Rozprawy doktorskie na temat „Computational stochastic dynamics”

The main limitations in performing uncertainty analysis of CFD models using conventional methods are associated with cost and effort. For these reasons, there is a need for the development and implementation of efficient stochastic CFD tools for performing uncertainty analysis. One of the main contributions of this research is the development and implementation of Intrusive and Non-Intrusive methods using polynomial chaos for uncertainty representation and propagation. In addition, a methodology was developed to address and quantify turbulence model uncertainty. In this methodology, a complex perturbation is applied to the incoming turbulence and closure coefficients of a turbulence model to obtain the sensitivity derivatives, which are used in concert with the polynomial chaos method for uncertainty propagation of the turbulence model outputs.
Ph. D.

Despite numerous advances in experimental methodologies capable of addressing the various phenomenon occurring on metal surfaces, atomic scale resolution of the microscopic dynamics remains elusive for most systems. Computational models of the processes may serve as an alternative tool to fill this void. To this end, parallel molecular dynamics simulations of self-diffusion on metal surfaces have been developed and employed to address microscopic details of the system. However these simulations are not without their limitations and prove to be computationally impractical for a variety of chemically relevant systems, particularly for diffusive events occurring in the low temperature regime. To circumvent this difficulty, a corresponding coarse-grained representation of the surface is also developed resulting in a reduction of the required computational effort by several orders of magnitude, and this description becomes all the more advantageous with increasing system size and complexity. This representation provides a convenient framework to address fundamental aspects of diffusion in nonequilibrium environments and an interesting mechanism for directing diffusive motion along the surface is explored. In the ensuing discussion, additional topics including transition state theory in noisy systems and the construction of a checking function for protein structure validation are outlined. For decades the former has served as a cornerstone for estimates of chemical reaction rates. However, in complex environments transition state theory most always provides only an upper bound for the true rate. An alternative approach is described that may alleviate some of the difficulties associated with this problem. Finally, one of the grand challenges facing the computational sciences is to develop methods capable of reconstructing protein structure based solely on readily-available sequence information. Herein a checking function is developed that may prove useful for addressing whether a particular proposed structure is a viable possibility.

Fluctuations, or "noise", can play a key role in determining the behaviour of living systems. The molecular-level fluctuations that occur in genetic networks are of particular importance. Here, noisy gene expression can result in genetically identical cells displaying significant variation in phenotype, even in identical environments. This variation can act as a basis for natural selection and provide a fitness benefit to cell populations under stress. This thesis focuses on the development of new conceptual knowledge about how gene expression noise and gene network topology influence drug resistance, as well as new simulation techniques to better understand cell population dynamics. Network topology may at first seem disconnected from expression noise, but genes in a network regulate each other through their expression products. The topology of a genetic network can thus amplify or attenuate noisy inputs from the environment and influence the expression characteristics of genes serving as outputs to the network. The main body of the thesis consists of five chapters: 1. A published review article on the physical basis of cellular individuality. 2. A published article presenting a novel method for simulating the dynamics of cell populations. 3. A chapter on modeling and simulating replicative aging and competition using an object-oriented framework. 4. A published research article establishing that noise in gene expression can facilitate adaptation and drug resistance independent of mutation. 5. An article submitted for publication demonstrating that gene network topology can affect the development of drug resistance. These chapters are preceded by a comprehensive introduction that covers essential concepts and theories relevant to the work presented.

Models computacionals basats en xarxes a gran escala d'inspiració neurobiològica permeten descriure els correlats neurals de la decisió observats en certes àrees corticals com una transició entre atractors de la xarxa cortical. L'estimulació provoca un canvi en el paisatge d'atractors que afavoreix la transició entre l'atractor neutre inicial a un dels atractors associats a les eleccions categòriques. El soroll present en el sistema introdueix indeterminació en les transicions. En aquest treball mostrem l'existència de dos mecanismes de decisió qualitativament diferents, cadascun amb signatures psicofísiques diferenciades. El mecanisme que apareix a baixes intensitats, induït exclusivament pel soroll, dóna lloc a temps de decisió distribuïts asimètricament, amb una mitjana dictada per l'amplitud del soroll.A més, tant els temps de decisió com el rendiment psicofísic són funcions decreixents de l'estimulació externa. També proposem dos mètodes, un basat en l'aproximació macroscòpica i un altre en la teoria de la varietat central, que simplifiquen la descripció de sistemes estocàstics multistables.
Computational models based on large-scale, neurobiologically-inspired networks describe the decision-related activity observed in some cortical areas as a transition between attractors of the cortical network. Stimulation induces a change in the attractor configuration and drives the system out from its initial resting attractor to one of the existing attractors associated with the categorical choices. The noise present in the system renders transitions random. We show that there exist two qualitatively different mechanisms for decision, each with distinctive psychophysical signatures. The decision mechanism arising at low inputs, entirely driven by noise, leads to skewed distributions of decision times, with a mean governed by the amplitude of the noise. Moreover, both decision times and performances are monotonically decreasing functions of the overall external stimulation. We also propose two methods, one based on the macroscopic approximation and one based on center manifold theory, to simplify the description of multistable stochastic neural systems.

Sudden cardiac death due to the development of lethal arrhythmias is the dominant cause of mortality in the UK, yet the mechanisms underlying their onset, maintenance and termination are still poorly understood. Therefore biomarkers are used to determine arrhythmic risk within patients and of new drug compounds. In recent years, the magnitude of variations in the length of successive beats, measured over a short period of time, has been shown to be a powerful predictor of arrhythmic risk. This beat-to-beat variability is thought to be the manifestation of the random opening and closing dynamics of individual ion channels that lie within the membrane of cardiac cells. Computational models have become an important tool in understanding the electrophysiology of the heart. However, current state-of-the-art electrophysiology models do not incorporate this intrinsic stochastic behaviour of ion channels. Those that do use computationally costly methods, restricting their use in complex tissue scale simulations, or employ stochastic simulation methods that result in negative numbers of channels and so are inaccurate. Therefore, using current stochastic modelling techniques to investigate the role of stochastic ion channel behaviour in beat-to-beat variability presents difficulties. In this thesis we take a mathematically rigorous and novel approach to develop accurate and computationally efficient models of stochastic ion channel dynamics that can be incorporated into existing electrophysiology models. Two different models of stochastic ion channel behaviour, both based on a system of stochastic differential equations (SDEs), are developed and compared. The first model is based on an existing SDE model from population dynamics called the Wright-Fisher model. The second approach incorporates boundary conditions into the SDE model of ion channel dynamics that is obtained in the limit from the discrete-state Markov chain model, and is called a reflected SDE. Of these two methods, the reflected SDE is found to more accurately capture the stochastic dynamics of the discrete-stateMarkov chain, seen as the ‘gold-standard’ model and also provides substantial computational speed up. Thus the reflected SDE is an accurate and efficient model of stochastic ion channel dynamics and so allows for detailed investigation into beat-to-beat variability using complex computational electrophysiology models. We illustrate the potential power of this method by incorporating it into a state-of-the-art canine cardiac cell electrophsyiology model so as to explore the effects of stochastic ion channel behaviour on beat-to-beat variability. The stochastic models presented in this thesis fulfil an important role in elucidating the effects of stochastic ion channel behaviour on beat-to-beat variability, a potentially important biomarker of arrhythmic risk.

There are a huge number of pathogens with multi-component transmission cycles, involving ampli_er hosts, vectors, complex pathogen life cycles and particular environmental conditions. These complex systems present challenges in terms of modeling and policy development. The deadliest tick-borne infectious disease in the world, the Brazilian Spotted Fever (BSF), is a relevant example of that. The current increase of human cases of BSF has been associated with the presence and expansion of capybaras Hydrochoerus hydrochaeris, amplifer host for the agent Rickettsia rickettsii and primary host for the tick vector Amblyomma sculptum. The objective of this thesis was to analyze the dynamics of the FMB with the purpose of providing bases for the planning of strategies focused on the prevention of human cases. We proposed diferent approaches to evaluating: i) the contribution of hosts and vectors in the transmission of BSF, ii) potential risk areas and anthropogenic parameters associated with the occurrence of human cases, iii) the pattern and the spatial propagation velocity of BSF, and iv) climatic and landscape factors that could be related to the distribution of the vector. The proposed approaches elucidated how BSF control and prevention strategies can be focused on the management of amplifier hosts populations. We found that geographical barriers generated, for example, by areas of riparian reforestation, could prevent the spatial spread of BSF, since a positive association between the occurrence of human cases and the increment of sugarcane crop was determined, as well as a higher propagation velocity of BSF in places with higher carrying capacity. This thesis was interdisciplinary and required, on one hand, expertise in biology, computational epidemiology, mathematics and statistics and on the other hand, a datarich environment such as the Laboratory of Parasitology of the VPS/FMVZ/USP. The results of this thesis can be usefulness in the planning of public health policies related to the prevention of BSF. Furthermore, this work will open the path to further mathematical and computational studies focused on the dynamics and prevention of other vector-borne infectious diseases.
Existe um grande número de agentes patogênicos com ciclos de transmissão complexos, envolvendo hospedeiros amplificadores, vetores e condições ambientais particulares. Esses sistemas complexos apresentam desafios quanto a modelagem e desenvolvimento de políticas públicas. A Febre Maculosa Brasileira (FMB) é a doença transmitida por carrapatos mais letal do mundo e é um claro exemplo de um sistema complexo. O aumento atual de casos humanos de BSF tem sido associado à presença e expansão de capivaras Hydrochoerus hydrochaeris, hospedeiros amplificadores do agente Rickettsia rickettsii e hospedeiros primários do carrapato vetor Amblyomma sculptum. O objetivo desta tese foi analisar a dinâmica da FMB com o propósito de fornecer bases para o delineamento de estratégias de prevenção de casos em humanos. Diferentes abordagens foram propostas para avaliar: i) a contribuição específica de hospedeiros e vetores na transmissão da FMB, ii) os parâmetros antropogênicos associados com a ocorrência dos casos e potenciais áreas de risco, iii) o padrão e a velocidade de propagação espacial e da doença, e iv) os fatores climáticos e paisagísticos que poderiam estar relacionados à distribuição do vetor. Os modelos propostos elucidaram que as estratégias de controle e prevenção da FMB podem estar focadas em práticas de manejo das populações de hospedeiros amplificadores. Uma vez que uma associação positiva entre ocorrência de casos humanos e o incremento de cultura de cana-de-açúcar foi determinada, assim como uma maior velocidade de propagação da FMB em locais com alta quantidade desta cultura, barreiras geográficas geradas, por exemplo, por zonas de reflorestamento ciliar, poderiam impedir a disseminação da FMB. Esta tese foi interdisciplinar e exigiu, por um lado, conhecimentos em biologia, epidemiologia computacional, matemática e estatística e, em contrapartida, um ambiente rico em dados biológicos como o Laboratório de Parasitologia do VPS/USP. Os resultados desta tese poderão ser utilizados na planificação de políticas de saúde pública enfocadas à prevenção da FMB. Complementarmente, este trabalho abrirá o caminho para futuros estudos matemáticos e computacionais orientados no estudo da dinâmica e prevenção de outras doenças infecciosas transmitidas por vetores.

Recent developments of high performance computing capabilities allow solving modern science problems employing sophisticated computational techniques. However, it is necessary to ensure the efficiency of state of the art computational methods to fully take advantage of modern technology capabilities. In this thesis we propose uncertainty quantification and high performance computing strategies to solve fluid dynamics systems characterized by uncertain conditions and unknown parameters. We verify that such techniques allow us to take decisions faster and ensure the reliability of simulation results. Different sources of uncertainties can be relevant in computational fluid dynamics applications. For example, we consider the shape and time variability of boundary conditions, as well as the randomness of external forces acting on the system. From a practical point of view, one has to estimate statistics of the flow, and a failure probability convergence criterion must be satisfied by the statistical estimator of interest to assess reliability. We use hierarchical Monte Carlo methods as uncertainty quantification strategy to solve stochastic systems. Such algorithms present three levels of parallelism: over levels, over realizations per level, and on the solution of each realization. We propose an improvement by adding a new level of parallelism, between batches, where each batch has its independent hierarchy. These new methods are called asynchronous hierarchical Monte Carlo, and we demonstrate that such techniques take full advantage of concurrency capabilities of modern high performance computing environments, while preserving the same reliability of state of the art methods. Moreover, we focus on reducing the wall clock time required to compute statistical estimators of chaotic incompressible flows. Our approach consists in replacing a single long-term simulation with an ensemble of multiple independent realizations, which are run in parallel with different initial conditions. The error analysis of the statistical estimator leads to the identification of two error contributions: the initialization bias and the statistical error. We propose an approach to systematically detect the burn-in time to minimize the initialization bias, accompanied by strategies to reduce the simulation cost. Finally, we propose an integration of Monte Carlo and ensemble averaging methods for reducing the wall clock time required for computing statistical estimators of time-dependent stochastic turbulent flows. A single long-term Monte Carlo realization is replaced by an ensemble of multiple independent realizations, each characterized by the same random event and different initial conditions. We consider different systems, relevant in the computational fluid dynamics engineering field, as realistic wind flowing around high-rise buildings or compressible potential flow problems. By solving such numerical examples, we demonstrate the accuracy, efficiency, and effectiveness of our proposals.
Los desarrollos relacionados con la computación de alto rendimiento de las últimas décadas permiten resolver problemas científicos actuales, utilizando métodos computacionales sofisticados. Sin embargo, es necesario asegurarse de la eficiencia de los métodos computacionales modernos, con el fin de explotar al máximo las capacidades tecnológicas. En esta tesis proponemos diferentes métodos, relacionados con la cuantificación de incertidumbres y el cálculo de alto rendimiento, con el fin de minimizar el tiempo de computación necesario para resolver las simulaciones y garantizar una alta fiabilidad. En concreto, resolvemos sistemas de dinámica de fluidos caracterizados por incertidumbres. En el campo de la dinámica de fluidos computacional existen diferentes tipos de incertidumbres. Nosotros consideramos, por ejemplo, la forma y la evolución en el tiempo de las condiciones de frontera, así como la aleatoriedad de las fuerzas externas que actúan sobre el sistema. Desde un punto de vista práctico, es necesario estimar valores estadísticos del flujo del fluido, cumpliendo los criterios de convergencia para garantizar la fiabilidad del método. Para cuantificar el efecto de las incertidumbres utilizamos métodos de Monte Carlo jerárquicos, también llamados hierarchical Monte Carlo methods. Estas estrategias tienen tres niveles de paralelización: entre los niveles de la jerarquía, entre los eventos de cada nivel y durante la resolución del evento. Proponemos agregar un nuevo nivel de paralelización, entre batches, en el cual cada batch es independiente de los demás y tiene su propia jerarquía, compuesta por niveles y eventos distribuidos en diferentes niveles. Definimos estos nuevos algoritmos como métodos de Monte Carlo asíncronos y jerárquicos, cuyos nombres equivalentes en inglés son asynchronous hierarchical Monte Carlo methods. También nos enfocamos en reducir el tiempo de computación necesario para calcular estimadores estadísticos de flujos de fluidos caóticos e incompresibles. Nuestro método consiste en reemplazar una única simulación de dinámica de fluidos, caracterizada por una ventana de tiempo prolongada, por el promedio de un conjunto de simulaciones independientes, caracterizadas por diferentes condiciones iniciales y una ventana de tiempo menor. Este conjunto de simulaciones se puede ejecutar en paralelo en superordenadores, reduciendo el tiempo de computación. El método de promedio de conjuntos se conoce como ensemble averaging. Analizando las diferentes contribuciones del error del estimador estadístico, identificamos dos términos: el error debido a las condiciones iniciales y el error estadístico. En esta tesis proponemos un método que minimiza el error debido a las condiciones iniciales, y en paralelo sugerimos varias estrategias para reducir el coste computacional de la simulación. Finalmente, proponemos una integración del método de Monte Carlo y del método de ensemble averaging, cuyo objetivo es reducir el tiempo de computación requerido para calcular estimadores estadísticos de problemas de dinámica de fluidos dependientes del tiempo, caóticos y estocásticos. Reemplazamos cada realización de Monte Carlo por un conjunto de realizaciones independientes, cada una caracterizada por el mismo evento aleatorio y diferentes condiciones iniciales. Consideramos y resolvemos diferentes sistemas físicos, todos relevantes en el campo de la dinámica de fluidos computacional, como problemas de flujo del viento alrededor de rascacielos o problemas de flujo potencial. Demostramos la precisión, eficiencia y efectividad de nuestras propuestas resolviendo estos ejemplos numéricos.
Gli sviluppi del calcolo ad alte prestazioni degli ultimi decenni permettono di risolvere problemi scientifici di grande attualità, utilizzando sofisticati metodi computazionali. È però necessario assicurarsi dell’efficienza di questi metodi, in modo da ottimizzare l’uso delle odierne conoscenze tecnologiche. A tal fine, in questa tesi proponiamo diversi metodi, tutti inerenti ai temi di quantificazione di incertezze e calcolo ad alte prestazioni. L’obiettivo è minimizzare il tempo necessario per risolvere le simulazioni e garantire alta affidabilità. Nello specifico, utilizziamo queste strategie per risolvere sistemi fluidodinamici caratterizzati da incertezze in macchine ad alte prestazioni. Nel campo della fluidodinamica computazionale esistono diverse tipologie di incertezze. In questo lavoro consideriamo, ad esempio, il valore e l’evoluzione temporale delle condizioni di contorno, così come l’aleatorietà delle forze esterne che agiscono sul sistema fisico. Dal punto di vista pratico, è necessario calcolare una stima delle variabili statistiche del flusso del fluido, soddisfacendo criteri di convergenza, i quali garantiscono l’accuratezza del metodo. Per quantificare l’effetto delle incertezze sul sistema utilizziamo metodi gerarchici di Monte Carlo, detti anche hierarchical Monte Carlo methods. Queste strategie presentano tre livelli di parallelizzazione: tra i livelli della gerarchia, tra gli eventi di ciascun livello e durante la risoluzione del singolo evento. Proponiamo di aggiungere un nuovo livello di parallelizzazione, tra gruppi (batches), in cui ogni batch sia indipendente dagli altri ed abbia una propria gerarchia, composta da livelli e da eventi distribuiti su diversi livelli. Definiamo questi nuovi algoritmi come metodi asincroni e gerarchici di Monte Carlo, il cui corrispondente in inglese è asynchronous hierarchical Monte Carlo methods. Ci focalizziamo inoltre sulla riduzione del tempo di calcolo necessario per stimare variabili statistiche di flussi caotici ed incomprimibili. Il nostro metodo consiste nel sostituire un’unica simulazione fluidodinamica, caratterizzata da un lungo arco temporale, con il valore medio di un insieme di simulazioni indipendenti, caratterizzate da diverse condizioni iniziali ed un arco temporale minore. Questo insieme 10 di simulazioni può essere eseguito in parallelo in un supercomputer, riducendo il tempo di calcolo. Questo metodo è noto come media di un insieme o, in inglese, ensemble averaging. Calcolando la stima di variabili statistiche, commettiamo due errori: l’errore dovuto alle condizioni iniziali e l’errore statistico. In questa tesi proponiamo un metodo per minimizzare l’errore dovuto alle condizioni iniziali, ed in parallelo suggeriamo diverse strategie per ridurre il costo computazionale della simulazione. Infine, proponiamo un’integrazione del metodo di Monte Carlo e del metodo di ensemble averaging, il cui obiettivo è ridurre il tempo di calcolo necessario per stimare variabili statistiche di problemi di fluidodinamica dipendenti dal tempo, caotici e stocastici. Ogni realizzazione di Monte Carlo è sostituita da un insieme di simulazioni indipendenti, ciascuna caratterizzata dallo stesso evento casuale, da differenti condizioni iniziali e da un arco temporale minore. Consideriamo e risolviamo differenti sistemi fisici, tutti rilevanti nel campo della fluidodinamica computazionale, come per esempio problemi di flusso del vento attorno a grattacieli, o sistemi di flusso potenziale. Dimostriamo l’accuratezza, l’efficienza e l’efficacia delle nostre proposte, risolvendo questi esempi numerici.
Enginyeria civil

Modelling and simulation are essential to modern research in cell biology. This thesis follows a journey starting from the construction of new stochastic methods for discrete biochemical systems to using them to simulate a population of interacting haematopoietic stem cell lineages. The first part of this thesis is on discrete stochastic methods. We develop two new methods, the stochastic extrapolation framework and the Stochastic Bulirsch-Stoer methods. These are based on the Richardson extrapolation technique, which is widely used in ordinary differential equation solvers. We believed that it would also be useful in the stochastic regime, and this turned out to be true. The stochastic extrapolation framework is a scheme that admits any stochastic method with a fixed stepsize and known global error expansion. It can improve the weak order of the moments of these methods by cancelling the leading terms in the global error. Using numerical simulations, we demonstrate that this is the case up to second order, and postulate that this also follows for higher order. Our simulations show that extrapolation can greatly improve the accuracy of a numerical method. The Stochastic Bulirsch-Stoer method is another highly accurate stochastic solver. Furthermore, using numerical simulations we find that it is able to better retain its high accuracy for larger timesteps than competing methods, meaning it remains accurate even when simulation time is speeded up. This is a useful property for simulating the complex systems that researchers are often interested in today. The second part of the thesis is concerned with modelling a haematopoietic stem cell system, which consists of many interacting niche lineages. We use a vectorised tau-leap method to examine the differences between a deterministic and a stochastic model of the system, and investigate how coupling niche lineages affects the dynamics of the system at the homeostatic state as well as after a perturbation. We find that larger coupling allows the system to find the optimal steady state blood cell levels. In addition, when the perturbation is applied randomly to the entire system, larger coupling also results in smaller post-perturbation cell fluctuations compared to non-coupled cells. In brief, this thesis contains four main sets of contributions: two new high-accuracy discrete stochastic methods that have been numerically tested, an improvement that can be used with any leaping method that introduces vectorisation as well as how to use a common stepsize adapting scheme, and an investigation of the effects of coupling lineages in a heterogeneous population of haematopoietic stem cell niche lineages.

Multi-period portfolio optimization (MPO) has gained a lot of interest in modern portfolio theory due to its consideration for inter-temporal trading e effects, especially market impacts and transactions costs, and for its subtle reliability on return predictability. However, because of the heavy computational demand, portfolio policies based on this approach have been sparsely explored. In that regard, a tractable MPO framework proposed by N. Gârleanu & L. H. Pedersen has been investigated. Using the stochastic control framework, the authors provided a closed form expression of the optimal policy. Moreover, they used a specific, yet flexible return predictability model. Excess returns were expressed using a linear factor model, and the predicting factors were modeled as mean reverting processes. Finally, transactions costs and market impacts were incorporated in the problem formulation as a quadratic function. The elaborated methodology considered that the market returns dynamics are governed by fast and slow mean reverting factors, and that the market transactions costs are not necessarily quadratic. By controlling the exposure to the market returns predicting factors, the aim was to uncover the importance of the mean reversion speeds in the performance of the constructed trading strategies, under realistic market costs. Additionally, for the sake of comparison, trading strategies based on a single-period mean variance optimization were considered. The findings suggest an overall superiority in performance for the studied MPO approach even when the market costs are not quadratic. This was accompanied with evidence of better usability of the factors' mean reversion speed, especially fast reverting factors, and robustness in adapting to transactions costs.
Portföljoptimering över era perioder (MPO) har fått stort intresse inom modern portföljteori. Skälet till detta är att MPO tar hänsyn till inter-temporala handelseffekter, särskilt marknadseffekter och transaktionskostnader, plus dess tillförlitlighet på avkastningsförutsägbarhet. På grund av det stora beräkningsbehovet har dock portföljpolitiken baserad på denna metod inte undersökts mycket. I det avseendet, har en underskriven MPO ramverk som föreslagits av N.Gârleanu L. H. Pedersen undersökts. Med hjälp av stokastiska kontrollramen tillhandahöll författarna formuläret för sluten form av den optimala politiken. Dessutom använde de en specifik, men ändå flexibel returförutsägbarhetsmodell. Överskjutande avkastning uttrycktes med hjälp av en linjärfaktormodell och de förutsägande faktorerna modellerades som genomsnittligaåterföringsprocesser. Slutligen inkorporerades transaktionskostnader och marknadseffekter i problemformuleringen som en kvadratisk funktion. Den utarbetade metodiken ansåg att marknadens avkastningsdynamik styrs av snabba och långsammaåterhämtningsfaktorer, och att kostnaderna för marknadstransaktioner inte nödvändigtvis är kvadratiska. Genom att reglera exponeringen mot marknaden återspeglar förutsägande faktorer, var målet att avslöja vikten av de genomsnittliga omkastningshastigheterna i utförandet av de konstruerade handelsstrategierna, under realistiska marknadskostnader. Dessutom, för jämförelses skull, övervägdes handelsstrategier baserade på en enstaka genomsnittlig variansoptimering. Resultaten tyder på en överlägsen överlägsenhet i prestanda för det studerade MPO-tillvägagångssättet, även när marknadsutgifterna inte är kvadratiska. Detta åtföljdes av bevis för bättre användbarhet av faktorernas genomsnittliga återgångshastighet, särskilt snabba återställningsfaktorer och robusthet vid anpassning till transaktionskostnader

Cette thèse s'inscrit dans un projet de modélisation numérique de la dispersion atmosphérique de polluants à travers le code de mécanique des fluides numérique Code_Saturne. L'objectif est de pouvoir simuler la dispersion atmosphérique de polluants en environnement complexe, c'est-à-dire autour de centrales, sites industriels ou en milieu urbain. Dans ce contexte, nous nous concentrons sur la modélisation de la dispersion des polluants à micro-échelle, c'est-à-dire pour des distances de l'ordre de quelques mètres à quelques kilomètres et correspondant à des échelles de temps de l'ordre de quelques dizaines de secondes à quelques dizaines de minutes : on parle de modélisation en champ proche. L’approche suivie dans ces travaux de recherche suit une formulation hybride eulérienne/lagrangienne, où les champs dynamiques moyens relatifs au fluide porteur (pression, vitesse, température, turbulence) sont calculés via une approche eulérienne et sont ensuite fournis au solveur lagrangien. Ce type de formulation est couramment utilisé dans la littérature atmosphérique pour son efficacité numérique. Le modèle lagrangien stochastique considéré dans nos travaux est le Simplified Langevin Model (SLM), développé par Pope (1985,2000). Ce modèle appartient aux méthodes communément appelées méthodes PDF (Probability Density Function), et, à notre connaissance, n'a pas été exploité auparavant dans le contexte de la dispersion atmosphérique. Premièrement, nous montrons que le SLM respecte le critère dit de mélange homogène (Thomson, 1987). Ce critère, essentiel pour juger de la bonne qualité d'un modèle lagrangien stochastique, correspond au fait que si des particules sont initialement uniformément réparties dans un fluide incompressible, alors elles doivent le rester. Nous vérifions le bon respect du critère de mélange homogène pour trois cas de turbulence inhomogène représentatifs d'une large gamme d'applications pratiques : une couche de mélange, un canal plan infini, ainsi qu'un cas de type atmosphérique mettant en jeu un obstacle au sein d'une couche limite neutre. Nous montrons que le bon respect du critère de mélange homogène réside simplement en la bonne introduction du terme de gradient de pression en tant que terme de dérive moyen dans le modèle de Langevin (Pope, 1987; Minier et al., 2014; Bahlali et al., 2018c). Nous discutons parallèlement de l'importance de la consistance entre champs eulériens et lagrangiens dans le cadre de telles formulations hybrides eulériennes/lagrangiennes. Ensuite, nous validons le modèle dans le cas d'un rejet de polluant ponctuel et continu, en conditions de vent uniforme et turbulence homogène. Dans ces conditions, nous disposons en effet d'une solution analytique nous permettant une vérification précise. Nous observons que dans ce cas, le modèle lagrangien discrimine bien les deux différents régimes de diffusion de champ proche et champ lointain, ce qui n'est pas le cas d'un modèle eulérien à viscosité turbulente (Bahlali et al., 2018b).Enfin, nous travaillons sur la validation du modèle sur plusieurs campagnes expérimentales en atmosphère réelle, en tenant compte de la stratification thermique de l'atmosphère et de la présence de bâtiments. Le premier programme expérimental considéré dans nos travaux concerne le site du SIRTA (Site Instrumental de Recherche par Télédétection Atmosphérique), dans la banlieue sud de Paris, et met en jeu une stratification stable de la couche limite atmosphérique. La seconde campagne étudiée est l'expérience MUST (Mock Urban Setting Test). Réalisée aux Etats-Unis, dans le désert de l'Utah, cette expérience a pour but de représenter une ville idéalisée, au travers d'un ensemble de lignées de conteneurs. Deux rejets ont été simulés et analysés, respectivement en conditions d'atmosphère neutre et stable (Bahlali et al., 2018a)
This Ph.D. thesis is part of a project that aims at modeling pollutant atmospheric dispersion with the Computational Fluid Dynamics code Code_Saturne. The objective is to simulate atmospheric dispersion of pollutants in a complex environment, that is to say around power plants, industrial sites or in urban areas. In this context, the focus is on modeling the dispersion at micro-scale, that is for distances of the order of a few meters to a few kilometers and corresponding to time scales of the order of a few tens of seconds to a few tens of minutes: this is also called the near field area. The approach followed in this thesis follows a hybrid Eulerian/Lagrangian formulation, where the mean dynamical fields relative to the carrier fluid (pressure, velocity, temperature, turbulence) are calculated through an Eulerian approach and are then provided to the Lagrangian solver. This type of formulation is commonly used in the atmospheric literature for its numerical efficiency. The Lagrangian stochastic model considered in our work is the Simplified Langevin Model (SLM), developed by Pope (1985,2000). This model belongs to the methods commonly referred to as PDF (Probability Density Function) methods, and, to our knowledge, has not been used before in the context of atmospheric dispersion. First, we show that the SLM meets the so-called well-mixed criterion (Thomson, 1987). This criterion, essential for any Lagrangian stochastic model to be regarded as acceptable, corresponds to the fact that if particles are initially uniformly distributed in an incompressible fluid, then they must remain so. We check the good respect of the well-mixed criterion for three cases of inhomogeneous turbulence representative of a wide range of practical applications: a mixing layer, an infinite plane channel, and an atmospheric-like case involving an obstacle within a neutral boundary layer. We show that the good respect of the well-mixed criterion lies simply in the good introduction of the pressure gradient term as the mean drift term in the Langevin model (Pope, 1987; Minier et al., 2014; Bahlali et al., 2018c). Also, we discuss the importance of consistency between Eulerian and Lagrangian fields in the framework of such Eulerian/Lagrangian hybrid formulations. Then, we validate the model in the case of continuous point source pollutant dispersion, under uniform wind and homogeneous turbulence. In these conditions, there is an analytical solution allowing a precise verification. We observe that in this case, the Lagrangian model discriminates well the two different near- and far-field diffusion regimes, which is not the case for an Eulerian model based on the eddy-viscosity hypothesis (Bahlali et al., 2018b).Finally, we work on the validation of the model on several experimental campaigns in real atmosphere, taking into account atmospheric thermal stratification and the presence of buildings. The first experimental program considered in our work has been conducted on the `SIRTA' site (Site Instrumental de Recherche par Télédétection Atmosphérique), in the southern suburb of Paris, and involves a stably stratified surface layer. The second campaign studied is the MUST (Mock Urban Setting Test) experiment. Conducted in the United States, in Utah's desert, this experiment aims at representing an idealized city, through several ranges of containers. Two cases are simulated and analyzed, respectively corresponding to neutral and stable atmospheric stratifications (Bahlali et al., 2018a)

Nos últimos anos, uma míriade de modelos de propagação de opinião foram propostos, motivados pelo interesse crescente dos físicos por problemas interdisciplinares tanto em sociologia, quanto em economia e biologia. Um dos objetivos desse trabalho é unificar alguns desses modelos em uma mesma formulação. Para isso, generalizamos a noção de confiança limitada para o que chamamos de regras de confiança, que podem ser interpretadas como a introdução de viéses ou preconceitos nas interações de agentes com opiniões distintas. Munidos dessa formulação, nos propusemos a estudar como modelos que promovem localmente conformidade (o que está de acordo com experimentos para grupos pequenos conduzidos por psicólogos), poderiam gerar diversidade globalmente (explicando a persistência de pontos de vista distintos em sociedades, por exemplo). Nós estudamos o campo médio do modelo do votante e de variantes do modelo Sznajd. Aplicando ferramentas de sistemas dinâmicos, conseguimos resolver analiticamente o comportamento qualitativo dos modelos na ausência de ruído e desenvolvemos uma teoria de perturbação para o modelo Sznajd com ruído infinitesimal, que nos forneceu um retrato parcial do comportamento na presença de ruído. Na ausência de ruído, chegamos a conclusão que o modelo do votante se comporta de maneira completamente diferente, enquanto que os outros modelos tem essencialmente o mesmo comportamento. Também fizemos simulações em redes Barabási-Albert e Watts-Strogatz para os modelos votante e Sznajd e, em colaboração com o grupo de pesquisa do Institute for Complex Systems and Mathematical Biology da Universidade de Aberdeen, estudamos um modelo de biodiversidade que pode ser encarado como uma variante do modelo do votante em uma rede quadrada. As nossas conclusões apontam que os resultados de campo médio podem ser compreendidos através de conexões com teoria de grafos e que os diversos modelos simulados se comportam em um certo sentido da mesma maneira, reforçando a idéia de universalidade entre eles (na verdade é essencial que existam aspectos universais no comportamento humano para que a modelagem de sistemas sociais seja factível, dadas as dificuldades óbvias de se construir um modelo realista para uma pessoa ou uma sociedade). Grosso modo, em todos os sistemas estudados, a coexistência ou não de pontos de vista diferentes parece depender mais crucialmente da rede e do tipo de regra de confiança, do que de outros detalhes específicos do modelo.
In the recent years, a great number of opinion propagation models were proposed, motivated by the increasing interest among physicists in interdisciplinary problems, not only in sociology, but also in economics and biology. One of the goals of this work is to unify some of these models under a same formulation. In order to do that, we generalized the notion of bounded confidence to what we called confidence rules, that can be interpreted as the introduction of biases and prejudices in the interactions among agents holding differing points of view. Using this formulation, we decided to study how models that locally breed conformity (what is in accordance with experiments conducted by psichologists for small groups) could sustain diversity globally (explaining the persistence of different points of view in societies, for example). We studied the mean field version of the voter model and of variants of the Sznajd model. We used dynamical systems techniques and were able to solve analytically the qualitative behaviour of the models in the absence of noise and developed a perturbation theory for the Sznajd model with infinitesimal noise, that yielded a partial picture of the behaviour with noise. In the absence of noise, we found that the voter model has a completely different behaviour, while the other models have essentially the same behaviour. We also did simulations in Barabási-Albert and Watts-Strogatz networks for the voter and the Sznajd models and we collaborated with the research group of the Institute for Complex Systems and Mathematical Biology from the University of Aberdeen, studying a biodiversity model that can be seen as a modification of the voter model in a square lattice. Our conclusions point that the mean field results can be understood through connections with graph theory problems and that the different models that were simulated, in some sense, have the same behaviour, reinforcing the idea of universality for these models (due to the obvious difficulties in modelling human beings in a reliable and realistic way, some degree of universality in human behaviour is actually essential, in order for social modelling to be feasible). Roughly speaking, in all the systems that were studied, the coexistence or not of differing opinions, seems to depend more strongly on the network and on the type of confidence rule used, than in other specific details of the model.

Durante as últimas décadas, pesquisas em biologia do tumor com a utilização de novas técnicas de biologia molecular produziram informações em profusão, motivando e dando condições para que fossem criados novos modelos matemáticos dedicados à análise de vários aspectos de crescimento e proliferação da população celular. Alguns desses modelos têm sido dedicados à descrição e análise do regime estacionário do processo de desenvolvimento de uma população celular sob condições químicas que se consideram favorecer a aceleração ou desaceleração do crescimento da população de células tumorais. Todavia, a dinâmica temporal do crescimento de uma população de células tumorais ainda não foi analisada nesses trabalhos. Uma das dificuldades é o estabelecimento da interação entre células de múltiplos tipos que sirvam como descrição para essa dinâmica. Nosso trabalho vem preencher essa lacuna e a presente dissertação tem como objetivo a apresentação do modelo, desenvolvido por nós, de simulação da dinâmica do crescimento e proliferação celular do melanoma (câncer de baixa incidência, mas de letalidade extremamente alta) e também dos resultados obtidos através das simulações deste modelo computacional
During the last decades, tumor biology research with the use of new techniques in molecular biology resulted in a profusion of information that have given conditions and motivated the development of new mathematical models dedicated to analyzing various aspects of growth and proliferation of the cell population. Some of these models have been devoted to the description and analysis of the steady state of the development process of a cell population under chemical conditions that, in theory, promote the acceleration or deceleration of the growth of tumor cell population. However, these studies have not yet analyzed the temporal dynamics of growth of a tumor cell population. One of the difficulties is the establishment of the interaction between cells of multiple types that serve as the description for this dynamic. Our work fills this gap and this dissertation aims to present the model, developed by us, to simulate the growth dynamics and cellular proliferation of melanoma (cancer of low incidence but of extremely high lethality) and the results obtained through the simulations of this computational model

An object-oriented framework is presented for developing and simulating individual-based models of cell populations. The framework supplies classes to define objects called simulation channels that encapsulate the algorithms that make up a simulation model. These may govern state-updating events at the individual level, perform global state changes, or trigger cell division. Simulation engines control the scheduling and execution of collections of simulation channels, while a simulation manager coordinates the engines according to one of two scheduling protocols. When the ensemble of cells being simulated reaches a specified maximum size, a procedure is introduced whereby random cells are ejected from the simulation and replaced by newborn cells to keep the sample population size constant but representative in composition. The framework permits recording of population snapshot data and/or cell lineage histories. Use of the framework is demonstrated through validation benchmarks and two case studies based on experiments from the literature.

Spatiotemporal activity dynamics with criticality have been widely observed in the cortex. In this thesis, we focus on elucidating the fundamental computational roles of these critical circuit dynamics in both biological and artificial neural networks. We first propose a novel neural computation mechanism, Computing by Modulating Spontaneous Activity (CMSA), for understanding visual perception. Using biophysically plausible circuit models, we demonstrate that spontaneous activity patterns with criticality are modulated by external stimuli to give rise to neural responses. We find that CMSA mechanism of generating neural responses provides profound computational advantages, such as speeding up cortical processing. CMSA mechanism provides a unifying explanation for many experimental findings at both the single-neuron and circuit levels. We further demonstrate that dynamical wave patterns, emerging from the non-equilibrium critical regime of a new type of models that integrate essential structural and neurophysiological properties of cortical circuits, exhibit Lévy walk-like movement. Such Lévy dynamics modulated by salient inputs provide a mechanistic account of recent key experimental findings on spatial attention sampling, including the theta-band sampling rate, theta-gamma coupling. This dynamical mechanism of attention, when applied to natural stimuli, can better explain the attention maps and attention sampling paths found in psychophysical studies than the classical winner-take-all model of attention. Finally, we demonstrate that Lévy walk-like learning dynamics also emerge from deep neural networks trained with stochastic gradient descent (SGD) algorithm, and that such learning dynamics enable the SGD optimizer to escape from local minima. This discovery of deep learning provides a framework for understanding the strengths and weaknesses of different network architectures and the development of new learning methods.

The study of social network dynamics has become an increasingly important component of many disciplines in the social sciences. In the past decade, statistical models and methods have been proposed which permit researchers to draw statistical inference on these dynamics. This thesis builds on one such family of models, the stochastic actor oriented model (SAOM) proposed by Snijders [2001]. Goodness of fit for SAOMs is an area that is only just beginning to be filled in with appropriate methods. This thesis proposes a Mahalanobis distance based, Monte Carlo goodness of fit test that can depend on arbitrary features of the observed network data and covariates. As remediating poor fit can be a difficult process, a modified model distance (MMD) estimator is devised that can help researchers to choose among a set of model elaborations. In practice, panel data is typically used to draw SAOM-based inference. This thesis also proposes a score-type test for time heterogeneity between the waves in the panel that is computationally cheap and fits into a convenient, forward model selecting workflow. Next, this thesis proposes a rigorous method for aggregating so-called relational event data (e.g. emails and phone calls) by extending the SAOM family to a family of hidden Markov models that suppose a latent social network is driving the observed relational events. Finally, this thesis proposes a measurement model for SAOMs inspired by error-in-variables (EiV) models employed in an array of disciplines. Like the relational event aggregation model, the measurement model is a hidden Markov model extension to the SAOM family. These models allow the researcher to specify the form of the mesurement error and buffer against potential attenuating biases and other problems that can arise if the errors are ignored.

In this thesis we discuss the synchronization of stochastic population oscillators in ecology and neuroscience. Traditionally, the synchronization of oscillators has been studied in deterministic systems with various modes of synchrony induced by coupling between the oscillators. However, recent developments have shown that an ensemble of uncoupled oscillators can be synchronized by a common noise source alone. By considering the effects of noise-induced synchronization on biological oscillators, we are able to explain various biological phenomena in ecological and neurobiological contexts - most importantly, the long-observed Moran effect. Our formulation of the systems as limit cycle oscillators arising from populations of individuals, each with a random element to its behaviour, also allows us to examine the interaction between an external noise source and this intrinsic stochasticity. This provides possible explanations as to why in ecological systems large-amplitude cycles may not be observed in the wild. In neural population oscillators, we were able to observe not just synchronization, but also clustering in some pa- rameter regimes. Finally, we are also able to extend our methods to include coupling in our models. In particular, we examine the competing effects of dispersal and extrinsic noise on the synchronization of a pair of Rosenzweig-Macarthur predator-prey systems. We discover that common environmental noise will ultimately synchronize the oscillators, but that the approach to synchrony depends on whether or not dispersal in the absence of noise supports any stable asynchronous states. We also show how the combination of correlated (shared) and uncorrelated (unshared) noise with dispersal can lead to a multistable steady-state probability density. Similar analysis on a coupled system of neural oscillators would be an interesting project for future work, which, among other future directions of research, is discussed in the concluding section of this thesis.

Le but de cette thèse est de développer des outils statistiques permettant d'initialiser et de calibrer les modèles de microsimulation dynamique stochastique, en partant de l'exemple du modèle SimVillages (développé dans le cadre du projet Européen PRIMA). Ce modèle couple des dynamiques démographiques et économiques appliquées à une population de municipalités rurales. Chaque individu de la population, représenté explicitement dans un ménage au sein d'une commune, travaille éventuellement dans une autre, et possède sa propre trajectoire de vie. Ainsi, le modèle inclut-il des dynamiques de choix de vie, d'étude, de carrière, d'union, de naissance, de divorce, de migration et de décès. Nous avons développé, implémenté et testé les modèles et méthodes suivants: * un modèle permettant de générer une population synthétique à partir de données agrégées, où chaque individu est membre d'un ménage, vit dans une commune et possède un statut au regard de l'emploi. Cette population synthétique est l'état initial du modèle. * un modèle permettant de simuler une table d'origine-destination des déplacements domicile-travail à partir de données agrégées. * un modèle permettant d'estimer le nombre d'emplois dans les services de proximité dans une commune donnée en fonction de son nombre d'habitants et de son voisinage en termes de service. * une méthode de calibration des paramètres inconnus du modèle SimVillages de manière à satisfaire un ensemble de critères d'erreurs définis sur des sources de données hétérogènes. Cette méthode est fondée sur un nouvel algorithme d'échantillonnage séquentiel de type Approximate Bayesian Computation.

In this study within quantitative portfolio optimization, stochastic programming is investigated as an investment decision tool. This research takes the direction of scenario based Mean-Absolute Deviation and is compared with the traditional Mean-Variance model and widely used Risk Parity portfolio. Furthermore, this thesis is done in collaboration with the First Swedish National Pension Fund, AP1, and the implemented multi-asset portfolios are thus tailored to match their investment style. The models are evaluated on two different fund management levels, in order to study if the portfolio performance benefits from a more restricted feasible domain. This research concludes that stochastic programming over the investigated time period is inferior to Risk Parity, but outperforms the Mean-Variance Model. The biggest aw of the model is its poor performance during periods of market stress. However, the model showed superior results during normal market conditions.
I denna studie inom kvantitativ portföljoptimering undersöks stokastisk programmering som ett investeringsbeslutsverktyg. Denna studie tar riktningen för scenariobaserad Mean-Absolute Deviation och jämförs med den traditionella Mean-Variance-modellen samt den utbrett använda Risk Parity-portföljen. Avhandlingen görs i samarbete med Första AP-fonden, och de implementerade portföljerna, med era tillgångsslag, är därför skräddarsydda för att matcha deras investeringsstil. Modellerna utvärderas på två olika fondhanteringsnivåer för att studera om portföljens prestanda drar nytta av en mer restrektiv optimeringsmodell. Den här undersökningen visar att stokastisk programmering under undersökta tidsperioder presterar något sämre än Risk Parity, men överträffar Mean-Variance. Modellens största brist är dess prestanda under perioder av marknadsstress. Modellen visade dock något bättre resultat under normala marknadsförhållanden.

This research aims at understanding the conditions that lead to reaction initiation of polymer-bonded explosives (PBXs) as they undergo mechanical and thermal processes subsequent to impact. To analyze this issue, a cohesive finite element method (CFEM) based finite deformation framework is developed and used to quantify the thermomechanical response of PBXs at the microstructure level. This framework incorporates the effects of large deformation, thermomechanical coupling, failure in the forms of micro-cracks in both bulk constituents and along grain/matrix interfaces, and frictional heating. A novel criterion for the ignition of heterogeneous energetic materials under impact loading is developed, which is used to quantify the critical impact velocity, critical time to ignition, and critical input work at ignition for non-shock conditions as functions of microstructure of granular HMX and PBX. A threshold relation between impact velocity and critical input energy at ignition for non-shock loading is developed, involving an energy cutoff and permitting the effects of microstructure and loading to be accounted for. Finally, a novel approach for computationally predicting and quantifying the stochasticity of the ignition process in energetic materials is developed, allowing prediction of the critical time to ignition and the critical impact velocity below which no ignition occurs based on basic material properties and microstructure attributes. Results are cast in the form of the Weibull distribution and used to establish microstructure-ignition behavior relations.

Thesis (M. S.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Reveliotis, Spyros; Committee Member: Ayhan, Hayriye; Committee Member: Goldsman, Dave; Committee Member: Shamma, Jeff; Committee Member: Zwart, Bert.

Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a new method, the MCR method, which is unique to stochastic models and provides significantly better estimates and smaller confidence intervals for parameter values. Initial analysis of the new MCR method indicates that this method might be a viable method for parameter estimation for continuous time Markov chain models.

Cette thèse examine une nouvelle façon d'étudier l'impact d'une voie de signalisation donnée sur l'évolution d'un tissu grâce à l'analyse multi-niveaux. Cette analyse est divisée en deux parties principales: La première partie considère les modèles décrivant la voie au niveau cellulaire. A l'aide de ces modèles, on peut calculer de manière résoluble la dynamique d'un groupe de cellules, en le représentant par une distribution multivariée sur des concentrations de molécules clés. La deuxième partie propose un modèle 3d de croissance tissulaire qui considère la population de cellules comme un ensemble de sous-populations, partitionnée de façon à ce que chaque sous-population partage les mêmes conditions externes. Pour chaque sous-population, le modèle résoluble présenté dans la première partie peut être utilisé. Cette thèse se concentre principalement sur la première partie, tandis qu'un chapitre couvre un projet de modèle pour la deuxième partie
This thesis examines a new way to study the impact of a given pathway on the dynamics of a tissue through Multi-Level Analysis. The analysis is split in two main parts: The first part considers models describing the pathway at the cellular level. Using these models, one can compute in a tractable manner the dynamics of a group of cells, representing it by a multivariate distribution over concentrations of key molecules. % of the distribution of the states of this pathway through groups of cells. The second part proposes a 3d model of tissular growth that considers the population of cell as a set of subpopulations, partitionned such as each subpopulation shares the same external conditions. For each subpopulation, the tractable model presented in the first part can be used. This thesis focuses mainly on the first part, whereas a chapter covers a draft of a model for the second part

In this thesis we focus on Stochastic combinatorial Optimization Problems (SCOPs), a wide class of combinatorial optimization problems under uncertainty, where part of the information about the problem data is unknown at the planning stage, but some knowledge about its probability distribution is assumed.

Optimization problems under uncertainty are complex and difficult, and often classical algorithmic approaches based on mathematical and dynamic programming are able to solve only very small problem instances. For this reason, in recent years metaheuristic algorithms such as Ant Colony Optimization, Evolutionary Computation, Simulated Annealing, Tabu Search and others, are emerging as successful alternatives to classical approaches.

In this thesis, metaheuristics that have been applied so far to SCOPs are introduced and the related literature is thoroughly reviewed. In particular, two properties of metaheuristics emerge from the survey: they are a valid alternative to exact classical methods for addressing real-sized SCOPs, and they are flexible, since they can be quite easily adapted to solve different SCOPs formulations, both static and dynamic. On the base of the current literature, we identify the following as the key open issues in solving SCOPs via metaheuristics:

(1) the design and integration of ad hoc, fast and effective objective function approximations inside the optimization algorithm;

(2) the estimation of the objective function by sampling when no closed-form expression for the objective function is available, and the study of methods to reduce the time complexity and noise inherent to this type of estimation;

(3) the characterization of the efficiency of metaheuristic variants with respect to different levels of stochasticity in the problem instances.

We investigate the above issues by focusing in particular on a SCOP belonging to the class of vehicle routing problems: the Probabilistic Traveling Salesman Problem (PTSP). For the PTSP, we consider the Ant Colony Optimization metaheuristic and we design efficient local search algorithms that can enhance its performance. We obtain state-of-the-art algorithms, but we show that they are effective only for instances above a certain level of stochasticity, otherwise it is more convenient to solve the problem as if it were deterministic.

The algorithmic variants based on an estimation of the objective function by sampling obtain worse results, but qualitatively have the same behavior of the algorithms based on the exact objective function, with respect to the level of stochasticity. Moreover, we show that the performance of algorithmic variants based on ad hoc approximations is strongly correlated with the absolute error of the approximation, and that the effect on local search of ad hoc approximations can be very degrading.

Finally, we briefly address another SCOP belonging to the class of vehicle routing problems: the Vehicle Routing Problem with Stochastic Demands (VRPSD). For this problem, we have implemented and tested several metaheuristics, and we have studied the impact of integrating in them different ad hoc approximations.

Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished

Living cells are made up of networks of interacting genes, proteins and other bio-molecules. Simple interactions between network components in forms of feedback regulations can lead to complex collective dynamics. A key task in cell biology is to gain a thorough understanding of the dynamics of intracellular systems and processes. In this thesis, a combined approach of mathematical modelling, computational simulation and analytical techniques, has been used to obtain a deeper insight into the dynamical aspects of a variety of feedback systems commonly encountered in cells. These systems range from model system with detailed available molecular knowledge to general regulatory motifs with varying network structures. Deterministic as well as stochastic modelling techniques have been employed, depending primarily on the specific questions asked. The first part of the thesis focuses on dissecting the principles behind the regulatory design of the Tryptophan Operon system in Escherichia coli. It has evolved three negative feedback loops, namely repression, attenuation and enzyme inhibition, as core regulator mechanisms to control the intracellular level of tryptophan amino acid, which is taken up for protein synthesis. Despite extensive experimental knowledge, the roles of these seemingly redundant loops remain unclear from a dynamical point of view. We aim to understand why three loops, rather than one, have evolved. Using a large-scale perturbation/response analysis through modelling and simulations and novel metrics for transient dynamics quantification, it has been revealed that the multiple negative feedback loops employed by the tryptophan operon are not redundant. In fact, they have evolved to concertedly give rise to a much more efficient, adaptive and stable system, than any single mechanism would provide. Since even the full topology of feedback interactions within a network is insufficient to determine its behavioural dynamics, other factors underlying feedback loops must be characterised to better predict system dynamics. In the second part of the thesis, we aim to derive these factors and explore how they shape system dynamics. We develop an analytical approach for stability and bifurcation analysis and apply it to class of feedback systems commonly encountered in cells. Our analysis showed that the strength and the Hill coefficient of a feedback loop play key role in determining the dynamics of the system carrying the loop. Not only that, the position of the loop was also found to be crucial in this decision. The analytical method we developed also facilitates parameter sensitivity analysis in which we investigate how the production and degradation rates affect system dynamics. We find that these rates are quite different in the way they shape up system behaviour, with the degradation rates exhibiting a more intricate manner. We demonstrated that coupled-loop systems display greater complexity and a richer repertoire of behaviours in comparison with single-loop ones. Different combinations of the feedback strengths of individual loops give rise to different dynamical regimes. The final part of the thesis aims to understand the effects of molecular noise on dynamics of specific systems, in this case the Tryptophan Operon. We developed two stochastic models for the system and compared their predictions to those given by the deterministic model. By means of simulations, we have shown that noise can induce oscillatory behaviour. On the other hand, incorporating noise in an oscillatory system can alter the characteristics of oscillation by shifting the bifurcation point of certain parameters by a substantial amount. Measurement of fluctuations reveals that that noise at the transcript level is most significant while noise at the enzyme level is smallest. This study highlights that noise should not be neglected if we want to obtain a complete understanding of the dynamic behaviour of cells.

Работа содержит описание построения доверительной полосы стохастического хаоса и реализацию алгоритмов исследования n-мерных моделей. В работе рассматривается дискретная модель, представленная в виде нелинейной динамической системы разностных уравнений, которая описывает динамику взаимодействия потребителей. Выделяются две задачи, которые были поставлены и выполнены в рамках данной работы для расширения программного инструментария исследования динамических систем такого рода. Для двумерного случая осуществляется стохастический анализ чувствительности хаоса через построение доверительной области с использованием критических линий. Помимо этого, описывается разработанный и реализованный алгоритм построения внешней границы хаоса. Производится переход к n-мерному варианту модели (взаимодействие n потребителей). Выделяется 4 алгоритма для исследования n-мерной модели: 1. построение фазовой траектории, 2. построение бифуркационной диаграммы, 3. построение карты режимов, 4. построение показателей Ляпунова. Описывается реализация данных алгоритмов с уклоном в параллельные вычисления. Реализация алгоритмов выполнена на языке программирования C# (платформа .NET) в виде консольного приложения для запуска параллельных вычислений на вычислительном кластере УрО РАН (суперкомпьютер «Уран»).
The work contains description of confidence band construction of a stochastic chaos and realization of algorithms for n-dimensional models studying. The thesis considers a discrete model presented in the form of a nonlinear dynamic system of difference equations, which describes the dynamic of consumer interaction. There are two task that were set and performed in this work to expand the software tools for research dynamic sys-tems of this kind. For the two-dimensional case, a stochastic analysis of the sensitivity of chaos is carried out through the construction of a confidence band using critical lines. In addition, there is description and implementation of algorithm, that can build outer boundary of chaos. A transition is made to the n-dimensional version of the model (interaction of n consumers). There are 4 algorithms for studying the n-dimensional model: 1. phase trajectory building, 2. bifurcation diagram building, 3. mode map building, 4. Lyapunov components building. Algorithm implementation is described with a bias in parallel computations. The algorithms are implemented with C# programming language (.NET platform) in the form of a console application for running parallel computations on the computing cluster of the Ural Branch of the Russian Academy of Sciences (supercomputer «Uranus»).

Cette thèse s'inscrit dans le cadre de systèmes complexes appliqués aux systèmes économiques. Dans cette thèse, un modèle multi-agent a été proposé, qui modélise le cycle de production. Il est consitué d'entreprises, ouvirers/foyers, et une banque, et repecte la conservation de la monnaie. Son hypothèse centrale est que les entreprises se basent sur une marge espérée pour déterminer leur production. Un scénario simple de ce modèle, ou les marges espérées sont homogènes, a été analysé dans le cadre de models de croissance stochastique. Les résultats sont la distribution de tailles d'entreprises rassemblant des lois de puissance, et leur distribution du taux de croissance de forme 'tente', ainsi qu'une dépendence de taille de la variance de la croissance. Ces résultats sont proches aux faits stylisés issus d'études empiriques. Dans un scénario plus complet, le modèle contient des caractéristiques supplémentaires: des marges espérées hétérogèges, ainsi que des paiements d'intérêts, la possibilité de faire faillite. Cela ramène le modèle aux modèles macro-économiques multi-agents. Les extensions sont décrites de façon théorique par des équations de replicateur. Les résultats nouveaux sont la distribution d'age d'entreprises actives, la distribution de leur taux de profit, la distribution de dette, des statistiques sur les faillites, et des cycles de vie caractéristiques. Tout ces résultats sont qualitativement en accord avec des résultats d'études empiriques de plusieurs pays.Le modèle proposé génère des résultats prometteurs, en respectant le principe que des résultats qui apparaissent simultanément peuvent soit etre générés par un même processus, soit par plusieurs aui qui sont compatibles
The thesis is in the field of complex systems, applied to an economic system. In this thesis, an agent-based model has been proposed to model the production cycle. It comprises firms, workers, and a bank, and respects stock-flow consistency. Its central assumption is that firms plan their production based on an expected profit margin. A simple scenario of the model, where the expected profit margin is the same for all firms, has been analyzed in the context of simple stochastic growth models. Results are a firms' size distribution close to a power law, and tent-shaped growth rate distribution, and a growth rate variance scaling with firm size. These results are close to empirically found stylized facts. In a more comprehensive version, the model contains additional features: heterogeneous profits margins, as well as interest payments and the possibility of bankruptcy. This relates the model to agent-based macroeconomic models. The extensions are described theoretically theoretically with replicator dynamics. New results are the age distribution of active firms, their profit rate distribution, debt distribution, bankruptcy statistics, as well as typical life cycles of firms, which are all qualitatively in agreement with studies of firms databases of various countries.The proposed model yields promising results by respecting the principle that jointly found results may be generated by the same process, or by several ones which are compatible

Random fields are frequently used in computational simulations of real-life processes. In particular, in this work they are used in modeling of flow and transport in porous media. Porous media as they arise in geological formations are intrinsically deterministic but there is significant uncertainty involved in determination of their properties such as permeability, porosity and diffusivity. In many situations description of properties of the porous media is aided by a limited number of observations at fixed points. These observations constrain the randomness of the field and lead to conditional simulations. In this work we propose a method of simulating the random fields which respect the observed data. An advantage of our method is that in the case that additional data becomes available it can be easily incorporated into subsequent representations. The proposed method is based on infinite series representations of random fields. We provide truncation error estimates which bound the discrepancy between the truncated series and the random field. We additionally provide the expansions for some processes that have not yet appeared in the literature. There are several approaches to efficient numerical computations for partial differential equations with random parameters. In this work we compare the solutions of flow and transport equations obtained by conditional simulations with Monte Carlo (MC) and stochastic collocation (SC) methods. Due to its simplicity MC method is one of the most popular methods used for the solution of stochastic equations. However, it is computationally expensive. The SC method is functionally similar to the MC method but it provides the faster convergence of the statistical moments of the solutions through the use of the carefully chosen collocation points at which the flow and transport equations are solved. We show that for both methods the conditioning on measurements helps to reduce the uncertainty of the solutions of the flow and transport equations. This especially holds in the neighborhood of the conditioning points. Conditioning reduces the variances of solutions helping to quantify the uncertainty in the output of the flow and transport equations.
Graduation date: 2013

This paper will analyze the effects of using hybrid optimization methods for optimizing objective functions that are determined by computational fluid dynamics solvers for compressible viscous flow for optimal design of airfoils. Previous studies on this topic by the authors had examined the application of deterministic optimization methods and stochastic optimization methods such as Simulated Annealing and Simultaneous Perturbation Stochastic Analysis (SPSA). The studies indicated that SPSA method has a greater or equal efficiency as compared with SA method in reaching optimal airfoil designs for the design problem in question. However, in some situations SPSA method has a tendency to demonstrate an oscillatory behavior in the vicinity of a local optima. To overcome this tendency, a hybrid method designed to take full advantage of SPSA’s high rate of reduction of the objective function at the inception of the design process to drive the design cycles towards the optimal zone at first, and then combining with other methods to perform the final stages of the convergence towards the optimal solutions is considered. SPSA method has been combined with the gradient-based Broydon-Fletcher-Goldfarb-Shanno (BFGS) method as well as Simulated Annealing method for the transonic inverse airfoil design problem that is concerned with the specification of a target airfoil surface pressure distribution and starting from an initial guess of an airfoil shape, the target airfoil shape is reached by way of minimization of a quantity that depends on the difference between the target and current airfoil surface pressure distribution. For a typical transonic flow test case, the effects of using hybrid optimization techniques such as SPSA+BFGS and SPSA+SA as opposed to using SPSA alone can be seen in Figure 1. After 800 design cycles using SPSA, the hybrid SPSA+SA method took 2521 function evaluations of SA while the SPSA+BFGS method took 271 function evaluations to reach similar values which are much better than that reached by using SPSA alone in the entire minimization process. Results indicate that both of the two hybrid methods have capability to find a global optimum more efficiently than the SPSA method. The paper will address issues related to hybridization and its impact on the optimal airfoil shape designs in various contexts.
Singapore-MIT Alliance (SMA)

Multi-query problems such as uncertainty quantification, optimization of a dynamical system require solving a governing differential equation at multiple parameter values. Therefore, for large systems, the computational cost becomes prohibitive. Replacing the original discretized higher dimensional model with a faster reduced order model (ROM) can alleviate this computationally prohibitive task significantly. However, a ROM incurs error in the solution due to approximation in a lower dimensional subspace. Moreover, ROMs lack robustness in terms of effectiveness over the entire parameter range. Accordingly, often they are classified as local and global, based on their construction in the parametric domain. Availability of an error bound or error estimator of a ROM helps in achieving this robustness, mainly by allowing adaptivity. The goal of this thesis is to propose such error estimators and use them to develop adaptive proper orthogonal decomposition-based ROM for uncertainty quantification. Therefore, two a posteriori error estimators, one for linear and another for nonlinear dynamical system, respectively, are developed based on the residual in the differential equation. To develop an a posteriori error estimator for nonlinear systems, first, an upper bound on the norm of the state transition matrix is derived and then it is used to develop the error estimator. Numerically they are compared with the error estimators available in the current literature. This comparison revealed that the proposed estimators follow the trend of the exact error more closely, thus serving as an improvement over the state-of-the-art. These error estimators are used in conjunction with a greedy search to develop adaptive algorithms for the construction of robust ROM. The adaptively trained ROM is subsequently deployed for uncertainty quantification by invoking it in a statistical simulation. For the linear dynamical system, two algorithms are proposed for building robust ROMs --- one for local, and another for global. For the nonlinear dynamical system, an adaptive algorithm is developed for the global ROM. In the training stage of global ROM, a modification is proposed --- at each iteration of the greedy search, the ROM is trained at a few local maxima in addition to the global maxima of the error estimator --- leading to an accelerated convergence. For this purpose, a multi-frequency vibrational particle swarm optimization is employed. It is shown that the proposed algorithm for adaptive training of ROMs poses ample scope of parallelization. Different numerical studies: (i) bladed disk assembly, (ii) Burgers' equation, and (iii) beam on nonlinear Winkler foundation, are performed to test the efficiency of the error estimators and the accuracy achieved by the modified greedy search. A speed-up of more than two orders of magnitude is achieved using the ROM, trained with the proposed algorithm, and error estimators. However, adaptive training of ROM is also expensive due to multiple evaluations of HDM. To address this issue, a novel random excitation-based training is proposed in this thesis. Accordingly, depending upon the parameter range of interest, bandlimited random white noise excitations are chosen and the ROM is trained from the corresponding responses. This is applied to linear and nonlinear vibrating systems with spatial periodicity and imperfection. From the numerical studies, it is found that the proposed method reduces the cost of training significantly, and successfully captures the behavior such as alternate pass- and stop-bands of vibration propagation, peak response.

Tesis (Lic. en Física)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2017.
¿Qué es lo que lleva a una sociedad a pasar de una situación social estable a un estado convulsionado o caótico? Los mejores ejemplos de esto son los procesos revolucionarios o las crisis económicas argentinas. En este trabajo presentamos un modelo simple en el que se observan transiciones abruptas en la opinión media del sistema dinámico. Consideramos una sociedad formada por agentes con distintos estados de opinión sobre una determinada cuestión. Dichos estados pueden ser modificados debido a dos procesos; una influencia externa (reflexión/propaganda) o por la interacción entre agentes (persuasión). Encontramos que si la dinámica de interacción no es homogénea en los estados de opinión, un pequeño cambio de alguno de los parámetros del modelo lleva a cambios drásticos en es el estado medio de opinión de la sociedad.
What leads a society to move from a stable social state to a troubled or chaotic one? Examples of this are the bank runs, Argentinian economical crisis, Political Crisis, Abrupts changes in the approval of a politician or distrust in the political sectors. To analize this problem we considered an agent based society with different state of opinion that can change their opinion due to two processes; an external influence (propaganda), and by the interaction between agents (persuasion), generated by the dynamical properties of the model.

Neural synchrony in the brain at rest is usually variable and intermittent, thus intervals of predominantly synchronized activity are interrupted by intervals of desynchronized activity. Prior studies suggested that this temporal structure of the weakly synchronous activity might be functionally significant: many short desynchronizations may be functionally different from few long desynchronizations, even if the average synchrony level is the same. In this thesis, we use computational neuroscience methods to investigate the effects of (i) spike-timing dependent plasticity (STDP) and (ii) noise on the temporal patterns of synchronization in a simple model. The model is composed of two conductance-based neurons connected via excitatory unidirectional synapses. In (i) these excitatory synapses are made plastic, in (ii) two different types of noise implementation to model the stochasticity of membrane ion channels is considered. The plasticity results are taken from our recently published article, while the noise results are currently being compiled into a manuscript.

The dynamics of this network is subjected to the time-series analysis methods used in prior experimental studies. We provide numerical evidence that both STDP and channel noise can alter the synchronized dynamics in the network in several ways. This depends on the time scale that plasticity acts on and the intensity of the noise. However, in general, the action of STDP and noise in the simple network considered here is to promote dynamics with short desynchronizations (i.e. dynamics reminiscent of that observed in experimental studies) over dynamics with longer desynchronizations.

Ο στόχος της παρούσας διατριβής είναι η ανάπτυξη μιας νέας κλάσης εξωτερικά εξαρτώμενων στοχαστικών συναρτησιακών μοντέλων για την αναγνώριση (identification) δυναμικών συστημάτων που παρουσιάζουν πολλαπλά σημεία λειτουργίας, τα οποία καθορίζονται από μετρήσιμη εξωτερική μεταβλητή (όπως για παράδειγμα, η θερμοκρασία, η υγρασία, κ.λ.π.). Επιπλέον, στόχος είναι η ανάπτυξη καινοτόμου μεθοδολογίας διάγνωσης (ανίχνευσης, προσδιορισμού και εκτίμησης) βλαβών σε δυναμικά συστήματα βάσει των στοχαστικών συναρτησιακών μοντέλων. Η διατριβή αρχικά πραγματεύεται την ανάπτυξη κατάλληλης μεθοδολογίας που αντιμετωπίζει τα επιμέρους προβλήματα της ανίχνευσης, του προσδιορισμού και της εκτίμησης βλαβών στη σύνθετη περίπτωση όπου η κατασκευή διεγείρεται υπό σεισμική διέγερση. Η αποτίμηση της μεθόδου αποτέλεσε και το έναυσμα για τη διαμόρφωση καινοτόμου μεθοδολογίας, η οποία βασίζεται σε μια νέα κλάση εξωτερικά εξαρτώμενων στοχαστικών συναρτησιακών μοντέλων. Τα μοντέλα αυτά έχουν την ικανότητα να αναπαριστούν, με μεγάλη ακρίβεια, μια κατασκευή για συγκεκριμένο τύπο βλάβης και συνεχές εύρος μεγεθών, χρησιμοποιώντας μοναδική μαθηματική αναπαράσταση παραμετροποιημένη ως προς το μέγεθος της βλάβης. Επισημαίνεται ότι τέτοιου τύπου συναρτησιακά μοντέλα δεν αναφέρονται στην βιβλιογραφία. Οι πιο συγγενείς οικογένειες μοντέλων προέρχονται από τις επιστήμες της στατιστικής και της οικονομετρίας, οι οποίες όμως δεν παρουσιάζουν συναρτησιακή μορφή και δεν μπορούν να καλύψουν συνεχή εύρη τιμών. Εξαιτίας αυτού του γεγονότος στη συνέχεια της διατριβής ορίζεται η νέα κλάση εξωτερικά εξαρτώμενων στοχαστικών Συναρτησιακών (F) μοντέλων Αυτοπαλινδρόμησης (AR) με Εξωγενή (X) είσοδο, των οποίων οι παράμετροι και η διασπορά του θορύβου είναι συναρτήσεις μετρήσιμης εξωτερικής μεταβλητής. Αυτή η συναρτησιακή εξάρτηση δίνει τη σημαντική ικανότητα στη νέα κλάση μοντέλων να μπορούν να χρησιμοποιηθούν: α) για τη δυναμική αναγνώριση συστημάτων με πολλαπλά σημεία λειτουργίας που καθορίζονται από μετρήσιμη εξωτερική μεταβλητή και, β) για την ανίχνευση, τον προσδιορισμό και την εκτίμηση βλαβών σε στοχαστικά δυναμικά συστήματα όπου η εξωτερική μεταβλητή είναι το μέγεθος της βλάβης. Επιπλέον, για τα μοντέλα αυτά αναπτύσσονται κατάλληλες μέθοδοι εκτίμησης των οποίων τα χαρακτηριστικά μελετώνται, και η αποτίμηση τους πραγματοποιείται μέσω προσομοιώσεων Monte Carlo. Στη συνέχεια ορίζεται η νέα κλάση εξωτερικά εξαρτώμενων στοχαστικών Συναρτησιακών (F) μοντέλων Αυτοπαλινδρόμησης (AR) και Κινητού Μέσου Όρου (ΜΑ) με Εξωγενή (X) είσοδο των οποίων επίσης οι παράμετροι και η διασπορά του θορύβου εκφράζονται ως συναρτήσεις μετρήσιμης εξωτερικής μεταβλητής. Τα μοντέλα FARΜΑX προσφέρουν επιπλέον ευελιξία σε σχέση με τα μοντέλα FARX εξαιτίας της εισαγωγής του πολυωνύμου ΜΑ. Για τα μοντέλα αυτά αναπτύσσονται επίσης κατάλληλες μεθοδολογίες εκτίμησης που βασίζονται στη μέγιστη πιθανοφάνεια και στην αρχή του σφάλματος πρόβλεψης. Επιπλέον, διαμορφώνονται δύο ακόμη μέθοδοι εκτίμησης που βασίζονται στην ελαχιστοποίηση του σφάλματος πρόβλεψης μέσω διαδοχικών γραμμικών σταδίων, οι οποίες παρουσιάζουν κάποια πρακτικά πλεονεκτήματα σε σχέση με τις προηγούμενες, μπορούν να συνδυαστούν με αυτές, αλλά απαιτούν την ανάπτυξη κατάλληλης άλγεβρας για τα μοντέλα FARΜΑX. Επίσης, μελετώνται ζητήματα όπως η συνέπεια και η ασυμπτωτική κατανομή της εκτιμήτριας σφάλματος πρόβλεψης. Η αποτίμηση όλων των μεθόδων εκτίμησης πραγματοποιείται μέσω προσομοιώσεων Monte Carlo. Τέλος, στα πλαίσια της παρούσας διατριβής αναπτύσσεται καινοτόμος μεθοδολογία ανίχνευσης, προσδιορισμού και εκτίμησης βλαβών σε δυναμικά συστήματα, η οποία βασίζεται στις νέες κλάσεις στοχαστικών συναρτησιακών μοντέλων των προηγούμενων κεφαλαίων. Η αποτίμηση της μεθοδολογίας πραγματοποιείται μέσω πειραματικής εφαρμογής σε διεθνές πρότυπο σκελετού αεροσκάφους υπό κλίμακα, όπου επιτυγχάνει με μεγάλη ακρίβεια, ανίχνευση, προσδιορισμό και εκτίμηση όλων των τύπων και μεγεθών βλάβης και επιπλέον ξεπερνά δυσκολίες που αντιμετωπίζουν άλλες τεχνικές της βιβλιογραφίας.
The aim of the present dissertation is the development of a new class of externally dependent stochastic functional models for the identification of dynamical systems under multiple operating conditions, which are defined by an external measurable variable (i.e. temperature, humidity, etc). The development of a novel methodology for fault diagnosis (fault detection, identification and estimation) in dynamical systems based upon the stochastic functional models is also an additional aim. The development of a proper method for fault detection, identification and estimation in structures under earthquake excitation is initially achieved. The method’s assessment was the motivation for the development of a novel methodology, which is based upon a new class of externally dependent stochastic functional models. These models are capable of accurately representing a structure for a certain type of fault in a continuous range of magnitudes by using a single mathematical representation parameterized in terms of the fault magnitude. It is noticed that such models are not referred in the literature until now. The most related families of models are found in sciences of statistics and econometrics. These models are mathematical representations without functional form and they are incapable of covering continuous ranges of values. Due to this fact, the new class of externally dependent stochastic Functional (F) AutoRegressive (AR) with eXogenous (X) excitation models, with parameters and innovations variance expressed as functions of a measurable external variable, is defined in the sequel of the dissertation. This functional dependence offers to the new class of models the important advantage of being used for: a) the identification of dynamical systems under multiple operating conditions which are defined by an external measurable variable and, b) fault detection, identification and estimation in stochastic dynamical systems where the external variable is the fault magnitude. Proper methods for FARX estimation are also developed and studied and their assessment is achieved via Monte Carlo simulations. In the following, the new class of externally dependent stochastic Functional (F) AutoRegressive (AR) Moving Average (MA) with eXogenous (X) excitation models, with parameters and innovations variance expressed as functions of a measurable external variable, is defined. The FARMAX models offer extra flexibility due to the MA part. Proper methods for FARMAX estimation, which are based upon the Maximum Likelihood and the Prediction Error principles, are also developed. Two further estimation methods are also formulated which are based upon minimization of the prediction error via successive linear stages. These methods offer some practical advantages comparing with the previous methods, they can be combined with the latter but they require the development of a proper algebra for FARMAX models. Additionally, the consistency and the asymptotic distribution of the prediction error estimator are considered. The assessment of all estimation methods is achieved via Monte Carlo simulations. In the last part of the dissertation a novel methodology for fault detection, identification and estimation in dynamical systems, which is based upon the new class of stochastic functional models of the previous chapters, is developed. The methodology’s assessment is accomplished via an experimental application in a prototype scale aircraft skeleton structure, where it achieves accurate fault detection, identification and estimation of several kinds and magnitudes of faults and also overcomes difficulties that are referred by other methods.