percolation under noise detecting explosive percolation using the second largest component we consider the problem of distinguishing between different rates of percolation under noise a statistical model of percolation is constructed allowing for the birth and death of edges as well as the presence of noise in the observations this graph valued stochastic process is composed of a latent and an observed nonstationary process where the observed graph process is corrupted by type i and type ii errors this produces a hidden markov graph model we show that for certain choices of parameters controlling the noise the classical erd s renyi percolation is visually indistinguishable from a more rapid form of percolation in this setting we compare two different criteria for discriminating between these two percolation models based on the interquartile range iqr of the first component s size and on the maximal size of the second largest component we show through data simulations that this second criterion outperforms the iqr of the first component s size in terms of discriminatory power the maximal size of the second component therefore provides a useful statistic for distinguishing between different rates of percolation under physically motivated conditions for the birth and death of edges and under noise the potential application of the proposed criteria for the detection of clinically relevant percolation in the context of applied neuroscience is also discussed

fixed time consensus of complex dynamical networks with nonlinear coupling and fuzzy state dependent uncertainties abstract in this paper the fixed time consensus problem for complex dynamical networks with nonlinear coupling and fuzzy state dependent uncertainties is discussed different from most existing publications the controller is designed as a fuzzy logic system which is applicable for complex dynamical networks with system uncertainties and unknown topology to ensure the fixed time consensus furthermore compared with the initial condition based finite time consensus the settling time is bounded by a constant within fixed time regardless of the initial condition based on the lyapunov stability theory and inequality techniques some sufficient criteria for fixed time consensus are obtained finally two numerical examples are granted to display the performance of the obtained results

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

synchronization of ts fuzzy complex dynamical networks with time varying impulsive delays and stochastic effects in this paper global exponential synchronization of takagi sugeno ts fuzzy complex dynamical networks with multiple time varying delays and stochastic perturbations is studied via delayed impulsive distributed control both impulsive and continuous parts of the fuzzy model have different multiple time varying delays which make the considered model general and practical a novel lemma on exponential stability of impulsive delayed differential equations was established in which the impulsive functions exhibit multiple time varying delays by utilizing the proposed lemma lyapunov functions the stochastic analysis techniques and the kronecker product general criteria ensuring global exponential synchronization in mean square of the addressed ts fuzzy complex networks are obtained moreover the theory of function minimum value is utilized to reduce the conservativeness of the obtained synchronization criteria which also makes them simple and easy to be verified in practical applications results of this paper improve and extend some existing ones numerical simulations including small world network coupled with time delayed lorenz system are given to show the effectiveness of the theoretical results

delay dependent synchronization of t s fuzzy markovian jump complex dynamical networks abstract in this paper a delay dependent synchronization criteria for markovian jump complex dynamical networks subject to time varying coupling delays and external disturbances are proposed via takagi sugeno t s fuzzy approach the class of markovian jump complex dynamical networks is described by a fuzzy model composed of two levels such as a crisp level which represents the jumps and a fuzzy level which describes the system nonlinearities an asymptotic synchronization criterion is obtained by employing fuzzy controller with the mixed h and passivity performance index 0 further by constructing a novel lyapunov krasovskii functional along with the extended integral inequality and using the properties of kronecker product and convex combination approach a set of sufficient constraints is derived in the form of linear matrix inequalities and checked for its feasibility using matlab software at last numerical simulations including the lorentz system are given to demonstrate the applicability and effectiveness of the developed results

robust fuzzy control for uncertain stochastic time delay takagi sugeno fuzzy models for achieving passivity this paper focuses on the robust passive stability and stabilization problems for uncertain nonlinear stochastic time delay systems via the fuzzy modeling approach the nonlinear stochastic system is described by takagi sugeno t s fuzzy model in which the consequent parts are presented by linear stochastic time delay differential equation with lyapunov krasovskii function and improved jensen s inequality the stability criteria are derived in addition the passivity theory is employed to discuss external disturbance effect on system for achieving attenuation performance according to the proposed design method the fuzzy controller is carried out by parallel distributed compensation pdc concept to guarantee the robust asymptotical stability and attenuation performance of system in the sense of mean square finally a synchronous generator power system is presented to manifest the application and effectiveness of the proposed fuzzy control method

receiver operating characteristic curves for a simple stochastic process that carries a static signal the detection of a weak signal in the presence of noise is an important problem that is often studied in terms of the receiver operating characteristic roc curve in which the probability of correct detection is plotted against the probability for a false positive this kind of analysis is typically applied to the situation in which signal and noise are stochastic variables the detection problem emerges however also often in a context in which both signal and noise are stochastic processes and the correct or false detection is said to take place when the process crosses a threshold in a given time window here we consider the problem for a combination of a static signal which has to be detected against a dynamic noise process the well known ornstein uhlenbeck process we give exact but difficult to evaluate quadrature expressions for the detection rates for false positives and correct detections investigate systematically a simple sampling approximation suggested earlier compare to an approximation by stratonovich for the limit of high threshold and briefly explore the case of multiplicative signal all theoretical results are compared to extensive numerical simulations of the corresponding langevin equation our results demonstrate that the sampling approximation provides a reasonable description of the roc curve for this system and it clarifies limit cases for the roc curve

cross bifix free codes within a constant factor of optimality a cross bifix free code is a set of words in which no prefix of any length of any word is the suffix of any word in the set cross bifix free codes arise in the study of distributed sequences for frame synchronization we provide a new construction of cross bifix free codes which generalizes the construction by bajic to longer code lengths and to any alphabet size the codes are shown to be nearly optimal in size we also establish new results on fibonacci sequences which are used in estimating the size of the cross bifix free codes

frame synchronization for gaussian channels the problem of locating a periodically inserted frame synchronization pattern in random data for a m ary digital communication system operating over the additive white gaussian noise channel is considered the optimum maximum likelihood decision rule high signal to noise approximate maximum likelihood decision rule and ordinary correlation decision rule for frame synchronization are derived for both coherent and noncoherent phase demodulation a general lower bound on synchronization probability is derived for the coherent correlation rule monte carlo computer simulations of all three decision rules along with evaluations of the lower bound for the coherent correlation rule were performed for the coherent mpsk coherent and noncoherent m ary orthogonal and 16 qam signaling schemes these results show that in each case the high signal to noise maximum likelihood rules have a performance nearly equal to that of the maximum likelihood rules over a wide range of practically interesting signal to noise ratios snr s these high snr decision rules also provide significant performance improvement over the simple correlation rules moreover they are much simpler to implement than the maximum likelihood decision rules and in fact are no more complex than the correlation rules

nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled data control this paper considers nonfragile exponential synchronization for complex dynamical networks cdns with time varying coupling delay the sampled data feedback control which is assumed to allow norm bounded uncertainty and involves a constant signal transmission delay is constructed for the first time in this paper by constructing a suitable augmented lyapunov function and with the help of introduced integral inequalities and employing the convex combination technique a sufficient condition is developed such that the nonfragile exponential stability of the error system is guaranteed as a result for the case of sampled data control free of norm bound uncertainties some sufficient conditions of sampled data synchronization criteria for the cdns with time varying coupling delay are presented as the formulations are in the framework of linear matrix inequality these conditions can be easily solved and implemented two illustrative examples are presented to demonstrate the effectiveness and merits of the proposed feedback control

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

frame synchronization for optical overlapping pulse position modulation systems the maximum likelihood rules for locating data frames in direct detection optical communication systems utilizing overlapping pulse position modulation oppm are derived under two distinct assumptions of symbol and chip synchronization respectively various approximations to the optimal rules are identified as well as upper and lower bounds on the probability of correct synchronization further the problem of sequence design based on a maximum peak to sidelobe distance criterion is studied and upper bounds on peak to sidelobe distance for sequences of oppm symbols are derived some good sequences are obtained through a computer search

on sequential frame synchronization in awgn channels we present a framework for the analysis of frame synchronization based on synchronization words sws where the detection is based on the following sequential algorithm the received samples are observed over a window of length equal to the sw over this window a metric e g correlation is computed an sw is declared if the computed metric is greater than a proper threshold otherwise the observation window is time shifted one sample we assume a gaussian channel antipodal signaling equally distributed data symbols and coherent detection where soft values are provided to the frame synchronizer we state the problem starting from the hypothesis testing theory deriving the optimum metric optimum likelihood ratio test lrt according to the neyman pearson lemma when the data distribution is unknown we design a simple and effective test based on the generalized lrt glrt we also analyze the performance of the commonly used correlation metric both with hard and soft values at the synchronizer input we show that synchronization can be greatly improved by using the lrt and glrt metrics instead of correlation and that among correlation based tests sometimes hard correlation is better than soft correlation the obtained closed form expressions allow the derivation of the receiver operating characteristic roc curves for the lrt and glrt synchronizers showing a remarkable gain with respect to synchronization based on correlation metric

global synchronization for discrete time stochastic complex networks with randomly occurred nonlinearities and mixed time delays in this paper the problem of stochastic synchronization analysis is investigated for a new array of coupled discrete time stochastic complex networks with randomly occurred nonlinearities rons and time delays the discrete time complex networks under consideration are subject to 1 stochastic nonlinearities that occur according to the bernoulli distributed white noise sequences 2 stochastic disturbances that enter the coupling term the delayed coupling term as well as the overall network and 3 time delays that include both the discrete and distributed ones note that the newly introduced rons and the multiple stochastic disturbances can better reflect the dynamical behaviors of coupled complex networks whose information transmission process is affected by a noisy environment e g internet based control systems by constructing a novel lyapunov like matrix functional the idea of delay fractioning is applied to deal with the addressed synchronization analysis problem by employing a combination of the linear matrix inequality lmi techniques the free weighting matrix method and stochastic analysis theories several delay dependent sufficient conditions are obtained which ensure the asymptotic synchronization in the mean square sense for the discrete time stochastic complex networks with time delays the criteria derived are characterized in terms of lmis whose solution can be solved by utilizing the standard numerical software a simulation example is presented to show the effectiveness and applicability 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

sampled data synchronization of complex networks with partial couplings and t s fuzzy nodes this paper is concerned with the synchronization of complex networks subject to partial couplings and takagi sugeno t s fuzzy nodes by adopting the aperiodic sampled data strategy a decoupling method is utilized to handle the partial couplings among connected nodes which enables us to investigate each channel of complex networks independently on the basis of the input delay approach the hybrid system about each channel is reformulated to a continuous time varying delay system then the free weighting matrix approach and a novel continuous lyapunov functional are adopted to capture the information of sampling pattern sufficient conditions are obtained to ensure that the complex networks achieves synchronization with the target node furthermore the proposed strategy is extended to more general case in which there exist constant transmission time delays in the local interactions of connected nodes based on wirtinger s inequality a simplified and efficient synchronization strategy is proposed moreover the corresponding optimization problem about the maximal sampling interval upper bound is addressed as well finally the communication frequency reduction potential of the proposed synchronization strategy is well demonstrated via a numerical example

generalized reciprocally convex combination lemmas and its application to time delay systems various efficient matrix inequalities have recently been proposed to deal with the stability analysis of linear systems with time varying delays this paper provides more insights on the relationship between some of them we present an equivalent formulation of moon et al s inequality allowing us to discover strong links not only with the most recent and efficient matrix inequalities such as the reciprocally convex combination lemma and also its relaxed version but also with some previous inequalities such as the approximation inequality introduced in 14 or free matrix based inequality more especially it is proved that these existing inequalities can be captured as particular cases of moon et al s inequality examples show the best tradeoff between the reduction of conservatism and the numerical complexity

on the search for a sequence from a predefined set of sequences in random and framed data streams in this paper we present a statistical analysis of the search for a set of predefined sequences in non equiprobable data streams both random and framed and derive a number of corresponding statistical parameters most importantly we derive the probability of occurrence of some sequence from the set at any given position from which all other statistical quantities of interest can be obtained the presented analysis is based on descriptors called cross bifices which express similarities among sequences in the set based on the obtained results we examine the problem of frame synchronization in synchronous transmission and derive parameters that could be used for the evaluation of the properties of frame synchronization sequences we introduce a survival probability of the search in a frame and a list miss probability for the list synchronizer which give exact bounds on the probability of correct frame synchronization when hard correlation is used as a sequence detection metric

analysis of optimum frame synchronization based on periodically embedded sync words we present new tight bounds for evaluating the performance of sync word based frame synchronization algorithms in the periodically embedded case we consider antipodal signaling with coherent detection over additive white gaussian noise and both optimal and suboptimal search techniques our bounds are very close to results obtained through simulation and tend asymptotically for increasing signal to noise ratios to the exact performance

a new approach to cross bifix free sets cross bifix free sets are sets of words such that no prefix of any word is a suffix of any other word in this paper we introduce a general constructive method for the sets of cross bifix free binary words of fixed length it enables us to determine a cross bifix free words subset which has the property to be non expandable

estimation of finite mixture distributions through bayesian sampling summary a formal bayesian analysis of a mixture model usually leads to intractable calculations since the posterior distribution takes into account all the partitions of the sample we present approximation methods which evaluate the posterior distribution and bayes estimators by gibbs sampling relying on the missing data structure of the mixture model the data augmentation method is shown to converge geometrically since a duality principle transfers properties from the discrete missing data chain to the parameters the fully conditional gibbs alternative is shown to be ergodic and geometric convergence is established in the normal case we also consider non informative approximations associated with improper priors assuming that the sample corresponds exactly to a k component mixture