a modified multiple relaxation time lattice boltzmann model for convection diffusion equation a modified lattice boltzmann model with multiple relaxation times mrt for the convection diffusion equation cde is proposed by modifying the relaxation matrix as well as choosing the corresponding equilibrium distribution function properly the present model can recover the cde with anisotropic diffusion coefficient with no deviation term even when the velocity vector varies generally with space or time through the chapman enskog analysis this model is firstly validated by simulating the diffusion of a gaussian hill which demonstrates it can handle the anisotropic diffusion problem correctly then it is adopted to calculate the longitudinal dispersion coefficient of the taylor aris dispersion numerical results show that the present model can further reduce the numerical error under the condition of non zero velocity vector especially when the dimensionless relaxation time is relatively large

finite difference lattice boltzmann method for compressible thermal fluids a splitting method to solve the modeled lattice boltzmann equation the splitting technique permits the boundary conditions for the lattice boltzmann equation to be set as conveniently as those required for the finite difference solution of the navier stokes equations it is shown that the compressible navier stokes equation can be recovered fully from this approach however the formulation requires the solution of a poisson equation governing a secondorder tensor thus constructed the method has no arbitrary constants the proposed method is used to simulate thermalcouette flow aeroacoustics andshockstructureswithanextendedthermodynamicsmodel thesimulations are carried out using a high order finite difference scheme with a two dimensional nine velocity lattice all simulations are performed using a single relaxation time and a set of constants deduced from the derivation it is found that the finite difference lattice boltzmann method is able to correctly replicate viscous effects in thermal couette flows aeroacoustics andshockstructures thesolutionsobtainedareidenticaleithertoanalyticalresults or obtained by solving the compressible navier stokes equations using a direct numerical simulation technique

recursive estimation of autoregressions this paper is concerned with the recursive estimation of autoregressive models in particular the realtime determination of the order of such a specification a model selection criterion based on the minimum description length principle due to rissanen is discussed and strong consistency in the stationary situation is shown alternative criteria are also considered and modifications required to introduce forgetting when the procedures are implemented in the non stationary case are presented some simulation evidence on the performance of the criteria when applied to stationary and non stationary processes is given

predictor selection for positive autoregressive processes let observations y1 yn be generated from a first order autoregressive ar model with positive errors in both the stationary and unit root cases we derive moment bounds and limiting distributions of an extreme value estimator of the ar coefficient these results enable us to provide asymptotic expressions for the mean squared error mse of and the mean squared prediction error mspe of the corresponding predictor of yn 1 based on these expressions we compare the relative performance of and the least squares predictor estimator from the mspe mse point of view our comparison reveals that the better predictor estimator is determined not only by whether a unit root exists but also by the behavior of the underlying error distribution near the origin and hence is difficult to identify in practice to circumvent this difficulty we suggest choosing the predictor estimator with the smaller accumulated prediction error and show that the predictor estimator chosen in this way is as

order selection for ar models by predictive least squares a criterion is presented for selecting the order of autoregressive models that unlike the existing criteria is amenable to online or adaptive operation it is based on the predictive least squares pls principle and is implemented in a computationally efficient way by predictive lattice filters the consistency of the criterion is proved and its performance is demonstrated by computer simulations assuming the data to be generated by an ar model of order p the order selection criterion should select the correct order p with probability that converges to 1 as the sample size grows to infinity it is proved that the pls criterion is indeed consistent thereby giving a solid justification for the criterion simulation results that demonstrate the performance of the pls criterion in comparison to h akaike s aic 1973 and the mdl criteria of j rissanen 1978 and g schwarz 1978 are given

implementation of diffuse reflection boundary conditions in a thermal lattice boltzmann model with flux limiters we discuss three new implementation versions of diffuse reflection boundary conditions in a thermal lattice boltzmann model their accuracy is investigated in the case of couette flow by considering the slip regime the best results are recovered with versions 2 and 3 which rely on outgoing fluxes to express the particle distribution functions in the ghost nodes outside the flow domain version 2 is found to be more economical since it involves no interpolation procedure this version was thereafter used to investigate the temperature profile in couette flow for various values of prandtl number as well as the capability of the thermal lb model to capture the knudsen minimum in poiseuille flow

structure selection for bounded parameter models consistency conditions and selection criterion strong consistency conditions for structure selection in bounded parameter models are studied a certain robust selection criterion based on the volume of the exact parameter bounding polytope is proposed for linear regression models the effectiveness of the polytope volume criterion is demonstrated on a model nonlinear in its variables but linear in its parameters its strong consistency is proved for a large class of noise distributions the usual assumptions on the noise namely independence constant variance or martingale difference properties need not be made but asymptotic independence is assumed

consistent order estimation for linear stochastic feedback control systems carma model abstract a new criterion cic is introduced to estimate orders p0 q0 r0 of the linear stochastic feedback control system with correlated noise described by a carma model it is proved that the estimate is strongly consistent when the upper bounds for p0 q0 and r0 are available but neither the stability condition nor the ergodicity of the input and output are imposed on the system

model selection and the principle of minimum description length this article reviews the principle of minimum description length mdl for problems of model selection by viewing statistical modeling as a means of generating descriptions of observed data the mdl framework discriminates between competing models based on the complexity of each description this approach began with kolmogorov s theory of algorithmic complexity matured in the literature on information theory and has recently received renewed attention within the statistics community here we review both the practical and the theoretical aspects of mdl as a tool for model selection emphasizing the rich connections between information theory and statistics at the boundary between these two disciplines we find many interesting interpretations of popular frequentist and bayesian procedures as we show mdl provides an objective umbrella under which rather disparate approaches to statistical modeling can coexist and be compared we illustrate the mdl principle by considering problems in regression nonpar

density estimation by stochastic complexity the results by p hall and e j hannan 1988 on optimization of histogram density estimators with equal bin widths by minimization of the stochastic complexity are extended and sharpened in two separate ways as the first contribution two generalized histogram estimators are constructed the first has unequal bin widths which together with the number of the bins are determined by minimization of the stochastic complexity using dynamic programming the other estimator consists of a mixture of equal bin width estimators each of which is defined by the associated stochastic complexity as the main contribution in the present work two theorems are proved which together extend the universal coding theorems to a large class of data generating densities the first gives an asymptotic upper bound for the code redundancy in the order of magnitude achieved with a special predictive type of histogram estimator which sharpens a related bound the second theorem states that this bound cannot be improved upon by any code whatsoever

coupled double distribution function lattice boltzmann method for the compressible navier stokes equations a coupled double distribution function lattice boltzmann method is developed for the compressible navier stokes equations different from existing thermal lattice boltzmann methods this method can recover the compressible navier stokes equations with a flexible specific heat ratio and prandtl number in the method a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations while the compressible energy equation is recovered by an energy distribution function the energy distribution function is then coupled to the density distribution function via the thermal equation of state in order to obtain an adjustable specific heat ratio a constant related to the specific heat ratio is introduced into the equilibrium energy distribution function two different coupled double distribution function lattice boltzmann models are also proposed in the paper numerical simulations are performed for the riemann problem the double mach reflection problem and the couette flow with a range of specific heat ratios and prandtl numbers the numerical results are found to be in excellent agreement with analytical and or other solutions

a lattice boltzmann model for elliptic equations with variable coefficient abstract a lattice boltzmann model is proposed to solve elliptic equations with variable coefficient compared with the previous model the present model is a more effective solver to the ellipse equation with variable coefficient and the ellipse equation is exactly recovered to order o e 2 the relaxation time is not fixed and is determined by the coefficient of the equation the limited numerical results show that the present model is valid for ellipse equations

relations between information criteria for model structure selection part 2 modelling by shortest data description the structure selection of stochastic dynamic models by the predictive least squares pls criterion introduced by rissanen and wertz 1985 is investigated in this paper in view of its relations to the bayesian estimator and to information criteria with a penalty term it is shown that in the autoregressive case the strong consistency of the pls criterion can be derived from the strong consistency of the bayesian order estimator

identification and adaptive control for systems with unknown orders delay and coefficients an analysis that gives recursive estimates for time delay system orders and coefficients of single input single output linear discrete time deterministic and stochastic systems with uncorrelated noise is presented it is assumed that a lower bound for the time delay and upper bounds for system order are known the optimal adaptive control is designed for both tracking and linear quadratic regulation when the system parameters including time delay orders and coefficients are unknown the rates of convergence are derived the coefficient estimates to their true values and the loss functions to their minima

a spectral difference lattice boltzmann method for solution of inviscid compressible flows on structured grids in this work a spectral difference lattice boltzmann method sdlbm is developed and applied for an accurate simulation of two dimensional inviscid compressible flows on structured grids the compressible form of the discrete boltzmann bgk equation is used in which multiple particle speeds have to be employed to correctly model the compressibility in a thermal fluid here the 2d compressible lattice boltzmann lb model proposed by watari is applied the spectral difference sd method is implemented for the solution of the lb equation in which the particle distribution function is stored at the solution points while the fluxes are computed at the flux points for calculating the particle distribution function for time accurate solutions the fourth order runge kutta scheme is used to discretize the temporal term in the lb equation note that the procedure of implementing the sd method to solve the lb equation is nearly the same as that procedure developed in the literature for the solution of the euler equations the accuracy and robustness of the present solution methodology are demonstrated by simulating different benchmark compressible flow problems a sensitivity study is also conducted to evaluate the effects of the numerical parameters and the grid size distribution on the accuracy and performance of the solution at first three inviscid compressible flow problems namely the stationary isentropic vortex the shock tube and the shock vortex interaction are solved by using the sdlbm to demonstrate the accuracy and robustness of the present solution methodology results computed for these test cases are in good agreement with the analytical and the available numerical solutions to more assess the accuracy and robustness of the sdlbm a third order finite volume lbm fvlbm is also developed and the solutions obtained by these two methods for the test cases simulated are thoroughly compared with each other it is demonstrated that the sdlbm is more accurate and robust compressible inviscid flow solver that can be used for evaluating the other compressible lb based flow solvers as the final problem the supersonic flow past a bump is simulated to demonstrate the accuracy and robustness of the sdlbm in reaching to a steady state solution

will the pls criterion for order estimation work with aml and a posteriori prediction error the general formula of the pls predictive least squares criterion for order estimation is worked out under the assumption that the parameter estimates are calculated via the aml approximate maximum likelihood a particular case is then carefully analysed and it is shown that depending on the system generating the data the pls critetion using the a posteriori prediction error can surprisingly almost surely overestimate the true order

on reflexive modules and abelian groups the class of a reflexive modules is investigated where a is a bimodule over rings s and r conditions are studied under which this class is closed under taking direct products or direct sums respectively furthermore it is shown that if a is free over a suitable ring r and s endr a then for every right r module m the natural map m m m is the completion of m in a certain functorial topology applications are given in the case that a is a free abelian group

error exponents for ar order testing this paper is concerned with error exponents in testing problems raised by autoregressive ar modeling the tests to be considered are variants of generalized likelihood ratio testing corresponding to traditional approaches to autoregressive moving average arma modeling estimation in several related problems such as markov order or hidden markov model order estimation optimal error exponents have been determined thanks to large deviations theory ar order testing is specially challenging since the natural tests rely on quadratic forms of gaussian processes in sharp contrast with empirical measures of markov chains the large deviation principles ldps satisfied by gaussian quadratic forms do not always admit an information theoretic representation despite this impediment we prove the existence of nontrivial error exponents for gaussian ar order testing and furthermore we exhibit situations where the exponents are optimal these results are obtained by showing that the log likelihood process indexed by ar models of a given order satisfy an ldp upper bound with a weakened information theoretic representation

nonstationary time series identification abstract in this paper strongly consistent estimates are given for both unknown parameters and orders of the nonstationary time series where the nonstationarity arises because 1 at any time n a feedback control is added to the usual arma process which is successfully applied to modelling economic systems and 2 det a z may have zeros on the unit circle in addition to those located outside the unit disk where a z is the matrix polynomial corresponding to the ar part of the arma process

strongly consistent estimation of the order of stochastic control systems carma model abstract in this paper a variant of the plc predictive least squares criterion for order estimation is combined with an adaptive control strategy and applied to multidimensional carma systems it is shown that with this combination we can estimate recursively and in a strongly consistent way both the order and coefficients of the controlled system while achieving asymptotically optimal cost

consistent estimation of the order of stochastic control systems a consistent estimate of the order of feedback control systems with unknown matrix coefficients estimated by the least squares method is derived by minimizing a modified version of the bayesian information criterion

a method for autoregressive moving average estimation summary the problem considered is that of estimating an autoregressive moving average system including estimating the degrees of the autoregressive and moving average lag operators the basic method is that introduced by hannan rissanen 1982 however that method may sometimes overestimate the degrees and modifications are here introduced to correct this the problem is itself due to the use of a long autoregression of order clog t when t is large in the first stage of the process the effect of this is investigated and in particular its effect on the speed of convergence of the estimates

ar infinity estimation and nonparametric stochastic complexity let h be the transfer function of a linear stochastic system such that h and its inverse are in h sup infinity d writing the system as an ar infinity system the best ar k approximation of the system is estimated using the method of least squares a useful representation theorem for the parameter estimation error is presented the effect of undermodeling and parameter uncertainty due to estimation on honest prediction and the optimal choice of k are questioned this question is answered and the result is applied to the ar approximation of arma systems the excess of the mean of the nonparametric stochastic complexity with respect to the ar class of an arma system with zeros less than 1 beta in moduli is found asymptotically to be less than sigma sup 2 log sup 2 n log beta after n samples

optimal adaptive control and consistent parameter estimates for armax model withquadratic cost we consider the multidimensional armax model a z y n b z u n c z w n with loss function j u mathop overline lim limits n to infty frac 1 n sum limits i 1 n left y i tau q 1 y i u i tau q 2 u i right where the coefficients in the matrix polynomials a z b z and c z are unknown conditions used here are 1 stability of a z and full rank of a p 2 strictly positive realness of c z frac 1 2 i and 3 controllability and observability of a matrix triple consisting of coefficients in a z b z and q 1 on the basis of the estimates given by the stochastic gradient algorithm for unknown parameters an adaptive control law is recursively defined it is proved that the parameter estimates are strongly consistent and the quadratic loss function reaches its minimum this paper also includes some general theorems on parameter estimation on which the results about adaptive control are essentially based

convergence rate of least squares identification and adaptive control for stochastic systems the strong consistency and the convergence rate of least squares identification for the multidimensional armax model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied the parameter identification results are applied to adaptive control systems with a quadratic loss function the rate of convergence of the loss function to its minimum is also obtained

a fractional step thermal lattice boltzmann model for high peclet number flow as a promising approach in hydrodynamics and thermodynamics modeling the lattice boltzmann method lbm still suffers severe numerical instability when the temperature field of the flow is convection dominant high peclet number despite a lot of research devoted to solve this problem worldwide to simulate high peclet number thermal flow at comparably few computational cost is still a hard work making it inefficient in practical use in this paper we combine the lbm and the fractional step method to propose a novel and stable thermal lattice boltzmann scheme for high peclet number flow without refining the lattice by numerical tests of thermal poiseuille flow and couette flow we quantify second order accuracy of the proposed model and through several cases of peclet number from low to high the superior stability and efficiency compared with existing thermal lattice boltzmann model

accumulated prediction errors information criteria and optimal forecasting for autoregressive time series the predictive capability of a modification of rissanen s accumulated prediction error ape criterion ape n is investigated in infinite order autoregressive ar oo models instead of accumulating squares of sequential prediction errors from the beginning ape n is obtained by summing these squared errors from stage n n where n is the sample size and 1 n n 1 1 n may depend on n under certain regularity conditions an asymptotic expression is derived for the mean squared prediction error mspe of an ar predictor with order determined by ape n this expression shows that the prediction performance of ape n can vary dramatically depending on the choice of n another interesting finding is that when n approaches 1 at a certain rate ape n can achieve asymptotic efficiency in most practical situations an asymptotic equivalence between ape n and an information criterion with a suitable penalty term is also established from the mspe point of view this offers new perspectives for understanding the information and prediction based model selection criteria finally we provide the first asymptotic efficiency result for the case when the underlying ar oo model is allowed to degenerate to a finite autoregression

extended least squares and their applications to adaptive control and prediction in linear systems herein strong consistency of recursive extended least squares is established under considerably weaker assumptions than previously assumed in the literature the argument used to establish consistency also leads to certain basic properties of adaptive predictors based on these recursive estimators making use of these properties of the adaptive predictors simple modifications of the astrom wittenmark self tuning regulator are proposed and shown to be asymptotically optimal

a rate of convergence result for a universal d semifaithful code the problem of optimal rate universal coding is considered in the context of rate distortion theory a d semifaithful universal coding scheme for discrete memoryless sources is given the main result is a refined covering lemma based on the random coding argument and the method of types the average codelength of the code is shown to approach its lower bound the rate distortion function at a rate o n sup 1 log n and this is conjectured to be optimal based on a result of a j pilc 1968 issues of constructiveness and universality are addressed

the minimum description length principle in coding and modeling we review the principles of minimum description length and stochastic complexity as used in data compression and statistical modeling stochastic complexity is formulated as the solution to optimum universal coding problems extending shannon s basic source coding theorem the normalized maximized likelihood mixture and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms we assess the performance of the minimum description length criterion both from the vantage point of quality of data compression and accuracy of statistical inference context tree modeling density estimation and model selection in gaussian linear regression serve as examples

brief on line order estimation and parameter identification for linear stochastic feedback control systems carma model this paper presents a new recursive estimate method for orders and coefficients of linear stochastic feedback control systems carma model under the assumption that the upper bounds of system orders are known the strong consistency of the estimates for orders and coefficients is proved and the convergence rate of coefficient estimates to their true values is also obtained the estimate algorithm is applied to adaptive tracking of the systems with unknown orders and unknown coefficients the resulting closed loop systems are then globally stable and the tracking sample mean square error is minimized as well simultaneously the estimates of the adaptive tracking for orders and coefficients are also strongly consistent the simulation results given here show that the new developed algorithms of both system identification and adaptive tracking are effective

recursive estimation of mixed autoregressive moving average order summary the order p q of an autoregressive moving average sequence y t may be estimated by minimizing a criterion log 2 p q log t t with respect to p and q where 2 is the maximum likelihood estimate of the variance of the innovations t it is suggested that instead a2 be estimated from a series of regressions of y t on y t 1 y t 2 y t p 5 t 1 t q where the t are obtained by fitting a long autoregression to the data it is shown how the sequence of regressions may for p q be economically recursively calculated by embedding them in a sequence of bivariate autoregressions asymptotic properties of the procedure are established under very general conditions

structure identification of parameter bounding models by use of noise structure bounds the selection of a model for a given set of records is discussed for the case when the output error is required to be always within some specified bounds a new selection criterion is proposed the model should be the simplest giving sufficiently unstructured output errors the lack of structure is specified by requiring the candidate model to be capable of giving sufficiently small sample autocorrelations of the model output errors over a range of lags computational algorithms to apply the criterion are presented and illustrated by tests on ar processes

the redundancy of source coding with a fidelity criterion 1 known statistics the problem of redundancy of source coding with respect to a fidelity criterion is considered for any fixed rate r 0 and any memoryless source with finite source and reproduction alphabets and a common distribution p the nth order distortion redundancy d sub n r of fixed rate coding is defined as the minimum of the difference between the expected distortion per symbol of any block code with length n and rate r and the distortion rate function d p r of the source p it is demonstrated that for sufficiently large n d sub n r is equal to spl part spl part r d p r ln n 2n o ln n n where spl part spl part r d p r is the partial derivative of d p r evaluated at r and assumed to exist for any fixed distortion level d 0 and any memoryless source p the nth order rate redundancy r sub n d of coding at fixed distortion level d or by using d semifaithful codes is defined as the minimum of the difference between the expected rate per symbol of any d semifaithful code of length n and the rate distortion function r p d of p evaluated at d it is proved that for sufficiently large n r sub n d is upper bounded by ln n n o ln n n and lower bounded by in n 2n o in n n as a by product the lower bound of r sub n d derived in this paper gives a positive answer to a conjecture proposed by yu and speed 1993

three dimensional finite difference lattice boltzmann model and its application to inviscid compressible flows with shock waves abstract in this paper a three dimensional 3d finite difference lattice boltzmann model for simulating compressible flows with shock waves is developed in the framework of the double distribution function approach in the model a density distribution function is adopted to model the flow field while a total energy distribution function is adopted to model the temperature field the discrete equilibrium density and total energy distribution functions are derived from the hermite expansions of the continuous equilibrium distribution functions the discrete velocity set is obtained by choosing the abscissae of a suitable gauss hermite quadrature with sufficient accuracy in order to capture the shock waves in compressible flows and improve the numerical accuracy and stability an implicit explicit finite difference numerical technique based on the total variation diminishing flux limitation is introduced to solve the discrete kinetic equations the model is tested by numerical simulations of some typical compressible flows with shock waves ranging from 1d to 3d the numerical results are found to be in good agreement with the analytical solutions and or other numerical results reported in the literature

selecting optimal multistep predictors for autoregressive processes of unknown order we consider the problem of choosing the optimal in the sense of mean squared prediction error multistep predictor for an autoregressive ar process of finite but unknown order if a working ar model which is possibly misspecified is adopted for multistep predictions then two competing types of multistep predictors i e plug in and direct predictors can be obtained from this model we provide some interesting examples to show that when both plug in and direct predictors are considered the optimal multistep prediction results cannot be guaranteed by correctly identifying the underlying model s order this finding challenges the traditional model order selection criteria which usually aim to choose the order of the true model a new prediction selection criterion which attempts to seek the best combination of the prediction order and the prediction method is proposed to rectify this difficulty when the underlying model is stationary the validity of the proposed criterion is justified theoretically to obtain this result asymptotic properties of accumulated squares of multistep prediction errors are investigated in addition to overcoming the above difficulty some other advantages of the proposed criterion are also mentioned

p adic and p cotorsion completions of nilpotent groups abstract the theory of cotorsion abelian groups is extended to the category of nilpotent groups and applications are given to the theory of p adic completions and exactness properties of the p adic completion functor the p cotorsion completion functor was first extended from abelian to nilpotent groups by bousfield and kan who defined and studied it using topological methods we develop the theory group theoretically and additional results and applications

a new order estimation technique for time series modeling a new approach to estimating the order of the autoregressive moving average model is proposed which is based on the approximate stochastic realization introduced in davis and fotopoulos 1991 the present approach is attractive because overparameterization a very common problem in order determination is avoided successfully simulation results are included to illustrate the effectiveness of the proposed order estimation approach