Due to changes of the thermal environment, thermal stresses are produced in structures. Two approaches based on the stochastic process theory are used to describe this phenomenon. The structure is idealized as a long hollow viscoelastic cylinder. Two sites are considered: Barrow (AK) and Yuma (AZ). First passage concepts are applied to characterize the reliability of the system. Crossings are assumed to follow either the behavior of the Poisson process or Markov process. In both cases, the distribution of the time to first passage is taken to be the exponential distribution. Because the material is viscoelastic, statistically and time varying barriers (strengths) with Normal, Log-Normal, or Neibull distributions are considered. Degradation of the barriers by aging and cumulative damage are incorporated in the analysis. / Ph. D. / incomplete_metadata

Thesis (MSc)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: We present a system that uses statistical machine learning to identify and extract bibliography information from scientific literature. Techniques for finding and gathering useful information from the ever growing volume of knowledge on the World Wide Web (WWW), are investigated. We use hidden Markov models both for recognition of bibliography styles and extraction of bibliographic information with an accuracy of up to 97%. The accuracy with which we are able to extract this information allows us to present a case study in which we apply methods of citation analysis to information extracted from three areas of machine learning. We use this information to identify core sets of papers that have made significant contributions to the fields of hidden Markov models, neural networks and recurrent neural networks. / AFRIKAANSE OPSOMMING: Ons bied 'n sisteem aan wat gebruik maak van statistiese masjiene wat leer om bibliografiese inligting uit wetenskaplikke literatuur te identifiseer en ontgin. Tegnieke wat aangewend word vir die verkenning en insameling van nuttige inligting vanaf die snel groeiende kennisbron van die WWW, word ondersoek. Ons gebruik verskuilde Markov modelle vir die herkenning van verwysingsstyl en ontginning van verwysingsinligting met 'n akuraatheidspeil van to 97%. Hierdie hoë ontginningsakuraatheid stelons in staat om 'n toepassing van die tegniek op die veld van masjiene wat leer toe te pas. Ons rapporteer hoe ons die tegnieke gebruik het om literatuur wat beduidende bydraes in die velde van verskuilde Markov modelle, neurale netwerke en terugkerende neurale netwerke, te identifiseer.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Computational molecular evolution is a field that attempts to characterize how genetic sequences evolve over phylogenetic trees – the branching processes that describe the patterns of genetic inheritance in living organisms. It has a long history of developing progressively more sophisticated stochastic models of evolution. Through a probabilist’s lens, this can be seen as a search for more appropriate ways to parameterize discrete state continuous time Markov chains to better encode biological reality, matching the historical processes that created empirical data sets, and creating useful tools that allow biologists to test specific hypotheses about the evolution of the organisms or the genes that interest them. This dissertation is an attempt to fill some of the gaps that persist in the literature, solving what we see as existing open problems. The overarching theme of this work is how to better model variation in the action of natural selection at multiple levels: across genes, between sites, and over time. Through four published journal articles and a fifth in preparation, we present amino acid and codon models that improve upon existing approaches, providing better descriptions of the process of natural selection and better tools to detect adaptive evolution. / AFRIKAANSE OPSOMMING: Komputasionele molekulêre evolusie is ’n navorsingsarea wat poog om die evolusie van genetiese sekwensies oor filogenetiese bome – die vertakkende prosesse wat die patrone van genetiese oorerwing in lewende organismes beskryf – te karakteriseer. Dit het ’n lang geskiedenis waartydens al hoe meer gesofistikeerde waarskynlikheidsmodelle van evolusie ontwikkel is. Deur die lens van waarskynlikheidsleer kan hierdie proses gesien word as ’n soektog na meer gepasde metodes om diskrete-toestand kontinuë-tyd Markov kettings te parametriseer ten einde biologiese realiteit beter te enkodeer – op so ’n manier dat die historiese prosesse wat tot die vorming van biologiese sekwensies gelei het nageboots word, en dat nuttige metodes geskep word wat bioloë toelaat om spesifieke hipotesisse met betrekking tot die evolusie van belanghebbende organismes of gene te toets. Hierdie proefskrif is ’n poging om sommige van die gapings wat in die literatuur bestaan in te vul en bestaande oop probleme op te los. Die oorkoepelende tema is verbeterde modellering van variasie in die werking van natuurlike seleksie op verskeie vlakke: variasie van geen tot geen, variasie tussen posisies in gene en variasie oor tyd. Deur middel van vier gepubliseerde joernaalartikels en ’n vyfde artikel in voorbereiding, bied ons aminosuur- en kodon-modelle aan wat verbeter op bestaande benaderings – hierdie modelle verskaf beter beskrywings van die proses van natuurlike seleksie sowel as beter metodes om gevalle van aanpassing in evolusie te vind.

This thesis relates to the design, implementation and evaluation of statistical face recognition techniques. In particular, the use of Hidden Markov Models in various forms is investigated as a recognition tool and critically evaluated. Current face recognition techniques are very dependent on issues like background noise, lighting and position of key features (ie. the eyes, lips etc.). Using an approach which specifically uses an embedded Hidden Markov Model along with spectral domain feature extraction techniques, shows that these dependencies may be lessened while high recognition rates are maintained.

在此篇論文中我們考慮連續時間架構下, 加入匯差風險與利率風險之跨國投資組合問題. 延續 Lioui, Poncet (2003) 的研究架構, 我們考慮 國內外債券股票與現金的投資組合, 以martingale方法求解避險操作與最佳投資策略. / In this study, we investigate the hedge demands in international portfolio management under a general continuous time framework for constant relative risk averse investors where, in particular, exchange rate risk and the interest rate risk are incorporated. Within this international economy, the changes of real exchange rates, real interest rates and stock prices are assumed to follow the Markovian processes whose drifts and diffusion parameters are driven by certain state variables. Our approach is through the use of the martingale methodology developed by Cox and Huang (1989, 1991) as proposed in the work of Lioui and Poncet (2003). Following their framework, we consider the economy of the investors that consists of one foreign currency and the domestic one, together with their bond portfolios and stock indices. Adding to the previous works, we have compared the obtained optimal strategies with some prevailing ad hoc ones in order to clarify the hedge effects in financial decision from the long term perspective.

Le présent travail porte sur l’estimation d’un système en temps discret dont l’évolution est décrite par une chaîne semi-markovienne (CSM) d’espace d’état fini. Nous présentons le principe d’invariance sous forme multidimensionnelle pour le noyau semi-markovien (NSM), ainsi que diverses mesures du processus. Ensuite, nous étudions l’estimation non-paramétrique de la loi stationnaire de la CSM, en considérant deux estimateurs différents, et nous montrons qu’ils ont le même comportement asymptotique. La probabilité de la première entrée est également introduite. Nous proposons un estimateur et nous étudions ses propriétés asymptotiques : la convergence forte et la normalité asymptotique.D’autre part, nous nous concentrons sur l’étude de la fiabilité des systèmes semi-markoviens. Nous définissons la fiabilité sur intervalle d’un système dont la fiabilité et la disponibilité sont des cas particuliers et nous étudions les propriétés asymptotiques d’un estimateur proposé. De plus, nous présentons une comparaison de l’estimation des différentes mesures de fiabilité fondées sur deux estimateurs du NSM, en réalisant une trajectoire unique et des observations multiples indépendantes. Ce travail fournit aussi des résultats dans le cas semi-markovien à temps discret avec espace d’état général. Nous évaluons l’approximation de moyenne et de diffusion des chaînes de renouvellement markovien. Enfin, nous nous sommes aussi intéressés à une autre classe des processus pour laquelle nous obtenons des résultats dans le cadre des files d’attente. Nous étudions l’approximation de moyenne pour le modèle d’Engset en temps continu et nous appliquons ce résultat aux files d’attente avec ré-essais. / The present work concerns the estimation of a discrete-time system whose evolution is governed by a semi-Markov chain (SMC) with finitely many states. We present the invariance principle in a multidimensional form for the semi-Markov kernel (SMK) and some associated measures of the process. Afterwards, we study the nonparametric estimation of the stationary distribution of the SMC, considering two different estimators, and we prove that they hold the same asymptotic behavior. We introduce also the first hitting probability. We propose an estimator and study its asymptotic properties : the strong consistency and the asymptotic normality. On the other hand, we focus on the study of the dependability of semi-Markovsystems. We introduce the interval reliability whose special cases are the reliability and the availability measures and we study the asymptotic properties of a proposed estimator. Moreover, we present a comparison of nonparametric estimation for various reliability measures based on two estimators of the SMK, realizing a unique trajectory and multiple independent observations.Furthermore, this work provides results on the discrete-time semi-Markov case with general state space. We evaluate the average and diffusion approximation of Markov renewal chains. Finally, we are also interested in another class of processes for which we obtain results in the framework of queueing systems. We establish the average approximationfor the Engset model in continuous time and we apply this result to retrial queues.

In dieser Arbeit werden zwei intrazelluläre Signalwege, betreffend den Tumorsuppressor p53 und das Signalmolekül Ca2+ , diskutiert und modelliert. Einzelzellmessungen des Tumorsuppressors p53 zeigen pulsatile Antwor- ten nach Zufügung von DNA Doppelstrangbrüchen (DSBs). Außer für sehr hohe Schadensdosen, ist das zeitliche auftreten dieser Pulse unregelmäßig. Mithilfe eines Wavelet basierten Pulsdetektors werden die einzelzell Trajek- torien untersucht und die inter-Puls Intervall (IPI) Verteilungen extrahiert. Diese weisen auf nicht-oszillatorische Regime in den Daten hin. Die Theorie der anregbaren Systeme angewendet auf regulatorische Netzwerke ermöglicht dieses komplexe Verhalten mathematisch zu beschreiben. Die Kopplung von Schadens-Sensor-Kinase Dynamik mit dem kanonischen p53 negativen feedback loop, ergibt ein anregbares p53 Modell. Detaillier- te Bifurkationsanalysen zeigen ein robustes anregbares Regime, welches durch ein starkes Schadenssignal auch in Oszillationen überführt werden kann. Treibt man das p53 Modell mit einem stochastischen DNA-Schadens-Prozess, kann sowohl das oszillatorische Verhalten nach hohem Schaden, als auch das unregelmäßige pulsatile Verhalten ohne äußere Stimulation reproduziert werden. Intrazelluläre Ca 2+ Spikes entstehen durch eine hierarchische Kaskade stochastischer prozesse. Die Anwendung einer semi-markovschen Beschreibung führt zu praktischen analytischen Lösungen des erstpassagezeiten Problems. Eine hierbei entdeckte Zeitskalenseparation ermöglicht ein neues allgemeines Ca2+ -Modell. Dieses erklärt auf äußerst prägnante Weise viele wesentliche experimentelle Ergebnisse, insbesondere die Momentenbeziehungen der inter-Spike Intervall Verteilungen. Schließlich erlaubt die hier vorgestellte Theorie Berechnungen der Stimulus-Enkodierung, also die Adaption des Ca 2+ Signals auf veränderliche extrazelluläre Stimuli. Die Vorhersage einer fold change Enkodierung kann durch Experimente gestützt werden. / In this work two signaling pathways, involving the tumor suppressor p53 and the second messenger Ca2+ , are to be discussed and modelled. The tumor suppressor p53 shows a pulsatile response in single cells after induction of DNA double strand breaks (DSBs). Except for very high amounts of damage, these pulses appear at irregular times. The concept of excitable systems is employed as a convenient way to model such observed dynamics. An application to biomolecular reaction networks shows the need for a positive feedback within the p53 regulatory network. Exploiting the reported ultrasensitive dynamics of the upstream damage sensor kinases, leads to a simplified excitable kinase-phosphatase model. Coupling that to the canonical negative feedback p53 regulatory loop, is the core idea behind the construction of the excitable p53 model. A detailed bifurcation analysis of the model establishes a robust excitable regime, which can be switched to oscillatory dynamics via a strong DNA damage signal. Driving the p53 model with a stochastic DSB process yields pulsatile dynamics which reflect different experimental scenarios. Intracellular Ca 2+ concentration spikes arise from a hierarchic cascade of stochastic events. An analytical solution strategy, employing a semi-Markovian description and involving Laplace transformations, is devised and successfully applied to a specific Ca2+ model. The new gained insights are then used, to construct a new generic Ca2+ model, which elegantly captures many known features of Ca2+ signaling. In particular the experimentally observed relations between the average and the standard deviation of the inter spike intervals (ISIs) can be explained in a concise way. Finally, the theoretical considerations allow to calculate the stimulus encoding relation, which governs the adaption of the Ca 2+ signals to varying extracellular stimuli. This is predicted to be a fold change response and new experimental results display a strong support of this idea.

Since the emergence of the Asynchronous Transfer Mode ( A TM ) concept, various switching architectures have been proposed. The multistage interconnection networks have been proposed for the switching architecture under the A TM environment. In this thesis, we propose a new model for the performance analysis of an A TM switching fabric based on single-buffered Banyan network. In this model, we use a three-state, i.e., "empty", "new" and "blocked" Markov chain model to describe the behavior of the buffer within a switching element. In addition to traditional statistical analysis including throughput and delay, we also examine the delay variation. Performance results show that the proposed model is more accurate in describing the switch behavior under uniform traffic environment in comparison with the "two-state" Markov chain model developed by Jenq, et. al.[4] [6] . Based on the "three-state" model, we study a packet priority scheme which gives the blocked packet higher priority to be routed forward during contention. It is found that the standard deviation of the network delay is reduced by about 30%.

The Aldous order is an ordering of representations of the symmetric group motivated by the Aldous Conjecture, a conjecture about random processes proved in 2009. In general, the Aldous order is very difficult to compute, and the proper relations have yet to be determined even for small cases. However, by restricting the problem down to Young-Jucys-Murphy elements, the problem becomes explicitly combinatorial. This approach has led to many novel insights, whose proofs are simple and elegant. However, there remain many open questions related to the Aldous Order, both in general and for the Young-Jucys-Murphy elements.

La Dominance Temporelle des Sensations (DTS) est une méthode d’analyse sensorielle qui mesure la perception temporelle d’un produit au cours de sa dégustation. Pour un panéliste, la DTS consiste à choisir parmi une liste de descripteurs lequel est dominant à chaque instant. Ce travail a pour but la modélisation des données DTS à l’aide de processus stochastiques et propose d’utiliser les processus semi-markoviens (PSM), une généralisation des chaînes de Markov qui permet de modéliser librement les durées de dominance. Le modèle obtenu peut être utilisé pour comparer des échantillons DTS en réalisant un rapport de vraisemblance. Étant donné que les probabilités de transition entre les descripteurs peuvent dépendre du temps, nous proposons d’utiliser des modèles différents par période et nous proposons un algorithme pour déterminer le nombre et les frontières de ces périodes de manière optimale. Le modèle est représenté sous forme d’un graphe montrant les transitions entre descripteurs les plus observées. Finalement, ce travail introduit les modèles de mélange de processus semi-markoviens afin de segmenter le panel en fonction des différences de perception interindividuelles.Les méthodes développées sont appliquées à des jeux de données DTS variés : chocolats, fromages frais et Goudas. Les résultats montrent que la modélisation par un PSM apporte de nouvelles informations sur la perception temporelle, en particulier sur la variabilité de perception au sein d’un panel, alors que les méthodes classiques se focalisent sur une vision moyenne de la perception du panel. De plus, à notre connaissance, ce travail est le premier à proposer l’identification d’un modèle de mélange de processus semi-markoviens. / Temporal Dominance of Sensations (TDS) is a technique to measure temporal perception of food product during tasting. For a panelist, it consists in choosing in a list of attributes which one is dominant at any time. This work aims to model TDS data with a stochastic process and proposes to use semi-Markov processes (SMP), a generalization of Markov chains which allows dominance durations to be modeled by any type of distribution. The model can then be used to compare TDS samples based on likelihood ratio. Because probabilities of transition from one attribute to another one can also depend on time, we propose to model TDS by period and we propose a method to select optimally the number of periods and the frontiers between periods. Graphs built upon the stochastic pattern can be plotted to represent main chronological transitions between attributes. Finally, this work introduces new statistical models based on finite mixtures of semi-Markov processes in order to derive consumer segmentation based on individual differences in temporal perception of a product.The methods are applied to various TDS datasets: chocolates, fresh cheeses and Gouda cheeses. Results show that SMP modeling gives new information about temporal perception compared to classical methods. It particularly emphasizes the existence of several perceptions for a same product in a panel, whereas classical methods only provide a mean panel overview. Furthermore, as far as we know, this work is the first one that considers mixtures of semi-Markov processes.