statistical complexity measure of pseudorandom bit generators abstract pseudorandom number generators prng are extensively used in monte carlo simulations gambling machines and cryptography as substitutes of ideal random number generators rng each application imposes different statistical requirements to prngs as l ecuyer clearly states the main goal for monte carlo methods is to reproduce the statistical properties on which these methods are based whereas for gambling machines and cryptology observing the sequence of output values for some time should provide no practical advantage for predicting the forthcoming numbers better than by just guessing at random in accordance with different applications several statistical test suites have been developed to analyze the sequences generated by prngs in a recent paper a new statistical complexity measure phys lett a 311 2003 126 has been defined here we propose this measure as a randomness quantifier of a prngs the test is applied to three very well known and widely tested prngs available in the literature all of them are based on mathematical algorithms another prngs based on lorenz 3d chaotic dynamical system is also analyzed prngs based on chaos may be considered as a model for physical noise sources and important new results are recently reported all the design steps of this prng are described and each stage increase the prng randomness using different strategies it is shown that the mpr statistical complexity measure is capable to quantify this randomness improvement the prng based on the chaotic 3d lorenz dynamical system is also evaluated using traditional digital signal processing tools for comparison

observability quadratic normal form for discrete time systems this note deals with quadratic observability normal form for nonlinear discrete time single input single output siso system first of all the main concept of quadratic equivalence with respect to the observability property is introduced for discrete time systems subsequently normal form structure for discrete time system is developed for system with unobservable linear approximation in one direction finally the effect of the so called resonant terms on the observer design and synchronization of chaotic systems is pointed out in an illustrative example

brief paper fault tolerant control for singular systems with actuator saturation and nonlinear perturbation in this paper the problem of robust fault tolerant control for a class of singular systems subject to both time varying state dependent nonlinear perturbation and actuator saturation is investigated a sufficient condition for the existence of a fixed gain controller is first proposed which guarantees the regularity impulse free and stability of the closed loop system under all possible faults an optimization problem with lmi constraints is formulated to determine the largest contractively invariant ellipsoid an adaptive fault tolerant controller is then developed to compensate for the failure effects on the system by estimating the fault and updating the design parameter matrices online both of these two controllers are in the form of a saturation avoidance feedback with the advantage of relatively small actuator capacities compared with the high gain counterpart an example is included to illustrate the proposed procedures and their effectiveness

a biobjective method for sample allocation in stratified sampling the two main and contradicting criteria guiding sampling design are accuracy of estimators and sampling costs in stratified random sampling the sample size must be allocated to strata in order to optimize both objectives in this note we address following a biobjective methodology this allocation problem a two phase method is proposed to describe the set of pareto optimal solutions of this nonlinear integer biobjective problem in the first phase all supported pareto optimal solutions are described via a closed formula which enables quick computation moreover for the common case in which sampling costs are independent of the strata all pareto optimal solutions are shown to be supported for more general cost structures the non supported pareto optimal solutions are found by solving a parametric knapsack problem bounds on the criteria can also be imposed directing the search towards implementable sampling plans our method provides a deeper insight into the problem than simply solving a scalarized version whereas the computational burden is reasonable

parametric solution for linear bicriteria knapsack models linear weighing is a common approach to handle multiple criteria and the knapsack is a well known combinatorial optimization problem a knapsack problem with two linearly weighted objective criteria is considered in this paper for better support it is important to provide the decision maker with information that covers the whole range of alternatives toward this goal an algorithm for the construction of a parametric solution to the problem i e for any combination of weights is developed which is based on finding a longest path in a network which compactly represents all feasible solutions to the knapsack problem exploiting the special structure of the knapsack model the algorithm efficiently constructs the parametric solution in time that is linear in the product of the number of variables the resource limit right hand side of the constraint and the finite number of vectors which constitute the solution the amount of memory required is linear in the product of the number of variables and the resource limit results of computational study are reported the results are used to assess the efficiency of the algorithm and characterize its behavior with respect to the parameter values

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

a novel dynamic model of pseudo random number generator an interesting hierarchy of random number generators is introduced in this paper based on the review of random numbers characteristics and chaotic functions theory the main objective of this paper is to produce an ergodic dynamical system which can be implemented in random number generators in order to check the efficacy of pseudo random number generators based on this map we have carried out certain statistical tests on a series of numbers obtained from the introduced hierarchy the results of the tests were promising as the hierarchy passed the tests satisfactorily and offers a great capability to be employed in a pseudo random number generator

nonlinear integer programming for optimal allocation in stratified sampling a stratified random sampling plan is one in which the elements of the population are first divided into nonoverlapping groups and then a simple random sample is selected from each group in this paper we focus on determining the optimal sample size of each group we show that various versions of this problem can be transformed into a particular nonlinear program with a convex objective function a single linear constraint and bounded variables two branch and bound algorithms are presented for solving the problem the first algorithm solves the transformed subproblems in the branch and bound tree using a variable pegging procedure the second algorithm solves the subproblems by performing a search to identify the optimal lagrange multiplier of the single constraint we also present linearization and dynamic programming methods that can be used for solving the stratified sampling problem computational testing indicates that the pegging branch and bound algorithm is fastest for some classes of problems and the linearization method is fastest for other classes of problems

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

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

brief paper set membership filtering for systems with sensor saturation this paper addresses the set membership filtering problem for a class of discrete time varying systems with sensor saturation in the presence of unknown but bounded process and measurement noises a sufficient condition for the existence of set membership filter is derived a convex optimisation method is proposed to determine a state estimation ellipsoid that is a set of states compatible with sensor saturation and unknown but bounded process and measurement noises a recursive algorithm is developed for computing the ellipsoid that guarantees to contain the true state by solving a time varying linear matrix inequality simulation results are provided to demonstrate the effectiveness of the proposed method

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

unequal probability sampling from a finite population a multicriteria approach abstract in this note we address the problem of determining selection probabilities for multipurpose surveys when the aim is the simultaneous minimization of variances for each variable under study a characterization of the set of pareto optimal designs is given for designs with replacement and also for a class of designs without replacement namely poisson designs as an application we describe a problem encountered in auditing where both the fraction of misstatements and the average amount of such misstatements are of interest

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

properties making a chaotic system a good pseudo random number generator we discuss the properties making a deterministic algorithm suitable to generate a pseudo random sequence of numbers high value of kolmogorov sinai entropy high dimensionality of the parent dynamical system and very large period of the generated sequence we propose the multidimensional anosov symplectic cat map as a pseudo random number generator we show what chaotic features of this map are useful for generating pseudo random numbers and investigate numerically which of them survive in the discrete state version of the map testing and comparisons with other generators are performed

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

algorithm for normal random numbers we propose a simple algorithm for generating normally distributed pseudorandom numbers the algorithm simulates n molecules that exchange energy among themselves following a simple stochastic rule we prove that the system is ergodic and that a maxwell like distribution that may be used as a source of normally distributed random deviates follows in the n limit the algorithm passes various performance tests including monte carlo simulation of a finite two dimensional ising model using wolff s algorithm it only requires four simple lines of computer code and is approximately ten times faster than the box muller algorithm s1063 651x 99 04409 8 pacs number s 02 70 lq 02 90 1p

logistic map a possible random number generator the logistic map is one of the simple systems exhibiting order to chaos transition in this work we have investigated the possibility of using the logistic map in the chaotic regime logmap for a pseudorandom number generator to this end we have performed certain statistical tests on the series of numbers obtained from the logmap we find that the logmap passes these tests satisfactorily and therefore it possesses many properties required of a pseudorandom number generator

non augmented state estimation for nonlinear stochastic coupling networks abstract this paper considers the state estimation problem for discrete time nonlinear stochastic coupling networks a non augmented filter is designed for each node to guarantee an optimized upper bound on the state estimation error covariance matrix despite nodes coupling as well as the linearization errors compared with the existing augmented filter the cross covariance matrices between coupling nodes are not required to be computed and the gain matrix can be obtained separately for each node by solving two riccati like difference equations

criteria for global pinning controllability of complex networks in this paper we study pinning controllability of networks of coupled dynamical systems in particular we study the problem of asymptotically driving a network of coupled identical oscillators onto some desired common reference trajectory by actively controlling only a limited subset of the whole network the reference trajectory is generated by an exogenous independent oscillator and pinned nodes are coupled to it through a linear state feedback we describe the time evolution of the complex dynamical system in terms of the error dynamics thereby we reformulate the pinning controllability problem as a global asymptotic stability problem by using lyapunov stability theory and algebraic graph theory we establish tractable sufficient conditions for global pinning controllability in terms of the network topology the oscillator dynamics and the linear state feedback

tendency towards maximum complexity in a nonequilibrium isolated system the time evolution equations of a simplified isolated ideal gas the open quotes tetrahedral close quotes gas are derived the dynamical behavior of the lopez ruiz endash mancini endash calbet complexity r lopez ruiz h l mancini and x calbet phys lett a 209 321 1995 is studied in this system in general it is shown that the complexity remains within the bounds of minimum and maximum complexity we find that there are certain restrictions when the isolated open quotes tetrahedral close quotes gas evolves towards equilibrium in addition to the well known increase in entropy the quantity called disequilibrium decreases monotonically with time furthermore the trajectories of the system in phase space approach the maximum complexity path as it evolves toward equilibrium

features of the extension of a statistical measure of complexity to continuous systems we discuss some aspects of the extension to continuous systems of a statistical measure of complexity introduced by l opez ruiz mancini and calbet phys lett a 209 321 1995 in general the extension of a magnitude from the discrete to the continuous case is not a trivial process and requires some kind of choice in the present study several possibilities appear available one of them is examined in detail some interesting properties desirable for any magnitude of complexity are discovered on this particular extension

hierarchy of chaotic maps with an invariant measure we give hierarchy of one parameter family x of maps at the interval 0 1 with an invariant measure using the measure we calculate kolmogorov sinai entropy or equivalently lyapunov characteristic exponent of these maps analytically where the results thus obtained have been approved with the numerical simulation in contrary to the usual one parameter family of maps such as logistic and tent maps these maps do not possess period doubling or period n tupling cascade bifurcation to chaos but they have single fixed point attractor for certain values of the parameter where they bifurcate directly to chaos without having period n tupling scenario exactly at those values of the parameter whose lyapunov characteristic exponent begins to be positive

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