Kalman filtering of a space-time Markov random field

In this paper, finite-dimensional recursive filters for space-time Markov random fields are derived. These filters can be used with the expectation maximization (EM) algorithm to yield maximum likelihood estimates of the parameters of the model.     

Measure change techniques in optimal control

Fully and partially observed stochastic control of systems with nonlinear dynamics and terminal and running costs are considered. Measure changes are introduced which allow both state and observation dynamics to be thought of as linear. In the case when the terms of the cost have a special form the measure change transformation “cancels out” the nonlinearities and changes the original nonlinear problem into a classical LQG one and standard results can be applied. We also consider unnormalized conditional densities of the whole path as state variables and obtain dynamic programming and verification results. R. J. Elliott wishes to acknowledge support of the Natural Sciences and Engineering Research Council of Canada, Grant A7964.     

Filtering,Smoothing and M-ary Detection with Discrete Time Poisson Observations

Abstract

In this article, we solve a class of estimation problems, namely, filtering smoothing and detection for a discrete time dynamical system with integer-valued observations. The observation processes we consider are Poisson random variables observed at discrete times. Here, the distribution parameter for each Poisson observation is determined by the state of a Markov chain. By appealing to a duality between forward (in time) filter and its corresponding backward processes, we compute dynamics satisfied by the unnormalized form of the smoother probability. These dynamics can be applied to construct algorithms typically referred to as fixed point smoothers, fixed lag smoothers, and fixed interval smoothers. M-ary detection filters are computed for two scenarios: one for the standard model parameter detection problem and the other for a jump Markov system.     

Bound States for a Klein–Gordon Particle in Vector Plus Scalar Generalized Hulthén Potentials in D Dimensions

The Green’s function associated with a Klein–Gordon particle moving in a D-dimensional space under the action of vector plus scalar q-deformed Hulthén potentials is constructed by path integration for \({q \geq 1}\) and \({\frac{1}{\alpha} \ln q < r < \infty}\). An appropriate approximation of the centrifugal potential term and the technique of space-time transformation are used to reduce the path integral for the generalized Hulthén potentials into a path integral for q-deformed Rosen–Morse potential. Explicit path integration leads to the radial Green’s function for any l state in closed form. The energy spectrum and the correctly normalized wave functions, for a state of orbital quantum number \({l \geq 0}\), are obtained. Eventually, the vector q-deformed Hulthén potential and the Coulomb potentials in D dimensions are considered as special cases.     

Optimal filters for a hidden Markov random field model

A Markov random field (MRF) is a useful technical tool for modeling dynamics systems exhibiting some type of spatio-temporal variability. In this paper, we propose optimal filters for the states of a partially observed temporal Markov random field. We also discuss parameters estimation. This generalizes an earlier work by Elliott and Aggoun [1].     

Recursive Estimation of Inventory Quality Classes Using Sampling

In this paper we propose a new discrete time discrete state inventory model for perishable items of a single product. Items in stock are assumed to belong to one of a finite number of quality classes that are ordered in such a way that Class 1 contains the best quality and the last class contains the pre-perishable quality. By the end of each epoch, items in each inventory class either stay in the same class or lose quality and move to a lower class. The movement between classes is not observed. Samples are drawn from the inventory and based on the observations of these samples, optimal estimates for the number of items in each quality classes are derived.     

Path Integral Solution for the Coulomb Potential in a Curved Space of Constant Positive Curvature

A new path integral treatment of a hydrogen-like atom in a uniformly curved space with a constant positive curvature is presented. By converting the radial path integral into a path integral for the modified Pöschl-Teller potential with the help of the space-time transformation technique, the radial Green’s function is expressed in closed form, from which the energy spectrum and the corresponding normalized wave functions of the bound states are extracted. In the limit of vanishing curvature, the Green’s function, the energy spectra and the correctly normalized wave functions of bound and scattering states for a standard hydrogen-like atom are found.     

State Estimation Schemes for Independent Component Coupled Hidden Markov Models

Conventional Hidden Markov models generally consist of a Markov chain observed through a linear map corrupted by additive noise. This general class of model has enjoyed a huge and diverse range of applications, for example, speech processing, biomedical signal processing and more recently quantitative finance. However, a lesser known extension of this general class of model is the so-called Factorial Hidden Markov Model (FHMM). FHMMs also have diverse applications, notably in machine learning, artificial intelligence and speech recognition [13 Ghahramani , Z. , and Jordan , M. 1997 . Factorial hidden Markov models . Machine Learning 29 : 245 – 273 .[Crossref], [Web of Science ®] , [Google Scholar], 17 Logan , B. , and Moreno , P.J. 1997 . Factorial Hidden Markov Models for Speech Recognition: Preliminary Experiments. Cambridge Research Laboratory, Technical Report CRL 97/7, September.  [Google Scholar]]. FHMMs extend the usual class of HMMs, by supposing the partially observed state process is a finite collection of distinct Markov chains, either statistically independent or dependent. There is also considerable current activity in applying collections of partially observed Markov chains to complex action recognition problems, see, for example, [6 Brand , M. , Oliver , N. , and Pentland , A. 1997 . Coupled hidden Markov models for complex action recognition . IEEE Conference on Computer Vision and Pattern Recognition , San Juan , Puerto Rico . [Google Scholar]].

In this article we consider the Maximum Likelihood (ML) parameter estimation problem for FHMMs. Much of the extant literature concerning this problem presents parameter estimation schemes based on full data log-likelihood EM algorithms. This approach can be slow to converge and often imposes heavy demands on computer memory. The latter point is particularly relevant for the class of FHMMs where state space dimensions are relatively large.

The contribution in this article is to develop new recursive formulae for a filter-based EM algorithm that can be implemented online. Our new formulae are equivalent ML estimators, however, these formulae are purely recursive and so, significantly reduce numerical complexity and memory requirements. A computer simulation is included to demonstrate the performance of our results.     

Synthesis,characterization and X-ray crystal structure of novel nickel Schiff base complexes and investigation of their catalytic activity in the electrocatalytic reduction of alkyl and aryl halides

Novel potentially bidentate NO Schiff base ligands, HL ¹ and HL ² derived from condensation reaction of 2′-methoxyphenyl-2-ethylamine with salicylaldehyde (HL ¹ ) and with 2-hydroxy-4-methoxybenzaldehyde (HL ² ), and their nickel complexes were synthesized and characterized by usual spectroscopic techniques such as FT-IR, UV–Vis, ¹H NMR, ¹³C NMR and elemental analysis. It was revealed that the bidentate Schiff base ligands coordinate with Ni(II) ions yielding mononuclear complexes with 1:2 (metal/ligand) stoichiometry. This result has been determined by using X-ray crystallographic technique of HL ² and the nickel complex derived from HL ¹ (Ni(II)-2L ¹ ). So, the structural studies showed that the two Ni(II) complexes adopt a square-planar geometry around the central metal ion. Cyclic voltammetry studies were investigated in 0.1 M TBAP in DMF solution and indicate that the nickel complexes show one reduction wave related to Ni(II)/Ni(I) redox couple. The electrocatalytical properties of these complexes were also studied in the same electrolyte medium. Their electrocatalytic performances have been tested toward the electroreduction reaction of bromocyclopentane and iodobenzene, showing a promoted activity in the case of the Ni(II)-2L ² complex.     

New quaternized poly(4-vinylpyridine-co-divinylbenzene) material containing nickel(II) Schiff base complex: synthesis,thermogravimetry, and application for heterogeneous electrooxidation of ethanol

Research on Chemical Intermediates - Poly(4-vinylpyridine) crosslinked by 2&nbsp;% divinylbenzene was partially quaternized (20&nbsp;% monomer equivalents) by a bidentate Schiff base nickel...