions by including an additional quenched disorder and we show that the phase coherence decreases with increasing strength of the quenched disorder these results complement the previous findings regarding ces and also fundamentally deepen the understanding of the interplay between topology and dynamics under the constraint of correlating natural frequencies and local structure

decreasing the spectral radius of a graph by link removals the decrease of the spectral radius an important characterizer of network dynamics by removing links is investigated the minimization of the spectral radius by removing m links is shown to be an np complete problem which suggests considering heuristic strategies several greedy strategies are compared and several bounds on the decrease of the spectral radius are derived the strategy that removes that link l i j with largest product x1 i x1 j of the components of the eigenvector x1 belonging to the largest adjacency eigenvalue is shown to be superior to other strategies in most cases furthermore a scaling law where the decrease in spectral radius is inversely proportional to the number of nodes n in the graph is deduced another sublinear scaling law of the decrease in spectral radius versus the number m of removed links is conjectured

inference for imputation estimators we derive an estimator of the asymptotic variance of both single and multiple imputation estimators we assume a parametric imputation model but allow for non and semiparametric analysis models our variance estimator in contrast to the estimator proposed by rubin 1987 is consistent even when the imputation and analysis models are misspecified and incompatible with one another

robust stability for switched positive systems with d perturbation and time varying delay this paper is focused on studying the robust stability of switched positive systems with d perturbation and time varying delay all subsystems are considered to be unstable based on the partition of state space on the nonnegative orthant sufficient conditions in terms of linear programming are obtained to guarantee such system to be asymptotically stable the hysteresis switching laws are designed to prevent chattering behavior via the single copositive lyapunov function and multiple copositive lyapunov functions approaches respectively two illustrative examples concerned with price model of goods are provided to display the effectiveness of the obtained results

asynchronously switched control of discrete impulsive switched systems with time delays this paper is concerned with the stabilization problem for a class of uncertain discrete impulsive switched delay systems under asynchronous switching the so called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous by using the average dwell time adt approach sufficient conditions for the existence of an asynchronously switched controller is derived such that the resulting closed loop system is exponentially stable the desired controller gains and the admissible switching signals are obtained in terms of a set of matrix inequalities a numerical example is given to illustrate the effectiveness of the proposed method

multiple imputation of missing categorical and continuous values via bayesian mixture models with local dependence abstractwe present a nonparametric bayesian joint model for multivariate continuous and categorical variables with the intention of developing a flexible engine for multiple imputation of missing values the model fuses dirichlet process mixtures of multinomial distributions for categorical variables with dirichlet process mixtures of multivariate normal distributions for continuous variables we incorporate dependence between the continuous and categorical variables by 1 modeling the means of the normal distributions as component specific functions of the categorical variables and 2 forming distinct mixture components for the categorical and continuous data with probabilities that are linked via a hierarchical model this structure allows the model to capture complex dependencies between the categorical and continuous data with minimal tuning by the analyst we apply the model to impute missing values due to item nonresponse in an evaluation of the redesign of the survey of income and program partic

complex macroscopic behavior in systems of phase oscillators with adaptive coupling abstract using recent dimensionality reduction techniques in large systems of coupled phase oscillators exhibiting bistability we analyze the complex macroscopic behavior arising when the coupling between oscillators is allowed to evolve slowly as a function of either macroscopic or local system properties for example we observe macroscopic excitability and intermittent synchrony in a system of time delayed kuramoto oscillators with hebbian and anti hebbian learning we demonstrate the robustness of our findings by considering systems with increasing complexity including time delayed oscillators with adaptive network structure and community interaction as well as a system with bimodally distributed frequencies

missing data methods for generalized linear models a comparative review missing data is a major issue in many applied problems especially in the biomedical sciences we review four common approaches for inference in generalized linear models glms with missing covariate data maximum likelihood ml multiple imputation mi fully bayesian fb and weighted estimating equations wees there is considerable interest in how these four methodologies are related the properties of each approach the advantages and disadvantages of each methodology and computational implementation we examine data that are missing at random and nonignorable missing for ml we focus on techniques using the em algorithm and in particular discuss the em by the method of weights and related procedures as discussed by ibrahim for mi we examine the techniques developed by rubin for fb we review approaches considered by ibrahim et al for wee we focus on the techniques developed by robins et al we use a real dataset and a detailed simulation study to compare the four methods

onset of synchronization in complex networks of noisy oscillators we study networks of noisy phase oscillators whose nodes are characterized by a random degree counting the number of its connections both these degrees and the natural frequencies of the oscillators are distributed according to a given probability density replacing the randomly connected network by an all to all coupled network with weighted edges allows us to formulate the dynamics of a single oscillator coupled to the mean field and to derive the corresponding fokker planck equation from the latter we calculate the critical coupling strength for the onset of synchronization as a function of the noise intensity the frequency distribution and the first two moments of the degree distribution our approach is applied to a dense small world network model for which we calculate the degree distribution numerical simulations prove the validity of the made replacement we also test the applicability to more sparsely connected networks and formulate homogeneity and absence of correlations in the degree distribution as limiting factors of our approach

stabilization for t s model based uncertain stochastic systems this paper considers the stabilization problem of a class of uncertain ito stochastic fuzzy systems driven by a multidimensional wiener process the uncertainty modeled in the systems is of the linear fractional type which includes the norm bounded uncertainty as a special case the objective is to design a state feedback fuzzy controller such that the closed loop system is robustly asymptotically stable under a stochastic setting by using a stochastic lyapunov approach sufficiency conditions for the stability and stabilization of this class of systems are established based on a novel matrix decomposition technique the derived stability conditions are then employed to design controllers which stabilize the uncertain ito stochastic fuzzy systems two simulation examples are given to illustrate the effectiveness of the approaches proposed

delay dependent exponential stabilization of positive 2d switched state delayed systems in the roesser model this paper deals with the controller synthesis for a class of positive two dimensional 2d switched delay systems described by the roesser model this kind of systems has the property that the states take nonnegative values whenever the initial boundaries are nonnegative some delay dependent sufficient conditions for the exponential stability of positive 2d switched systems with state delays are given furthermore the design of positive state feedback controller under which the resulting closed loop system meets the requirements of positivity and exponential stability is presented in terms of linear matrix inequalities lmis an example is included to illustrate the effectiveness of the proposed approach

hole structures in nonlocally coupled noisy phase oscillators we demonstrate that a system of nonlocally coupled noisy phase oscillators can collectively exhibit a hole structure which manifests itself in the spatial phase distribution of the oscillators the phase model is described by a nonlinear fokker planck equation which can be reduced to the complex ginzburg landau equation near the hopf bifurcation point of the uniform solution by numerical simulations we show that the hole structure clearly appears in the space dependent order parameter which corresponds to the nozaki bekki hole solution of the complex ginzburg landau equation

wavelet bispectral analysis for the study of interactions among oscillators whose basic frequencies are significantly time variable bispectral analysis recently introduced as a technique for revealing time phase relationships is extended to make use of wavelets rather than fourier analysis it is thus able to encompass instantaneous phase time dependence for the case of two or more coupled nonlinear oscillators the method is demonstrated and evaluated by use of test signals from a pair of coupled poincare oscillators it promises to be useful in a wide range of scientific contexts for studies of interacting oscillators whose basic frequencies are significantly time variable

onset of synchronization in large networks of coupled oscillators we study the transition from incoherence to coherence in large networks of coupled phase oscillators we present various approximations that describe the behavior of an appropriately defined order parameter past the transition and generalize recent results for the critical coupling strength we find that under appropriate conditions the coupling strength at which the transition occurs is determined by the largest eigenvalue of the adjacency matrix we show how with an additional assumption a mean field approximation recently proposed is recovered from our results we test our theory with numerical simulations and find that it describes the transition when our assumptions are satisfied we find that our theory describes the transition well in situations in which the mean field approximation fails we study the finite size effects caused by nodes with small degree and find that they cause the critical coupling strength to increase

observer design for switched recurrent neural networks an average dwell time approach this paper is concerned with the problem of observer design for switched recurrent neural networks with time varying delay the attention is focused on designing the full order observers that guarantee the global exponential stability of the error dynamic system based on the average dwell time approach and the free weighting matrix technique delay dependent sufficient conditions are developed for the solvability of such problem and formulated as linear matrix inequalities the error state decay estimate is also given then the stability analysis problem for the switched recurrent neural networks can be covered as a special case of our results finally four illustrative examples are provided to demonstrate the effectiveness and the superiority of the proposed methods

on the bias of the multiple imputation variance estimator in survey sampling summary multiple imputation is a method of estimating the variances of estimators that are constructed with some imputed data we give an expression for the bias of the multiple imputation variance estimator for data that are collected with a complex sample design the bias may be sizable for certain estimators such as domain means when a large fraction of the values are imputed a bias adjusted variance estimator is suggested

laplacian spectra as a diagnostic tool for network structure and dynamics we examine numerically the three way relationships among structure laplacian spectra and frequency synchronization dynamics on complex networks we study the effects of clustering degree distribution and a particular type of coupling asymmetry input normalization all of which are known to have effects on the synchronizability of oscillator networks we find that these topological factors produce marked signatures in the laplacian eigenvalue distribution and in the localization properties of individual eigenvectors using a set of coordinates based on the laplacian eigenvectors as a diagnostic tool for synchronization dynamics we find that the process of frequency synchronization can be visualized as a series of quasi independent transitions involving different normal modes particular features of the partially synchronized state can be understood in terms of the behavior of particular modes or groups of modes for example there are important partially synchronized states in which a set of low lying modes remain unlocked while those in the main spectral peak are locked we find therefore that spectra are correlated with dynamics in ways that go beyond results relating a single threshold to a single extremal eigenvalue

erosion of synchronization coupling heterogeneity and network structure we study the dynamics of network coupled phase oscillators in the presence of coupling frustration it was recently demonstrated that in heterogeneous network topologies the presence of coupling frustration causes perfect phase synchronization to become unattainable even in the limit of infinite coupling strength here we consider the important case of heterogeneous coupling functions and extend previous results by deriving analytical predictions for the total erosion of synchronization our analytical results are given in terms of basic quantities related to the network structure and coupling frustration in addition to fully heterogeneous coupling where each individual interaction is allowed to be distinct we also consider partially heterogeneous coupling and homogeneous coupling in which the coupling functions are either unique to each oscillator or identical for all network interactions respectively we demonstrate the validity of our theory with numerical simulations of multiple network models and highlight the interesting effects that various coupling choices and network models have on the total erosion of synchronization finally we consider some special network structures with well known spectral properties which allows us to derive further analytical results

on robust stabilization for neutral delay differential systems with parametric uncertainties and its application this paper considers the problem of robust stabilization for uncertain neutral delay differential systems based on the lyapunov method a delay dependent criterion for determining the stability of systems is obtained in terms of matrix inequalities which can be easily solved by efficient convex optimization algorithms then the method presented is extended to systems with controller gain variations that is the design problem for the nonfragile controller is considered a numerical example is included to illustrate the design procedure of the proposed method

effect of node degree correlation on synchronization of identical pulse coupled oscillators we explore the effect of correlations between the in and out degrees of random directed networks on the synchronization of identical pulse coupled oscillators numerical experiments demonstrate that the proportion of initial conditions resulting in a globally synchronous state prior to a large but finite time is an increasing function of node degree correlation for those networks observed to globally synchronize both the mean and standard deviation of time to synchronization are decreasing functions of node degree correlation pulse coupled oscillator networks with negatively correlated node degree often exhibit multiple coherent attracting states with trajectories performing fast transitions between them these effects of node degree correlation on dynamics of pulse coupled oscillators are consistent with aspects of network topology e g the effect of node degree correlation on the eigenvalues of the laplacian matrix that have been shown to affect synchronization in other contexts

self organized network of phase oscillators coupled by activity dependent interactions we investigate a network of coupled phase oscillators whose interactions evolve dynamically depending on the relative phases between the oscillators we found that this coevolving dynamical system robustly yields three basic states of collective behavior with their self organized interactions the first is the two cluster state in which the oscillators are organized into two synchronized groups the second is the coherent state in which the oscillators are arranged sequentially in time the third is the chaotic state in which the relative phases between oscillators and their coupling weights are chaotically shuffled furthermore we demonstrate that self assembled multiclusters can be designed by controlling the weight dynamics note that the phase patterns of the oscillators and the weighted network of interactions between them are simultaneously organized through this coevolving dynamics we expect that these results will provide new insight into self assembly mechanisms by which the collective behavior of a rhythmic system emerges as a result of the dynamics of adaptive interactions

large sample significance levels from multiply imputed data using moment based statistics and an f reference distribution abstract we present a procedure for computing significance levels from data sets whose missing values have been multiply imputed data this procedure uses moment based statistics m 3 repeated imputations and an f reference distribution when m we show first that our procedure is essentially the same as the ideal procedure in cases of practical importance and second that its deviations from the ideal are basically a function of the coefficient of variation of the canonical ratios of complete to observed information for small m our procedure s performance is largely governed by this coefficient of variation and the mean of these ratios using simulation techniques with small m we compare our procedure s actual and nominal large sample significance levels and conclude that it is essentially calibrated and thus represents a definite improvement over previously available procedures furthermore we compare the large sample power of the procedure as a function of m and other factors such as the di

random line graphs and a linear law for assortativity for a fixed number n of nodes the number of links l in the line graph h n l can only appear in consecutive intervals called a band of l we prove that some consecutive integers can never represent the number of links l in h n l and they are called a bandgap of l we give the exact expressions of bands and bandgaps of l we propose a model which can randomly generate simple graphs which are line graphs of other simple graphs the essence of our model is to merge step by step a pair of nodes in cliques which we use to construct line graphs obeying necessary rules to ensure that the resulting graphs are line graphs two nodes to be merged are randomly chosen at each step if the cliques are all of the same size the assortativity of the line graphs in each step are close to 0 and the assortativity of the corresponding root graphs increases linearly from 1 to 0 with the steps of the nodal merging process if we dope the constructing elements of the line graphs the cliques of the same size with a relatively smaller number of cliques of different size the characteristics of the assortativity of the line graphs is completely altered we also generate line graphs with the cliques whose sizes follow a binomial distribution the corresponding root graphs with binomial degree distributions zero assortativity and semicircle eigenvalue distributions are equivalent to erd s renyi random graphs

spectral properties of the hierarchical product of graphs the hierarchical product of two graphs represents a natural way to build a larger graph out of two smaller graphs with less regular and therefore more heterogeneous structure than the cartesian product here we study the eigenvalue spectrum of the adjacency matrix of the hierarchical product of two graphs introducing a coupling parameter describing the relative contribution of each of the two smaller graphs we perform an asymptotic analysis for the full spectrum of eigenvalues of the adjacency matrix of the hierarchical product specifically we derive the exact limit points for each eigenvalue in the limits of small and large coupling as well as the leading order relaxation to these values in terms of the eigenvalues and eigenvectors of the two smaller graphs given its central roll in the structural and dynamical properties of networks we study in detail the perron frobenius or largest eigenvalue finally as an example application we use our theory to predict the epidemic threshold of the susceptible infected susceptible model on a hierarchical product of two graphs

small sample degrees of freedom with multiple imputation an appealing feature of multiple imputation is the simplicity of the rules for combining the multiple complete data inferences into a final inference the repeated imputation inference rubin 1987 this inference is based on a t distribution and is derived from a bayesian paradigm under the assumption that the complete data degrees of freedom com are infinite but the number of imputations m is finite when com is small and there is only a modest proportion of missing data the calculated repeated imputation degrees of freedom m for the t reference distribution can be much larger than com which is clearly inappropriate following the bayesian paradigm we derive an adjusted degrees of freedom m with the following three properties for fixed m and estimated fraction of missing information m monotonically increases in com m is always less than or equal to com and m equals m when com is infinite a small simulation study demonstrates the superior frequentist performance when using m rather than m

imputation and variable selection in linear regression models with missing covariates across multiply imputed data sets variable selection methods such as stepwise regression and other criterion based strategies that include or exclude particular variables typically result in models with different selected predictors thus presenting a problem for combining the results from separate complete data analyses here drawing on a bayesian framework we propose two alternative strategies to address the problem of choosing among linear regression models when there are missing covariates one approach which we call impute then select its involves initially performing multiple imputation and then applying bayesian variable selection to the multiply imputed data sets a second strategy is to conduct bayesian variable selection and missing data imputation simultaneously within one gibbs sampling process which we call simultaneously impute and select sias the methods are implemented and evaluated using the bayesian procedure known as stochastic search variable selection for multivariate normal data sets but both strategies offer general frameworks within which different bayesian variable selection algorithms could be used for other types of data sets a study of mental health services utilization among children in foster care programs is used to illustrate the techniques simulation studies show that both its and sias outperform complete case analysis with stepwise variable selection and that sias slightly outperforms its

hamiltonian mean field model effect of network structure on synchronization dynamics the hamiltonian mean field model of coupled inertial hamiltonian rotors is a prototype for conservative dynamics in systems with long range interactions we consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix by studying the linear stability of the incoherent state we find that the transition to synchrony begins when the coupling constant k is inversely proportional to the largest eigenvalue of the adjacency matrix we derive a closed system of equations for a set of local order parameters to study the effect of network heterogeneity on the synchronization of the rotors when k is just beyond the transition to synchronization we find that the degree of synchronization is highly dependent on the network s heterogeneity but that for large k the degree of synchronization is robust to changes in the degree distribution our results are illustrated with numerical simulations on erd os renyi networks and networks with power law degree distributions

large sample theory for parametric multiple imputation procedures we consider the asymptotic behaviour of various parametric multiple imputation procedures which include but are not restricted to the proper imputation procedures proposed by rubin 1978 the asymptotic variance structure of the resulting estimators is provided this result is used to compare the relative efficiencies of different imputation procedures it also provides a basis to understand the behaviour of two monte carlo iterative estimators stochastic em celeux diebolt 1985 wei tanner 1990 and simulated em ruud 1991 we further develop properties of these estimators when they stop at iteration k with imputation size m an application to a mcasurement error problem is used to illustrate the results

robust reliable stabilization of uncertain switched neutral systems with delayed switching this paper investigates the problem of robust reliable control for a class of uncertain switched neutral systems under asynchronous switching where the switching instants of the controller experience delays with respect to those of the system and the parameter uncertainties are assumed to be norm bounded a state feedback controller is proposed to guarantee exponential stability and reliability for switched neutral systems and the dwell time approach is utilized for the stability analysis and controller design a numerical example is given to illustrate the effectiveness of the proposed method

network connectivity during mergers and growth optimizing the addition of a module the principal eigenvalue of a network s adjacency matrix often determines dynamics on the network e g in synchronization and spreading processes and some of its structural properties e g robustness against failure or attack and is therefore a good indicator for how strongly a network is connected we study how is modified by the addition of a module or community which has broad applications ranging from those involving a single modification e g introduction of a drug into a biological process to those involving repeated additions e g power grid and transit development we describe how to optimally connect the module to the network to either maximize or minimize the shift in noting several applications of directing dynamics on networks

multiple imputation of industry and occupation codes in census public use samples using bayesian logistic regression abstract we describe methods used to create a new census data base that can be used to study comparability of industry and occupation classification systems this project represents the most extensive application of multiple imputation to date and the modeling effort was considerable as well hundreds of logistic regressions were estimated one goal of this article is to summarize the strategies used in the project so that researchers can better understand how the new data bases were created another goal is to show how modifications of maximum likelihood methods were made for the modeling and imputation phases of the project to multiply impute 1980 census comparable codes for industries and occupations in two 1970 census public use samples logistic regression models were estimated with flattening constants for many of the regression models considered the data were too sparse to support conventional maximum likelihood analysis so some alternative had to be employed these methods solve existence and

network ensemble comparisons with stochastic rewiring and von neumann entropy assessing whether a given network is typical or atypical for a random network ensemble i e network ensemble comparison has widespread applications ranging from null model selection and hypothesis testing to clustering and classifying networks we develop a framework for network ensemble comparison by subjecting the network to stochastic rewiring we study two rewiring processes uniform and degree preserved rewiring which yield random network ensembles that converge to the erdos renyi and configuration model ensembles respectively we study convergence through von neumann entropy vne a network summary statistic measuring information content based on the spectra of a laplacian matrix and develop a perturbation analysis for the expected effect of rewiring on vne our analysis yields an estimate for how many rewires are required for a given network to resemble a typical network from an ensemble offering a computationally efficient quantity for network ensemble comparison that does not require

spontaneous synchronization of coupled oscillator systems with frequency adaptation we study the synchronization of kuramoto oscillators with all to all coupling in the presence of slow noisy frequency adaptation in this paper we develop a new model for oscillators which adapt both their phases and frequencies it is found that this model naturally reproduc es some observed phenomena that are not qualitatively produced by the standard kuramoto model such as long waiting times before the synchronization of clapping audiences by assuming a self consistent steady state solution we find three stability regimes for the coupling constant k separated by critical points k1 and k2 i for k k2 the incoherent state becomes unstable and only the synchronized state exists iii for k1 k2 the average waiting time grows logarithmically with the number of oscillators

approximate solution to the stochastic kuramoto model we study kuramoto phase oscillators with temporal fluctuations in the frequencies the infinite dimensional system can be reduced in a gaussian approximation to two first order differential equations this yields a solution for the time dependent order parameter which characterizes the synchronization between the oscillators the known critical coupling strength is exactly recovered by the gaussian theory extensive numerical experiments further show that the analytical results are very accurate below and sufficiently above the critical value we obtain the asymptotic order parameter in closed form which suggests a tighter upper bound for the corresponding scaling as a last point we elaborate the gaussian approximation in complex networks with distributed degrees

stability and l2 gain analysis for switched delay systems a delay dependent method in this paper we study stability and l 2 gain for a class of switched systems with time varying delays sufficient conditions for exponential stability and weighted l 2 gain are developed for a class of switching signals with average dwell time these conditions are delay dependent and are given in the form of linear matrix inequalities lmis as a special case of such switching signals we can obtain exponential stability and normal l 2 gain under arbitrary switching signals the state decay estimate is explicitly given two examples illustrate the effectiveness and applicability of the proposed method

multiple imputation after 18 years abstract multiple imputation was designed to handle the problem of missing data in public use data bases where the data base constructor and the ultimate user are distinct entities the objective is valid frequency inference for ultimate users who in general have access only to complete data software and possess limited knowledge of specific reasons and models for nonresponse for this situation and objective i believe that multiple imputation by the data base constructor is the method of choice this article first provides a description of the assumed context and objectives and second reviews the multiple imputation framework and its standard results these preliminary discussions are especially important because some recent commentaries on multiple imputation have reflected either misunderstandings of the practical objectives of multiple imputation or misunderstandings of fundamental theoretical results then criticisms of multiple imputation are considered and finally comparisons are made to alt

stabilization of switched linear systems with time delay in detection of switching signal a feedback stabilization problem for switched linear systems with time delay in detection of switching signal is formulated first online state feedback controller design method for asymptotic stability and exponential stability is given then offline state feedback controller design method for asymptotic stability and exponential stability is given as well

synchronization transition of heterogeneously coupled oscillators on scale free networks we investigate the synchronization transition of the modified kuramoto model where the oscillators form a scale free network with degree exponent ensuremath lambda an oscillator of degree k i is coupled to its neighboring oscillators with asymmetric and degree dependent coupling in the form of j k i ensuremath eta ensuremath 1 by invoking the mean field approach we find eight different synchronization transition behaviors depending on the values of ensuremath eta and ensuremath lambda and derive the critical exponents associated with the order parameter and the finite size scaling in each case the synchronization transition point j c is determined as being zero finite when ensuremath eta g ensuremath lambda ensuremath 2 ensuremath eta l ensuremath lambda ensuremath 2 the synchronization transition is also studied from the perspective of cluster formation of synchronized vertices the cluster size distribution and the largest cluster size as a function of the system size are derived for each case using the generating function technique our analytic results are confirmed by numerical simulations

network evolution based on centrality we study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality we show that the same network dynamics arise under various centrality measures and solve analytically the network evolution during the complete evolution the network is characterized by nestedness the neighborhood of a node is contained in the neighborhood of the nodes with larger degree we find a discontinuous transition in the network density between hierarchical and homogeneous networks depending on the rate of link decay we also show that this evolution mechanism leads to double power law degree distributions with interrelated exponents

top eigenpair statistics for weighted sparse graphs we develop a formalism to compute the statistics of the top eigenpair of weighted sparse graphs with finite mean connectivity and bounded maximal degree framing the problem in terms of optimisation of a quadratic form on the sphere and introducing a fictitious temperature we employ the cavity and replica methods to find the solution in terms of self consistent equations for auxiliary probability density functions which can be solved by population dynamics this derivation allows us to identify and unpack the individual contributions to the top eigenvector s components coming from nodes of degree k the analytical results are in perfect agreement with numerical diagonalisation of large weighted adjacency matrices and are further cross checked on the cases of random regular graphs and sparse markov transition matrices for unbiased random walks

maximum performance at minimum cost in network synchronization we consider two optimization problems on synchronization of oscillator networks maximization of synchronizability and minimization of synchronization cost we first develop an extension of the well known master stability framework to the case of non diagonalizable laplacian matrices we then show that the solution sets of the two optimization problems coincide and are simultaneously characterized by a simple condition on the laplacian eigenvalues among the optimal networks we identify a subclass of hierarchical networks characterized by the absence of feedback loops and the normalization of inputs we show that most optimal networks are directed and non diagonalizable necessitating the extension of the framework we also show how oriented spanning trees can be used to explicitly and systematically construct optimal networks under network topological constraints our results may provide insights into the evolutionary origin of structures in complex networks for which synchronization plays a significant role

queue length synchronization in communication networks we study the synchronization in the context of network traffic on a 2 d communication network with local clustering and geographic separations the network consists of nodes and randomly distributed hubs where the top five hubs ranked according to their coefficient of betweenness centrality cbc are connected by random assortative and gradient mechanisms for multiple message traffic messages can trap at the high cbc hubs and congestion can build up on the network with long queues at the congested hubs the queue lengths are seen to synchronize in the congested phase both complete and phase synchronization are seen between pairs of hubs in the decongested phase the pairs start clearing and synchronization is lost a cascading master slave relation is seen between the hubs with the slower hubs which are slow to decongest driving the faster ones these are usually the hubs of high cbc similar results are seen for traffic of constant density total synchronization between the hubs of high cbc is also seen in the congested regime similar behavior is seen for traffic on a network constructed using the waxman random topology generator we also demonstrate the existence of phase synchronization in real internet traffic data

detecting couplings between interacting oscillators with time varying basic frequencies instantaneous wavelet bispectrum and information theoretic approach in the natural world the properties of interacting oscillatory systems are not constant but evolve or fluctuating continuously in time thus the basic frequencies of the interacting oscillators are time varying which makes the system analysis complex for studying their interactions we propose a complementary approach combining wavelet bispectral analysis and information theory we show how these methods uncover the interacting properties and reveal the nature strength and direction of coupling wavelet bispectral analysis is generalized as a technique for detecting instantaneous phase time dependence for the case of two or more coupled nonlinear oscillators whereas the information theory approach can uncover the directionality of coupling and extract driver response relationships in complex systems we generate bivariate time series numerically to mimic typical situations that occur in real measured data apply both methods to the same time series and discuss the results the approach is applicable quite generally to any system of coupled nonlinear oscillators

strong effects of network architecture in the entrainment of coupled oscillator systems random networks of coupled phase oscillators representing an approximation for systems of coupled limit cycle oscillators are considered entrainment of such networks by periodic external forcing applied to a subset of their elements is numerically and analytically investigated for a large class of interaction functions we find that the entrainment window with a tongue shape becomes exponentially narrow for networks with higher hierarchical organization however the entrainment is significantly facilitated if the networks are directionally biased i e closer to the feedforward networks furthermore we show that the networks with high entrainment ability can be constructed by evolutionary optimization processes the neural network structure of the master clock of the circadian rhythm in mammals is discussed from the viewpoint of our results

multiple edit multiple imputation for multivariate continuous data multiple imputation replaces an incomplete dataset with m 1 simulated complete versions that are analyzed separately by standard methods we present a natural extension of multiple imputation for handling the dual problems of nonresponse and response error this extension which we call multiple edit multiple imputation memi replaces an observed dataset containing missing values and errors with m 1 simulated versions of the ideal dataset that is complete and error free these ideal data sets are analyzed separately and the results are combined using the same rules as for multiple imputation the resulting inferences simultaneously reflect uncertainty due to nonresponse and response error memi may be an attractive alternative to deterministic or quasi statistical edit and imputation procedures used by many data collecting agencies producing memi s requires assumptions about the distribution of the ideal data the nature of nonresponse and a model for the response error mechanism however fittin

collective frequency variation in network synchronization and reverse pagerank a wide range of natural and engineered phenomena rely on large networks of interacting units to reach a dynamical consensus state where the system collectively operates here we study the dynamics of self organizing systems and show that for generic directed networks the collective frequency of the ensemble is not the same as the mean of the individuals natural frequencies specifically we show that the collective frequency equals a weighted average of the natural frequencies where the weights are given by an outflow centrality measure that is equivalent to a reverse pagerank centrality our findings uncover an intricate dependence of the collective frequency on both the structural directedness and dynamical heterogeneity of the network and also reveal an unexplored connection between synchronization and pagerank which opens the possibility of applying pagerank optimization to synchronization finally we demonstrate the presence of collective frequency variation in real world networks by considering the uk and scandinavian power grids

the multiple adaptations of multiple imputation multiple imputation was first conceived as a tool that statistical agencies could use to handle nonresponse in large sample public use surveys in the last two decades the multiple imputation framework has been adapted for other statistical contexts for example individual researchers use multiple imputation to handle missing data in small samples statistical agencies disseminate multiply imputed data sets for purposes of protecting data confidentiality and survey methodologists and epidemiologists use multiple imputation to correct for measurement errors in some of these settings rubin s original rules for combining the point and variance estimates from the multiply imputed data sets are not appropriate because what is known and thus the conditional expectations and variances used to derive inferential methods differs from that in the missing data context these applications require new combining rules and methods of inference in fact more than 10 combining rules exist in the published literatur

synchronization is optimal in nondiagonalizable networks we consider maximization of the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology by extending the master stability formalism to all possible network structures we show that unless some oscillator is linked to all the others maximally synchronizable networks are necessarily nondiagonalizable and can always be obtained by imposing unidirectional information flow with normalized input strengths the results provide insights into hierarchical structures observed in complex networks in which synchronization is important

sliding mode control for stochastic systems subject to packet losses this paper investigates the problem of sliding mode control for stochastic system under the effect of packet dropout in this work a new sliding function dependent on the probability of packet dropout is constructed by means of a lyapunov function involved in sliding mode variable and system state both the reachabiltiy and the stability are analyzed simultaneously and the sufficient condition is derived via linear matrix inequalities finally numerical simulation results are given

extreme value statistics of networks with inhibitory and excitatory couplings inspired by the importance of inhibitory and excitatory couplings in the brain we analyze the largest eigenvalue statistics of random networks incorporating such features we find that the largest real part of eigenvalues of a network which accounts for the stability of an underlying system decreases linearly as a function of inhibitory connection probability up to a particular threshold value after which it exhibits rich behaviors with the distribution manifesting generalized extreme value statistics fluctuations in the largest eigenvalue remain somewhat robust against an increase in system size but reflect a strong dependence on the number of connections indicating that systems having more interactions among its constituents are likely to be more unstable

technical communique a new result on stability analysis for stochastic neutral systems this paper discusses the mean square exponential stability of stochastic linear systems of neutral type applying the lyapunov krasovskii theory a linear matrix inequality based delay dependent stability condition is presented the use of model transformations cross term bounding techniques or additional matrix variables is all avoided thus the method leads to a simple criterion and shows less conservatism the new result is derived based on the generalized finsler lemma gfl gfl reduces to the standard finsler lemma in the absence of stochastic perturbations and it can be used in the analysis and synthesis of stochastic delay systems moreover gfl is also employed to obtain stability criteria for a class of stochastic neutral systems which have different discrete and neutral delays numerical examples including a comparison with some recent results in the literature are provided to show the effectiveness of the new results

inference from coarse data via multiple imputation with application to age heaping abstract multiple imputation is applied to a demographic data set with coarse age measurements for tanzanian children the heaped ages are multiply imputed with plausible true ages using a a simple naive model and b a new relatively complex model that relates true age to the observed values of heaped age sex and anthropometric variables the imputed true ages are used to create valid inferences under the models and compare inferences across models thereby revealing sensitivity of inferences to prior specifications from naive to complex in addition diagnostic analyses applied to the imputed data are used to suggest which models appear most appropriate because it is not clear just what set of heaping intervals should be used the models are applied under various assumptions about the heaping rounding to the nearest year or half year versus a combination of rounding and truncation as practiced in the united states and medium versus wide heaping interval sizes the most striking conclusions ar

relaxation of synchronization on complex networks point of information transfer or the dynamics of system recovery from a perturbation we measure the relaxation time that is required to establish global synchronization by varying the structural properties of the networks it is found that the relaxation time in a strong coupling regime kkc logarithmically increases with network size n which is attributed to the initial random phase fluctuation given by on 1 2 after elimination of the initial phase fluctuation the relaxation time is found to be independent of the system size this implies that the local interaction that depends on the structural connectivity is irrelevant in the relaxation dynamics of the synchronization in the strong coupling regime the relaxation dynamics is analytically derived in a form independent of the system size and it exhibits good consistency with numerical simulations as an application we also explore the recovery dynamics of the oscillators when perturbations enter the system

emergence of synchronization in complex networks of interacting dynamical systems abstract we study the emergence of coherence in large complex networks of interacting heterogeneous dynamical systems we show that for a large class of dynamical systems and network topologies there is a critical coupling strength at which the systems undergo a transition from incoherent to coherent behavior we find that the critical coupling strength at which this transition takes place is k c z 1 where z depends only on the uncoupled dynamics of the individual systems on each node while is the largest eigenvalue of the network adjacency matrix thus we achieve a separation of the problem into two parts one depending solely on the node dynamics and one depending solely on network topology

erosion of synchronization in networks of coupled oscillators we report erosion of synchronization in networks of coupled phase oscillators a phenomenon where perfect phase synchronization is unattainable in steady state even in the limit of infinite coupling an analysis reveals that the total erosion is separable into the product of terms characterizing coupling frustration and structural heterogeneity both of which amplify erosion the latter however can differ significantly from degree heterogeneity finally we show that erosion is marked by the reorganization of oscillators according to their node degrees rather than their natural frequencies

perturbation analysis of complete synchronization in networks of phase oscillators the behavior of weakly coupled self sustained oscillators can often be well described by phase equations here we use the paradigm of kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections to the frequency of the fully synchronized state for nonidentical oscillators the topology of the underlying coupling network is reflected in the eigenvalues and eigenvectors of the network laplacian which influence the synchronization frequency in a particular way they characterize the importance of nodes in a network and the relations between them expected values for the synchronization frequency are obtained for oscillators with quenched random frequencies on a class of scale free random networks and for a erdos renyi random network we briefly discuss an application of the perturbation theory in the second order to network structural analysis

small sample degrees of freedom for multi component significance tests with multiple imputation for missing data summary when performing multi component significance tests with multiply imputed datasets analysts can use a wald like test statistic and a reference f distribution the currently employed degrees of freedom in the denominator of this f distribution are derived assuming an infinite sample size for modest complete data sample sizes this degrees of freedom can be unrealistic for example it may exceed the complete data degrees of freedom this paper presents an alternative denominator degrees of freedom that is always less than or equal to the complete data denominator degrees of freedom and equals the currently employed denominator degrees of freedom for infinite sample sizes its advantages over the currently employed degrees of freedom are illustrated with a simulation

finite size scaling of synchronized oscillation on complex networks the onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated using a mean field approximation we characterize sample to sample fluctuations for networks of finite size and derive the corresponding scaling properties in the critical region for scale free networks with the degree distribution p k approximately k gamma at large k we found that the finite size exponent nu takes on the value 5 2 when gamma 5 the same as in the globally coupled kuramoto model for highly heterogeneous networks 3 gamma 5 nu and the order parameter exponent beta depend on gamma the analytical expressions for these exponents obtained from the mean field theory are shown to be in excellent agreement with data from extensive numerical simulations

stabilization for switched stochastic neutral systems under asynchronous switching in this paper the mean square exponential stability of switched stochastic neutral systems with time varying delay under asynchronous switching is investigated a new lyapunov function dependent on the controllers switching signal is constructed which can counteract the difficulty of controller design to stabilize the system under asynchronous switching moreover the value of the lyapunov function is allowed to increase during mismatched periods based on the average dwell time approach a sufficient condition expressed by a set of linear matrix inequalities lmis is derived to guarantee the mean square exponential stability for the closed loop system and the controllers with asynchronous switching are designed finally a numerical example illustrates the effectiveness of the results

synchronization processes in complex networks we present an extended analysis based on the dynamics towards synchronization of a system of coupled oscillators of the hierarchy of communities in complex networks in the synchronization process different structures corresponding to well defined communities of nodes appear in a hierarchical way the analysis also provides a useful connection between synchronization dynamics complex networks topology and spectral graph analysis

performing likelihood ratio tests with multiply imputed data sets summary existing procedures for obtaining significance levels from multiply imputed data either i require access to the completed data point estimates and variance covariance matrices which may not be available in practice when the dimensionality of the estimand is high or ii directly combine p values with less satisfactory results taking advantage of the well known relationship between the wald and log likelihood ratio test statistics we propose a complete data log likelihood ratio based procedure it is shown that for any number of multiple imputations the proposed procedure is equivalent in large samples to the existing procedure based on the point estimates and the variance covariance matrices yet it only requires the point estimates and evaluations of the complete data log likelihood ratio statistic as a function of these estimates and the completed data the proposed procedure therefore is especially attractive with highly multiparameter incomplete data problems since it does not involve the computation of any matrices

two order parameters for the kuramoto model on complex networks we investigate the behavior of two different order parameters for the kuramoto model in the desynchronized phase since the primary role of the order parameter is to distinguish different phases we focus on the ability to discern the desynchronized phase from the synchronized one on complex networks with the size n from the exact derivation of the difference between two order parameters on a star network we find that these order parameters disagree in the desynchronized phase we also show that the hub plays an important role and provide an analytic conjecture on the condition that the two order parameters agree with each other as n the conjecture is numerically confirmed