Non-Markovian Momentum Computing: Universal and Efficient

All computation is physically embedded. Reflecting this, a growing body of results embraces rate equations as the underlying mechanics of thermodynamic computation and biological information processing. Strictly applying the implied continuous-time Markov chains, however, excludes a universe of natural computing. We show that expanding the toolset to continuous-time hidden Markov chains substantially removes the constraints. The general point is made concrete by our analyzing two eminently-useful computations that are impossible to describe with a set of rate equations over the memory states. We design and analyze a thermodynamically-costless bit flip, providing a first counterexample to rate-equation modeling. We generalize this to a costless Fredkin gate---a key operation in reversible computing that is computation universal. Going beyond rate-equation dynamics is not only possible, but necessary if stochastic thermodynamics is to become part of the paradigm for physical information processing.Comment: 6 pages, 3 figures; Supplementary Material, 1 page; http://csc.ucdavis.edu/~cmg/compmech/pubs/cbdb.ht

A refined and asymptotic analysis of optimal stopping problems of Bruss and Weber

The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of a specific kind. We follow Dendievel, (where a bibliography can be found) who studies several types of such problems, mainly initiated by Bruss and Weber. Whether in discrete time or continuous time, whether all parameters are known or must be sequentially estimated, we shall call such problems simply "Bruss-Weber problems". Our contribution in the present paper is a refined analysis of several problems in this class and a study of the asymptotic behaviour of solutions. The problems we consider center around the following model. Let $X_1,X_2,\ldots,X_n$ be a sequence of independent random variables which can take three values: $\{+1,-1,0\}.$ Let p:=\P(X_i=1), p':=\P(X_i=-1), \qt:=\P(X_i=0), p\geq p', where p+p'+\qt=1. The goal is to maximize the probability of stopping on a value $+1$ or $-1$ appearing for the last time in the sequence. Following a suggestion by Bruss, we have also analyzed an x-strategy with incomplete information: the cases $p$ known, $n$ unknown, then $n$ known, $p$ unknown and finally $n,p$ unknown are considered. We also present simulations of the corresponding complete selection algorithm.Comment: 22 pages, 19 figure

Color Image Segmentation Using the Bee Algorithm in the Markovian Framework

This thesis presents color image segmentation as a vital step of image analysis in computer vision. A survey of the Markov Random Field (MRF) with four different implementation methods for its parameter estimation is provided. In addition, a survey of swarm intelligence and a number of swarm based algorithms are presented. The MRF model is used for color image segmentation in the framework. This thesis introduces a new image segmentation implementation that uses the bee algorithm as an optimization tool in the Markovian framework. The experiments show that the new proposed method performs faster than the existing implementation methods with about the same segmentation accuracy

Pattern Recognition for Command and Control Data Systems

To analyze real-world events, researchers collect observation data from an underlying process and construct models to represent the observed situation. In this work, we consider issues that affect the construction and usage of a specific type of model. Markov models are commonly used because their combination of discrete states and stochastic transitions is suited to applications with both deterministic and stochastic components. Hidden Markov Models (HMMs) are a class of Markov model commonly used in pattern recognition. We first demonstrate how to construct HMMs using only the observation data, and no a priori information, by extending a previously developed approach from J.P. Crutchfield and C.R. Shalizi. We also show how to determine with a level of statistical confidence whether or not the model fully encapsulates the underlying process. Once models are constructed from observation data, the models are used to identify other types of observations. Traditional approaches consider the maximum likelihood that the model matches the observation, solving a classification problem. We present a new method using confidence intervals and receiver operating characteristic curves. Our method solves a detection problem by determining if observation data matches zero, one, or more than one model. To detect the occurrence of a behavior in observation data, one must consider the amount of data required. We consider behaviors to be \u27serial Markovian,\u27 when the behavior can change from one model to another at any time. When analyzing observation data, considering too much data induces high delay and could lead to confusion in the system if multiple behaviors are observed in the data stream. If too little data is used, the system has a high false positive rate and is unable to correctly detect behaviors. We demonstrate the effectiveness of all methods using illustrative examples and consumer behavior data