tractable inference and observation likelihood evaluation in latent structure influence models latent structure influence models lsims are a particular kind of coupled hidden markov models chmms against chmms lsims overcome the exponential growth of state space parameters by considering the influence model for coupled markov chains nevertheless the exact inference in lsims requires exponential complexity we propose a new recursive formulation to compute marginal forward and backward parameters by mathcal o t nc 2 instead of mathcal o tn text 2 c for c channels of n states apiece observing t data points this formulation is derived systematically and carefully to increase the inference accuracy furthermore a solution is presented for the evaluation problem of lsims based on the proposed marginal forward parameter this solution is essential in statistical multi channel time series classification the results show that the proposed algorithm is generally more accurate and reliable than other existing algorithms novelties in deriving the marginal backward parameter plays an important role in this superiority the hellinger distance is computed between the proposed and exact forward and one slice parameters for various simulation scenarios distances are small enough indicating that the proposed inference algorithm is sufficiently close to exact inference for various channels hidden state numbers and other parameters statistical multi channel time series classification is also considered for both proposed and exact algorithms classification results are almost similar indicating that the proposed approximate inference is proper and acceptable in the classification task finally the ieeg dataset s parameter learning indicates that the proposed inference algorithm leads to a higher log likelihood than the existing algorithms

on the box counting dimension of graphs of harmonic functions on the sierpinski gasket abstract the objective of this paper is to study the box counting dimension of graphs of fractal interpolation functions and harmonic functions on the sierpinski gasket firstly we give construction of a fractal interpolation function on the sierpinski gasket and then with the help of fractal interpolation functions we show the existence of fractal functions in the space dom e consisting of all finite energy functionals on the sierpinski gasket later we provide bounds for the box counting dimension of graphs of some functions belonging to the family of continuous functions which arise as fractal interpolation functions moreover we also obtain bounds for the box counting dimension of graphs of harmonic functions and piecewise harmonic functions also we obtain upper and lower bounds for the box counting dimension of graphs of functions that belong to dom e

some properties of fractal interpolation functions on sierpinski gasket abstract in this paper we discuss some basic properties of uniform fractal interpolation functions fifs which is a special class of fifs on sierpinski gasket we firstly study the min max property of uniform fifs then we present a necessary and sufficient condition such that uniform fifs have finite energy normal derivative and laplacian of uniform fifs are also discussed

an approach to critical phenomena from one subsystem based on the cam analysis two systematic series of multi body effective field approximations are constructed and the cam analyses are performed for the ising mode on the two dimensional square lattice in the first series a two body effective field is introduced in addition to the usual one body one and a set of strips are used the critical temperature and the critical index of the susceptibility are estimated as t c approximately 2 2697 j kb and gamma approximately 1 749 in the second series only a three line strip is used and applied with increasing numbers of multi body effective fields the expected cam scaling behaviour has also been observed

finite size scaling and universality in the 2 1 d ising model the energy and magnetisation density of the 2 1 d ising model are investigated for the thermal exponent the author finds xepsilon 1 42 or 0 02 in agreement with hyperscaling the privman fisher universality hypothesis is confirmed by two methods first the author presents at the critical point numerical data for the finite size scaling amplitudes of the singular free energy magnetisation susceptibility and surface tension and checks them for universality second using the explicitly computed eigenvectors of the hamiltonian it is shown that the ratios of matrix elements of the energy and magnetisation density are universal

an em algorithm for markov modulated markov processes an expectation maximization em algorithm for estimating the parameter of a markov modulated markov process in the maximum likelihood sense is developed this is a doubly stochastic random process with an underlying continuous time finite state homogeneous markov chain conditioned on that chain the observable process is a continuous time finite state nonhomogeneous markov chain the generator of the observable process at any given time is determined by the state of the underlying markov chain at that time the parameter of the process comprises the set of generators for the underlying and conditional markov chains the proposed approach generalizes an earlier approach by ryden for estimating the parameter of a markov modulated poisson process

bayes smoothing algorithms for segmentation of binary images modeled by markov random fields a new image segmentation algorithm is presented based on recursive bayes smoothing of images modeled by markov random fields and corrupted by independent additive noise the bayes smoothing algorithm yields the a posteriori distribution of the scene value at each pixel given the total noisy image in a recursive way the a posteriori distribution together with a criterion of optimality then determine a bayes estimate of the scene the algorithm presented is an extension of a 1 d bayes smoothing algorithm to 2 d and it gives the optimum bayes estimate for the scene value at each pixel computational concerns in 2 d however necessitate certain simplifying assumptions on the model and approximations on the implementation of the algorithm in particular the scene noiseless image is modeled as a markov mesh random field a special class of markov random fields and the bayes smoothing algorithm is applied on overlapping strips horizontal vertical of the image consisting of several rows columns it is assumed that the signal scene values vector sequence along the strip is a vector markov chain since signal correlation in one of the dimensions is not fully used along the edges of the strip estimates are generated only along the middle sections of the strips the overlapping strips are chosen such that the union of the middle sections of the strips gives the whole image the bayes smoothing algorithm presented here is valid for scene random fields consisting of multilevel discrete or continuous random variables

using iterated function systems to model discrete sequences two iterated function system ifs models are explored for the representation of single valued discrete time sequences the self affine fractal model and the piecewise self affine fractal model algorithms are presented one of which is suitable for a multiprocessor implementation for identification of the parameters of each model applications of these models to a variety of data types are given where signal to noise ratios are presented quantization effects of the model parameters are investigated and compression ratios are computed

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

cluster expansions for the ising and heisenberg spin models in hamiltonian lattice field theory cluster expansion methods are applied to calculate high temperature series for the vacuum energy the susceptibility and the mass gap for the ising model and the o 2 and o 3 heisenberg models in 1 1 dimensions and 2 1 dimensions critical points and critical indices are estimated for the line the square and the triangular lattices the results demonstrate universality with the normal euclidean versions of these models within errors

series expansions for the zero temperature transverse ising model series expansions are presented for the magnetisation susceptibility magnetic field derivatives of the susceptibility and specific heat of the zero temperature transverse ising model coefficients in these series have been calculated to tenth order in lambda 2 where lambda is the transverse field for the linear chain to eighth order for the square lattice and to seventh order for the triangular lattice these series yield estimates of the low temperature critical exponents alpha beta gamma and delta of the two and three dimensional ising models they provide good evidence for the symmetry of exponents above and below the critical point e g gamma gamma

multi effective field theory applications to the cam analysis of the two dimensional ising model abstract a multi effective field theory is formulated and applied to the two dimensional ising model from the viewpoint of the coherent anomaly method cam two necessary conditions to construct the cam canonical series are shown two series of approximations are derived on 3 3 and 4 4 clusters and with the use of the cam we estimate the critical exponent of the susceptibility within an error of 0 37 and 0 45 percent respectively for the exact value 1 75 where the exact t c is assumed this accuracy of the estimation shows the effectiveness of this theory it is generally proved that certain kinds of approximations with different combinations of effective fields yield exactly the same approximate critical temperature and mean field coefficient

cluster expansions in the 2 1 d ising model the cluster expansion methods of nickel are applied to calculate high temperature series for the vacuum energy and specific heat the susceptibility and the mass gap in the 2 1 d ising model critical points and critical exponents are estimated for the square and triangular lattices the results demonstrate universality with the 3d ising model within errors exact linked cluster expansions are formulated for the quantities above and their convergence and scaling properties are investigated

practical implementation of an efficient forward backward algorithm for an explicit duration hidden markov model this correspondence addresses several practical problems in implementing a forward backward fb algorithm for an explicit duration hidden markov model first the fb variables are redefined in terms of posterior probabilities to avoid possible underflows that may occur in practice then a forward recursion is used that is symmetric to the backward one and can reduce the number of logic gates required to implement on a field programmable gate array fpga chip

causal recursive parameter estimation for discrete time hidden bivariate markov chains an algorithm for causal recursive parameter estimation of a discrete time hidden bivariate markov chain is developed in this model a discrete time bivariate markov chain is observed through a discrete time memoryless channel the algorithm relies on the em based recursive approach developed by stiller and radons for hidden markov models a distinct advantage of the discrete time hidden bivariate markov chain model is that the sojourn time distribution of its observable process in each state is phase type rather than geometric as in the hidden markov model phase type distributions can approximate any desired sojourn time distribution particular phase type distributions include mixtures and convolutions of geometric distributions the parameter estimation algorithm requires causal recursive estimation of the relevant statistics in each em step these statistics include the number of jumps of the bivariate markov chain from one state to another including self transitions in the given observation interval and first and second order statistical averages of the observable process in each state when the memoryless channel is gaussian we develop the explicit recursions and demonstrate the performance of the algorithm in estimating the model s parameter and its sojourn time distribution in a numerical example

coherent anomaly method with a new mean field type approximation abstract in the present paper we propose a new mean field type approximation based on multispin effective fields determined from self consistency conditions for some correlation functions of a cluster using the transfer matrix method we investigate finite width strips of spins for square honeycomb and triangle lattices the results obtained exhibit good scaling properties and can be analyzed with suzuki s coherent anomaly method yielding a very accurate estimation of the critical temperature and the critical exponent

fractal interpolation on the sierpinski gasket abstract we prove for the sierpinski gasket sg an analogue of the fractal interpolation theorem of barnsley let v 0 p 1 p 2 p 3 be the set of vertices of sg and u i x 1 2 x p i the three contractions of the plane of which the sg is the attractor fix a number n and consider the iterations u w u w 1 u w 2 u w n for any sequence w w 1 w 2 w n 1 2 3 n the union of the images of v 0 under these iterations is the set of nth stage vertices v n of sg let f v n r be any function given any numbers w w 1 2 3 n with 0 w 1 there exists a unique continuous extension f sg r of f such that f u w x w f x h w x for x sg where h w are harmonic functions on sg for w 1 2 3 n interpreting the harmonic functions as the degree 1 polynomials on sg is thus a self similar interpolation obtained for any start function f v n r

cam approach to the ground state phase transition in the two dimensional transverse ising model the double cluster approximation dca and the multi effective field approximation mefa are formulated for the two dimensional s 1 2 transverse ising model on a square lattice in the ground state these two cluster effective field approximations expand the sizes of clusters effectively combining some suitable series of these approximations with the coherent anomaly method cam the authors have analysed the critical phenomenon of this model they have obtained g c 1 528 or 0 016 and gamma 1 25 or 0 08 using the dca and gamma 1 26 or 0 10 using the mefa these estimates are consistent with the other results g c approximately 1 52 and gamma approximately 1 24 their scheme is expected to be useful in the study of frustrated systems because various shapes of clusters can be used in their calculations

on the asymptotic stability of boundary trajectories for a class of dynamical systems it is shown that trajectories which remain on the boundary of a non empty connected subset of a reachable set must be asymptotically stable using this result and a reachability maximum principle we obtain a control law which will drive the system from the origin to the boundary of the reachable set for a class of two dimensional linear control systems using this control law the reachable set is easily constructed

a recursive algorithm for the bayes solution of the smoothing problem the optimum fixed interval smoothing problem is solved using a bayesian approach assuming that the signal is markov and is corrupted by independent noise not necessarily additive a recursive algorithm to compute the a posteriori smoothed density is obtained using this recursive algorithm the smoothed estimate of a binary markov signal corrupted by an independent noise in a nonlinear manner is determined demonstrating that the bayesian approach presented in this paper is not restricted to the gauss markov problem

recursive algorithms for the bayes solution of the fixed point and fixed lag smoothing problems recursive algorithms for the bayes solutions of the fixed point and fixed lag smoothing problems are obtained recursive algorithms for the respective smoothed a posteriori densities are derived under assumptions that the signal to be estimated is a markov process and the observation is a signal embedded in independent noise not necessarily additive which is also independent of the signal the recursive algorithm for the fixed point smoothing is applied to a binary markov signal corrupted by an independent noise in a nonlinear manner