maximum likelihood estimation of functionals of discrete distributions we consider the problem of estimating functionals of discrete distributions and focus on a tight up to universal multiplicative constants for each specific functional nonasymptotic analysis of the worst case squared error risk of widely used estimators we apply concentration inequalities to analyze the random fluctuation of these estimators around their expectations and the theory of approximation using positive linear operators to analyze the deviation of their expectations from the true functional namely their bias we explicitly characterize the worst case squared error risk incurred by the maximum likelihood estimator mle in estimating the shannon entropy h p sum i 1 s p i ln p i and the power sum f alpha p sum i 1 s p i alpha alpha 0 up to universal multiplicative constants for each fixed functional for any alphabet size s leq infty and sample size n for which the risk may vanish as a corollary for shannon entropy estimation we show that it is necessary and sufficient to have n gg s observations for the mle to be consistent in addition we establish that it is necessary and sufficient to consider n gg s 1 alpha samples for the mle to consistently estimate f alpha p 0 the minimax rate optimal estimators for both problems require s ln s and s 1 alpha ln s samples which implies that the mle has a strictly sub optimal sample complexity when 1 we show that the worst case squared error rate of convergence for the mle is n 2 alpha 1 for infinite alphabet size while the minimax squared error rate is n ln n 2 alpha 1 when alpha geq 3 2 the mle achieves the minimax optimal rate n 1 regardless of the alphabet size as an application of the general theory we analyze the dirichlet prior smoothing techniques for shannon entropy estimation in this context one approach is to plug in the dirichlet prior smoothed distribution into the entropy functional while the other one is to calculate the bayes estimator for entropy under the dirichlet prior for squared error which is the conditional expectation we show that in general such estimators do not improve over the maximum likelihood estimator no matter how we tune the parameters in the dirichlet prior this approach cannot achieve the minimax rates in entropy estimation the performance of the minimax rate optimal estimator with n samples is essentially at least as good as that of dirichlet smoothed entropy estimators with n ln n samples

passivity based synchronization of a class of complex dynamical networks with time varying delay this paper proposes a complex delayed dynamical network consisting of n linearly and diffusively coupled identical reaction diffusion neural networks by utilizing some inequality techniques a sufficient condition ensuring the output strict passivity is derived for the proposed network model then we reveal the relationship between output strict passivity and synchronization of the proposed network model moreover based on the obtained passivity result and the relationship between output strict passivity and synchronization a criterion for synchronization is established finally a numerical example is provided to illustrate the correctness and effectiveness of the proposed results

uniform estimates for the finite time ruin probability in the dependent renewal risk model abstract this paper investigates the finite time ruin probability in the dependent renewal risk model where the claim sizes are independent and identically distributed random variables with strongly subexponential tails and the interarrival times are negatively dependent we establish an asymptotic estimate which holds uniformly for the time horizon varying in the positive half line

reliability properties under a stopping time shift abstract considering a series representation of a coherent system using a shift transform of the components lifetime t i at its critical level y i we study two problems first under such a shift transform we analyse the preservation properties of the non parametric distribution classes and secondly the association preserving property of the components lifetime under such transformations

delay induced stability of vector second order systems via simple lyapunov functionals it is well known that some important classes of systems e g inverted pendulums oscillators double integrators that cannot be stabilized by a static output feedback may be stabilized by inserting an artificial time delay in the feedback static output feedback controllers have advantages over observer based controllers in the presence of uncertainties in the system matrices and or uncertain input output delays where the observer based design becomes complicated the existing lyapunov based methods that may treat the case of stabilizing delays and that lead to stability conditions in terms of linear matrix inequalities lmis suffer from high dimensionality of the resulting lmis with a large number of decision variables in this paper we suggest simple lyapunov functionals for vector second order systems with stabilizing delays that lead to reduced order lmis with a small number of decision variables moreover differently from the existing methods we show that the presented lmis are always feasible for small enough delays

independence via uncorrelatedness under certain dependence structures a characterization of independence via uncorrelatedness is shown to hold for the families satisfying positive and negative dependence conditions for the associated random variables the bounds on covariance functions obtained by lebowitz comm math phys 28 1972 313 321 readily yield such a characterization an elementary proof for the same characterization is also given for a condition weaker than association labeled as strong positive negative orthant dependence this condition is compared with the linear positive dependence under which newman and wright ann probab 9 1981 671 675 obtained the characterization

deconvolving multivariate kernel density estimates from contaminated associated observations we consider the estimation of the multivariate probability density function f x sub 1 x sub p of x sub 1 x sub p of a stationary positively or negatively associated pa or na random process x sub i sub i 1 sup spl infin from noisy observations both ordinary smooth and super smooth noise are considered quadratic mean and asymptotic normality results are established

the consistency of the nearest neighbor estimator of the density function based on wod samples abstract in this paper the consistency of the nearest neighbor estimator of the density function based on widely orthant dependent wod in short samples is investigated the convergence rate of strong consistency the complete consistency the uniformly complete consistency and uniformly strong consistency of the nearest neighbor estimator of the density function based on wod samples are established our results established in the paper generalize or improve the corresponding ones for independent samples and some negatively dependent samples

on h control for linear systems with interval time varying delay this paper deals with the problem of delay dependent robust h control for linear time delay systems with norm bounded and possibly time varying uncertainty the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available and no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function based on an integral inequality which is introduced in this paper and lyapunov krasovskii functional approach a delay dependent bounded real lemma brl is first established without using model transformation and bounding techniques on the related cross product terms then employing the obtained brl a delay dependent condition for the existence of a state feedback controller which ensures asymptotic stability and a prescribed h performance level of the closed loop systems for all admissible uncertainties is proposed in terms of a linear matrix inequality lmi a numerical example is also given to illustrate the effectiveness of the proposed method

validity of dependent bootstrapping in finite populations abstract the traditional bootstrap resamples with replacement from the original sample observations to form arrays of row wise independent and identically distributed bootstrap random variables there are situations for example when sampling from finite populations where resampling without replacement provides a more realistic bootstrap procedure and produces dependent bootstrap random variables the desired properties of consistency and asymptotic validity are shown to hold for certain nonparametric dependent bootstrap estimators in addition it is shown that the smaller variation in dependent bootstrap estimators can be used to increase precision in some of the estimators

synchronization of a complex dynamical network with coupling time varying delays via sampled data control abstract in this paper the synchronization problem of a complex dynamical network with coupling time varying delays via delayed sampled data controller is investigated in order to make full use of the sawtooth structure characteristic of the sampling input delay a discontinuous lyapunov functional is proposed based on the extended wirtinger inequality from a convex representation of the sector restricted nonlinearity in system dynamics the stability condition based on lyapunov stability theory is obtained by utilization of linear matrix inequality formulation to find the controller which achieves the synchronization of a complex dynamical network with coupling time varying delay finally two numerical examples are given to illustrate the effectiveness of the proposed methods

the law of the iterated logarithm for positively dependent random variables the levy s type maximal inequality is a key to establish the law of the iterated logarithm for associated random variables unfortunately this type inequality cannot be obtained for a generalization of association i e linear positive quadrant dependence because of their special dependence structure the purpose of this paper is to provide a different approach to obtain a law of the iterated logarithm for a sequence of linear positive quadrant dependent random variables

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

exact rates in log law for positively associated random variables abstract let x n n 1 be a strictly stationary sequence of positively associated random variables with mean zero and finite variance set s n k 1 n x k m n max k n s k n 1 suppose 2 e x 1 2 2 k 2 e x 1 x k in this paper we study the exact convergence rates of a kind of weighted infinite series of p m n e n log n p s n e n log n and i s n e n log n as e 0 respectively

a novel approach to reliable output feedback control of fuzzy affine systems with time delays and sensor faults this paper proposes a novel system augmentation approach to the delay dependent reliable piecewise affine mathscr h infty static output feedback control for nonlinear systems with time varying delay and sensor faults in the piecewise markovian lyapunov functional based framework the nonlinear plant is described by a continuous time takagi sugeno fuzzy affine model with parametric uncertainties and the sensor faults are characterized by a markov process specifically by applying a state input augmentation technique the original closed loop system is first reformulated into a descriptor fuzzy affine system based on a new piecewise markovian lyapunov krasovskii functional combined with a wirtinger based integral inequality improved reciprocally convex inequality and s procedure a novel bounded real lemma is then derived for the underlying closed loop system furthermore by taking advantage of the redundancy of descriptor system formulation together with a linearization procedure the piecewise affine controller synthesis is carried out it is shown that the desired piecewise affine controller gains can be attained by solving a linear matrix inequality based optimization problem finally simulation examples are performed to confirm the effectiveness and less conservatism of the presented approach

k connectivity in random k out graphs intersecting erdős renyi graphs we investigate k connectivity in secure wireless sensor networks under the random pairwise key predistribution scheme with unreliable links when wireless communication links are modeled as independent on off channels this amounts to analyzing a random graph model formed by intersecting a random k out graph and an erd s renyi graph we present conditions on how to scale the parameters of this intersection model so that the resulting graph is k connected with probability approaching to one resp zero as the number of nodes gets large the resulting zero one law is shown to improve and sharpen the previous result on the 1 connectivity of the same model we also provide numerical results to support our analysis

mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability abstract from the classical notion of uniform integrability of a sequence of random variables a new concept of integrability called h integrability is introduced for an array of random variables concerning an array of constants we prove that this concept is weaker than other previous related notions of integrability such as cesaro uniform integrability chandra sankhy ser a 51 1989 309 317 uniform integrability concerning the weights ordonez cabrera collect math 45 1994 121 132 and cesaro integrability chandra and goswami j theoret probab 16 2003 655 669 under this condition of integrability and appropriate conditions on the array of weights mean convergence theorems and weak laws of large numbers for weighted sums of an array of random variables are obtained when the random variables are subject to some special kinds of dependence a rowwise pairwise negative dependence b rowwise pairwise non positive correlation c when the sequence of random variables in every row is mixing finally we consider the general weak law of large numbers in the sense of gut statist probab lett 14 1992 49 52 under this new condition of integrability for a banach space setting

stochastic maximum principle for mean field type optimal control under partial information this technical note is concerned with a partially observed optimal control problem whose novel feature is that the cost functional is of mean field type hence determining the optimal control is time inconsistent in the sense that bellman s dynamic programming principle does not hold a maximum principle is established using girsanov s theorem and convex variation some nonlinear filtering results for backward stochastic differential equations bsdes are developed by expressing the solutions of the bsdes as some ito s processes an illustrative example is demonstrated in terms of the maximum principle and the filtering

convergence rates in the slln for some classes of dependent random fields abstract let x n n n r be a random field i e a family of random variables indexed by n r r 2 we discuss complete convergence and convergence rates under assumption on dependence structure of random fields in the case of nonidentical distributions results are obtained for negatively associated random fields mixing random fields having maximal coefficient of correlation strictly smaller then 1 and martingale random fields

mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables abstract under some conditions of uniform integrability and appropriate conditions mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables are obtained our results extend and improve the results of h s sung s lisawadi a volodin weak laws of large numbers for arrays under a condition of uniform integrability j korean math soc 45 2008 289 300 and m ordonez cabrera a volodin mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability j math anal appl 305 2005 644 658

improved delay dependent stabilization for a class of networked control systems with nonlinear perturbations and two delay components abstract this paper focuses on the problem of delay dependent state feedback control for a class of networked control systems ncss with nonlinear perturbations and two delay components based on the dynamic delay interval ddi method and the wirtinger integral inequality some improved delay dependent stability analysis are obtained furthermore the results are extended to the conditions of ncss with one time delay and the corresponding stability analysis results and state feedback controller are obtained finally some numerical examples and simulations are given to show the effectiveness of the proposed methods

directional dependence of random vectors in this paper we define and study several properties of the concept of multivariate directional dependence and study the new concept in terms of copulas and provide new measures of multivariate association based on directional dependence finally we show the relationships of directional dependence with other dependence concepts such as association and conditional dependence

some concepts of negative dependence abstract the theory of positive dependence notions cannot yield useful results for some widely used distributions such as the multinomial dirichlet and the multivariate hypergeometric some conditions of negative dependence that are satisfied by these distributions and which have practical meaning are introduced preservation results for some of these concepts are derived useful inequalities for some widely used distributions are obtained results of mallows 1969 that apply to the multinomial distributions are extended to more distributions examples are listed author

tail behavior of random sums of negatively associated increments abstract let x x k k 1 be a sequence of negatively associated random variables with a common distribution function and finite expectation and let be a nonnegative integer valued random variable independent of x k k 1 in this paper we give unified form for the asymptotic behavior of the random sums s k 1 x k in the case of lim x p x x p x c 0 the results extend the earlier results of aleskeviciene et al 2008 2

maximum principle for mean field jump diffusion stochastic delay differential equations and its application to finance abstract this paper investigates a stochastic optimal control problem with delay and of mean field type where the controlled state process is governed by a mean field jump diffusion stochastic delay differential equation two sufficient maximum principles and one necessary maximum principle are established for the underlying system as an application a bicriteria mean variance portfolio selection problem with delay is studied to demonstrate the effectiveness and potential of the proposed techniques under certain conditions explicit expressions are provided for the efficient portfolio and the efficient frontier which are as elegant as those in the classical mean variance problem without delays

restricted isometry property for general p norms the restricted isometry property rip is a fundamental property of a matrix which enables sparse recovery informally an m times n matrix satisfies rip of order k for the ell p norm if ax p approx x p for every vector x with at most k non zero coordinates for every 1 leq p we obtain almost tight bounds on the minimum number of rows m necessary for the rip property to hold prior to this paper only the cases p 1 1 1 log n and 2 were studied interestingly our results show that the case p 2 is a singularity point the optimal number of rows m is widetilde theta k p for all p in 1 infty setminus 2 as opposed to widetilde theta k for p 2 we also obtain almost tight bounds for the column sparsity of rip matrices and discuss the implications of our results for the stable sparse recovery problem as defined by candes et al

precise asymptotics for the linear processes generated by associated random variables in hilbert spaces let e k k z be a strictly stationary associated sequence of random variables taking values in a real separable hilbert space and a k k z be a sequence of bounded linear operators for a linear process x k i a i e k i the precise probability and moment convergence rates of i 1 nx i in some limit theorems are discussed

delay dependent robust stability of uncertain neutral type it stochastic systems with markovian jumping parameters this paper investigates the problem of mean square exponential stability for uncertain neutral stochastic systems with time delays and markovian jumping parameters based on the new results on expectations of stochastic cross terms containing the it o integral by song et al 2013 a new lyapunov krasovskii function is established and then an improved mean square exponential stability criterion is derived the derived results extend the conclusions recently presented in song et al 2013 in fact the system discussed in song et al 2013 is a special case of ours finally two examples are provided to demonstrate the effectiveness of the proposed results

towards a theory of negative dependence the fkg theorem says that the positive lattice condition an easily checkable hypothesis which holds for many natural families of events implies positive association a very useful property thus there is a natural and useful theory of positively dependent events there is as yet no corresponding theory of negatively dependent events there is however a need for such a theory this paper unfortunately contains no substantial theorems its purpose is to present examples that motivate a need for such a theory give plausibility arguments for the existence of such a theory outline a few possible directions such a theory might take and state a number of specific conjectures which pertain to the examples and to a wish list of theorems

on the strong convergence rate for positively associated random variables abstract for sequences of the positively associated random variables which are strictly weaker than the classical associated random ones introduced by esary et al 1967 7 strong convergence rate n 1 2 log n 1 2 is obtained which reaches the available one for independent random variables in terms of berstein type inequality further we give the corresponding precise asymptotics with respect to the rate mentioned above which extend and improve the relevant results in fu 2009 8

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

brief paper new delay dependent stability criteria for systems with interval delay this paper provides a new delay dependent stability criterion for systems with a delay varying in an interval with a different lyapunov functional defined a tight upper bound of its derivative is given the resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism which is established theoretically examples are provided to demonstrate the advantage of the stability result

non fragile h control for markovian jump fuzzy systems with time varying delays abstract this paper focuses on the non fragile h control of markovian jump fuzzy systems with time varying delays in order to obtain less conservatism an improved delay partitioning method is introduced which divides the delay interval into multiple segments with a geometric sequence a modified lyapunov krasovskii functional is constructed and some less conservative delay dependent stability criteria are derived by using linear matrix inequalities technique then a non fragile controller is designed finally two numerical examples are given to show the effectiveness of the obtained results

modeling activity times by the parkinson distribution with a lognormal core theory and validation abstract based on theoretical arguments and empirical evidence we advocate the use of the lognormal distribution as a model for activity times however raw data on activity times are often subject to rounding and to the parkinson effect we address those factors in our statistical tests by using a generalized version of the parkinson distribution with random censoring of earliness ultimately validating our model with field data from several sources we also confirm that project activities exhibit stochastic dependence that can be modeled by linear association

normal approximation for associated point processes via stein s method with applications to determinantal point processes abstract we use stein s method to provide non asymptotic l 1 bounds also known as wasserstein bounds to the normal for functionals of associated point processes as for supporting tools we use the connection between association and mixing properties that was recently uncovered by 29 we apply our main results to determinantal point processes which are known to be negatively associated a potential application to determinantal point processes in the laguerre gaussian family is also presented

bootstrap inference in partially identified models defined by moment inequalities coverage of the identified set this paper introduces a novel bootstrap procedure to perform inference in a wide class of partially identi ed econometric models we consider econometric models de ned by nitely many weak moment inequalities y which encompass many applications of economic interest the objective of our inferential procedure is to cover the identi ed set with a prespeci ed probability z we compare our bootstrap procedure a competing asymptotic approximation and subsampling proce dures in terms of the rate at which they achieve the desired coverage level also known as the error in the coverage probability under certain conditions we show that our bootstrap procedure and the asymp totic approximation have the same order of error in the coverage probability which is smaller than the one obtained by using subsampling this implies that inference based on our bootstrap and asymptotic approximation should eventually be more precise than inference based on subsampling a monte carlo study con rms this nding in a small sample simulation

improved linear matrix inequality approach to stability analysis of linear systems with interval time varying delays this paper investigates the problem of stability analysis for a class of linear systems with interval time varying delay in order to develop a less conservative stability condition a lyapunov krasovskii functional comprising novel integral terms is introduced convex combination idea is utilized to derive a stability criterion in terms of linear matrix inequalities lmis without any additional free weighting matrices which increase drastically the computational burden of the stability test numerical examples are presented to illustrate the superiority of the proposed approach compared to some existing ones in the literature

precise rates in the law of the logarithm for negatively associated random variables let x n n 1 be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance set s email protected k 1 nx k m n max k n s k n 1 suppose s 2 ex 1 email protected k 2 ex 1x k we study the precise rates of a kind of weighted infinite series of p m n email protected snlogn and p s n email protected snlogn as email protected 0 and p m email protected email protected email protected 2n8logn as email protected the results are related to the convergence rates of the law of the logarithm and the chung type law of the logarithm

on partial information optimal singular control problem for mean field stochastic differential equations driven by teugels martingales measures abstractthis paper is concerned with partial information mixed optimal stochastic continuous singular control problem for mean field stochastic differential equation driven by teugels martingales and an independent brownian motion where the teugels martingales are a family of pairwise strongly orthonormal martingales associated with levy processes the control variable has two components the first being absolutely continuous and the second singular partial information necessary and sufficient conditions of optimal continuous singular control for these mean field models are investigated as an illustration this paper studies a partial information linear quadratic control problem of mean field type involving continuous singular control

optimal control of mean field jump diffusion systems with delay this paper is concerned with an optimal control problem under mean field jump diffusion systems with delay firstly some existence and uniqueness results are proved for a jump diffusion mean field stochastic delay differential equation and a jump diffusion mean field advanced backward stochastic differential equation then necessary and sufficient maximum principles for control systems of mean field type and with delay are established under certain conditions a mean field delayed linear quadratic control problem is finally discussed using the obtained maximum principles

reduced feedback schemes using random beamforming in mimo broadcast channels a random beamforming scheme for the gaussian mimo broadcast channel with channel quality feedback is investigated and extended considering the case where the n receivers each have n receive antennas the effects of feeding back various amounts of signal to interference plus noise ratio sinr information are analyzed using the results from order statistics of the ratio of a linear combination of exponential random variables the distribution function of the maximum order statistic of the sinr observed at the receiver is found the analysis from viewing each antenna as an individual user is extended to allow combining at the receivers where it is known that the linear mmse combiner is the optimal linear receiver and the cdf for the sinr after optimal combining is derived analytically using the delta method the asymptotic distribution of the maximum order statistic of the sinr with and without combining is shown to be in the nomenclature of extreme order statistics of type 3 the throughput of the feedback schemes are shown to exhibit optimal scaling asymptotically in the number of users finally to further reduce the amount of feedback a hard threshold is applied to the sinr feedback the amount of feedback saved by implementing a hard threshold is determined and the effect on the system throughput is analyzed and bounded

solving optimization problems with diseconomies of scale via decoupling we present a new framework for solving optimization problems with a diseconomy of scale in such problems our goal is to minimize the cost of resources used to perform a certain task the cost of resources grows superlinearly as xq q 1 with the amount x of resources used we define a novel linear programming relaxation for such problems and then show that the integrality gap of the relaxation is aq where aq is the q th moment of the poisson random variable with parameter 1 using our framework we obtain approximation algorithms for the minimum energy efficient routing minimum degree balanced spanning tree load balancing on unrelated parallel machines and unrelated parallel machine scheduling with nonlinear functions of completion times problems our analysis relies on the decoupling inequality for nonnegative random variables the inequality states that ie1nxi q cq ie1nyi q where xi are independent nonnegative random variables yi are possibly dependent nonnegative random variables and each yi has the same distribution as xi the inequality was proved by de la pena in 1990 de la pena ibragimov and sharakhmetov showed that cq 2 for qi 1 2 and cq aq1 q for q 2 we show that the optimal constant is cqe aq1 q for any q 1 we then prove a more general inequality for every convex function v elv ie1nxi r elv p ie1n yi r and for every concave function el ie1n xi r el p ie1n yi r where p is a poisson random variable with parameter 1 independent of the random variables yi

negative association of random variables with applications random variables x 1 cdots x k are said to be negatively associated na if for every pair of disjoint subsets a 1 a 2 of 1 2 cdots k operatorname cov lbrack f x 1 i in a 1 g x j j in a 2 rbrack leq 0 for all nondecreasing functions f g the basic properties of negative association are derived especially useful is the property that nondecreasing functions of mutually exclusive subsets of na random variables are na this property is shown not to hold for several other types of negative dependence recently proposed one consequence is the inequality p x i leq x i i 1 cdots k leq prod k 1p x i leq x i for na random variables x 1 cdots x k and the dual inequality resulting from reversing the inequalities inside the square brackets in another application it is shown that negatively correlated normal random variables are na other na distributions are the a multinomial b convolution of unlike multinomials c multivariate hypergeometric d dirichlet and e dirichlet compound multinomial negative association is shown to arise in situations where the probability measure is permutation invariant applications of this are considered for sampling without replacement as well as for certain multiple ranking and selection procedures in a somewhat striking example na and positive association representing quite strong opposing types of dependence are shown to exist side by side in models of categorical data analysis

on optimal control of mean field stochastic systems driven by teugels martingales via derivative with respect to measures this paper deals with partial information stochastic optimal control problem for general controlled mean field systems driven by teugels martingales associated with some levy process having moments

stability criteria for bam neural networks with leakage delays and probabilistic time varying delays this paper is concerned with the stability criteria for bidirectional associative memory bam neural networks with leakage time delay and probabilistic time varying delays by establishing a stochastic variable with bernoulli distribution the information of probabilistic time varying delay is transformed into the deterministic time varying delay with stochastic parameters based on the lyapunov krasovskii functional and stochastic analysis approach delay probability distribution dependent sufficient conditions are derived to achieve the globally asymptotically mean square stable of the considered bam neural networks the criteria are formulated in terms of a set of linear matrix inequalities lmis which can be checked efficiently by use of some standard numerical packages finally a numerical example and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results

synchronization criteria of fuzzy complex dynamical networks with interval time varying delays this paper presents new delay dependent synchronization criteria for fuzzy complex dynamical networks with interval time varying delays by construction of a suitable lyapunov krasovskii s l k functional and utilization of finsler s lemma new synchronization criteria for the networks are established in terms of linear matrix inequalities lmis which can be easily solved by various effective optimization algorithms one numerical example is given to illustrate the effectiveness of the proposed methods

m matrices as covariance matrices of multinormal distributions abstract the class of multivariate normal densities n 0 whose inverse covariance matrix 1 is an m matrix is equivalent to this normal density being multivariate totally positive of order 2 mtp 2 equivalent characterizations are given in terms of certain partial correlation coefficients being positive it is further shown that related partial and multiple regression coefficients and canonical correlation are positive when is an m matrix the corresponding normal random vector components are negatively associated this concept and some extensions are discussed

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

a strong approximation theorem for positively dependent gaussian sequences and its applications abstract under the polynomial decay rates and finite second moment a strong approximation theorem for partial sums of linear positive quadrant dependent gaussian sequences is derived as applications the law of the iterated logarithm the chung type law of the iterated logarithm and the almost sure central limit theorem are obtained with minimal conditions

passivity based synchronization of markovian jump complex dynamical networks with time varying delays parameter uncertainties reaction diffusion terms and sampled data control abstract the problem of passivity analysis of reaction diffusion complex dynamical networks with time varying delays and markovian jumping parameters is considered in this article to reflect most of the dynamical behaviors of the system the parameter uncertainties are considered specially the time varying delays are taken into consideration to describe the sample data control of the system the control objective is that the trajectories of the system by designing suitable control schemes track the trajectories of the system with sample data control it is shown that through lyapunov stability theory the proposed sample data controllers are successful in ensuring the achievement of passivity based synchronization of complex dynamical networks even in the case of uncertainty and markovian jumping parameters by utilizing the lyapunov functional method jensen s inequality wirtinger s inequality and reciprocal convex techniques we establish a sufficient criterion such that for all admissible parameter uncertainties the complex dynamical network is passive the derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software illustrative example is presented to demonstrate the effectiveness and usefulness of the proposed results

on the failure of the bootstrap for matching estimators matching estimators are widely used in empirical economics for the evaluation of programs or treatments researchers using matching methods often apply the bootstrap to calculate the standard errors however no formal justification has been provided for the use of the bootstrap in this setting in this article we show that the standard bootstrap is in general not valid for matching estimators even in the simple case with a single continuous covariate where the estimator is root n consistent and asymptotically normally distributed with zero asymptotic bias valid inferential methods in this setting are the analytic asymptotic variance estimator of abadie and imbens 2006a as well as certain modifications of the standard bootstrap like the subsampling methods in politis and romano 1994

improved delay dependent stability results of recurrent neural networks abstract by using the fact that the activation functions are sector bounded and a tighter inequality this paper presents a new method to the stability analysis of a class of recurrent neural networks rnns with time varying delays this method includes more the slope of activation functions and less variables matrices in constructed lyapunov krasovskii functional with the present stability conditions the computational burden and conservatism are largely reduced both theoretical analysis and numerical example are given to illustrate the effectiveness and the benefits of the proposed method

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

negative dependence and the geometry of polynomials we introduce the class of strongly rayleigh probability measures by means of geometric properties of their generating polynomials that amount to the stability of the latter this class covers important models such as determinantal measures e g product measures and uniform random spanning tree measures and distributions for symmetric exclusion processes we show that strongly rayleigh measures enjoy all virtues of negative dependence and we also prove a series of conjectures due to liggett pemantle and wagner respectively moreover we extend lyons recent results on determinantal measures and we construct counterexamples to several conjectures of pemantle and wagner on negative dependence and ultra log concave rank sequences

state estimation of t s fuzzy delayed neural networks with markovian jumping parameters using sampled data control abstract in this paper we are concerned with the problem of state estimation of takagi sugeno t s fuzzy delayed neural networks with markovian jumping parameters via sampled data control based on the fuzzy model based control approach and linear matrix inequality lmi technique several novel conditions are derived to guarantee the stability of the suggested system a new class of lyapunov functional which contains integral terms is constructed to derive delay dependent stability criteria some characteristics of the sampling input delay are proposed based on the input delay approach numerical examples are given to illustrate the usefulness and effectiveness of the proposed theoretical results

diffusion equation techniques in stochastic monotonicity and positive correlations a diffusion equation approach is investigated for the study of stochastic monotonicity positive correlations and the preservation of lipschitz functions necessary and sufficient conditions are given for diffusion semigroups to be stochastically monotonic and to preserve the class of positively correlated measures applications are given which discuss the shape of the ground state for schrodinger operators v with fkg potentialsv

a new type of compact uniform integrability with application to degenerate mean convergence of weighted sums of banach space valued random elements abstract in this correspondence for an array x n k u n k v n n n of integrable random elements in a real separable banach space and an array a n k u n k v n n n of real numbers a new type of compact uniform integrability is introduced and it is used to obtain degenerate mean convergence theorems for the weighted sums k u n v n a n k x n k e x n k n n more specifically conditions are provided under which lim n e k u n v n a n k x n k e x n k 0

unknown input observer design for one sided lipschitz discrete time systems subject to time delay in this paper we address the problem of unknown input observer design which simultaneously estimates state and unknown input of a class of nonlinear discrete time systems with time delay a novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the one sided lipschitz and quadratically inner bounded conditions is proposed this approach also allows us to reconstruct the unknown inputs of the systems the nonlinear system is first transformed to a new system which can be decomposed into unknown input free and unknown input dependent subsystems the estimation problem is then reduced to designing observer for the unknown input free subsystem rather than full order observer design in this paper we propose observer design of reduced order which is more practical and cost effective by utilizing several mathematical techniques the time delay issue as well as the bilinear terms which often emerge when designing observers for nonlinear discrete time systems are handled and less conservative observer synthesis conditions are derived in the linear matrix inequalities form two numerical examples are given to show the efficiency and high performance of our results

convergence of series of dependent φ subgaussian random variables the almost sure convergence of weighted sums of subgaussian m acceptable random variables is investigated as corollaries the main results are applied to the case of negatively dependent and m dependent subgaussian random variables finally an application to random fourier series is presented

stabilization by using artificial delays an lmi approach abstract static output feedback stabilization for the n th order vector differential equations by using artificial multiple delays is considered under assumption of the stabilizability of the system by a static feedback that depends on the output and its derivatives up to the order n 1 a delayed static output feedback is found that stabilizes the system the conditions for the stability analysis of the resulting closed loop system are given in terms of simple lmis it is shown that the lmis are always feasible for appropriately chosen gains and small enough delays robust stability analysis in the presence of uncertain time varying delays and stochastic perturbation of the system coefficients is provided numerical examples including chains of three and four integrators that are stabilized by static output feedbacks with multiple delays illustrate the efficiency of the method

approximations for finite time ruin probability in a dependent discrete time risk model with cmc simulations consider a discrete time risk model in which the insurer is allowed to invest its wealth into a risk free or a risky portfolio under a certain regulation then the insurer is said to be exposed to a stochastic economic environment that contains two kinds of risks the insurance risk and financial risk within period i the net insurance loss is denoted by xi and the stochastic discount factor from time i to zero is denoted by i for any integer n assume that x1 xn form a sequence of pairwise asymptotically independent but not necessarily identically distributed real valued random variables with distributions f1 fn respectively 1 2 n are another sequence of arbitrarily dependent positive random variables and the two sequences are mutually independent under the assumption that the average distribution n1i 1nfi is dominatedly varying tailed and some moment conditions on i i 1 n we derive a weakly equivalent formula for the finite time ruin probability we demonstrate our obtained results through a crude monte carlo simulation with asymptotics

passivity of delayed reaction diffusion networks with application to a food web model this paper is concerned with the passivity problem of a class of delayed reaction diffusion networks in which the input and output variables are varied with the time and space variables firstly two new passivity definitions are proposed which are totally different from some existing concepts of passivity then we establish several criteria for the passivity input strict passivity and output strict passivity by using the lyapunov functional method combined with the inequality techniques and also reveal the relationship between passivity and stability of the reaction diffusion networks moreover these results are applied to investigate the asymptotic stability and control design of a food web model with time delay and reaction diffusion terms numerical simulations are presented finally to demonstrate the effectiveness of the proposed results

association of normal random variables and slepian s inequality abstract a simple extension of slepian s inequality is given which implies the original inequality and the result that positively correlated normal variables are associated author

posterior convergence given the mean for various applications one wants to know the asymptotic behavior of x the posterior density of a parameter given the mean x of the data rather than the full data set here we show that x is asymptotically normal in an l 1 sense and we identify the mean of the limiting normal and its asymptotic variance the main results are first proved assuming that x 1 x n are independent and identical suitable modifications to obtain results for the nonidentical case are given separately our results may be used to construct approximate hpd highest posterior density sets for the parameter which is of use in the statistical theory of standardized educational tests they may also be used to show the covariance between two test items conditioned on the mean is asymptotically nonpositive this has implications for constructing tests of item independence

stability analysis and dynamic output feedback controller design of t s fuzzy systems with time varying delays and external disturbances abstract this paper investigates the stability analysis and takagi sugeno t s fuzzy dynamic output feedback control for a class of t s fuzzy systems with multiple time varying delays and unmatched disturbances firstly the t s fuzzy model is employed to represent the system based on the system input matrix and output matrix secondly the t s fuzzy dynamic output feedback controller is designed based on the t s fuzzy model thirdly the line integral fuzzy lyapunov functional is employed and the boundary information of membership functions is considered in the stability analysis compared with previous works the multiple time varying delays and unmatched disturbances are considered in the t s fuzzy system the t s fuzzy dynamic output feedback controller and t s fuzzy system employ the same number of fuzzy rules but different membership functions to relax the control design conditions the line integral fuzzy lyapunov functional is employed and the boundary information of membership functions is considered to obtain the less conservative stability conditions finally two simulation examples are performed and some comparison figures results are presented to show the effectiveness and advantage of proposed method respectively

lower bounds on the restitution error in the hopfield model this paper contains a first rigorous results at the direction of the converse to newman s bounds 11 on the storage capacity for the hopfield model of associative memory let m denote the number of stored patterns and n that of neurons assuming that m n to alpha as n to infty we show that for alpha 0 the memory necessarily commits a positive fraction of errors on memorized patterns that becomes superior to some threshold value approximately 0 05 as alpha to infty

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

manifest characterization and testing for certain latent properties work due to junker and more recently due to junker and ellis characterized desired latent properties of an educational testing procedure in terms of a collection of other manifest properties this is important because one can only propose tests for manifest quantities not latent ones here we complete the conversion of a pair of latent properties to equivalent conditions in terms of four manifest quantities and identify a general method for producing tests for manifest properties 1 introduction item response theory irt is the statistical theory of standardized tests which are commonly used in educational testing applications the goal is to combine the data generated by many examinees answering a collection of test items so as to estimate the value of a parameter or trait say for each of the examinees the parameter is intended to quantify a latent trait such as mathematics ability the traits are latent in the sense that they cannot be measured directly more specifically desired properties of suchtesting procedures are called latent when their statement depends explicitly on the the latent trait being estimated most efforts at modeling involve the introduction of latent parameters one specifies parameters to reflect aspects of the physical problem such as the individual achievement of each examinee the difficulty of each test item specialized knowledge that certain examinees might possess etc this is in contrast to the manifest properties of a testing procedure which can be phrased in a way that does not explicitly depend on the latent trait the limitation of a latent model is that it contains parameters for the latent trait the experimenter wants to estimate each examinee s parameter value and so cannot perform hypothesis tests on a conjectured model in the usual way the solution to this problem is to convert latent models or latent statements about them to physically meaningful manifest properties which are provably mathematically equivalent to the latent properties actually wanted manifest statements are amenable to conventional hypothesis testing and the problem then becomes the identification of optimal hypothesis tests for the manifest quantities in this way one can test hypotheses that are independent of the latent structure at least in principle the goal of characterizing latent properties in terms of manifest properties to be tested begins with stout 1987 stout considers the requirement that

synchronization of coupled reaction diffusion neural networks with time varying delays via pinning impulsive controller in this paper global exponential synchronization stability in an array of linearly diffusively coupled reaction diffusion neural networks with time varying delays is investigated by adding impulsive controller to a small fraction of nodes pinning impulsive controller in order to overcome the difficulty resulting from the fact that the impulsive controller affects only the dynamical behaviors of the controlled nodes a new analysis method is developed by using the developed method two known lemmas on stability of delayed functional differential equation with and without impulses and lyapunov stability theory several novel and easily verified synchronization criteria guaranteeing the whole network will be pinned to a homogenous solution are derived moreover the effects of the pinning impulsive controller and the dynamics of the uncontrolled nodes and the diffusive couplings on the synchronization process are explicitly expressed in the obtained criteria our results also show that we can always de

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

on the connectivity of sensor networks under random pairwise key predistribution we investigate the connectivity of wireless sensor networks under the random pairwise key predistribution scheme of chan under the assumption of full visibility this reduces to studying the connectivity in the so called random k out graph h n k here n is the number of nodes and k n is an integer parameter affecting the number of keys stored at each node we show that if k 2 respectively k 1 the probability that h n k is a connected graph approaches 1 respectively 0 as n goes to infinity for the one law this is done by establishing an explicitly computable lower bound on the probability of connectivity using this bound we see that with high probability network connectivity can already be guaranteed with k 2 by a relatively small number of sensors this corrects earlier predictions made on the basis of a heuristic transfer of connectivity results available for erdos renyi graphs

a max norm constrained minimization approach to 1 bit matrix completion we consider in this paper the problem of noisy 1 bit matrix completion under a general non uniform sampling distribution using the max norm as a convex relaxation for the rank a max norm constrained maximum likelihood estimate is introduced and studied the rate of convergence for the estimate is obtained information theoretical methods are used to establish a minimax lower bound under the general sampling model the minimax upper and lower bounds together yield the optimal rate of convergence for the frobenius norm loss computational algorithms and numerical performance are also discussed

matrix characterization of a statistical convergence abstract the main objective of the paper is to characterize multipliers of summability fields of regular methods while relaxing the usual boundedness condition for this purpose we use the sequence spaces of a bounded sequences and a uniformly integrable sequences among the main results it is shown that the space of multipliers is closely related to the space of a statistically convergent sequences and that a statistical convergence over l is equivalent to a regular matrix method this observation eliminates the need for separate proofs of several a statistical convergence results

conditional covariance structure of generalized compensatory multidimensional items some nonparametric dimensionality assessment procedures such as dimtest and detect use nonparametric estimates of item pair conditional covariances given an appropriately chosen subtest score as their basic building blocks such conditional covariances given some subtest score can be regarded as an approximation to the conditional covariances given an appropriately chosen unidimensional latent composite where the composite is oriented in the multidimensional test space direction in which the subtest score measures best in this paper the structure and properties of such item pair conditional covariances given a unidimensional latent composite are thoroughly investigated assuming a semiparametric irt modeling framework called a generalized compensatory model it is shown that such conditional covariances are highly informative about the multidimensionality structure of a test the theory developed here is very useful in establishing properties of dimensionality assessment procedures current and yet to be developed that are based upon estimating such conditional covariances in particular the new theory is used to justify the dimtest procedure because of the importance of conditional covariance estimation a new bias reducing approach is presented a byproduct of likely independent importance beyond the study of conditional covariances is a rigorous score information based definition of an item s and a score s direction of best measurement in the multidimensional test space

on the exponential inequalities for negatively dependent random variables a number of exponential inequalities for identically distributed negatively dependent and negatively associated random variables have been established by many authors the proofs use the truncation technique together with the control of the bounded terms and unbounded terms in this paper we improve essentially the control of bounds for the unbounded terms and obtain exponential inequalities for negatively dependent random variables which include negatively associated random variables our results improve on the corresponding ones in the literature

an almost sure central limit theorem for products of sums of partial sums under association abstract let x n n 1 be a strictly stationary positively or negatively associated sequence of positive random variables with e x 1 0 and var x 1 2 denote s n i 1 n x i t n i 1 n s i and the coefficient of variation under suitable conditions we show that x lim n 1 log n k 1 n 1 k i 2 k j 1 k t j k k 1 k 1 1 k x f x a s where 1 2 1 2 2 j 2 cov x 1 x j f is the distribution function of the random variables e 10 3 n and n is a standard normal random variable

multiprocess parallel antithetic coupling for backward and forward markov chain monte carlo antithetic coupling is a general stratification strategy for reducing monte carlo variance without increasing the simulation size the use of the antithetic principle in the monte carlo literature typically employs two strata via antithetic quantile coupling we demonstrate here that further stratification obtained by using k 2 e g k 3 10 antithetically coupled variates can offer substantial additional gain in monte carlo efficiency in terms of both variance and bias the reason for reduced bias is that antithetically coupled chains can provide a more dispersed search of the state space than multiple independent chains the emerging area of perfect simulation provides a perfect setting for implementing the k process parallel antithetic coupling for mcmc because without antithetic coupling this class of methods delivers genuine independent draws furthermore antithetic backward coupling provides a very convenient theoretical tool for investigating antithetic forward coupling however the generation of k 2 antithetic variates that are negatively associated that is they preserve negative correlation under monotone transformations and extremely antithetic that is they are as negatively correlated as possible is more complicated compared to the case with k 2 in this paper we establish a theoretical framework for investigating such issues among the generating methods that we compare latin hypercube sampling and its iterative extension appear to be generalpurpose choices making another direct link between monte carlo and quasi monte carlo