initial boundary value problem for the system of compressible adiabatic flow through porous media abstract we study the initial value problem for the system of compressible adiabatic flow through porous media in the one space dimension with fixed boundary condition under the restriction on the oscillations in the initial data we establish the global existence and large time behavior for the classical solutions via the combination of characteristic analysis and energy estimate methods the time asymptotic states for the solution are found and the exponential convergence to the asymptotic states is proved it is also shown that this problem can be approximated very well time asymptotically by an initial boundary problem for the related diffusion equations obtained from the original hyperbolic system by darcy s law provided that the initial total mass is the same the difference between these two solutions tends to zero exponentially fast as time goes to infinity in the sense of h 1 the diffusive phenomena caused by damping mechanism with boundary effects are thus observed

a note on bayes factors for log linear contingency table models with vague prior information spiegelhalter and smith 1982 hereafter ssproposed an approximate method for calculating the bayes factor for a log linear model mo for a contingency table against the saturated model m1 with vague prior information we adopt their notation and denote by ss n equation n of ss suppose x1 xk have a multinomial distribution with parameters 014 4k where xi 0 0 x4i 1 we write yt log x1 log xk 01 log 01 log dk and y diag x1 xk then if m1 is the saturated model and mo is the nested log linear model defined by setting the contrasts co1 0 where c is an s x k matrix with rank s and rows summing to zero the approximate bayes factor bo1 for mo against m1 is given by ss 32 this however is indeterminate if any of the cell frequencies in the table is zero this is because of the use by ss of a prior density proportional to h i if however we use instead the standard jeffreys prior density proportional to i1i 1 2 the problem no longer arises then by the arguments of ss and lindley 1964 the resulting bayes factor is still given by ss 32 with xi replaced by xi 2 in the definitions of y and y i 1 k and ss 33 replaced by c 1 2 s2 1 cct i 1 2 if this solution is adopted the prior is proper and so in principle the problem of assigning an arbitrary multiplicative constant for which the ss approach was primarily devised need not arise one could in theory simply apply bayes theorem directly and so obtain the bayes factor exactly however in practice this is difficult to do and i know of no general solution to the problem even for simpler more specific contingency table and related models such as those of independence or equiprobability finding the bayes factor exactly is not too easy see for example crook and good 1982 altham 1971 gunel and dickey 1974 gunel 1982 broniatowski 1981 and references therein the second purpose of this note is to point out that conditionally on mo

estimating the errors on measured entropy and mutual information abstract information entropy and the related quantity mutual information are used extensively as measures of complexity and to identify nonlinearity in dynamical systems expressions for the probability distribution of entropies and mutual informations calculated from finite amounts of data exist in the literature but the expressions have seldom been used in the field of nonlinear dynamics in this paper formulae for estimating the errors on observed information entropies and mutual informations are derived using the standard error analysis familiar to physicists their validity is demonstrated by numerical experiment for illustration the formulae are then used to evaluate the errors on the time lagged mutual information of the logistic map

assessing the order of dependence for partially exchangeable binary data abstract the problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences we obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts these tests are facilitated with a new monte carlo scheme asymptotic tests are also discussed in particular we show that the likelihood ratio tests have an asymptotic chi squared distribution thus generalizing the results of billingsley for the particular case of markov chains we apply these methods to several datasets and perform a simulation to study their properties

decomposition of conditional probability for high order symbolic markov chains the main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet we elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high order markov chains we represent the conditional probability function as the sum of multilinear memory function monomials of different orders from zero up to the chain order this allows us to introduce a family of markov chain models and to construct artificial sequences via a method of successive iterations taking into account at each step increasingly high correlations among random elements at weak correlations the memory functions are uniquely expressed in terms of the high order symbolic correlation functions the proposed method fills the gap between two approaches namely the likelihood estimation and the additive markov chains the obtained results may have applications for sequential approximation of artificial neural network training

the tsallis entropy of natural information abstract estimating the information contained in natural data such as electroencephalography data is unusually difficult because the relationship between the physical data and the information that it encodes is unknown this unknown relationship is often called the encoding problem the present work provides a solution to this problem by deriving a method to estimate the tsallis entropy in natural data the method is based on two findings the first finding is that the physical instantiation of any information event that is the physical occurrence of a symbol of information must begin and end at a discontinuity or critical point maximum minimum or saddle point in the data the second finding is that in certain data types such as the encephalogram eeg the variance within of an eeg waveform event is directly proportional to its probability of occurrence these two outcomes yield two results the first is the easy binning of data into separate information events the second is the ability to estimate probabilities in two ways frequency counting and computing the variance within of an eeg waveform these results are used to derive a linear estimator of the tsallis entropy functional allowing it to be estimated without deducing the encoding this method for estimating the tsallis entropy is first used to estimate the information in simple signals the amount of information estimated is highly accurate the method is then applied to two problems in electroencephalography the first is distinguishing normal aging from very early alzheimer s disease mild cognitive impairment and the second is medication monitoring of alzheimer s disease treatment the former is done with an accuracy of 92 and the latter with an accuracy of 91 this detection accuracy is the highest published accuracy in the literature which suggests that this method for tsallis entropy estimation is both accurate and useful

estimating functions of probability distributions from a finite set of samples this paper addresses the problem of estimating a function of a probability distribution from a finite set of samples of that distribution a bayesian analysis of this problem is presented the optimal properties of the bayes estimators are discussed and as an example of the formalism closed form expressions for the bayes estimators for the moments of the shannon entropy function are derived then numerical results are presented that compare the bayes estimator to the frequency counts estimator for the shannon entropy we also present the closed form estimators all derived elsewhere for the mutual information mathrm ensuremath chi 2 covariance and some other statistics c 1995 the american physical society

convergence of controlled models and finite state approximation for discounted continuous time markov decision processes with constraints abstract in this paper we consider the convergence of a sequence m n of the models of discounted continuous time constrained markov decision processes mdp to the limit one denoted by m for the models with denumerable states and unbounded transition rates under reasonably mild conditions we prove that the constrained optimal policies and the optimal values of m n converge to those of m respectively using a technique of occupation measures as an application of the convergence result developed here we show that an optimal policy and the optimal value for countable state continuous time mdp can be approximated by those of finite state continuous time mdp finally we further illustrate such finite state approximation by solving numerically a controlled birth and death system and also give the corresponding error bound of the approximation

best asymptotic profile for linear damped p system with boundary effect abstract this paper is devoted to the study of the 2 2 linear damped p system with boundary effect by a heuristic analysis we realize that the best asymptotic profile for the original solution is the parabolic solution of the ibvp for the corresponding porous media equation with a specified initial data in particular we further show the convergence rates of the original solution to its best asymptotic profile which are much better than the existing rates obtained in the previous works the approach adopted in the paper is the elementary weighted energy method with green function method together

l 1 convergence to the barenblatt solution for compressible euler equations with damping we study the asymptotic behavior of compressible isentropic flow through a porous medium when the initial mass is finite the model system is the compressible euler equation with frictional damping as t the density is conjectured to obey the well known porous medium equation and the momentum is expected to be formulated by darcy s law in this paper we prove that any l weak entropy solution to the cauchy problem of damped euler equations with finite initial mass converges strongly in the natural l1 topology with decay rates to the barenblatt profile of the porous medium equation the density function tends to the barenblatt solution of the porous medium equation while the momentum is described by darcy s law the results are achieved through a comprehensive entropy analysis capturing the dissipative character of the problem

applying experimental design and regression splines to high dimensional continuous state stochastic dynamic programming in stochastic dynamic programming sdp with continuous state and decision variables the future value function is computed at discrete points in the state spac e interpolation can be used to approximate the values of the future value function between these discrete points however for large dimensional problems the number of discrete points required to obtain a good approximation of the future value function can be prohibitively large statistical methods of experimental design and function estimation may be employed to overcome this curse of dimensionality in this paper we describe a method for estimating the future value function by multivariate adaptive regression splines mars fit over a discretization scheme based on orthogonal array oa experimental designs because orthogonal arrays only grow polynomially in the state space dimension our oa mars method is accurately able to solve higher dimensional sdp problems than previously possible to our knowledge the most efficient method published prior to this work employs tensor product cubic splines to approximate the future value function johnson et al 1993 the computational advantages of oa ma rs are demonstrated in comparisons with the method using tensor product cubic splines for applications of an inventory forecasting sdp with up to nine state variables computed on a small workstation in particular the storage of an adequate tensor product cubic spline for six dimensions exceeds the memory of our workstation and the run time for an accurate oa mars sdp solution would be at least an order of magnitude faster than using tensor product cubic splines for higher than six dimensions

tsallis conditional mutual information in investigating long range correlation in symbol sequences abstract the presence of long range correlation lrc as opposed to markov chain of a finite order is of primary interest in the study of symbol sequences such as dna among others methods using information theory have been developed for markov chain order estimation in this work we consider the tsallis entropy and define the tsallis conditional mutual information tcmi for markov chain order estimation which is more suitable to identify large orders suggesting effectively lrc the tcmi of order m for a tsallis parameter q is computed for increasing m and a significance test is performed for each m until tcmi is found non significant randomization and parametric significance tests for tcmi are developed for the latter the null distribution of tcmi is approximated with a gamma distribution deriving analytic expressions for its parameters we assess the accuracy of order estimation with the two tests for tcmi and compare them to the respective tests using the shannon entropy extended simulations on markov chains of different orders and structures of the transition probability matrix show that shannon and tsallis tests with parameter q 2 have similar performance for small orders when the problem becomes more demanding for higher markov chain orders and lrcs tsallis tests for q 2 have better approximation to the correct order with the sequence length n finally the tsallis tests are favorably compared to shannon tests to real dna sequences

shock reflection for a system of hyperbolic balance laws abstract this paper concerns shock reflection for a system of hyperbolic balance laws in one space dimension it is shown that the generalized nonlinear initial boundary riemann problem for a system of hyperbolic balance laws with nonlinear boundary conditions in the half space t x t 0 x 0 admits a unique global piecewise c 1 solution u u t x containing only shocks with small amplitude and this solution possesses a global structure similar to that of self similar solution u u x t of the corresponding homogeneous riemann problem if each characteristic field with positive velocity is genuinely nonlinear and the corresponding homogeneous riemann problem has only shocks but no centered rarefaction waves and contact discontinuities this result is also applied to shock reflection for the flow equations of a model class of fluids with viscosity induced by fading memory

exact significance test for markov order abstract we describe an exact significance test of the null hypothesis that a markov chain is n th order the procedure utilizes surrogate data to yield an exact test statistic distribution valid for any sample size surrogate data are generated using a novel algorithm that guarantees per shot a uniform sampling from the set of sequences that exactly match the n th order properties of the observed data using the test the markov order of tel aviv rainfall data is examined

context tree based image contour coding using a geometric prior efficient encoding of object contours in images can facilitate advanced image video compression techniques such as shape adaptive transform coding or motion prediction of arbitrarily shaped pixel blocks we study the problem of lossless and lossy compression of detected contours in images specifically we first convert a detected object contour into a sequence of directional symbols drawn from a small alphabet to encode the symbol sequence using arithmetic coding we compute an optimal variable length context tree vct mathcal t via a maximum a posterior map formulation to estimate symbols conditional probabilities map can avoid overfitting given a small training set mathcal x of past symbol sequences by identifying a vct mathcal t with high likelihood p mathcal x mathcal t of observing mathcal x given mathcal t using a geometric prior p mathcal t stating that image contours are more often straight than curvy for the lossy case we design fast dynamic programming dp algorithms that optimally trade off coding rate of an approximate contour hat text x given a vct mathcal t with two notions of distortion of hat text x with respect to the original contour x to reduce the size of the dp tables a total suffix tree is derived from a given vct mathcal t for compact table entry indexing reducing complexity experimental results show that for lossless contour coding our proposed algorithm outperforms state of the art context based schemes consistently for both small and large training datasets for lossy contour coding our algorithms outperform comparable schemes in the literature in rate distortion performance

almost global existence of classical discontinuous solutions to genuinely nonlinear hyperbolic systems of conservation laws with small bv initial data abstract in the present paper the author investigates the initial problem for genuinely nonlinear quasilinear hyperbolic systems of conservation laws under small bv perturbations of the riemann initial data where the perturbations are in bv but they are assumed to be c 1 smooth with bounded and possibly large c 1 norms combining the techniques employed by li and kong with the modified glimm s functional the author obtains the almost global existence and lifespan of classical discontinuous solutions to the above problem this result is also applied to the system of one dimensional isentropic flow

the generalized nonlinear initial boundary riemann problem for linearly degenerate quasilinear hyperbolic systems of conservation laws abstract this work is a continuation of our previous work in the present paper we study the generalized nonlinear initial boundary riemann problem with small bv data for linearly degenerate quasilinear hyperbolic systems of conservation laws with nonlinear boundary conditions in a half space t x t 0 x 0 we prove the global existence and uniqueness of piecewise c 1 solution containing only contact discontinuities to a class of the generalized nonlinear initial boundary riemann problem which can be regarded as a small bv perturbation of the corresponding nonlinear initial boundary riemann problem for general n n linearly degenerate quasilinear hyperbolic system of conservation laws moreover this solution has a global structure similar to the one of the self similar solution u u x t to the corresponding nonlinear initial boundary riemann problem some applications to quasilinear hyperbolic systems of conservation laws arising in the string theory and high energy physics are also given

a mixture of transition models for heterogeneous longitudinal ordinal data with applications to longitudinal bacterial vaginosis data markov models used to analyze transition patterns in discrete longitudinal data are based on the limiting assumption that individuals follow the common underlying transition process however when one is interested in diseases with different disease or severity subtypes explicitly modeling subpopulation specific transition patterns may be appropriate we propose a model which captures heterogeneity in the transition process through a finite mixture model formulation and provides a framework for identifying subpopulations at different risks we apply the procedure to longitudinal bacterial vaginosis bv study data and demonstrate that the model fits the data well further we show that under the mixture model formulation we can make the important distinction between how covariates affect transition patterns unique to each of the subpopulations and how they affect which subgroup a participant will belong to practically covariate effects on subpopulation specific transition behavior and those on subpopulation membership can be interpreted as effects on short term and long term transition behavior we further investigate models with higher order subpopulation specific transition dependence

approximate stochastic dynamic programming for hydroelectric production planning abstract this paper presents a novel approach for approximate stochastic dynamic programming asdp over a continuous state space when the optimization phase has a near convex structure the approach entails a simplicial partitioning of the state space bounds on the true value function are used to refine the partition we also provide analytic formulae for the computation of the expectation of the value function in the uni basin case where natural inflows are strongly correlated the approach is experimented on several configurations of hydro energy systems it is also tested against actual industrial data

convergence to nonlinear diffusion waves for solutions of p system with time dependent damping abstract in this paper we study the cauchy problem for the hyperbolic p system with time gradually degenerate damping term 1 1 t u for 0 1 and show that the damped p system has a couple of global solutions uniquely and such solutions tend time asymptotically to the shifted nonlinear diffusion waves which are the solutions of the corresponding nonlinear parabolic equation governed by the darcy s law we further derive the convergence rates when the initial perturbations are in l 2 the approach adopted is the technical time weighted energy method

higher order multivariate markov chains and their applications abstract markov chains are commonly used in modeling many practical systems such as queuing systems manufacturing systems and inventory systems they are also effective in modeling categorical data sequences in a conventional n th order multivariate markov chain model of s chains and each chain has the same set of m states the total number of parameters required to set up the model is o m ns such huge number of states discourages researchers or practitioners from using them directly in this paper we propose an n th order multivariate markov chain model for modeling multiple categorical data sequences such that the total number of parameters are of o ns 2 m 2 the proposed model requires significantly less parameters than the conventional one we develop efficient estimation methods for the model parameters an application to demand predictions in inventory control is also discussed

entropy and long range memory in random symbolic additive markov chains the goal of this paper is to develop an estimate for the entropy of random symbolic sequences with elements belonging to a finite alphabet as a plausible model we use the high order additive stationary ergodic markov chain with long range memory supposing that the correlations between random elements of the chain are weak we express the conditional entropy of the sequence by means of the symbolic pair correlation function we also examine an algorithm for estimating the conditional entropy of finite symbolic sequences we show that the entropy contains two contributions i e the correlation and the fluctuation the obtained analytical results are used for numerical evaluation of the entropy of written english texts and dna nucleotide sequences the developed theory opens the way for constructing a more consistent and sophisticated approach to describe the systems with strong short range and weak long range memory

on some criteria for estimating the order of a markov chain tong 1975 has proposed a procedure for estimating the order of a markov chain based on akaike s information criterion aic in this paper the asymptotic distribution of the aic estimator is derived and it is shown that the estimator is inconsistent as an alternative to the aic procedure the bayesian information criterion bic proposed by schwarz 1978 is shown to be consistent these two procedures yield different estimated orders when applied to specific samples of meteorological observations for parameters based on these meteorological examples the aic and bic procedures are compared by means of simulation for finite samples the results obtained have practical implications concerning whether in the routine fitting of precipitation data it is necessary to consider higher than first order markov chains

on the relation between various entropy concepts and the valoric interpretation abstract the valoric interpretation developed already by clausius helmholtz and ostwald is taken as the basis for a reinterpretation of the various entropy concepts developed by clausius boltzmann gibbs shannon and kolmogorov as the key points we consider the value of energy with respect to work and the value of entropy with respect to informmation processing

a comparison of global and semi local approximation in t stage stochastic optimization the paper presents a comparison between two different flavors of nonlinear models to be used for the approximate solution of t stage stochastic optimization tso problems a typical paradigm of markovian decision processes specifically the well known class of neural networks is compared with a semi local approach based on kernel functions characterized by less demanding computational requirements to this purpose two alternative methods for the numerical solution of tso are considered one corresponding to the classic approximate dynamic programming adp and the other based on a direct optimization of the optimal control functions introduced here for the first time advantages and drawbacks in the tso context of the two classes of approximators are analyzed in terms of computational burden and approximation capabilities then their performances are evaluated through simulations in two important high dimensional tso test cases namely inventory forecasting and water reservoirs management

testing the order of discrete markov chains using surrogate data tests of the null hypothesis that a symbolic sequence is of nth markov order are described these tests are based on resampling methods similar to the method of surrogate data used to test continuous time series for nonlinear structure the size and power of these symbolic surrogate tests are estimated using binary and heptary test sequences of known order conditioning on a sufficient statistic under the null hypothesis yields an estimated true size which closely approximates the nominal size and increases the power of the test with respect to the unconditional test we apply one method to a symbolic sequence derived from the rossler system and to a binary and heptary representation of an interspike interval sequence of an electroreceptor of the weakly electric eel apteronotus leptorhynchus

method for generating long range correlations for large systems we propose a new method to generate a sequence of random numbers with long range power law correlations that overcomes known difficulties associated with large systems the new method presents an improvement on the commonly used methods we apply the algorithm to generate enhanced diffusion isotropic and anisotropic self affine surfaces and isotropic and anisotropic correlated percolation

numerical solution of continuous state dynamic programs using linear and spline interpolation this paper demonstrates that the computational effort required to develop numerical solutions to continuous state dynamic programs can be reduced significantly when cubic piecewise polynomial functions rather than tensor product linear interpolants are used to approximate the value function tensor product cubic splines represented in either piecewise polynomial or b spline form and multivariate hermite polynomials are considered computational savings are possible because of the improved accuracy of higher order functions and because the smoothness of higher order functions allows efficient quasi newton methods to be used to compute optimal decisions the use of the more efficient piecewise polynomial form of the spline was slightly superior to the use of hermite polynomials for the test problem and easier to program in comparison to linear interpolation use of splines in piecewise polynomial form reduced the cpu time to obtain results of equivalent accuracy by a factor of 250 330 for a stochastic

relative entropy and identification of gibbs measures in dynamical systems in this work we explore the idea of using the relative entropy of ergodic measures for the identification of gibbs measures in dynamical systems the question we face is how to estimate the thermodynamic potential together with a grammar from a sample produced by the corresponding gibbs state

markov chain order estimation with conditional mutual information abstract we introduce the conditional mutual information cmi for the estimation of the markov chain order for a markov chain of k symbols we define cmi of order m i c m as the mutual information of two variables in the chain being m time steps apart conditioning on the intermediate variables of the chain we find approximate analytic significance limits based on the estimation bias of cmi and develop a randomization significance test of i c m where the randomized symbol sequences are formed by random permutation of the components of the original symbol sequence the significance test is applied for increasing m and the markov chain order is estimated by the last order for which the null hypothesis is rejected we present the appropriateness of cmi testing on monte carlo simulations and compare it to the akaike and bayesian information criteria the maximal fluctuation method peres shields estimator and a likelihood ratio test for increasing orders using divergence the order criterion of cmi testing turns out to be superior for orders larger than one but its effectiveness for large orders depends on data availability in view of the results from the simulations we interpret the estimated orders by the cmi testing and the other criteria on genes and intergenic regions of dna chains

human brain dynamics the analysis of eeg signals with tsallis information measure we undertake the study of human eeg signals by recourse to a wavelet based multiresolution analysis as adapted to an information measure scenario dierent information measures are employed it is shown that non extensive ones seem to be of particular usefulness their use opens up perspectives of building up automatic detection devices conjectures concerning general characteristics of focal epilepsy are formulated on the basis of a tsallis type of analysis c 1999 elsevier science b v all rights reserved

convergence to strong nonlinear diffusion waves for solutions to p system with damping on quadrant in this paper we consider the so called p system with linear damping on quadrant we show that for a certain class of given large initial data v0 x u0 x the corresponding initial boundary value problem admits a unique global smooth solution v x t u x t and such a solution tends time asymptotically at the lp 2 p optimal decay rates to the corresponding nonlinear diffusion wave v x t u x t which satisfies 1 9 provided the corresponding prescribed initial error function v0 x u0 x lies in h3 r l1 r h2 r l1 r

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

lifespan of classical discontinuous solutions to general quasilinear hyperbolic systems of conservation laws with small bv initial data shocks and contact discontinuities abstract this work is a continuation of our previous work z q shao global structure stability of riemann solutions for linearly degenerate hyperbolic conservation laws under small bv perturbations of the initial data nonlinear anal real world appl 11 2010 3791 3808 in the present paper we investigate the global structure stability of riemann solutions for general quasilinear hyperbolic systems of conservation laws under small bv perturbations of the initial data where the riemann solution only contains the shocks and contact discontinuities and at least a shock wave the perturbations are in bv but they are assumed to be c 1 smooth with bounded and possibly large c 1 norms we get a lower bound of the lifespan of the piecewise c 1 solution to a class of the generalized riemann problem which can be regarded as a small bv perturbation of the corresponding riemann problem some applications to quasilinear hyperbolic systems of conservation laws arising in physics particularly to one dimensional euler equations of gas dynamics for a compressible inviscid non heat conducting gas in eulerian coordinates are also given

newton noda iteration for finding the perron pair of a weakly irreducible nonnegative tensor we present a newton noda iteration nni for computing the perron pair of a weakly irreducible nonnegative mth order tensor mathscr a a by combining the idea of newton s method with the idea of the noda iteration the method requires the selection of a positive parameter theta k k in the kth iteration and produces a scalar sequence approximating the spectral radius of mathscr a a and a positive vector sequence approximating the perron vector we propose a halving procedure to determine the parameters theta k k starting with theta k 1 k 1 for each k such that the scalar sequence is monotonically decreasing convergence of this sequence to the spectral radius of mathscr a a and convergence of the vector sequence to the perron vector is guaranteed for any initial positive unit vector as long as the sequence theta k k so chosen is bounded below by a positive constant in this case we always have theta k 1 k 1 near convergence and the convergence is quadratic very often the halving procedure will return theta k 1 k 1 i e no halving is actually used for each k if the tensor is semisymmetric m ge 4 m 4 and theta k 1 k 1 then the computational work in the kth iteration of nni is roughly the same as that for one iteration of the ng qi zhou algorithm which is linearly convergent for the smaller class of weakly primitive tensors

asymptotic behaviors of solutions of quasilinear hyperbolic equations with linear damping ii this paper as a follow up to the recent work of k nishihara 1997 j differential equations133 384 395 is concerned with the asymptotic behaviors of the solution of quasilinear hyperbolic equation with linear damping vtt a vx x vt 0 a v 0forallv r which satisfies the following prescribed initial condition v t x vt t x t 0 v0 x v1 x x r compared with the results obtained by k nishihara the main novelties of our present paper lie in the following first we recover all the results obtained by k nishihara under some other smallness assumptions on the initial data v0 x v1 x which are much weaker than those needed in k nishihara s arguments second under some additional assumptions on the nonlinear function a v and on the initial data v0 x v1 x when 0 0 1 0 we succeed in proving that t x is still an asymptotic profile of v t x and this answers partially the open problem left by k nishihara

two general models that generate long range correlation abstract in this paper we study two models that generate sequences with lrc long range correlation for the ift inverse fourier transform model our conclusion is the low frequency part leads to lrc while the high frequency part tends to eliminate it therefore a typical method to generate a sequence with lrc is multiplying the spectrum of a white noise sequence by a decaying function a special case is analyzed the linear combination of a smooth curve and a white noise sequence in which the dfa plot consists of two line segments for the patch model our conclusion is long subsequences leads to lrc while short subsequences tend to eliminate it therefore we can generate a sequence with lrc by using a fat tailed pdf probability distribution function of the length of the subsequences a special case is also analyzed if a patch model with long subsequences is mixed with a white noise sequence the dfa plot will consist of two line segments we have checked known models and actual data and found they are all consistent with this study

guessing probability distributions from small samples we propose a new method for the calculation of the statistical properties e g the entropy of unknown generators of symbolic sequences the probability distributionp k of the elementsk of a population can be approximated by the frequenciesf k of a sample provided the sample is long enough so that each elementk occurs many times our method yields an approximation if this precondition does not hold for a givenf k we recalculate the zipf ordered probability distribution by optimization of the parameters of a guessed distribution we demonstrate that our method yields reliable results

learning with kernel smoothing models and low discrepancy sampling this brief presents an analysis of the performance of kernel smoothing models used to estimate an unknown target function addressing the case where the choice of the training set is part of the learning process in particular we consider a choice of the points at which the function is observed based on low discrepancy sequences which is a family of sampling methods commonly employed for efficient numerical integration we prove that under suitable regularity assumptions consistency of the empirical risk minimization is guaranteed with a good rate of convergence of the estimation error as well as the convergence of the approximation error simulation results confirm in practice the good theoretical properties given by the combination of kernel smoothing models with low discrepancy sampling

low discrepancy points for deterministic assignment of hidden weights in extreme learning machines the traditional extreme learning machine elm approach is based on a random assignment of the hidden weight values while the linear coefficients of the output layer are determined analytically this brief presents an analysis based on geometric properties of the sampling points used to assign the weight values investigating the replacement of random generation of such values with low discrepancy sequences ldss such sequences are a family of sampling methods commonly employed for numerical integration yielding a more efficient covering of multidimensional sets with respect to random sequences without the need for any computationally intensive procedure in particular we prove that the universal approximation property of the elm is guaranteed when ldss are employed and how an efficient covering affects the convergence positively furthermore since ldss are generated deterministically the results do not have a probabilistic nature simulation results confirm in practice the good theoretical properties given by the combination of elm with ldss

the lp lq estimates of solutions to one dimensional damped wave equations and their application to the compressible flow through porous media we first obtain the lp lq estimates of solutions to the cauchy problem for one dimensional damped wave equation vtt vxx vt 0 v vt t 0 v0 v1 x x t r r corresponding to that for the parabolic equation t xx 0 t 0 v0 v1 x the estimates are shown by v t e t 2v0 t v0 t 2lp ct 121q 1p 1 v0 v1 lq t 1 etc for 1 q p to show the explicit formula of the damped wave equation will be used to apply the estimates to nonlinear problems is the second aim we will treat the system of a compressible flow through porous media the solution is expected to behave as the diffusion wave which is the solution to the porous media equation due to the darcy law when the initial data has the same constant state at a sharp lp convergence rate for p 2 has been recently obtained by nishihara proc roy soc edinburgh sect a 133a 2003 1 20 by choosing a suitably located diffusion wave we will show the l1 convergence applying

local linear regression for function learning an analysis based on sample discrepancy local linear regression models a kind of nonparametric structures that locally perform a linear estimation of the target function are analyzed in the context of empirical risk minimization erm for function learning the analysis is carried out with emphasis on geometric properties of the available data in particular the discrepancy of the observation points used both to build the local regression models and compute the empirical risk is considered this allows to treat indifferently the case in which the samples come from a random external source and the one in which the input space can be freely explored both consistency of the erm procedure and approximating capabilities of the estimator are analyzed proving conditions to ensure convergence since the theoretical analysis shows that the estimation improves as the discrepancy of the observation points becomes smaller low discrepancy sequences a family of sampling methods commonly employed for efficient numerical integration are also analyzed simulation results involving two different examples of function learning are provided

some applications of the useful mutual information abstract the useful mutual information statistic is considered and its asymptotic properties are investigated either considering random sampling or stratified random sampling under different assumptions it is shown that the asymptotic distribution of this statistic is either normal or a linear form in gc 2 variables finally its application to testing hypotheses of independence in multinomial populations is given

determining and interpreting the order of a two state markov chain application to models of daily precipitation we illustrate the result that lumping together some of the states of a many state first order markov chain does not in general give a first order markov chain with a smaller number of states if a series generated in this way is nevertheless assumed to have been produced by a two state markov chain standard statistical procedures using the akaike and bayesian information criteria may indicate that it should be fitted by a higher order than first stochastic models based on a markov chain are often used to model precipitation series it is normal to classify days as dry and wet and fit a two state process in some cases second or higher order chains are preferred by reference to information criteria in the light of the foregoing we suggest that this might be because a many state process possibly of only first order would actually be a better choice than a two state process

statistical analysis of gene and intergenic dna sequences abstract much of the on going statistical analysis of dna sequences is focused on the estimation of characteristics of coding and non coding regions that would possibly allow discrimination of these regions in the current approach we concentrate specifically on genes and intergenic regions to estimate the level and type of correlation in these regions we apply various statistical methods inspired from nonlinear time series analysis namely the probability distribution of tuplets the mutual information and the identical neighbour fit the methods are suitably modified to work on symbolic sequences and they are first tested for validity on sequences obtained from well known simple deterministic and stochastic models then they are applied to the dna sequence of chromosome 1 of arabidopsis thaliana the results suggest that correlations do exist in the dna sequence but they are weak and that intergenic sequences tend to be more correlated than gene sequences the use of statistical tests with surrogate data establish these findings in a rigorous statistical manner

dynamical complexity detection in pre seismic emissions using nonadditive tsallis entropy abstract we investigate within the framework of nonextensive tsallis entropy particular aspects of the relation between signal analysis and signals originating in a very special nonlinear system the focal area of an impending earthquake the tsallis like time dependent entropy is shown to be a rather powerful tool for providing a novel quantitative strategy for monitoring the focal area states just before the earthquake occurrence

a model for high order markov chains on introduit un modele pour des chaines de markov du leme ordre qui comporte seulement un parametre additionnel pour chaque retard

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

functional optimization through semilocal approximate minimization an approach based on semilocal approximation is introduced for the solution of a general class of operations research problems such as markovian decision problems multistage optimal control and maximum likelihood estimation because it is extremely hard to derive analytical solutions that minimize the cost in most instances of the problem we must look for approximate solutions here it is shown that good solutions can be obtained with a moderate computational effort by exploiting properties of semilocal approximation through kernel models and efficient sampling of the state space the convergence of the proposed method called semilocal approximate minimization slam is discussed and the consistency of the solution is derived simulation results show the efficiency of slam also through its application to a classic operations research problem i e inventory forecasting

convergence to the barenblatt solution for the compressible euler equations with damping and vacuum we study the asymptotic behavior of a compressible isentropic flow through a porous medium when the initial mass is finite the model system is the compressible euler equation with frictional damping as t the density is conjectured to obey the well known porous medium equation and the momentum is expected to be formulated by darcy s law in this paper we give a definite answer to this conjecture without any assumption on smallness or regularity for the initial data we prove that any l weak entropy solution to the cauchy problem of damped euler equations with finite initial mass converges strongly in lp with decay rates to matching barenblatt s profile of the porous medium equation the density function tends to the barenblatt s solution of the porous medium equation while the momentum is described by darcy s law

asymptotic behavior of the solutions to the damped compressible euler equations with vacuum abstract the asymptotic behavior of solutions of the damped compressible euler equations is conjectured to obey to the famous porous media equations pmes the previous works on this topic concern the case away from vacuum where the system is strictly hyperbolic in present paper we prove that the l entropy weak solution with vacuum obtained by the compensated compactness theory converges strongly in l loc p 1 p space to the unique similarity solution of the related pme as time goes to infinity

convergence rate for compressible euler equations with damping and vacuum we study the asymptotic behavior of l weak entropy solutions to the compressible euler equations with damping and vacuum previous works on this topic are mainly concerned with the case away from the vacuum and small initial data in the present paper we prove that the entropy weak solution strongly converges to the similarity solution of the porous media equations in lp r 2 p with decay rates the initial data can contain vacuum and can be arbitrary large a new approach is introduced to control the singularity near vacuum for the desired estimates

global structure and asymptotic behavior of weak solutions to flood wave equations abstract the present paper concerns with the global structure and asymptotic behavior of the discontinuous solutions to flood wave equations by solving a free boundary problem we first obtain the global structure and large time behavior of the weak solutions containing two shock waves for the cauchy problem with a class of initial data we use glimm scheme to obtain a uniform bv estimate both with respect to time and the relaxation parameter this yields the global existence of bv solution and convergence to the equilibrium equation as the relaxation parameter tends to 0

correlation function inadequacy in random sequence entropy measures considering symbolic and numerical random sequences in the framework of the additive markov chain approach we establish a relation between their correlation functions and conditional entropies we express the entropy by means of the two point probability distribution functions and then evaluate the entropy for the numerical random chain in terms of the correlation function we show that such approximation gives a satisfactory result only for special types of random sequences in general case the conditional entropy of numerical sequences obtained in the two point distribution function approach is lower we derive the conditional entropy of the additive markov chain as a sum of the kullback leibler mutual information and give an example of random sequence with the exactly zero correlation function and the nonzero correlations

global existence of classical solutions to the cauchy problem on a semi bounded initial axis for a nonhomogeneous quasilinear hyperbolic system abstract it is proven that if the leftmost eigenvalue is weakly linearly degenerate then the cauchy problem for a class of nonhomogeneous quasilinear hyperbolic systems with small and decaying initial data given on a semi bounded axis admits a unique global c 1 solution on the domain t x t 0 x x n t where x x n t is the fastest forward characteristic emanating from the origin as an application of our result we prove the existence of global classical c 1 solutions of the flow equations of a model class of fluids with viscosity induced by fading memory with small smooth initial data given on a semi bounded axis

asymptotics of the partition function of a general markov random field on an infinite rectangular lattice abstract we investigate theoretically and numerically the asymptotics of the partition function of a general markov random field mrf on an infinite rectangular lattice we first propose the general local energy function lef parameterized mrf then we prove that the thermodynamic limit of the free energy of the mrf can be exactly characterized by the perron root of the fundamental transfer matrix of a particular markov additive process map this matrix possesses a special structure and many interesting properties that enable parallel computation of the perron root and may be beneficial for deriving an analytical form of the free energy we also develop another transfer matrix for numerical computation of the desired perron root specifically the former is a site to site transfer matrix on a twisted cylindrical lattice while the latter is the one associated with a row to row transition on a vertical strip numerical results show that our methods exhibit consistent finite size scaling behavior even for small values of the lattice width this study reveals that the fundamental transfer matrix is an alternative direction of research on the analysis of the partition function of general mrfs within the scope of matrix algebra

optimization of a large scale water reservoir network by stochastic dynamic programming with efficient state space discretization a numerical solution to a 30 dimensional water reservoir network optimization problem based on stochastic dynamic programming is presented in such problems the amount of water to be released from each reservoir is chosen to minimize a nonlinear cost or maximize benefit function while satisfying proper constraints experimental results show how dimensionality issues given by the large number of basins and realistic modeling of the stochastic inflows can be mitigated by employing neural approximators for the value functions and efficient discretizations of the state space such as orthogonal arrays latin hypercube designs and low discrepancy sequences

global solutions with shock waves to the generalized riemann problem for a system of hyperbolic conservation laws with linear damping abstract it is proven that a class of the generalized riemann problem for quasilinear hyperbolic systems of conservation laws with the uniform damping term admits a unique global piecewise c 1 solution u u t x containing only n shock waves with small amplitude on t 0 and this solution possesses a global structure similar to that of the similarity solution u u x t of the corresponding homogeneous riemann problem as an application of our result we prove the existence of global shock solutions piecewise continuous and piecewise smooth solution with shock discontinuities of the flow equations of a model class of fluids with viscosity induced by fading memory with a single jump initial data we also give an example to show that the uniform damping mechanism is not strong enough to prevent the formation of shock waves

global solutions with shock waves to the generalized riemann problem for a class of quasilinear hyperbolic systems of balance laws it is proven that the generalized riemann problem for a class of quasilinear hyperbolic systems of balance laws admits a unique global piecewise c1 solution u u t x containing only n shock waves with small amplitude on t 0 and this solution possesses a global structure similar to that of the similarity solution u u x t of the corresponding homogeneous riemann problem as an application of our result we prove the existence of global shock solutions piecewise continuous and piecewise smooth solution with shock discontinuities of the flow equations of a model class of fluids with viscosity induced by fading memory with a single jump initial data

approximate confidence intervals for the parameters of a stationary binary markov chain the power divergence family of test statistics introduced by cressie and read 1984 is used to obtain approximate confidence intervals for the parameters of a stationary first order binary markov chain intervals based on inverting the likelihood ratio pearson and freeman tukey statistics are included in this family small sample comparisons are used to select the best intervals for the different parameters the results show that the best power divergence intervals for the probability of success and in particular the likelihood ratio interval have error rates closer to nominal levels than the sample proportion based intervals suggested by crow 1979 the properties of power divergence joint confidence regions for the transition probabilities are also explored

spectral analysis for categorical time series scaling and the spectral envelope summary many studies produce categorical time series in which harmonic analysis is of interest although there exist time domain approaches for the analysis of categorical time series such as markov chains or link function based regression models there is apparently little statistical theory or methodology for analyzing qualitative valued time series in the frequency domain the purpose of this paper is to initiate the development of a general framework for the frequency domain analysis of categorical time series in doing so we discuss the scaling of categorical time series and introduce a new concept that we call the spectral envelope of a categorical time series we demonstrate our methodology on a data set from a problem in molecular biology

long range memory elementary 1d cellular automata dynamics and nonextensivity abstract we numerically study the dynamics of elementary 1d cellular automata ca where the binary state i t 0 1 of a cell i does not only depend on the states in its local neighborhood at time t 1 but also on the memory of its own past states i t 2 i t 3 i t we assume that the weight of this memory decays proportionally to with 0 the limit corresponds to the usual ca since the memory function is summable for 1 and nonsummable for 0 1 we expect pronounced changes of the dynamical behavior near 1 this is precisely what our simulations exhibit particularly for the time evolution of the hamming distance h of initially close trajectories we typically expect the asymptotic behavior h t t 1 1 q where q is the entropic index associated with nonextensive statistical mechanics in all cases the function q exhibits a sensible change at 1 we focus on the class ii rules 61 99 and 111 for rule 61 q 0 for 0 c 1 3 and q 0 for c whereas the opposite behavior is found for rule 111 for rule 99 the effect of the long range memory on the spread of damage is quite dramatic these facts point at a rich dynamics intimately linked to the interplay of local lookup rules and the range of the memory finite size scaling studies varying system size n indicate that the range of the power law regime for h t typically diverges n z with 0 z 1

tsallis like information measures and the analysis of complex signals abstract a tsallis like information measure that elaborates upon those of the tsallis type is shown to be a rather powerful tool for the analysis of complex non stationary signals as exemplified by the henon map and eegs the ensuing results could be of importance concerning the automatic detection of epileptic spikes

application of statistical information criteria for optimal fuzzy model construction theoretical studies have shown that fuzzy models are capable of approximating any continuous function on a compact domain to any degree of accuracy however constructing a good fuzzy model requires finding a good tradeoff between fitting the training data and keeping the model simple a simpler model is not only easily understood but also less likely to overfit the training data even though heuristic approaches to explore such a tradeoff for fuzzy modeling have been developed few principled approaches exist in the literature due to the lack of a well defined optimality criterion in this paper we propose several information theoretic optimality criteria for fuzzy models construction by extending three statistical information criteria 1 the akaike information criterion aic 1974 2 the bhansali downham information criterion bdic 1977 and 3 the information criterion of schwarz 1978 and rissanen 1978 sric we then describe a principled approach to explore the fitness complexity tradeoff using these optimality criteria together with a fuzzy model reduction technique based on the singular value decomposition svd the role of these optimality criteria in fuzzy modeling is discussed and their practical applicability is illustrated using a nonlinear system modeling example

nonlinear diffusion waves for hyperbolic p system with nonlinear damping abstract this paper is concerned with the p system of hyperbolic conservation laws with nonlinear damping when the constant states are small the solutions of the cauchy problem for the damped p system globally exist and converge to their corresponding nonlinear diffusion waves which are the solutions of the corresponding nonlinear parabolic equation given by the darcy s law the optimal convergence rates are also obtained in order to overcome the difficulty caused by the nonlinear damping a couple of correction functions have been technically constructed the approach adopted is the elementary energy method together with the technique of approximating green function on the other hand when the constant states are large the solutions of the cauchy problem for the p system will blow up at a finite time

some models for the analysis of association in multiway cross classifications having ordered categories abstract goodman recently presented a class of models for the analysis of association between two discrete ordinal variables the association was measured in terms of the odds ratios in 2 2 subtables formed from adjacent rows and adjacent columns of the cross classification and models were devised that allowed the odds ratios to depend on an overall effect on row effects on column effects and on other effects this article presents some generalizations of this approach appropriate for multiway cross classifications including a models for the analysis of conditional association b models for the analysis of partial association and c models for the analysis of symmetric association three cross classifications are analyzed with these models and methods and rather simple interpretations of the association in each are provided

symbolic stochastic dynamical systems viewed as binary n step markov chains a theory of systems with long range correlations based on the consideration of binary n step markov chains is developed in the model the conditional probability that the ith symbol in the chain equals zero or unity is a linear function of the number of unities among the preceding n symbols the correlation and distribution functions as well as the variance of the number of symbols in the words of arbitrary length l are obtained analytically and numerically a self similarity of the studied stochastic process is revealed and the similarity group transformation of the chain parameters is presented the diffusion fokker planck equation governing the distribution function of the l words is explored if the persistent correlations are not extremely strong the distribution function is shown to be the gaussian with the variance being nonlinearly dependent on l the applicability of the developed theory to the coarse grained written and dna texts is discussed

wavelet analysis and nonlinear dynamics in a nonextensive setting abstract we undertake the study of signals originated in time dependent nonlinear systems by recourse to a wavelet based multiresolution analysis as adapted to a nonextensive tsallis scenario diverse applications are discussed it is shown that the tsallis environment provides one with more detailed information than the conventional shannon one

methods and criteria for model selection model selection is an important part of any statistical analysis and indeed is central to the pursuit of science in general many authors have examined the question of model selection from both frequentist and bayesian perspectives and many tools for selecting the best model have been suggested in the literature this paper considers the various proposals from a bayesian decision theoretic perspective

uniform attractor for non autonomous hyperbolic equation with critical exponent abstract in this paper we study the uniform attractor for semilinear wave equation with mixed differential quotient terms and critical nonlinearity we prove the existence of the uniform attractor in h 0 1 l 2