H ∞ state feedback control of discrete-time Markov jump linear systems through linear matrix inequalities

This paper addresses the H ∞ state-feedback control design problem of discretetime Markov jump linear systems. First, under the assumption that the Markov parameter is measured, the main contribution is on the LMI characterization of all linear feedback controllers such that the closed loop output remains bounded by a given norm level. This results allows the robust controller design to deal with convex bounded parameter uncertainty, probability uncertainty and cluster availability of the Markov mode. For partly unknown transition probabilities, the proposed design problem is proved to be less conservative than one available in the current literature. An example is solved for illustration and comparisons. © 2011 IFAC.

SINGULARLY PERTURBED DISCOUNTED MARKOV CONTROL PROCESSES IN A GENERAL STATE SPACE

This paper studies the asymptotic optimality of discrete-time Markov decision processes (MDPs) with general state space and action space and having weak and strong interactions. By using a similar approach as developed by Liu, Zhang, and Yin [Appl. Math. Optim., 44 (2001), pp. 105-129], the idea in this paper is to consider an MDP with general state and action spaces and to reduce the dimension of the state space by considering an averaged model. This formulation is often described by introducing a small parameter epsilon > 0 in the definition of the transition kernel, leading to a singularly perturbed Markov model with two time scales. Our objective is twofold. First it is shown that the value function of the control problem for the perturbed system converges to the value function of a limit averaged control problem as epsilon goes to zero. In the second part of the paper, it is proved that a feedback control policy for the original control problem defined by using an optimal feedback policy for the limit problem is asymptotically optimal. Our work extends existing results of the literature in the following two directions: the underlying MDP is defined on general state and action spaces and we do not impose strong conditions on the recurrence structure of the MDP such as Doeblin's condition.

Theoretical analysis of hidden photon searches in high-precision experiments

Although the Standard Model of particle physics (SM) provides an extremely successful description of the ordinary matter, one knows from astronomical observations that it accounts only for around 5% of the total energy density of the Universe, whereas around 30% are contributed by the dark matter. Motivated by anomalies in cosmic ray observations and by attempts to solve questions of the SM like the (g-2)_mu discrepancy, proposed U(1) extensions of the SM gauge group have raised attention in recent years. In the considered U(1) extensions a new, light messenger particle, the hidden photon, couples to the hidden sector as well as to the electromagnetic current of the SM by kinetic mixing. This allows for a search for this particle in laboratory experiments exploring the electromagnetic interaction. Various experimental programs have been started to search for hidden photons, such as in electron-scattering experiments, which are a versatile tool to explore various physics phenomena. One approach is the dedicated search in fixed-target experiments at modest energies as performed at MAMI or at JLAB. In these experiments the scattering of an electron beam off a hadronic target e+(A,Z)->e+(A,Z)+l^+l^- is investigated and a search for a very narrow resonance in the invariant mass distribution of the lepton pair is performed. This requires an accurate understanding of the theoretical basis of the underlying processes. For this purpose it is demonstrated in the first part of this work, in which way the hidden photon can be motivated from existing puzzles encountered at the precision frontier of the SM. The main part of this thesis deals with the analysis of the theoretical framework for electron scattering fixed-target experiments searching for hidden photons. As a first step, the cross section for the bremsstrahlung emission of hidden photons in such experiments is studied. Based on these results, the applicability of the Weizsäcker-Williams approximation to calculate the signal cross section of the process, which is widely used to design such experimental setups, is investigated. In a next step, the reaction e+(A,Z)->e+(A,Z)+l^+l^- is analyzed as signal and background process in order to describe existing data obtained by the A1 experiment at MAMI with the aim to give accurate predictions of exclusion limits for the hidden photon parameter space. Finally, the derived methods are used to find predictions for future experiments, e.g., at MESA or at JLAB, allowing for a comprehensive study of the discovery potential of the complementary experiments. In the last part, a feasibility study for probing the hidden photon model by rare kaon decays is performed. For this purpose, invisible as well as visible decays of the hidden photon are considered within different classes of models. This allows one to find bounds for the parameter space from existing data and to estimate the reach of future experiments.

A Pseudolikelihood Approach for Simultaneous Analysis of Array Comparative Genomic Hybridizations (aCGH)

DNA sequence copy number has been shown to be associated with cancer development and progression. Array-based Comparative Genomic Hybridization (aCGH) is a recent development that seeks to identify the copy number ratio at large numbers of markers across the genome. Due to experimental and biological variations across chromosomes and across hybridizations, current methods are limited to analyses of single chromosomes. We propose a more powerful approach that borrows strength across chromosomes and across hybridizations. We assume a Gaussian mixture model, with a hidden Markov dependence structure, and with random effects to allow for intertumoral variation, as well as intratumoral clonal variation. For ease of computation, we base estimation on a pseudolikelihood function. The method produces quantitative assessments of the likelihood of genetic alterations at each clone, along with a graphical display for simple visual interpretation. We assess the characteristics of the method through simulation studies and through analysis of a brain tumor aCGH data set. We show that the pseudolikelihood approach is superior to existing methods both in detecting small regions of copy number alteration and in accurately classifying regions of change when intratumoral clonal variation is present.

A comparison of Markov and generalized linear models of hospital mortality

This paper reports a comparison of three modeling strategies for the analysis of hospital mortality in a sample of general medicine inpatients in a Department of Veterans Affairs medical center. Logistic regression, a Markov chain model, and longitudinal logistic regression were evaluated on predictive performance as measured by the c-index and on accuracy of expected numbers of deaths compared to observed. The logistic regression used patient information collected at admission; the Markov model was comprised of two absorbing states for discharge and death and three transient states reflecting increasing severity of illness as measured by laboratory data collected during the hospital stay; longitudinal regression employed Generalized Estimating Equations (GEE) to model covariance structure for the repeated binary outcome. Results showed that the logistic regression predicted hospital mortality as well as the alternative methods but was limited in scope of application. The Markov chain provides insights into how day to day changes of illness severity lead to discharge or death. The longitudinal logistic regression showed that increasing illness trajectory is associated with hospital mortality. The conclusion is reached that for standard applications in modeling hospital mortality, logistic regression is adequate, but for new challenges facing health services research today, alternative methods are equally predictive, practical, and can provide new insights. ^

LiDAR simulation in modelled orchards to optimise the use of terretrial laser scanners and derived vegetative measures

Light detection and ranging (LiDAR) technology is beginning to have an impact on agriculture. Canopy volume and/or fruit tree leaf area can be estimated using terrestrial laser sensors based on this technology. However, the use of these devices may have different options depending on the resolution and scanning mode. As a consequence, data accuracy and LiDAR derived parameters are affected by sensor configuration, and may vary according to vegetative characteristics of tree crops. Given this scenario, users and suppliers of these devices need to know how to use the sensor in each case. This paper presents a computer program to determine the best configuration, allowing simulation and evaluation of different LiDAR configurations in various tree structures (or training systems). The ultimate goal is to optimise the use of laser scanners in field operations. The software presented generates a virtual orchard, and then allows the scanning simulation with a laser sensor. Trees are created using a hidden Markov tree (HMT) model. Varying the foliar structure of the orchard the LiDAR simulation was applied to twenty different artificially created orchards with or without leaves from two positions (lateral and zenith). To validate the laser sensor configuration, leaf surface of simulated trees was compared with the parameters obtained by LiDAR measurements: the impacted leaf area, the impacted total area (leaves and wood), and th impacted area in the three outer layers of leaves.

Efficiency improvement of HF communications using cognitive radio principles

Cognitive Radio principles can be applied to HF communications to make a more efficient use of the extremely scarce spectrum. In this contribution we focus on analyzing the usage of the available channels done by the legacy users, which are regarded as primary users since they are allowed to transmit without resorting any smart procedure, and consider the possibilities for our stations -over the HFDVL (HF Data+Voice Link) architecture- to participate as secondary users. Our goal is to enhance an efficient use of the HF band by detecting the presence of uncoordinated primary users and avoiding collisions with them while transmitting in different HF channels using our broad-band HF transceiver. A model of the primary user activity dynamics in the HF band is developed in this work. It is based on Hidden Markov Models (HMM) which are a powerful tool for modelling stochastic random processes, and is trained with real measurements from the 14 MHz band.

MBIS: Multivariate Bayesian Image Segmentation Tool

We present MBIS (Multivariate Bayesian Image Segmentation tool), a clustering tool based on the mixture of multivariate normal distributions model. MBIS supports multi-channel bias field correction based on a B-spline model. A second methodological novelty is the inclusion of graph-cuts optimization for the stationary anisotropic hidden Markov random field model. Along with MBIS, we release an evaluation framework that contains three different experiments on multi-site data. We first validate the accuracy of segmentation and the estimated bias field for each channel. MBIS outperforms a widely used segmentation tool in a cross-comparison evaluation. The second experiment demonstrates the robustness of results on atlas-free segmentation of two image sets from scan-rescan protocols on 21 healthy subjects. Multivariate segmentation is more replicable than the monospectral counterpart on T1-weighted images. Finally, we provide a third experiment to illustrate how MBIS can be used in a large-scale study of tissue volume change with increasing age in 584 healthy subjects. This last result is meaningful as multivariate segmentation performs robustly without the need for prior knowledge.

Training and search methods for speech recognition.

Speech recognition involves three processes: extraction of acoustic indices from the speech signal, estimation of the probability that the observed index string was caused by a hypothesized utterance segment, and determination of the recognized utterance via a search among hypothesized alternatives. This paper is not concerned with the first process. Estimation of the probability of an index string involves a model of index production by any given utterance segment (e.g., a word). Hidden Markov models (HMMs) are used for this purpose [Makhoul, J. & Schwartz, R. (1995) Proc. Natl. Acad. Sci. USA 92, 9956-9963]. Their parameters are state transition probabilities and output probability distributions associated with the transitions. The Baum algorithm that obtains the values of these parameters from speech data via their successive reestimation will be described in this paper. The recognizer wishes to find the most probable utterance that could have caused the observed acoustic index string. That probability is the product of two factors: the probability that the utterance will produce the string and the probability that the speaker will wish to produce the utterance (the language model probability). Even if the vocabulary size is moderate, it is impossible to search for the utterance exhaustively. One practical algorithm is described [Viterbi, A. J. (1967) IEEE Trans. Inf. Theory IT-13, 260-267] that, given the index string, has a high likelihood of finding the most probable utterance.

Cortical activity flips among quasi-stationary states.

Parallel recordings of spike trains of several single cortical neurons in behaving monkeys were analyzed as a hidden Markov process. The parallel spike trains were considered as a multivariate Poisson process whose vector firing rates change with time. As a consequence of this approach, the complete recording can be segmented into a sequence of a few statistically discriminated hidden states, whose dynamics are modeled as a first-order Markov chain. The biological validity and benefits of this approach were examined in several independent ways: (i) the statistical consistency of the segmentation and its correspondence to the behavior of the animals; (ii) direct measurement of the collective flips of activity, obtained by the model; and (iii) the relation between the segmentation and the pair-wise short-term cross-correlations between the recorded spike trains. Comparison with surrogate data was also carried out for each of the above examinations to assure their significance. Our results indicated the existence of well-separated states of activity, within which the firing rates were approximately stationary. With our present data we could reliably discriminate six to eight such states. The transitions between states were fast and were associated with concomitant changes of firing rates of several neurons. Different behavioral modes and stimuli were consistently reflected by different states of neural activity. Moreover, the pair-wise correlations between neurons varied considerably between the different states, supporting the hypothesis that these distinct states were brought about by the cooperative action of many neurons.

Contexto e modularização em redes neurais recorrentes para aprendizagem de seqüências temporais

Este trabalho apresenta um sistema neural modular, que processa separadamente informações de contexto espacial e temporal, para a tarefa de reprodução de sequências temporais. Para o desenvolvimento do sistema neural foram considerados redes neurais recorrentes, modelos estocásticos, sistemas neurais modulares e processamento de informações de contexto. Em seguida, foram estudados três modelos com abordagens distintas para aprendizagem de seqüências temporais: uma rede neural parcialmente recorrente, um exemplo de sistema neural modular e um modelo estocástico utilizando a teoria de modelos markovianos escondidos. Com base nos estudos e modelos apresentados, esta pesquisa propõe um sistema formado por dois módulos sucessivos distintos. Uma rede de propagação direta (módulo estimador de contexto espacial) realiza o processamento de contexto espacial identificando a seqüência a ser reproduzida e fornecendo um protótipo do contexto para o segundo módulo. Este é formado por uma rede parcialmente recorrente (módulo de reprodução de sequências temporais) para aprender as informações de contexto temporal e reproduzir em suas saídas a seqüência identificada pelo módulo anterior. Para a finalidade mencionada, este mestrado utiliza a distribuição de Gibbs na saída do módulo para contexto espacial de forma que este forneça probabilidades de contexto espacial, indicando o grau de certeza do módulo e possibilitando a utilização de procedimentos especiais para os casos de dúvida. O sistema neural foi testado em conjuntos contendo trajetórias abertas, fechadas, e com diferentes situações de ambigüidade e complexidade. Duas situações distintas foram avaliadas: (a) capacidade do sistema em reproduzir trajetórias a partir de pontos iniciais treinados; e (b) capacidade de generalização do sistema reproduzindo trajetórias considerando pontos iniciais ou finais em situações não treinadas. A situação (b) é um problema de difícil ) solução em redes neurais devido à falta de contexto temporal, essencial na reprodução de seqüências. Foram realizados experimentos comparando o desempenho do sistema modular proposto com o de uma rede parcialmente recorrente operando sozinha e um sistema modular neural (TOTEM). Os resultados sugerem que o sistema proposto apresentou uma capacidade de generalização significamente melhor, sem que houvesse uma deterioração na capacidade de reproduzir seqüências treinadas. Esses resultados foram obtidos em sistema mais simples que o TOTEM.

Search of Method for Analyzing "Viability" of Innovative Projects

Questions of "viability" evaluation of innovation projects are considered in this article. As a method of evaluation Hidden Markov Models are used. Problem of determining model parameters, which reproduce test data with highest accuracy are solving. For training the model statistical data on the implementation of innovative projects are used. Baum-Welch algorithm is used as a training algorithm.

Treatment-seeking behavior and delay in children with severe malaria in Uganda: results of a Markov analysis

Thesis (Master's)--University of Washington, 2016-06

Wurst: a protein threading server with a structural scoring function, sequence profiles and optimized substitution matrices

Wurst is a protein threading program with an emphasis on high quality sequence to structure alignments (http://www.zbh.uni-hamburg.de/wurst). Submitted sequences are aligned to each of about 3000 templates with a conventional dynamic programming algorithm, but using a score function with sophisticated structure and sequence terms. The structure terms are a log-odds probability of sequence to structure fragment compatibility, obtained from a Bayesian classification procedure. A simplex optimization was used to optimize the sequence-based terms for the goal of alignment and model quality and to balance the sequence and structural contributions against each other. Both sequence and structural terms operate with sequence profiles.