synchronization in scale free networks with degree correlation in this paper we study a model of synchronization process on scale free networks with degree degree correlations this model was already studied on this kind of networks without correlations by pastore y piontti et al a l pastore y piontti p a macri l a braunstein phys rev e 76 2007 046117 here we study the effects of the degree degree correlation on the behavior of the load fluctuationsw s in the steady state we found that for assortative networks there exist a specific correlation where the system is optimally synchronized in addition we found that close to this optimal value the fluctuations does not depend on the system size and therefore the system becomes fully scalable this result could be very important for some technological applications on the other hand far from the optimal correlation w s scales logarithmically with the system size

assessing normality in random effects models when one uses the unbalanced mixed linear model mathbf y i mathbf x i mathbf alpha mathbf z i mathbf beta i varepsilon i i 1 cdots n to analyze data from longitudinal experiments with continuous outcomes it is customary to assume varepsilon i sim operatorname ind mathscr n mathbf 0 sigma 2 mathbf i i independent of mathbf beta i sim operatorname iid mathscr n mathbf 0 delta where sigma 2 and the elements of an arbitrary mathbf delta are unknown variance and covariance components in this paper we describe a method for checking model adequacy and in particular the distributional assumption on the random effects mathbf beta i we generalize the weighted normal plot to accommodate dependent nonidentically distributed observations subject to multiple random effects for each individual unit under study one can detect various departures from the normality assumption by comparing the expected and empirical cumulative distribution functions of standardized linear combinations of estimated residuals for each of the individual units through application of distributional results for a certain class of estimators to our context we adjust the estimated covariance of the empirical cumulative distribution function to account for estimation of unknown parameters several examples of our method demonstrate its usefulness in the analysis of longitudinal data

an approximate generalized linear model with random effects for informative missing data this paper develops a class of models to deal with missing data from longitudinal studies we assume that separate models for the primary response and missingness e g number of missed visits are linked by a common random parameter such models have been developed in the econometrics heckman 1979 econometrica 47 153 161 and biostatistics wu and carroll 1988 biometrics 44 175 188 literature for a gaussian primary response we allow the primary response conditional on the random parameter to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness the resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects an example is given to illustrate the approximate approach and simulations are performed to critique the adequacy of the approximation for repeated binary data

estimation and comparison of changes in the presence of information right censoring by modeling the censoring process abstract in estimating and comparing the rates of change of a continuous variable between two groups the unweighted averages of individual simple least squares estimates from each group are often used under a linear random effects model when all individuals have completed observations at identical time points these statistics are maximum likelihood estimates for the expected rates of change however with censored of missing data these estimates are no longer efficient when compared to generalized least squares estimates when in addition the right censoring process is dependent upon the individual rates of change i e informative right censoring the generalized least squares estimates will be biased likelihood ratio test for informativeness of the censoring process and maximum likelihood estimates for the expected rates of change and the parameters of the right censoring process are developed under a linear random effect models with a probit model for the right censoring process in realistic situations we illustrate that the bias in estimating group rate of change and the reduction of power in comparing group difference could be substantial when strong dependency of the right censoring process on individual rates of change is ignored author

model for the analysis of binary longitudinal pain data subject to informative dropout through remedication abstract we address the problem of accounting for informative dropout in the form of rescue medication when comparing pain relievers with respect to longitudinal binary pain relief outcomes we present a selection model approach for binary longitudinal data that accommodates informative dropout the relationship between dropout or remedication and the binary pain relief response is assumed to be characterized by a random effect that is conditional on this random effect response and dropout are independent unlike previous approaches to this problem which rely on numerical or approximation methods we obtain a closed form expression for the marginal log likelihood of response and dropout by specifying a complementary log log link function for both components and a conjugate log gamma random effect distribution a data analysis supported by simulation results suggest that the model fits reasonably well results are compared to those obtained from conventional but somewhat inappropriate analyses

accelerated growth in outgoing links in evolving networks deterministic versus stochastic picture in several real world networks such as the internet world wide web etc the number of links grow in time in a nonlinear fashion we consider growing networks in which the number of outgoing links is a nonlinear function of time but new links between older nodes are forbidden the attachments are made using a preferential attachment scheme in the deterministic picture the number of outgoing links m t at any time t is taken as n t ensuremath theta where n t is the number of nodes present at that time the continuum theory predicts a power law decay of the degree distribution p k ensuremath propto k ensuremath 1 ensuremath 2 1 ensuremath ensuremath theta while the degree of the node introduced at time t i is given by k t i t t i ensuremath theta phantom rule 0 2em 0ex t t i 1 ensuremath theta 2 when the network is evolved till time t numerical results show a growth in the degree distribution for small k values at any nonzero ensuremath theta in the stochastic picture m t is a random variable as long as m t is independent of time the network shows a behavior similar to the barab asi albert ba model different results are obtained when m t is time dependent e g when m t follows a distribution p m ensuremath propto m ensuremath ensuremath lambda the behavior of p k changes significantly as ensuremath lambda is varied for ensuremath lambda g3 the network has a scale free distribution belonging to the ba class as predicted by the mean field theory for smaller values of ensuremath lambda it shows different behavior characteristic features of the clustering coefficients in both models have also been discussed

range limited centrality measures in complex networks here we present a range limited approach to centrality measures in both nonweighted and weighted directed complex networks we introduce an efficient method that generates for every node and every edge its betweenness centrality based on shortest paths of lengths not longer than ensuremath ell 1 l in the case of nonweighted networks and for weighted networks the corresponding quantities based on minimum weight paths with path weights not larger than w ensuremath ell ensuremath ell ensuremath delta ensuremath ell 1 2 l r ensuremath delta these measures provide a systematic description on the positioning importance of a node edge with respect to its network neighborhoods one step out two steps out etc up to and including the whole network they are more informative than traditional centrality measures as network transport typically happens on all length scales from transport to nearest neighbors to the farthest reaches of the network we show that range limited centralities obey universal scaling laws for large nonweighted networks as the computation of traditional centrality measures is costly this scaling behavior can be exploited to efficiently estimate centralities of nodes and edges for all ranges including the traditional ones the scaling behavior can also be exploited to show that the ranking top list of nodes edges based on their range limited centralities quickly freezes as a function of the range and hence the diameter range top list can be efficiently predicted we also show how to estimate the typical largest node to node distance for a network of n nodes exploiting the afore mentioned scaling behavior these observations were made on model networks and on a large social network inferred from cell phone trace logs ensuremath sim 5 5 ifmmode times else texttimes fi 10 6 nodes and ensuremath sim 2 7 ifmmode times else texttimes fi 10 7 edges finally we apply these concepts to efficiently detect the vulnerability backbone of a network defined as the smallest percolating cluster of the highest betweenness nodes and edges and illustrate the importance of weight based centrality measures in weighted networks in detecting such backbones

local preferential attachment model for hierarchical networks abstract in real life networks incomers may only connect to a few others in a local area for their limited information and individuals in a local area are likely to have close relations accordingly we propose a local preferential attachment model here a local area network stands for a node and all its neighbors and the new nodes perform nonlinear preferential attachment k i k i in local areas the stable degree distribution and clustering degree correlations are analytically obtained with the increasing of the clustering coefficient increases while assortativity decreases from positive to negative in addition by adjusting the parameter the model can generate different kinds of degree distribution from exponential to power law the hierarchical organization independent of is the most significant character of this model

synchronizability in complex ad hoc dynamical networks with accelerated growth recent research works have been pursued in connection with network synchronizability under various constraints for different topological structures and evolving mechanisms however the fundamental question of how the synchronizability of the networks relates to accelerated growth and ad hoc property in the evolving processes remains underexplored here we study the ad hoc dynamical models with accelerated growth where the total number of edges increases faster than linearly with network size by adopting three attachment mechanisms random rewired and preferential attachment we investigate the second largest eigenvalues and the ratios of the extremal eigenvalues of coupled matrices in the accelerated models with different evolving parameters for the new models we demonstrate the robustness and fragility of synchronization against random and specific attacks by numerical simulations we find that accelerated growth represents a convenient tool for improving the synchronizability of an evolving network furthermore we show that not only network synchronization but also topological periodicity has robustness and fragility against random failures and specifical removal of the nodes respectively in particular when ad hoc property is suggested in the evolving networks we find that the deletion of nodes is easier to change network synchronizability and robustness compared to the addition of nodes

enhancing the spectral gap of networks by node removal dynamics on networks are often characterized by the second smallest eigenvalue of the laplacian matrix of the network which is called the spectral gap examples include the threshold coupling strength for synchronization and the relaxation time of a random walk a large spectral gap is usually associated with high network performance such as facilitated synchronization and rapid convergence in this study we seek to enhance the spectral gap of undirected and unweighted networks by removing nodes because practically the removal of nodes often costs less than the addition of nodes addition of links and rewiring of links in particular we develop a perturbative method to achieve this goal the proposed method realizes better performance than other heuristic methods on various model and real networks the spectral gap increases as we remove up to half the nodes in most of these networks

network growth under the constraint of synchronization stability while it is well recognized that realistic networks are typically growing with time the dynamical features of their growing processes remain to be explored in the present paper incorporating the requirement of synchronization stability into the conventional models of network growth we will investigate how the growing process of a complex network is influenced by and also will influence the network collective dynamics our study shows that constrained by the synchronization stability the network will be growing in a selective and dynamical fashion in particular we find that the chance for a new node to be accepted by the growing network could have a large variation i e it follows roughly a power law distribution furthermore we find that with the dynamical growth the network is always developed into structures of clear scale free features despite the form of the link attachment preferential or random the dynamical properties of network growth are studied using the method of eigenvalue analysis and they are verified by direct simulations of coupled chaotic oscillators our study implies that driven by the network collective dynamics network growth could also be highly dynamical

noise induced synchronization in small world networks of phase oscillators a small world sw network of similar phase oscillators interacting according to the kuramoto model is studied numerically it is shown that deterministic kuramoto dynamics on sw networks has various stable stationary states this can be attributed to the so called defect patterns in an sw network which it inherits from deformation of helical patterns in its regular parent turning on an uncorrelated random force causes vanishing of the defect patterns hence increasing the synchronization among oscillators for moderate noise intensities this phenomenon called stochastic synchronization is generally observed in some natural networks such as the brain neural network

marginal models for the analysis of longitudinal measurements with nonignorable non monotone missing data summary we propose methods for the analysis of continuous responses subject to nonignorable non monotone missing data we form a pseudolikelihood by naively assuming independence over time and using a product of marginal likelihoods at each time point and we obtain consistent and asymptotically normal estimators of the mean and missingness parameters our primary interest is in estimating the parameters of the marginal model at each time point and we make no assumption about the correlation structure an approximate variance is found for the parameter estimates using a sandwich estimate we provide an example and present a simulation study that assesses the performance of the model

modelling progression of cd4 lymphocyte count and its relationship to survival time the purpose of this article is to model the progression of cd4 lymphocyte count and the relationship between different features of this progression and survival time the complicating factors in this analysis are that the cd4 lymphocyte count is observed only at certain fixed times and with a high degree of measurement error and that the length of the vector of observations is determined in part by the length of survival if probability of death depends on the true unobserved cd4 lymphocyte count then the survival process must be modelled wu and carroll 1988 biometrics 44 175 188 proposed a random effects model for two sample longitudinal data in the presence of informative censoring in which the individual effects included only slopes and intercepts we propose methods for fitting a broad class of models of this type in which both the repeated cd4 lymphocyte counts and the survival time are modelled using random effects these methods permit us to estimate parameters describing the progression of cd4 lymphocyte count as well as the effect of differences in the cd4 trajectory on survival we apply these methods to results of aids clinical trials

the physical position neighbourhood evolving network model abstract many social technological biological and economical systems are properly described by evolved network models in this paper a new evolving network model with the concept of physical position neighbourhood connectivity is proposed and studied this concept exists in many real complex networks such as communication networks the simulation results for network parameters such as the first nonzero eigenvalue and maximal eigenvalue of the graph laplacian clustering coefficients average distances and degree distributions for different evolving parameters of this model are presented the dynamical behaviour of each node on the consensus problem is also studied it is found that the degree distribution of this new model represents a transition between power law and exponential scaling while the barabasi albert scale free model is only one of its special limiting cases it is also found that the time to reach a consensus becomes shorter sharply with increasing of neighbourhood scale of the nodes

predicting links based on knowledge dissemination in complex network abstract link prediction is the task of mining the missing links in networks or predicting the next vertex pair to be connected by a link a lot of link prediction methods were inspired by evolutionary processes of networks in this paper a new mechanism for the formation of complex networks called knowledge dissemination kd is proposed with the assumption of knowledge disseminating through the paths of a network accordingly a new link prediction method knowledge dissemination based link prediction kdlp is proposed to test kd kdlp characterizes vertex similarity based on knowledge quantity kq which measures the importance of a vertex through h index extensive numerical simulations on six real world networks demonstrate that kdlp is a strong link prediction method which performs at a higher prediction accuracy than four well known similarity measures including common neighbors local path index average commute time and matrix forest index furthermore based on the common conclusion that an excellent link prediction method reveals a good evolving mechanism the experiment results suggest that kd is a considerable network evolving mechanism for the formation of complex networks

adjusting for nonignorable drop out using semiparametric nonresponse models abstract consider a study whose design calls for the study subjects to be followed from enrollment time t 0 to time t t at which point a primary endpoint of interest y is to be measured the design of the study also calls for measurements on a vector v t of covariates to be made at one or more times t during the interval 0 t we are interested in making inferences about the marginal mean 0 of y when some subjects drop out of the study at random times q prior to the common fixed end of follow up time t the purpose of this article is to show how to make inferences about 0 when the continuous drop out time q is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables in particular we consider two models for the conditional hazard of drop out given v t y where v t denotes the history of the process v t through time t t 0 t in the first model we assume that q t v t y exp 0 y where 0 is a scalar paramet

scale free property of complex ad hoc networks with accelerated growth a complex ad hoc network model with accelerated growth is proposed in this paper in the evolving process of the model at each time step with the addition probability c1c1 a new vertex with m t m t edges is added into the model which new adding edges are connected with the old vertices according to the preferential attachment rule and with the deletion probability c2 c1 c2 c1 a random chosen vertex is deleted and its associated edges are disappeared simultaneously the accelerated growth means that at each time step the number of new adding edges is the increasing function of the time tt we consider mainly m t t m t t where 0 10 1 to analyze the degree distribution of the model using the continuous approach we prove theoretically and numerically that the model follows the scale free degree distribution and generates both the barabasi and albert ba model and the model introduced by sarshar and roychowdhury sr in addition we present the appropriate numerical range of c1c1 c2c2 and according to theoretical analyzes and numerical simulation the model takes on a certain universality to complex evolving network and has the guiding significance to the application of the peer to peer networks and complex ad hoc networks

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

spectra of real world graphs beyond the semicircle law results on the spectra of adjacency matrices corresponding to models of real world graphs we find that when the number of links grows as the number of nodes the spectral density of uncorrelated random matrices does not converge to the semicircle law furthermore the spectra of real world graphs have specific features depending on the details of the corresponding models in particular scale free graphs develop a trianglelike spectral density with a power law tail while small world graphs have a complex spectral density consisting of several sharp peaks these and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks

anomalous physical transport in complex networks the emergence of scaling in transport through interconnected systems is a consequence of the topological structure of the network and the physical mechanisms underlying the transport dynamics we study transport by advection and diffusion in scale free and erd ifmmode mbox h o else h o fi s r enyi networks velocity distributions derived from a flow potential exhibit power law scaling with exponent ensuremath nu ensuremath approx ensuremath gamma 1 where ensuremath gamma is the exponent of network connectivity using stochastic particle simulations we find anomalous nonlinear scaling of the mean square displacement with time we show the connection with existing descriptions of anomalous transport in disordered systems and explain the mean transport behavior from the coupled nature of particle jump lengths and transition times

mixed effects logistic regression models for longitudinal binary response data with informative drop out a shared parameter model with logistic link is presented for longitudinal binary response data to accommodate informative drop out the model consists of observed longitudinal and missing response components that share random effects parameters to our knowledge this is the first presentation of such a model for longitudinal binary response data comparisons are made to an approximate conditional logit model in terms of a clinical trial dataset and simulations the naive mixed effects logit model that does not account for informative drop out is also compared the simulation based differences among the models with respect to coverage of confidence intervals bias and mean squared error mse depend on at least two factors whether an effect is a between or within subject effect and the amount of between subject variation as exhibited by variance components of the random effects distributions when the shared parameter model holds the approximate conditional model provides confidence intervals with good coverage for within cluster factors but not for between cluster factors the converse is true for the naive model under a different drop out mechanism when the probability of drop out is dependent only on the current unobserved observation all three models behave similarly by providing between subject confidence intervals with good coverage and comparable mse and bias but poor within subject confidence intervals mse and bias the naive model does more poorly with respect to the within subject effects than do the shared parameter and approximate conditional models the data analysis which entails a comparison of two pain relievers and a placebo with respect to pain relief conforms to the simulation results based on the shared parameter model but not on the simulation based on the outcome driven drop out process this comparison between the data analysis and simulation results may provide evidence that the shared parameter model holds for the pain data

scale free networks via attaching to random neighbors abstract preferential attachment is considered one of the key factors in the formation of scale free networks however complete random attachment without a preferential mechanism can also generate scale free networks in nature such as protein interaction networks in cells this article presents a new scale free network model that applies the following general mechanisms i networks expand continuously by the addition of new vertices and ii new vertices attach to random neighbors of random vertices that are already well connected the proposed model does not require global based preferential strategies and utilizes only the random attachment method theoretical analysis and numerical simulation results denote that the proposed model has steady scale free network characteristics and random attachment without a preferential mechanism may generate scale free networks

weighted estimating equations for longitudinal studies with death and non monotone missing time dependent covariates and outcomes we propose a marginal modeling approach to estimate the association between a time dependent covariate and an outcome in longitudinal studies where some study participants die during follow up and both variables have non monotone response patterns the proposed method is an extension of weighted estimating equations that allows the outcome and covariate to have different missing data patterns we present methods for both random and non random missing data mechanisms a study of functional recovery in a cohort of elderly female hip fracture patients motivates the approach

a correlated random effects model for normal longitudinal data with nonignorable missingness the missing data problem is common in longitudinal or hierarchical structure studies in this paper we propose a correlated random effects model to fit normal longitudinal or cluster data when the missingness mechanism is nonignorable computational challenges arise in the model fitting due to intractable numerical integrations we obtain the estimates of the parameters based on an accurate approximation of the log likelihood which has higher order accuracy but with less computational burden than the existing approximation we apply the proposed method it to a real data set arising from an autism study

self organized scale free networks growth and preferential attachments have been coined as the two fundamental mechanisms responsible for the scale free feature in complex networks as characterized by an algebraic degree distribution there are situations particularly in biological networks where growth is absent or not important yet some of these networks still exhibit the scale free feature with a small degree exponent here we propose two classes of models to account for this phenomenon we show analytically and numerically that in the first model a spectrum of algebraic degree distributions with a small exponent can be generated the second model incorporates weights for nodes and it is able to generate robust scale free degree distribution with larger algebraic exponents our results imply that it is natural for a complex network to self organize itself into a scale free

spatially self organized resilient networks by a distributed cooperative mechanism abstract the robustness of connectivity and the efficiency of paths are incompatible in many real networks we propose a self organization mechanism for incrementally generating onion like networks with positive degree degree correlations whose robustness is nearly optimal as a spatial extension of the generation model based on cooperative copying and adding shortcut we show that the growing networks become more robust and efficient through enhancing the onion like topological structure on a space the reasonable constraint for locating nodes on the perimeter in typical surface growth as a self propagation does not affect these properties of the tolerance and the path length moreover the robustness can be recovered in the random growth damaged by insistent sequential attacks even without any remedial measures

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

fubini s theorem in codimension two we classify codimension two analytic submanifolds of projective space x cp having the property that any line through a general point x x having contact to order two with x at x automatically has contact to order three we give applications to the study of the debarre de jong conjecture and of varieties whose fano variety of lines has dimension 2n 4

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

semiparametric regression for repeated outcomes with nonignorable nonresponse abstract we consider inference about the parameter indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values that is nonresponse is nonignorable we propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal can for estimating when the response probabilities can be parametrically modeled and a can estimator exists the proposed estimators do not require full specification of a parametric likelihood and their computation does not require numerical integration our estimators can be viewed as an extension of generalized estimating equation estimators that allows for nonignorable nonresponse we show that our class essentially consists of all can estimators of we also show that the asymptotic variance of the optimal estimator in our

hub synchronization in scale free networks heterogeneity in the degree distribution is known to suppress global synchronization in complex networks of symmetrically coupled oscillators scale free networks display a great deal of heterogeneity containing a few nodes termed hubs that are highly connected while most nodes receive only a few connections here we show that a group of synchronized nodes may appear in scale free networks hubs undergo a transition to synchronization while the other nodes remain unsynchronized this general phenomenon can occur even in the absence of global synchronization our results suggest that scale free networks may have evolved to complement various levels of synchronization

epidemic dynamics behavior in some bus transport networks abstract we abstract bus transport networks btns to complex networks using the space p approach first we select three actual btns in three major cities in china namely beijing shanghai and hangzhou using the sis model we simulate and study the epidemic spreading in the three btns we obtain the density of infected vertices varying with time and the stationary density of infected vertices varying with infection rate second we simulate and study the epidemic spreading in a recently introduced btn evolution model the network properties of which correspond well with those of actual btns third we use mean field theory to analyze the epidemic dynamics behavior of the btn evolution model and obtain the theoretical epidemic threshold of this model the theoretical value agrees well with the simulation results based on the work in this paper we provide the following possible forecasts for epidemic dynamics in actual btns an actual btn should have a finite positive epidemic threshold if the effective infection rate is above this threshold the epidemic spread in the network and the density of infected vertices finally stabilizes in a balanced state below this threshold the number of infected vertices decays exponentially fast and the epidemic cannot spread on a large scale

finite mixture modeling with mixture outcomes using the em algorithm summary this paper discusses the analysis of an extended finite mixture model where the latent classes corresponding to the mixture components for one set of observed variables influence a second set of observed variables the research is motivated by a repeated measurement study using a random coefficient model to assess the influence of latent growth trajectory class membership on the probability of a binary disease outcome more generally this model can be seen as a combination of latent class modeling and conventional mixture modeling the em algorithm is used for estimation as an illustration a random coefficient growth model for the prediction of alcohol dependence from three latent classes of heavy alcohol use trajectories among young adults is analyzed

stock market networks the dynamic conditional correlation approach we demonstrate the economic relevance of minimum spanning trees msts constructed from dynamic conditional correlations dcc for a sample of s p 100 constituents an empirical comparison of mst properties shows that using the standard approach of rolling or sliding window correlations yields trees that are more robust have higher densities and exhibit higher industry clustering than msts based on dcc our results suggest that these properties are achieved at the expense of the smoothing of market dynamics which is better preserved by dcc the dcc approach offers a new perspective for the analysis of complex systems such as stock markets

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

optimizing controllability of complex networks by minimum structural perturbations to drive a large complex networked dynamical system toward some desired state using as few external signals as possible is a fundamental issue in the emerging field of controlling complex networks optimal control is referred to the situation where such a network can be fully controlled using only one driving signal we propose a general approach to optimizing the controllability of complex networks by judiciously perturbing the network structure the principle of our perturbation method is validated theoretically and demonstrated numerically for homogeneous and heterogeneous random networks and for different types of real networks as well the applicability of our method is discussed in terms of the relative costs of establishing links and imposing external controllers besides the practical usage of our approach its implementation elucidates interestingly the intricate relationship between certain structural properties of the network and its controllability

a random effects ordinal regression model for multilevel analysis a random effects ordinal regression model is proposed for analysis of clustered or longitudinal ordinal response data this model is developed for both the probit and logistic response functions the threshold concept is used in which it is assumed that the observed ordered category is determined by the value of a latent unobservable continuous response that follows a linear regression model incorporating random effects a maximum marginal likelihood mml solution is described using gauss hermite quadrature to numerically integrate over the distribution of random effects an analysis of a dataset where students are clustered or nested within classrooms is used to illustrate features of random effects analysis of clustered ordinal data while an analysis of a longitudinal dataset where psychiatric patients are repeatedly rated as to their severity is used to illustrate features of the random effects approach for longitudinal ordinal data

variance components testing in the longitudinal mixed effects model this article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by laird and ware 1982 biometrics 38 963 974 our discussion of the large sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by self and liang 1987 journal of the american statistical association 82 605 610

bus transport network model with ideal n depth clique network topology abstract we propose an ideal n depth clique network model in this model the original network is composed of cliques maximal complete subgraphs that overlap with each other the network expands continuously by the addition of new cliques the final diameter of the network can be set in advance namely it is controllable assuming that the diameter of the network is n the network exhibits a logistic structure with n 1 layers in this structure the 0th layer represents the original network and each node of the m th layer 1 m n corresponds to a clique in the m 1 th layer in the growth process of the network we ensure that any m th layer network is composed of overlapping cliques any node in an m th layer network corresponds to an m depth community in the original network and the diameter of an m depth community is m therefore the n 1 th layer network will contain only one clique the n th layer network will contain only one node and the diameter of the corresponding original network is n then an ideal n depth clique network will be obtained based on the ideal n depth clique network model we construct a bus transport network model with an ideal n depth clique network topology icnbtn moreover our study compares this model with the real bus transport network realbtn of three major cities in china and a recently introduced bus transport network model btn whose network properties correspond well with those of real btns the network properties of the icnbtn are much closer to those of the realbtn than those of the btn are at the same time the icnbtn has higher clustering extent of bus routes smaller network diameter which corresponds to shorter maximum transfer times in a bus network and lower average shortest path time coefficient than the btn and the realbtn therefore the icnbtn can achieve higher transfer efficiency for a bus transport system

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

characterization of calabi yau variations of hodge structure over tube domains by characteristic forms sheng and zuo s characteristic forms are invariants of a variation of hodge structure we show that they characterize gross s canonical variations of hodge structure of calabi yau type over hermitian symmetric tube domains

phase synchronization in small world networks of chaotic oscillators abstract small world networks are highly clustered networks with small average distance among the vertices there are many natural and technological networks that present this kind of connections we study the phase synchronization of small world chaotic oscillator networks in this paper we find that for rossler oscillator networks in the synchronous regime the oscillation phases are locked while the amplitudes vary chaotically we further show the dependence of phase synchronization on the network coupling strength the product of the shortcuts adding probability and the number of chaotic oscillators as well as the maximal frequency mismatch

degree distribution rank size distribution and leadership persistence in mediation driven attachment networks abstract we investigate the growth of a class of networks in which a new node first picks a mediator at random and connects with m randomly chosen neighbors of the mediator at each time step we show that the degree distribution in such a mediation driven attachment mda network exhibits power law p k k m with a spectrum of exponents depending on m to appreciate the contrast between mda and barabasi albert ba networks we then discuss their rank size distribution to quantify how long a leader the node with the maximum degree persists in its leadership as the network evolves we investigate the leadership persistence probability f i e the probability that a leader retains its leadership up to time we find that it exhibits a power law f m with persistence exponent m 1 51 m in mda networks and m 1 53 exponentially with m in ba networks

scale free and stable structures in complex ad hoc networks unlike the well studied models of growing networks where the dominant dynamics consist of insertions of new nodes and connections and rewiring of existing links we study ad hoc networks where one also has to contend with rapid and random deletions of existing nodes and hence the associated links we first show that dynamics based only on the well known preferential attachments of new nodes do not lead to a sufficiently heavy tailed degree distribution in ad hoc networks in particular the magnitude of the power law exponent increases rapidly from 3 with the deletion rate becoming ensuremath infty in the limit of equal insertion and deletion rates we then introduce a local and universal compensatory rewiring dynamic and show that even in the limit of equal insertion and deletion rates true scale free structures emerge where the degree distributions obey a power law with a tunable exponent which can be made arbitrarily close to 2 the dynamics reported in this paper can be used to craft protocols for designing highly dynamic peer to peer networks and also to account for the power law exponents observed in existing popular services

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

a two part random effects model for semicontinuous longitudinal data a semicontinuous variable has a portion of responses equal to a single value typically 0 and a continuous often skewed distribution among the remaining values in cross sectional analyses variables of this type may be described by a pair of regression models for example a logistic model for the probability of nonzero response and a conditional linear model for the mean response given that it is nonzero we extend this two part regression approach to longitudinal settings by introducing random coefficients into both the logistic and the linear stages fitting a two part random effects model poses computational challenges similar to those found with generalized linear mixed models we obtain maximum likelihood estimates for the fixed coefficients and variance components by an approximate fisher scoring procedure based on high order laplace approximations to illustrate we apply the technique to data from the adolescent alcohol prevention trial examining reported recent alcohol use for students in g

bias correction in generalized linear mixed models with multiple components of dispersion abstract general formulas are derived for the asymptotic bias in regression coefficients and variance components estimated by penalized quasi likelihood pql in generalized linear mixed models with canonical link function and multiple sets of independent random effects easily computed correction matrices result in variance component estimates that have satisfactory asymptotic behavior for small values of the variance components and significantly reduce bias for larger values both first order and second order correction procedures are developed for regression coefficients estimated by pql the methods are illustrated through an analysis of an experiment on salamander matings involving crossed male and female random effects and their properties are evaluated in a simulation study

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved