maximum likelihood extracting unbiased information from complex networks the choice of free parameters in network models is subjective since it depends on what topological properties are being monitored however we show that the maximum likelihood ml principle indicates a unique statistically rigorous parameter choice associated with a well defined topological feature we then find that if the ml condition is incompatible with the built in parameter choice network models turn out to be intrinsically ill defined or biased to overcome this problem we construct a class of safely unbiased models we also propose an extension of these results that leads to the fascinating possibility to extract only from topological data the hidden variables underlying network organization making them no longer hidden we test our method on world trade web data where we recover the empirical gross domestic product using only topological information

structured condition numbers and small sample condition estimation of symmetric algebraic riccati equations abstract this paper is devoted to a structured perturbation analysis of the symmetric algebraic riccati equations by exploiting the symmetry structure based on the analysis the upper bounds for the structured normwise mixed and componentwise condition numbers are derived due to the exploitation of the symmetry structure our results are improvements of the previous work on the perturbation analysis and condition numbers of the symmetric algebraic riccati equations our preliminary numerical experiments demonstrate that our condition numbers provide accurate estimates for the change in the solution caused by the perturbations on the data moreover by applying the small sample condition estimation method we propose a statistical algorithm for practically estimating the condition numbers of the symmetric algebraic riccati equations

estimating and understanding exponential random graph models we introduce a method for the theoretical analysis of exponential random graph models the method is based on a large deviations approximation to the normalizing constant shown to be consistent using theory developed by chatterjee and varadhan european j combin 32 2011 1000 1017 the theory explains a host of difficulties encountered by applied workers many distinct models have essentially the same mle rendering the problems practically ill posed we give the first rigorous proofs of degeneracy observed in these models here almost all graphs have essentially no edges or are essentially complete we supplement recent work of bhamidi bresler and sly 2008 ieee 49th annual ieee symposium on foundations of computer science focs 2008 803 812 ieee showing that for many models the extra sufficient statistics are useless most realizations look like the results of a simple erd s renyi model we also find classes of models where the limiting graphs differ from erd s renyi graphs a limitation of our approach inherited from the limitation of graph limit theory is that it works only for dense graphs

the average distances in random graphs with given expected degrees abstract random graph theory is used to examine the small world phenomenon any two strangers are connected through a short chain of mutual acquaintances we will show that for certain families of random graphs with given expected degrees the average distance is almost surely of order log n log d where d is the weighted average of the sum of squares of the expected degrees of particular interest are power law random graphs in which the number of vertices of degree k is proportional to 1 k for some fixed exponent for the case of 3 we prove that the average distance of the power law graphs is almost surely of order log n log d however many internet social and citation networks are power law graphs with exponents in the range 2 3 for which the power law random graphs have average distance almost surely of order log log n but have diameter of order log n provided having some mild constraints for the average distance and maximum degree in particular these graphs contain a dense subgraph which we call the core having nc log log n vertices almost all vertices are within distance log log n of the core although there are vertices at distance log n from the core

accurate solutions of m matrix algebraic riccati equations this paper is concerned with the relative perturbation theory and its entrywise relatively accurate numerical solutions of an m matrix algebraic riccati equations mare xdx ax xb c 0 by which we mean the following conformally partitioned matrix left begin array ll b d c a end array right is a nonsingular or an irreducible singular m matrix it is known that such an mare has a unique minimal nonnegative solution phi it is proved that small relative perturbations to the entries of a b c and d introduce small relative changes to the entries of the nonnegative solution phi thus the smaller entries phi do not suffer bigger relative errors than its larger entries unlike the existing perturbation theory for general algebraic riccati equations we then discuss some minor but crucial implementation changes to three existing numerical methods so that they can be used to compute phi as accurately as the input data deserve current study is based on a previous paper of the authors on m matrix sylvester equation for which d 0

an exponential family of probability distributions for directed graphs abstract directed graph or digraph data arise in many fields especially in contemporary research on structures of social relationships we describe an exponential family of distributions that can be used for analyzing such data a substantive rationale for the general model is presented and several special cases are discussed along with some possible substantive interpretations a computational algorithm based on iterative scaling procedures for use in fitting data is described as are the results of a pilot simulation study an example using previously reported empirical data is worked out in detail an extension to multiple relationship data is discussed briefly

hyperbolic geometry of complex networks we develop a geometric framework to study the structure and function of complex networks we assume that hyperbolic geometry underlies these networks and we show that with this assumption heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry conversely we show that if a network has some metric structure and if the network degree distribution is heterogeneous then the network has an effective hyperbolic geometry underneath we then establish a mapping between our geometric framework and statistical mechanics of complex networks this mapping interprets edges in a network as noninteracting fermions whose energies are hyperbolic distances between nodes while the auxiliary fields coupled to edges are linear functions of these energies or distances the geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures finally we show that targeted transport processes without global topology knowledge made possible by our geometric framework are maximally efficient according to all efficiency measures in networks with strongest heterogeneity and clustering and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure

hamiltonian dynamics of preferential attachment prediction and control of network dynamics are grand challenge problems in network science the lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades here we study the dynamics of networks evolving according to preferential attachment pa known to approximate well the large scale growth dynamics of a variety of real networks we show that this dynamics is hamiltonian thus casting the study of complex networks dynamics to the powerful canonical formalism in which the time evolution of a dynamical system is described by hamilton s equations we derive the explicit form of the hamiltonian that governs network growth in pa this hamiltonian turns out to be nearly identical to graph energy in the configuration model which shows that the ensemble of random graphs generated by pa is nearly identical to the ensemble of random graphs with scale free degree distributions in other words pa generates nothing but random graphs with power law degree distribution the extension of the developed canonical formalism for network analysis to richer geometric network models with non degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales

mixed and componentwise condition numbers for matrix decompositions abstract we present normwise and componentwise perturbation bounds for the lu the cholesky the l d l t and the qr decompositions by using a new approach the explicit expressions of mixed and componentwise condition numbers for these matrix decompositions are derived the condition numbers improve known results of the normwise and componentwise cases and reveal the characterizations of the structured perturbations the exact explicit perturbation expressions are derived for the factors l and u of the lu decomposition and the rigorous normwise and componentwise perturbation bounds are presented for the lu decomposition

condition numbers of algebraic riccati equations in the frobenius norm consider the continuous time algebraic riccati equation care and the discrete time algebraic riccati equation dare which arise in linear control and system theory it is known that appropriate assumptions on the coefficient matrices guarantee the existence and uniqueness of hermitian positive semidefinite stabilizing solutions in this note we apply the theory of condition developed by rice to define condition numbers of the care and dare in the frobenius norm and derive explicit expressions of the condition numbers in a uniform manner both the complex case and real case are considered and connections to certain existing condition numbers of the care and dare are discussed

a new class of nonsymmetric algebraic riccati equations abstract motivated by the study of linear quadratic differential games we introduce a new class of nonsymmetric algebraic riccati equations it is shown that every equation in this class has a unique stabilizing solution which is the solution required to find the open loop nash equilibrium for the differential game we show that the doubling algorithm can be used to find this solution efficiently the solution may also be found by the schur method and under further assumptions by newton s method and a basic fixed point iteration

mixed and componentwise condition numbers of nonsymmetric algebraic riccati equation abstract in this paper the mixed and componentwise condition numbers of nonsymmetric algebraic riccati equation are considered the explicit expressions of two kinds of condition numbers are derived in the uniform manner and the upper bounds are proposed some simple numerical experiments show that the mixed and componentwise condition numbers can be sharp

latent space approaches to social network analysis network models are widely used to represent relational information among interacting units in studies of social networks recent emphasis has been placed on random graph models where the nodes usually represent individual social actors and the edges represent the presence of a specified relation between actors we develop a class of models where the probability of a relation between actors depends on the positions of individuals in an unobserved social space we make inference for the social space within maximum likelihood and bayesian frameworks and propose markov chain monte carlo procedures for making inference on latent positions and the effects of observed covariates we present analyses of three standard datasets from the social networks literature and compare the method to an alternative stochastic blockmodeling approach in addition to improving on model fit for these datasets our method provides a visual and interpretable model based spatial representation of social relationships and improv

consistent inference of probabilities for reproducible experiments the need for inducing a probability distribution from partial data and the complementary problem of the analysis of an observed distribution in terms of fewer relevant variables occur in many branches of physics for reproducible experiments consistency conditions which must be satisfied by any algorithm for inferring a discrete probability distribution with given averages are formulated the only consistent algorithm is the one leading to the distribution of maximal entropy subject to the given constraints

design of inner coupling matrix for robustly self synchronizing networks abstract a self synchronizing network may undergo change of scale and topology during its functioning thus adjustment of parameters is necessary to enable the synchronization the adjustment cost and runtime break demand a method to maintain continuous operation of the network to address these issues this paper presents an analytical method for the design of the inner coupling matrix the proposed method renders the synchronization robust to change of network scale and topology it is usual in network models that scale and topology are represented by outer coupling matrix in this paper we only consider diffusively coupled networks for these networks the eigenvalues of the outer coupling matrix are all non positive by utilizing this property the designed inner coupling matrix can cover the entire left half of complex plane within the synchronized region to underlie robustness of synchronization after elaborating the applicability of several types of synchronization state for a robustly self synchronizing network the analytical design method is given for the stable equilibrium point case sometimes the jacobian matrix of the node dynamical equation may lead to an unrealizable complex inner coupling matrix in the method we then introduce a lemma of matrix transformation to prevent this possibility additionally we investigated the choice of inner coupling matrix to get a desirable self synchronization speed the corresponding condition in the design procedure is given to drive the network synchronization faster than convergence of each node finally the article includes examples that show effectiveness and soundness of the method

on the augmented system approach to sparse least squares problems we study the augmented system approach for the solution of sparse linear least squares problems it is well known that this method has better numerical properties than the method based on the normal equations we use recent work by arioli et al 1988 to introduce error bounds and estimates for the components of the solution of the augmented system in particular we find that using iterative refinement we obtain a very robust algorithm and our estimates of the error are accurate and cheap to compute the final error and all our error estimates are much better than the classical or skeel s error analysis 1979 indicates moreover we prove that our error estimates are independent of the row scaling of the augmented system and we analyze the influence of the bjorck scaling 1967 on these estimates we illustrate this with runs both on large scale practical problems and contrived examples comparing the numerical behaviour of the augmented systems approach with a code using the normal equations these experiments show that while the augmented system approach with iterative refinement can sometimes be less efficient than the normal equations approach it is comparable or better when the least squares matrix has a full row and is in any case much more stable and robust

mixed and componentwise condition numbers for a linear function of the solution of the total least squares problem abstract in this paper we consider the mixed and componentwise condition numbers for a linear function lx of the solution to the total least squares tls problem we derive the explicit expressions of the mixed and componentwise condition numbers through the dual techniques under both unstructured and structured componentwise perturbations the sharp upper bounds for condition numbers are obtained an efficient condition estimation algorithm is proposed which can be integrated into the iterative method for solving large scale tls problems moreover the new derived condition number expressions can recover the previous results on the condition analysis for the tls problem when l i n numerical experiments show the effectiveness of the introduced condition numbers and condition estimation algorithm

brief paper robust filtering with stochastic nonlinearities and multiple missing measurements this paper is concerned with the filtering problem for a class of discrete time uncertain stochastic nonlinear time delay systems with both the probabilistic missing measurements and external stochastic disturbances the measurement missing phenomenon is assumed to occur in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval 01 such a probabilistic distribution could be any commonly used discrete distribution over the interval 01 the multiplicative stochastic disturbances are in the form of a scalar gaussian white noise with unit variance the purpose of the addressed filtering problem is to design a filter such that for the admissible random measurement missing stochastic disturbances norm bounded uncertainties as well as stochastic nonlinearities the error dynamics of the filtering process is exponentially mean square stable by using the linear matrix inequality lmi method sufficient conditions are established that ensure the exponential mean square stability of the filtering error and then the filter parameters are characterized by the solution to a set of lmis illustrative examples are exploited to show the effectiveness of the proposed design procedures

on level 2 condition number for the weighted moore penrose inverse in this paper we present characterizations for the level 2 condition number of the weighted moore penrose inverse i e cond m n a cond m n 2 a cond m n a 1 where cond m n a is the condition number of the weighted moore penrose inverse of a rectangular matrix and cond m n 2 a is the level 2 condition number of this problem this paper extends the result by cucker diao and wei f cucker h diao y wei on the level 2 condition number for moore penrose inversion 2005 unpublished report and improves the results by wei and wang y wei d wang condition numbers and perturbation of weighted moore penrose inverse and weighted linear least squares problem appl math comput 145 2003 45 58

brief paper perturbation analysis and condition numbers of symmetric algebraic riccati equations this paper is devoted to the perturbation analysis of symmetric algebraic riccati equations based on our perturbation analysis the upper bounds for the normwise mixed and componentwise condition numbers are presented the results are demonstrated by our preliminary numerical experiments

convergent sequences of dense graphs i subgraph frequencies metric properties and testing we consider sequences of graphs gn and define various notions of convergence related to these sequences left convergence defined in terms of the densities of homomorphisms from small graphs into gn right convergence defined in terms of the densities of homomorphisms from gn into small graphs and convergence in a suitably defined metric in part i of this series we show that left convergence is equivalent to convergence in metric both for simple graphs gn and for graphs gn with nodeweights and edgeweights one of the main steps here is the introduction of a cut distance comparing graphs not necessarily of the same size we also show how these notions of convergence provide natural

h_ infty state estimation for discrete time complex networks with randomly occurring sensor saturations and randomly varying sensor delays in this paper the state estimation problem is investigated for a class of discrete time delay nonlinear complex networks with randomly occurring phenomena from sensor measurements the randomly occurring phenomena include randomly occurring sensor saturations rosss and randomly varying sensor delays rvsds that result typically from networked environments a novel sensor model is proposed to describe the rosss and the rvsds within a unified framework via two sets of bernoulli distributed white sequences with known conditional probabilities rather than employing the commonly used lipschitz type function a more general sector like nonlinear function is used to describe the nonlinearities existing in the network the purpose of the addressed problem is to design a state estimator to estimate the network states through available output measurements such that for all probabilistic sensor saturations and sensor delays the dynamics of the estimation error is guaranteed to be exponentially mean square stable and the effect from the exogenous disturbances to the estimation accuracy is attenuated at a given level by means of an h norm in terms of a novel lyapunov krasovskii functional and the kronecker product sufficient conditions are established under which the addressed state estimation problem is recast as solving a convex optimization problem via the semidefinite programming method a simulation example is provided to show the usefulness of the proposed state estimation conditions

entropy measures for networks toward an information theory of complex topologies the quantification of the complexity of networks is today a fundamental problem in the physics of complex systems a possible roadmap to solve the problem is via extending key concepts of information theory to networks in this rapid communication we propose how to define the shannon entropy of a network ensemble and how it relates to the gibbs and von neumann entropies of network ensembles the quantities we introduce here will play a crucial role for the formulation of null models of networks through maximum entropy arguments and will contribute to inference problems emerging in the field of complex networks

on mixed and componentwise condition numbers for moore penrose inverse and linear least squares problems classical condition numbers are normwise they measure the size of both input perturbations and output errors using some norms to take into account the relative of each data component and in particular a possible data sparseness componentwise condition numbers have been increasingly considered these are mostly of two kinds mixed and componentwise in this paper we give explicit expressions computable from the data for the mixed and componentwise condition numbers for the computation of the moore penrose inverse as well as for the computation of solutions and residues of linear least squares problems in both cases the data matrices have full column row rank

state estimation for stochastic complex networks with switching topology this technical note studies the state estimation problem for stochastic complex networks with switching topology a set of bernoulli random variables are used to describe the switching behavior of the network by using the structure of the extended kalman filter ekf a recursive estimator is developed for each node to guarantee an optimized upper bound on the state estimation error covariance despite the switching coupling and linearization errors compared with the existing results on state estimation for stochastic complex networks a distinct feature for the proposed estimator is that the estimation errors for all nodes are not formulated in an augmented vector so that the gain matrix can be determined separately for each node by solving two riccati like difference equations based on the stochastic analysis theory it is shown that the estimation error is bounded in mean square under certain conditions simulation results are provided to verify the effectiveness of the proposed estimator

two kinds of condition numbers for the quadratic matrix equation in the situation that the quadratic matrix equation has the dominant or minimal solvents the mixed and componentwise condition numbers of the quadratic matrix equation are considered the explicit approximate expressions of two kinds of condition numbers are derived in the uniform manner and the upper bounds are proposed the theoretical results are illustrated by using some simple numerical examples

consistency under sampling of exponential random graph models the growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure typically however these are models for the entire network while the data consists only of a sampled sub network parameters for the whole network which is what is of interest are estimated by applying the model to the sub network this assumes that the model is consistent under sampling or in terms of the theory of stochastic processes that it defines a projective family focusing on the popular class of exponential random graph models ergms we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models and that satisfying it drastically limits ergm s expressive power these results are actually special cases of more general results about exponential families of dependent random variables which we also prove using such results we offer easily checked conditions for the consistency of maximum likelihood estimation in ergms and discuss some possible constructive responses

bounded h_ infty synchronization and state estimation for discrete time varying stochastic complex networks over a finite horizon in this paper new synchronization and state estimation problems are considered for an array of coupled discrete time varying stochastic complex networks over a finite horizon a novel concept of bounded h synchronization is proposed to handle the time varying nature of the complex networks such a concept captures the transient behavior of the time varying complex network over a finite horizon where the degree of bounded synchronization is quantified in terms of the h norm a general sector like nonlinear function is employed to describe the nonlinearities existing in the network by utilizing a timevarying real valued function and the kronecker product criteria are established that ensure the bounded h synchronization in terms of a set of recursive linear matrix inequalities rlmis where the rlmis can be computed recursively by employing available matlab toolboxes the bounded h state estimation problem is then studied for the same complex network where the purpose is to design a state estimator to estimate the network states through available output measurements such that over a finite horizon the dynamics of the estimation error is guaranteed to be bounded with a given disturbance attenuation level again an rlmi approach is developed for the state estimation problem finally two simulation examples are exploited to show the effectiveness of the results derived in this paper

synchronization in complex networks with stochastically switching coupling structures synchronization in complex networks with time dependent coupling and stochastically switching coupling structure is discussed a novel approach investigating synchronization based on the scramblingness property of the coupling matrix is proposed some sufficient condition for a network with general time varying coupling structure to reach complete synchronization is provided based on the general theorem networks with stochastically switching coupling structures is investigated in particular two kinds of stochastic switching coupling networks are addressed a independent and identically distributed switching processes and b markov jump processes in both cases some sufficient condition for almost sure synchronization of the networks is given also numerical simulations are provided to illustrate the theoretical results

synchronization of complex networks via aperiodically intermittent pinning control in this note synchronization for linearly coupled network is investigated by pinning a simple aperiodically intermittent controller nodes dynamical behaviors in the network are described by continuous time ordinary differential equations some sufficient conditions to guarantee global synchronization are presented furthermore an adaptive algorithm is designed for the pinning control gain and its validity is also proved rigorously finally numerical simulations are given to demonstrate the correctness of obtained results

robust kalman filtering for uncertain discrete time systems this paper is concerned with the problem of a kalman filter design for uncertain discrete time systems the system under consideration is subjected to time varying norm bounded parameter uncertainty in both the state and output matrices the problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties furthermore the guaranteed cost can be optimized by appropriately searching a scaling design parameter

robust discrete time minimum variance filtering the bounded variance filtered estimation of the state of an uncertain linear discrete time system with an unknown norm bounded parameter matrix is considered an upper bound on the variance of the estimation error is found for all admissible systems and estimators are derived that minimize the latter bound we treat the finite horizon time varying case and the infinite time case where the nominal system model is time invariant in the special stationary case where it is known that the uncertain system is time invariant we provide a robust filter for all uncertainties that still keep the system asymptotically stable

condition number and backward errors of nonsymmetric algebraic riccati equation abstract the normwise condition number and two kinds of backward errors are considered when nonsymmetric algebraic riccati equation nare has the minimal nonnegative solution based on the techniques for the symmetric case we apply the condition number theory developed by rice to define condition number for nare the explicit expression is derived in a uniform manner meanwhile two kinds of backward errors are defined and evaluated by the explicit formulas numerical experiments are listed to illustrate and compare the practical performance

a contraction theory based analysis of the stability of the deterministic extended kalman filter the contraction properties of the extended kalman filter viewed as a deterministic observer for nonlinear systems are analyzed the approach relies on the study of an auxiliary virtual dynamical system some conditions under which exponential convergence of the state error can be guaranteed are derived moreover contraction provides a simple formalism to study some robustness properties of the filter especially with respect to measurement errors as illustrated by a simplified inertial navigation example this technical note sheds another light on the theoretical properties of this popular observer

sensitivity analysis of the discrete time algebraic riccati equation abstract consider the discrete time algebraic riccati equation dare a t xa x a t xb s r b t xb 1 b t xa s t q 0 where a r n n b s r n m r rt r m m q qt r n n the available perturbation theory for the dare can only be applied to the case r 0 however in some control problems the matrix r can be singular in this paper we study perturbation properties of the dare without the restriction r 0 perturbation bounds and a relative condition number for the stabilizing solution of the dare are derived computable residual bounds for an approximate solution are also derived the theoretical results are illustrated by numerical examples

state estimation for coupled uncertain stochastic networks with missing measurements and time varying delays the discrete time case this paper is concerned with the problem of state estimation for a class of discrete time coupled uncertain stochastic complex networks with missing measurements and time varying delay the parameter uncertainties are assumed to be norm bounded and enter into both the network state and the network output the stochastic brownian motions affect not only the coupling term of the network but also the overall network dynamics the nonlinear terms that satisfy the usual lipschitz conditions exist in both the state and measurement equations through available output measurements described by a binary switching sequence that obeys a conditional probability distribution we aim to design a state estimator to estimate the network states such that for all admissible parameter uncertainties and time varying delays the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square by employing the lyapunov functional method combined with the stochastic analysis approach several delay dependent criteria are established that ensure the existence of the desired estimator gains and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities lmis two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes

perturbation analysis of a quadratic matrix equation associated with an m matrix this paper is devoted to the perturbation analysis for the quadratic matrix equation x 2 e x f 0 where e is a diagonal matrix and f is an m matrix the quadratic matrix equation of this type arises in noisy wiener hopf problems for markov chains the solution of practical interest is a particular m matrix solution in this paper the perturbation bound of the m matrix solution is presented meanwhile the residual bound for an approximate solution to the m matrix solution is obtained the theoretical results are illustrated by using simple numerical examples

exponential synchronization of linearly coupled neural networks with impulsive disturbances this brief investigates globally exponential synchronization for linearly coupled neural networks nns with time varying delay and impulsive disturbances since the impulsive effects discussed in this brief are regarded as disturbances the impulses should not happen too frequently the concept of average impulsive interval is used to formalize this phenomenon by referring to an impulsive delay differential inequality we investigate the globally exponential synchronization of linearly coupled nns with impulsive disturbances the derived sufficient condition is closely related with the time delay impulse strengths average impulsive interval and coupling structure of the systems the obtained criterion is given in terms of an algebraic inequality which is easy to be verified and hence our result is valid for large scale systems the results extend and improve upon earlier work as a numerical example a small world network composing of impulsive coupled chaotic delayed nn nodes is given to illustrate our theoretical result

h_ infty state estimation for discrete time nonlinear singularly perturbed complex networks under the round robin protocol this paper investigates the h infty state estimation problem for a class of discrete time nonlinear singularly perturbed complex networks spcns under the round robin rr protocol a discrete time nonlinear spcn model is first devised on two time scales with their discrepancies reflected by a singular perturbation parameter spp the network measurement outputs are transmitted via a communication network where the data transmissions are scheduled by the rr protocol with hope to avoid the undesired data collision the error dynamics of the state estimation is governed by a switched system with a periodic switching parameter a novel lyapunov function is constructed that is dependent on both the transmission order and the spp by establishing a key lemma specifically tackling the spp sufficient conditions are obtained such that for any spp less than or equal to a predefined upper bound the error dynamics of the state estimation is asymptotically stable and satisfies a prescribed h infty performance requirement furthermore the explicit parameterization of the desired state estimator is given by means of the solution to a set of matrix inequalities and the upper bound of the spp is then evaluated in the feasibility of these matrix inequalities moreover the corresponding results for linear discrete time spcns are derived as corollaries a numerical example is given to illustrate the effectiveness of the proposed state estimator design scheme

on mixed and componentwise condition numbers for indefinite least squares problem in this paper we mainly consider the mixed and componentwise condition numbers for the indefinite least squares problem without constraints or with least squares constraints the explicit expressions and the easily computable upper bounds for these condition numbers are presented two numerical examples are given to test these results and illustrate their superiority compared with the corresponding normwise condition numbers furthermore we also provide the mixed and componentwise condition numbers for the moore penrose inverse in indefinite inner product spaces

low rank approximation to the solution of a nonsymmetric algebraic riccati equation from transport theory abstract we consider the solution of the large scale nonsymmetric algebraic riccati equation xcx xd ax b 0 from transport theory juang 1995 with m d c b a r 2 n 2 n being a nonsingular m matrix in addition a d are rank 1 updates of diagonal matrices with the products a 1 u a u d 1 v and d v computable in o n complexity for some vectors u and v and b c are rank 1 the structure preserving doubling algorithm by guo et al 2006 is adapted with the appropriate applications of the sherman morrison woodbury formula and the sparse plus low rank representations of various iterates the resulting large scale doubling algorithm has an o n computational complexity and memory requirement per iteration and converges essentially quadratically as illustrated by the numerical examples

a variance constrained approach to recursive state estimation for time varying complex networks with missing measurements in this paper the recursive state estimation problem is investigated for an array of discrete time varying coupled stochastic complex networks with missing measurements a set of random variables satisfying certain probabilistic distributions is introduced to characterize the phenomenon of the missing measurements where each sensor can have individual missing probability the taylor series expansion is employed to deal with the nonlinearities and the high order terms of the linearization errors are estimated the purpose of the addressed state estimation problem is to design a time varying state estimator such that in the presence of the missing measurements and the random disturbances an upper bound of the estimation error covariance can be guaranteed and the explicit expression of the estimator parameters is given by using the riccati like difference equations approach the estimator parameter is characterized by the solutions to two riccati like difference equations it is shown that the obtained upper bound is minimized by the designed estimator parameters and the proposed state estimation algorithm is of a recursive form suitable for online computation finally an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation scheme

h_ infty state estimation for complex networks with uncertain inner coupling and incomplete measurements in this paper the h state estimation problem is investigated for a class of complex networks with uncertain coupling strength and incomplete measurements with the aid of the interval matrix approach we make the first attempt to characterize the uncertainties entering into the inner coupling matrix the incomplete measurements under consideration include sensor saturations quantization and missing measurements all of which are assumed to occur randomly by introducing a stochastic kronecker delta function these incomplete measurements are described in a unified way and a novel measurement model is proposed to account for these phenomena occurring with individual probability with the measurement model a set of h state estimators is designed such that for all admissible incomplete measurements as well as the uncertain coupling strength the estimation error dynamics is exponentially mean square stable and the h performance requirement is satisfied the characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem that can be easily solved using the semidefinite program method finally a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach

a contribution to the theory of condition in this paper the use of the condition number of a problem as defined by rice in 1966 is discussed for the eigenvalue eigenvector and linear least squares problems either condition numbers according to various norms are determined or lower and upper bounds for them are derived

extended kalman filtering with stochastic nonlinearities and multiple missing measurements in this paper the extended kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon both deterministic and stochastic nonlinearities are included in the system model where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances the phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval 0 1 such a probability distribution is allowed to be any commonly used distribution over the interval 0 1 with known conditional probability the aim of the addressed filtering problem is to design a filter such that in the presence of both the stochastic nonlinearities and multiple missing measurements there exists an upper bound for the filtering error covariance subsequently such an upper bound is minimized by properly designing the filter gain at each sampling instant it is shown that the desired filter can be obtained in terms of the solutions to two riccati like difference equations that are of a form suitable for recursive computation in online applications an illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme

scale free networks from varying vertex intrinsic fitness a new mechanism leading to scale free networks is proposed in this letter it is shown that in many cases of interest the connectivity power law behavior is neither related to dynamical properties nor to preferential attachment assigning a quenched fitness value x i to every vertex and drawing links among vertices with a probability depending on the fitnesses of the two involved sites gives rise to what we call a good get richer mechanism in which sites with larger fitness are more likely to become hubs i e to be highly connected

duality between equilibrium and growing networks in statistical physics any given system can be either at an equilibrium or away from it networks are not an exception most network models can be classified as either equilibrium or growing here we show that under certain conditions there exists an equilibrium formulation for any growing network model and vice versa the equivalence between the equilibrium and nonequilibrium formulations is exact not only asymptotically but even for any finite system size the required conditions are satisfied in random geometric graphs in general and causal sets in particular and to a large extent in some real networks

accurate solutions of m matrix sylvester equations this paper is concerned with a relative perturbation theory and its entrywise relatively accurate numerical solutions of an m matrix sylvester equation ax xb c by which we mean both a and b have positive diagonal entries and nonpositive off diagonal entries and p i m otimes a b rm t otimes i n is a nonsingular m matrix and c is entrywise nonnegative it is proved that small relative perturbations to the entries of a b and c introduce small relative errors to the entries of the solution x thus the smaller entries of x do not suffer bigger relative errors than its larger entries unlikely the existing perturbation theory for general sylvester equations we then discuss some minor but crucial implementation changes to three existing numerical methods so that they can be used to compute x as accurately as the input data deserve

entropy distribution and condensation in random networks with a given degree distribution the entropy of network ensembles characterizes the amount of information encoded in the network structure and can be used to quantify network complexity and the relevance of given structural properties observed in real network datasets with respect to a random hypothesis in many real networks the degrees of individual nodes are not fixed but change in time while their statistical properties such as the degree distribution are preserved here we characterize the distribution of entropy of random networks with given degree sequences where each degree sequence is drawn randomly from a given degree distribution we show that the leading term of the entropy of scale free network ensembles depends only on the network size and average degree and that entropy is self averaging meaning that its relative variance vanishes in the thermodynamic limit we also characterize large fluctuations of entropy that are fully determined by the average degree in the network finally above a certain threshold large fluctuations of the average degree in the ensemble can lead to condensation meaning that a single node in a network of size n can attract o n links

a structure preserving doubling algorithm for nonsymmetric algebraic riccati equation in this paper we propose a structure preserving doubling algorithm sda for the computation of the minimal nonnegative solution to the nonsymmetric algebraic riccati equation nare based on the techniques developed for the symmetric cases this method allows the simultaneous approximation to the minimal nonnegative solutions of the nare and its dual equation requiring only the solutions to two linear systems and several matrix multiplications per iteration similar to newton s method and the fixed point iteration methods for solving nares we also establish global convergence for sda under suitable conditions using only elementary matrix theory we show that sequences of matrices generated by sda are monotonically increasing and quadratically convergent to the minimal nonnegative solutions of the nare and its dual equation numerical experiments show that the sda algorithm is feasible and effective and outperforms newton s iteration and the fixed point iteration methods

a survey of nonsymmetric riccati equations abstract we survey recent and also older results on nonsymmetric matrix riccati differential equations and in the time invariant case on the corresponding algebraic riccati equations in particular we cite various applications connected with matrix riccati equations

singularities in the entropy of asymptotically large simple graphs we prove that the asymptotic entropy of large simple graphs as a function of fixed edge and triangle densities is nondifferentiable along a certain curve we also determine the precise modified bipartite structure of asymptotic graphs with edge density 1 2 and triangle density in the interval displaystyle 0 1 8

entropy of network ensembles in this paper we generalize the concept of random networks to describe network ensembles with nontrivial features by a statistical mechanics approach this framework is able to describe undirected and directed network ensembles as well as weighted network ensembles these networks might have nontrivial community structure or in the case of networks embedded in a given space they might have a link probability with a nontrivial dependence on the distance between the nodes these ensembles are characterized by their entropy which evaluates the cardinality of networks in the ensemble in particular in this paper we define and evaluate the structural entropy i e the entropy of the ensembles of undirected uncorrelated simple networks with given degree sequence we stress the apparent paradox that scale free degree distributions are characterized by having small structural entropy while they are so widely encountered in natural social and technological complex systems we propose a solution to the paradox by proving that scale free degree distributions are the most likely degree distribution with the corresponding value of the structural entropy finally the general framework we present in this paper is able to describe microcanonical ensembles of networks as well as canonical or hidden variable network ensembles with significant implications for the formulation of network constructing algorithms

mode dependent stochastic synchronization for markovian coupled neural networks with time varying mode delays this paper investigates the stochastic synchronization problem for markovian hybrid coupled neural networks with interval time varying mode delays and random coupling strengths the coupling strengths are mutually independent random variables and the coupling configuration matrices are nonsymmetric a mode dependent augmented lyapunov krasovskii functional lkf is proposed where some terms involving triple or quadruple integrals are considered which makes the lkf matrices mode dependent as much as possible this gives significant improvement in the synchronization criteria i e less conservative results can be obtained in addition by applying an extended jensen s integral inequality and the properties of random variables new delay dependent synchronization criteria are derived the obtained criteria depend not only on upper and lower bounds of mode delays but also on mathematical expectations and variances of the random coupling strengths finally two numerical examples are provided to demonstrate the feasibility of the proposed results

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

synchronization of complex dynamical networks with switching topology a switched system point of view in this paper we study the synchronization problem for complex dynamical networks with switching topology from a switched system point of view the synchronization problem is transformed into the stability problem for time varying switched systems we address two basic problems synchronization under arbitrary switching topology and synchronization via design of switching within a pre given collection of topologies when synchronization cannot be achieved by using any topology alone in this collection for the both problems we first establish synchronization criteria for general connection topology then under the condition of simultaneous triangularization of the connection matrices a common lyapunov function for the first problem and a single lyapunov and multiple lyapunov functions for the second problem are systematically constructed respectively by those of several lower dimensional dynamic systems in order to achieve synchronization using multiple lyapunov functions a stability condition and switching law design method for time varying switched systems are also presented which avoid the usual non increasing condition

finite time state estimation for coupled markovian neural networks with sensor nonlinearities this paper investigates the issue of finite time state estimation for coupled markovian neural networks subject to sensor nonlinearities where the markov chain with partially unknown transition probabilities is considered a luenberger type state estimator is proposed based on incomplete measurements and the estimation error system is derived by using the kronecker product by using the lyapunov method sufficient conditions are established which guarantee that the estimation error system is stochastically finite time bounded and stochastically finite time stable respectively then the estimator gains are obtained via solving a set of coupled linear matrix inequalities finally a numerical example is given to illustrate the effectiveness of the proposed new design method

class of correlated random networks with hidden variables we study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices we find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices the expressions obtained are checked by means of numerical simulations in a particular example the general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure we also present an extension of the class to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system

on condition numbers for least squares with quadric inequality constraint abstract in this paper we will study normwise mixed and componentwise condition numbers for the linear mapping of the solution for general least squares with quadric inequality constraint glsqi and its standard form lsqi we will introduce the mappings from the data space to the interested data space and the frechet derivative of the introduced mapping can deduced through matrix differential techniques based on condition number theory we derive the explicit expressions of normwise mixed and componentwise condition numbers for the linear function of the solution for glsqi and lsqi also easier computable upper bounds for mixed and componentwise condition numbers are given numerical example shows that the mixed and componentwise condition numbers can tell us the true conditioning of the problem when its data is sparse or badly scaled compared with normwise condition numbers the mixed and componentwise condition number can give sharp perturbation bounds

sparse maximum entropy random graphs with a given power law degree distribution even though power law or close to power law degree distributions are ubiquitously observed in a great variety of large real networks the mathematically satisfactory treatment of random power law graphs satisfying basic statistical requirements of realism is still lacking these requirements are sparsity exchangeability projectivity and unbiasedness the last requirement states that entropy of the graph ensemble must be maximized under the degree distribution constraints here we prove that the hypersoft configuration model belonging to the class of random graphs with latent hyperparameters also known as inhomogeneous random graphs or w random graphs is an ensemble of random power law graphs that are sparse unbiased and either exchangeable or projective the proof of their unbiasedness relies on generalized graphons and on mapping the problem of maximization of the normalized gibbs entropy of a random graph ensemble to the graphon entropy maximization problem showing that the two entropies converge to each other in the large graph limit

mixed h_2 h_ infty state estimation for discrete time switched complex networks with random coupling strengths through redundant channels this article investigates the mixed h 2 h infty state estimation problem for a class of discrete time switched complex networks with random coupling strengths through redundant communication channels a sequence of random variables satisfying certain probability distributions is employed to describe the stochasticity of the coupling strengths a redundant channel based data transmission mechanism is adopted to enhance the reliability of the transmission channel from the sensor to the estimator the purpose of the addressed problem is to design a state estimator for each node such that the error dynamics achieves both the stochastic stability with probability 1 and the prespecified mixed h 2 h infty performance requirement by using the switched system theory an extensive stochastic analysis is carried out to derive the sufficient conditions ensuring the stochastic stability as well as the mixed h 2 h infty performance index the desired state estimator is also parameterized by resorting to the solutions to certain convex optimization problems a numerical example is provided to illustrate the validity of the proposed estimation scheme

structured mixed and componentwise condition numbers of some structured matrices structured matrices such as cauchy vandermonde toeplitz hankel and circulant matrices are considered in this paper we apply a kronecker product based technique to deduce the structured mixed and componentwise condition numbers for the matrix inversion and for the corresponding linear systems