extracting randomness using few independent sources in this work we give the first deterministic extractors from a constant number of weak sources whose entropy rate is less than 1 2 specifically for every delta 0 we give an explicit construction for extracting randomness from a constant depending polynomially on 1 delta number of distributions over bits n each having min entropy delta n these extractors output n bits that are 2 n close to uniform this construction uses several results from additive number theory and in particular a recent result of bourgain et al we also consider the related problem of constructing randomness dispersers for any constant output length m our dispersers use a constant number of identical distributions each with requires min entropy omega log n and outputs every possible m bit string with positive probability the main tool we use is a variant of the stepping up lemma of erdods and hajnal used in establishing a lower bound on the ramsey number for hypergraphs

extracting information is hard a turing degree of non integral effective hausdorff dimension abstract we construct a 2 0 infinite binary sequence with effective hausdorff dimension 1 2 that does not compute a sequence of higher dimension introduced by lutz effective hausdorff dimension can be viewed as a measure of the information density of a sequence in particular the dimension of a 2 is the lim inf of the ratio between the information content and length of initial segments of a thus the main result demonstrates that it is not always possible to extract information from a partially random source to produce a sequence that has higher information density

generalised theory on asymptotic stability and boundedness of stochastic functional differential equations asymptotic stability and boundedness have been two of most popular topics in the study of stochastic functional differential equations sfdes see e g appleby and reynolds 2008 appleby and rodkina 2009 basin and rodkina 2008 khasminskii 1980 mao 1995 mao 1997 mao 2007 rodkina and basin 2007 shu lam and xu 2009 yang gao lam and shi 2009 yuan and lygeros 2005 and yuan and lygeros 2006 in general the existing results on asymptotic stability and boundedness of sfdes require i the coefficients of the sfdes obey the local lipschitz condition and the linear growth condition ii the diffusion operator of the sfdes acting on a c 2 1 function be bounded by a polynomial with the same order as the c 2 1 function however there are many sfdes which do not obey the linear growth condition moreover for such highly nonlinear sfdes the diffusion operator acting on a c 2 1 function is generally bounded by a polynomial with a higher order than the c 2 1 function hence the existing criteria on stability and boundedness for sfdes are not applicable and we see the necessity to develop new criteria our main aim in this paper is to establish new criteria where the linear growth condition is no longer needed while the up bound for the diffusion operator may take a much more general form

occupancy numbers in testing random number generators the classical occupancy problem where n balls are placed in n cells is used for testing of random number generators we show that the statistics of appropriately chosen occupancy numbers are incompatible with the statistics of many pseudorandom number generators prngs evenif they are trun cated more thanthat the in compatibility shows up onrelatively small samples long before the period of the prng is reached we introduce generalized fermi dirac models as idealized models for prngs these models are used to make educated guesses of how large the sample sizes should be to detect the deficiencies of the prngs under study we use the developed occupancy tests together with some other ones to examine the performance of several widely used random number generators including random of the unix c library we found that random failed two of the conducted tests rather badly we also tested a true random number generator based on decay which passed all our relevant tests successfully

stabilization of highly nonlinear hybrid systems by feedback control based on discrete time state observations given an unstable hybrid stochastic differential equation sde can we design a feedback control based on the discrete time observations of the state at times 0 tau 2 tau ldots so that the controlled hybrid sde becomes asymptotically stable it has been proved that this is possible if the drift and diffusion coefficients of the given hybrid sde satisfy the linear growth condition however many hybrid sdes in the real world do not satisfy this condition namely they are highly nonlinear and there is no answer to the question yet if the given sde is highly nonlinear the aim of this paper is to tackle the stabilization problem for a class of highly nonlinear hybrid sdes under some reasonable conditions on the drift and diffusion coefficients we show how to design the feedback control function and give an explicit bound on tau the time duration between two consecutive state observations whence the new theory established in this paper is implementable

exponential stability of stochastic delay interval systems with markovian switching in the past few years a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with markovian switching however little research has been on the stability of interval systems with markovian switching which is the topic of this paper the system discussed is the stochastic delay interval system with markovian switching it is a very advanced system and takes all the features of interval systems ito equations and markovian switching as well as time lag into account the theory developed is applicable in many different and complicated situations so the importance of the paper is clear

stabilisation of hybrid stochastic differential equations by delay feedback control this paper is concerned with the exponential mean square stabilisation of hybrid stochastic differential equations also known as stochastic differential equations with markovian switching by delay feedback controls although the stabilisation by non delay feedback controls for such equations has been discussed by several authors there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap to make our theory more understandable as well as to avoid complicated notations we will restrict our underlying hybrid stochastic differential equations to a relatively simple form however our theory can certainly be developed to cope with much more general equations without any difficulty

independent minimum length programs to translate between given strings a string p is called a program to compute y given x if u p x y where u denotes universal programming language kolmogorov complexity k y x of y relative to x is defined as minimum length of a program to compute y given x let k x denote k x emptystring kolmogorov complexity of x and let i x y k x k y k x y the amount of mutual information in x y in the present paper we answer in the negative the following question posed in bennett et al ieee trans inform theory 44 4 1998 1407 1423 is it true that for any strings x y there are independent minimum length programs p q to translate between x y that is is it true that for any x y there are p q such that u p x y u q y x the length of p is k y x the length of q is k x y and i p q 0 where the last three equalities hold up to an additive o log k x y k y x term

symmetry based inference in an instrumental variable setting we describe exact inference based on group invariance assumptions that specify various forms of symmetry in the distribution of a disturbance vector in a general nonlinear model it is shown that such mild assumptions can be equivalently formulated in terms of exact confidence sets for the parameters of the functional form when applied to the linear model this exact inference provides a unified approach to a variety of parametric and distribution free tests in particular we consider exact instrumental variable inference based on symmetry assumptions the unboundedness of exact confidence sets is related to the power to reject a hypothesis of underidentification in a multivariate instrumental variables context generalizations of anderson rubin confidence sets are considered

on asymptotic convergence and boundedness of stochastic systems with time delay analyzing the long term behavior of a nonlinear dynamical system is an important but challenging task especially in the presence of noise and delays this paper investigates asymptotic convergence and boundedness properties of stochastic systems with time delay we are particularly interested in asymptotic convergence that may not be exponential as observed in many practical applications general criteria for checking both moment and almost sure asymptotic convergence and boundedness are established such criteria are mainly motivated by stochastic systems with time varying coefficients and multiple delays and or different orders of nonlinearities as shown by several examples the existing results cannot be applied to analyze such systems thus we generalize the existing theory by allowing the diffusion operator associated with a lyapunov function to satisfy a weaker assumption which involves time varying coefficients and several auxiliary functions to cope with possible multiple delays and or different orders of nonlinearities the results presented in this paper provide an effective tool for checking asymptotic convergence and boundedness properties of general stochastic nonlinear systems with time delay

new criteria for mean square exponential stability of stochastic delay differential equations by a novel approach we present several new criteria for the mean square exponential stability of general non linear stochastic delay differential equations both delay independent and delay depend

delay dependent stability of highly nonlinear hybrid stochastic systems abstract there are lots of papers on the delay dependent stability criteria for differential delay equations ddes stochastic differential delay equations sddes and hybrid sddes a common feature of these existing criteria is that they can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions namely satisfy the linear growth condition in other words there is so far no delay dependent stability criterion on nonlinear equations without the linear growth condition we will refer to such equations as highly nonlinear ones this paper is the first to establish delay dependent criteria for highly nonlinear hybrid sddes it is therefore a breakthrough in the stability study of highly nonlinear hybrid sddes

delay dependent exponential stability of stochastic systems with time varying delay nonlinearity and markovian switching the problem of delay dependent stability in the mean square sense for stochastic systems with time varying delays markovian switching and nonlinearities is investigated both the slowly time varying delays and fast time varying delays are considered based on a linear matrix inequality approach delay dependent stability criteria are derived by introducing some relaxation matrices which can be chosen properly to lead to a less conservative result numerical examples are given to illustrate the effectiveness of the method and significant improvement of the estimate of stability limit over some existing results in the literature

quantum hypothesis testing for gaussian states quantum analogues of χ 2 t and f tests we consider quantum counterparts of testing problems for which the optimal tests are the 2 t and f tests these quantum counterparts are formulated as quantum hypothesis testing problems concerning gaussian state families and they contain nuisance parameters which have group symmetry the quantum hunt stein theorem removes some of these nuisance parameters but other difficulties remain in order to remove them we combine the quantum hunt stein theorem and other reduction methods to establish a general reduction theorem that reduces a complicated quantum hypothesis testing problem to a fundamental quantum hypothesis testing problem using these methods we derive quantum counterparts of the 2 t and f tests as optimal tests in the respective settings

optimal geostatistical model selection in many fields of science predicting variables of interest over a study region based on noisy data observed at some locations is an important problem two popular methods for the problem are kriging and smoothing splines the former assumes that the underlying process is stochastic whereas the latter assumes it is purely deterministic kriging performs better than smoothing splines in some situations but is outperformed by smoothing splines in others however little is known regarding selecting between kriging and smoothing splines in addition how to perform variable selection in a geostatistical model has not been well studied in this article we propose a general methodology for selecting among arbitrary spatial prediction methods based on approximately unbiased estimation of mean squared prediction errors using a data perturbation technique the proposed method accounts for estimation uncertainty in both kriging and smoothing spline predictors and is shown to be optimal in terms of two mean sq

a note on delay dependent stability of ito type stochastic time delay systems different from the existing delay dependent stability criteria which depend on the size of the delays in both the drift and diffusion parts of stochastic time delay systems stdss this paper shows that the delay dependent stability criterion depends only on the drift part and works for arbitrary large delays of the diffusion part of stdss by developing the stochastic version descriptor system approach simple stability criterion is further derived for aperiodic sampled data stochastic systems the theoretical results are illustrated by means of a numerical example

robust stability and boundedness of nonlinear hybrid stochastic differential delay equations one of the important issues in the study of hybrid stochastic differential delay equations sddes is the automatic control with consequent emphasis being placed on the asymptotic analysis of stability and boundedness in the study of asymptotic properties the robust stability has received a great deal of attention the theory of robust stability shows how much perturbation a given stable hybrid sdde can tolerate so that its perturbed system remains stable almost all results so far on the robust stability require that the underlying sddes be either linear or nonlinear with linear growth condition however little is known on the robust stability of nonlinear hybrid sddes without the linear growth condition which is one of the key topics in this paper the other key topic is the robust boundedness the aim here is to answer the question how much perturbation can a given asymptotically bounded hybrid sdde tolerate so that its perturbed system remains asymptotically bounded

a new approach to specificity in possibility theory decision making point of view abstract the paper investigates the problem of defining a specificity relation in pyt ev possibility theory that branch of possibility theory developed by prof yu p pyt ev in the late 1990s defines possibility as a monotone measure which numerical values except 0 and 1 are meaningless the following information and its consequent implications are meaningful a 0 a is impossible or a b a is more possible than b or a b a and b are equally possible all results obtained with pyt ev possibility theory are invariant to any strictly increasing lower semi continuous transformation of all possibility values with the fixed points 0 and 1 this fact allows anyone to assign numerical values to possibilities using an individual subjective scale of possibility values unlike zadeh possibility theory based on fuzzy sets where specificity of possibility distributions is evaluated by means of fuzzy set inclusion and distribution 1 is more specific than 2 iff 1 2 pointwise in pyt ev possibility theory such an approach can not be applied if numerical values of 1 and 2 are assigned through different subjective scales a thesis we put forward in this paper states that the specificity relation definition has to be consistent with the possibilistic decision making approaches the following is intended to be true the more specific an underlying possibility and a corresponding possibility distribution are the narrower more specific a set of the optimal decisions is a decision is optimal if it minimizes the possibility of error a specificity relation satisfying such a requirement is defined and studied