This thesis addresses chemotherapy-induced peripheral neuropathy (CIPN)- a form of pain sensation and a prevalent dose-limiting side-effect of several chemotherapy agents such as vincristine, paclitaxel, and oxaliplatin. These agents are used for treating various cancers such as leukemia, brain tumor, lung cancer. Peripheral neuropathy is a numbing, tingling, and burning sensation felt in the palms and feet, which occurs due to damage to neurons (nerve cells). Prolonged CIPN can impact the quality of life of cancer patients. Occasionally, severe CIPN can result in termination of chemotherapy treatment altogether. Currently, there are no established strategies for treating CIPN due to a lack of understanding of its mechanisms. Moreover, different patients react differently to the same treatment; a subgroup of patient population may never experience CIPN, while another may experience severe CIPN for the same dose. In addition, there are no established strategies for predicting CIPN either. This thesis addresses both prediction and mechanisms of CIPN.<br><br>The following paragraphs reflect the organization of this thesis. Each paragraph introduces a research problem, the approaches taken to investigate it, and states the key results.<br><br>First, a metabolomics-based approach was used to investigate CIPN prediction. Blood samples of pediatric leukemic cancer patients who underwent treatment with a chemotherapy agent - vincristine were provided. These blood samples were analyzed at different treatment time points using mass spectrometry to obtain the metabolite profiles. Machine learning was then employed to identify specific metabolites that can predict overall susceptibility to peripheral neuropathy in those patients at specific treatment time points. Subsequently, selected metabolites were used to train machine learning models to predict neuropathy susceptibility. Finally, the models were deployed into an open-source interactive tool- <i>VIPNp</i>- that can be used by researchers to predict CIPN in new pediatric leukemic cancer patients.<br><br>Second, the focus was shifted to the pathophysiology of pain and the pain-sensing neuron; specifically: (i) investigating pain sensation mutations and the dynamics of the pain-sensing neuron, and (ii) exploring chemotherapy-induced peripheral neuropathy mechanisms. <br><br>While pain is a common experience, genetic mutations in individuals can alter their experience of pain, if any at all (certain mutations yield individuals insensitive to pain). Despite its ubiquity, we do not have a complete understanding of the onset and/or mechanisms of pain sensation. Pain sensation can be broadly classified into three types: (i) nociceptive, (ii) neuropathic, and (iii) inflammatory. Nociceptive pain arises due to a noxious external stimulus (e.g., upon touching a hot object). Neuropathic pain (which is felt as a side-effect of the aforementioned chemotherapy agents) is the numbing and tingling sensation due to nerve damage. Inflammatory pain occurs due to damage to internal tissues. Pain in any form can be characterized in terms of electrical signaling by the pain-sensing neuron. Signal transmission regarding pain occurs through generation of an electrical signal called the action potential- a peak in neuron membrane potential. Excessive firing of action potentials by a pain-sensing neuron indicates pain of a specific form and intensity. In order to investigate this electrical signaling, a mathematical modeling approach was employed. The neuron membrane was assumed to be an electrical circuit and the potential across the membrane was modeled in terms of the sodium and potassium ions flowing across it via voltage-gated sodium and potassium channels, respectively. Generation of a single action potential followed by a resting state corresponds to a normal state, whereas periodic firing of action potentials (an oscillatory state) corresponds to pain of some form and intensity <i>in vitro</i>. Therefore, an investigation into the switch from a resting state to an oscillatory state was proposed. A bifurcation theory approach (generally useful in exploring changes in qualitative behavior of a model) was used to explore possible bifurcations to explain this switch. Firstly, genetic mutations that can shift the pain sensation threshold in the pain-sensing neuron were explored. The detected bifurcation points were found to be sensitive to specific sodium channels’ model parameters, implying sodium channels’ sensitivity towards the pain sensation threshold. This was corroborated by experimental evidence in existing literature. Secondly, a theoretical analysis was performed to explore all possible bifurcations that can explain the dynamics of this pain-sensing neuron model. The mathematical modeling simulations revealed a mixture of small amplitude and large amplitude membrane potential oscillations (mixed-mode oscillations) for specific parameter values. The onset and disappearance of the oscillations were investigated. Model simulations further demonstrated that the mixed-mode oscillations solutions belonged to Farey sequences. Furthermore, regions of bistability- where stable steady state and periodic solutions coexisted- were explored. Additionally, chaotic behavior was observed for specific model parameters.<br><br>Finally, this thesis investigated the role of voltage-gated ion channels in inducing CIPN using the same mathematical model. Repetitive firing of action potentials in the absence of any external stimulus was used as an indicator of peripheral neuropathy. Bifurcation analysis revealed that specific sodium and potassium conductances can induce repetitive firing without any external stimulus. The findings were supplemented by recording the firing rate of a sensory neuron culture. Next, a chemotherapy agent - paclitaxel, was introduced in the model to investigate its potential effects on the firing behavior. It was seen that a medium dose of paclitaxel increased repetitive firing. This was supported by the firing rate recordings of the sensory neuron culture.<br><br>In summary, this thesis presents a prediction strategy for CIPN. Moreover, it presents a bifurcation theory-based framework that can be used to investigate pain sensation, in particular, genetic mutations related to pain sensation and chemotherapy-induced peripheral neuropathy. This framework can be used to find potential voltage-gated ion channels that can be targeted to control the pain sensation threshold in individuals, and can be extended to investigate various degeneracies in CIPN mechanisms to find therapeutic cures for it.

Dans cette thèse, nous avons étudié le problème de l'estimation de mouvement chez les mammifères et nous proposons que passer à l’échelle des modèles ancrés dans la biologie pour les applications du monde réel peut nous donner de nouvelles perspectives en vision biologique. En utilisant un modèle classique qui décrit l'activité des neurones dans les aires corticales V1 et MT du cerveau des primates, nous avons proposé une architecture montante pour l'estimation de mouvement et l’avons évaluée sur des exemples de référence de vision par ordinateur (une première pour ce type de modèles), révélant des lacunes telles que le manque de sélectivité au niveau des frontières de mouvement et l'absence d'association spatiale du champ de vitesses. Pour y remédier, nous avons proposé deux extensions, une stratégie d’intégration modulée par la forme pour minimiser les erreurs aux discontinuités de texture et un schéma de régression pour le décodage. Ces extensions ont amélioré la précision de l'estimation, mais aussi souligné à nouveau le débat sur le rôle des différents types de cellules dans le codage mouvement, par exemple le rôle relatif des cellules “pattern” par rapport aux cellules “component”. Pour comprendre cela, nous avons utilisé un modèle de champs neuronaux représentant une population de cellules MT pour comprendre le rôle des récurrences. Nos résultats montrent qu'une variété de comportements peuvent être reproduits, ils expliquent les changements dynamiques en fonction des stimuli, et nous conduisent à remettre en cause les régimes élevés d'inhibition généralement choisis dans la littérature. / In this thesis, we studied the problem of motion estimation in mammals and propose that scaling up models rooted in biology for real world applications can give us fresh insights into the biological vision. Using a classic model that describes the activity of directionally-selective neurons in V1 and MT areas of macaque brain, we proposed a feedforward V1-MT architecture for motion estimation and benchmarked it on computer vision datasets (first publicly available evaluation for this kind of models), revealing interesting shortcomings such as lack of selectivity at motion boundaries and lack of spatial association of the flow field. To address these, we proposed two extensions, a form modulated pooling strategy to minimize errors at texture boundaries and a regression based decoding scheme. These extensions improved estimation accuracy but also reemphasized the debate about the role of different cell types (characterized by their tuning curves) in encoding motion, for example relative role of pattern cells versus component cells. To understand this, we used a phenomenological neural fields model representative of a population of directionally tuned MT cells to check whether different tuning behaviors could be reproduced by a recurrently interacting population or if we need different types of cells explicitly. Our results indicated that a variety of tuning behavior can be reproduced by a minimal network, explaining dynamical changes in the tuning with change of stimuli leading us to question the high inhibition regimes typically considered by models in the literature.

Applications of distributed-power systems are on the rise. They are already used in telecommunication power supplies, aircraft and shipboard power-distribution systems, motor drives, plasma applications, and they are being considered for numerous other applications. The successful operation of these multi-converter systems relies heavily on a stable design. Conventional analyses of power converters are based on averaged models, which ignore the fast-scale instability and analyze the stability on a reduced-order manifold. As such, validity of the averaged models varies with the switching frequency even for the same topological structure. The prevalent procedure for analyzing the stability of switching converters is based on linearized smooth averaged (small-signal) models. Yet there are systems (in active use) that yield a non-smooth averaged model. Even for systems for which smooth averaged models are realizable, small-signal analyses of the nominal solution/orbit do not provide anything about three important characteristics: region of attraction of the nominal solution, dependence of the converter dynamics on the initial conditions of the states, and the post-instability dynamics. As such, converters designed based on small-signal analyses may be conservative. In addition, linear controllers based on such analysis may not be robust and optimal. Clearly, there is a need to analyze the stability of power converters from a different perspective and design nonlinear controllers for such hybrid systems. In this Dissertation, using bifurcation analysis and Lyapunov's method, we analyze the stability and dynamics of some of the building blocks of distributed-power systems, namely standalone, integrated, and parallel converters. Using analytical and experimental results, we show some of the differences between the conventional and new approaches for stability analyses of switching converters and demonstrate the shortcomings of some of the existing results. Furthermore, using nonlinear analyses we attempt to answer three fundamental questions: when does an instability occur, what is the mechanism of the instability, and what happens after the instability? Subsequently, we develop nonlinear controllers to stabilize parallel dc-dc and parallel multi-phase converters. The proposed controllers for parallel dc-dc converters combine the concepts of multiple-sliding-surface and integral-variable-structure control. They are easy to design, robust, and have good transient and steady-state performances. Furthermore, they achieve a constant switching frequency within the boundary layer and hence can be operated in interleaving or synchronicity modes. The controllers developed for parallel multi-phase converters retain many of the above features. In addition, they do not require any communication between the modules; as such, they have high redundancy. One of these control schemes combines space-vector modulation and variable-structure control. It achieves constant switching frequency within the boundary layer and a good compromise between the transient and steady-state performances. / Ph. D.

Cette thèse a pour objectif principal de développer un outil numérique capable de prédire la ductilité des matériaux polycristallins. Cet outil est basé sur le couplage de l’approche multi-échelles autocohérente à deux critères d’instabilités plastiques : la théorie de bifurcation et l’approche d’imperfection initiale. Le schéma autocohérent est utilisé pour déterminer le comportement d’un agrégat polycristallin (supposé représentatif du matériau étudié) à partir du comportement des monocristaux constitutifs. Le comportement à l’échelle monocristalline est formulé dans le cadre des grandes déformations élastoplastiques. Deux différentes versions du critère de Schmid sont successivement utilisées pour modéliser l’écoulement plastique monocristallin : la version classique et une version régularisée. Pour intégrer numériquement les équations constitutives à l’échelle monocristalline, deux algorithmes ont été développés : un algorithme de type évolutif et un algorithme de type retour radial. Les équations gouvernant le schéma autocohérent ont été revisitées. Pour résoudre ces équations, un nouvel algorithme numérique a été proposé, qui est montré être plus efficace que les algorithmes existants communément basés sur la méthode du point fixe. De plus, une approche numérique robuste a été développée, qui permet de coupler le modèle autocohérent à l’approche d’imperfection initiale. La performance ainsi que la robustesse des différents algorithmes et schémas numériques développés ont été mis en évidence à travers plusieurs résultats de simulation. L’effet de plusieurs paramètres et choix de modélisation sur la prédiction de formabilité des tôles métalliques a été extensivement analysé. / The main objective of this PhD thesis is to develop a numerical tool capable of predicting the ductility of polycrystalline materials. This tool is based on the coupling of the self-consistent multiscale approach with two plastic instability criteria: the bifurcation theory and the initial imperfection approach. The self-consistent scheme is used to derive the mechanical behavior of a polycrystalline aggregate (assumed to be representative of the studied material) from that of its microscopic constituents (the single crystals). The constitutive framework at the single crystal scale follows a finite strain rate-independent formulation. Two different versions of the Schmid law are successively used to model the plastic flow: the classical version and a regularized one. To solve the constitutive equations at the single crystal scale, two numerical algorithms have been developed: one is based on the usual return-mapping scheme and the other on the so-called ultimate scheme. The equations governing the self-consistent approach have been revisited. To solve these equations, a new numerical scheme has been developed, which is shown to be more efficient than the existing schemes commonly based on the fixed point method. Also, a robust numerical approach has been developed to couple the self-consistent model to the initial imperfection approach. The performance and the robustness of the different numerical schemes and algorithms developed have been highlighted through several simulation results. The impact of various parameters and modeling choices on the formability prediction of sheet metals has been extensively analyzed.

Cette thèse a pour sujet les effets que l’information a sur les incitations. Les trois articles fournissent et explorent des résultats lorsque l’information est la principale variable d’intérêt, est endogène, pas homogène entre les acteurs et évolue dans le temps d’une manière qui n’est pas nécessairement rationnelle. Le premier article étudie les problèmes de hold-up dans les hiérarchies verticales avec la sélection adverse montrant qu’alors que le pouvoir de négociation des travailleurs augmente, les distorsions provenant de l’asymétrie d’information disparaissent. En outre, il étudie l’effet de la scolarité et du degré d’hétérogénéité de la population de travailleurs sur la répartition du pouvoir de négociation dans les marchés réglementés. Le deuxième article assouplit l’hypothèse des croyances homogènes dans les relations principal-agent avec sélection adverse. Dans un apprentissage évolutif qui est imitatif, les principaux peuvent avoir des croyances différentes sur la répartition des types d’agents dans la population. La convergence à une croyance uniforme dépend de la taille relative de la polarisation dans les croyances. En outre, le modèle est une version d’un cobweb stable. Notre approche offre des explications pour l’alternance des périodes avec quantité oscillante et relativement stable. Le troisième article étudie la fac¸on dont le contenu informatif des politiques juridiques, comme la responsabilité stricte et négligence, en cas de soucis morales, influence la conception optimale des régimes de responsabilité. Plusieurs cas récents ont montré qu’un individu ayant causé un dommage s’expose non seulement a une sanction légale — par exemple, une amende — mais aussi a un boycott social, la désapprobation ou la stigmatisation. L’article montre que le choix d’une stratégie dépend de façon complexe de l’importance du dommage et du “coût moral”. / This thesis focuses on the effects that information has on incentives. The three papers provide and explore some results when the information is the main variable of interest, it is made endogenous, not homogeneous between actors and evolving over time in a way that is not necessarily rational. The first paper studies hold-up problems in vertical hierarchies with adverse selection showing that as the bargaining power of the worker increases, distortions coming from asymmetric information vanish. Moreover, it studies the effect of schooling and degree of heterogeneity in the workforce on the allocation of bargaining power in regulating markets. The second paper relaxes the common assumption of homogeneous beliefs in principal-agent relationships with adverse selection. In an evolutionary learning set-up, which is imitative, principals can have different beliefs about the distribution of agents’ types in the population. Convergence to a uniform belief depends on the relative size of the bias in beliefs. In addition, the set-up is a version of a stable cobweb model. Our approach offers explanations for alternating periods of oscillating and relatively steady quantity. The third paper studies how the informative content of legal policies as strict-liability and fault-based, in case of moral concerns, influences the optimal design of liability regimes. Many recent cases show that an individual found to have caused harm faces not only the possibility of a legal sanction — e.g., the damages he must pay — but also social boycott, disapproval or stigma. The paper shows that the choice of a policy depends in a complex way on the magnitude of the harm and the “moral cost”.Keywords: Bargaining, Adverse Selection, Hold-up, Evolutionary Game Theory, Heterogeneous Beliefs, Bifurcation Theory, Boycott, Law Enforcement, Strict Liability, Negligence.

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Cette thèse présente quelques contributions à l'étude qualitative de solutions d'équations aux dérivées partielles non linéaires dans des modèles issus de l'optique et de la mécanique des fluides. Nous nous intéressons plus précisément à l'existence de solutions et à leur stabilité temporelle. Le Chapitre 1 est consacré à l'équation de Lugiato-Lefever, qui est une variante de l'équation de Schrödinger non linéaire et qui a été dérivée dans plusieurs contextes en optique. En utilisant des outils de la théorie des bifurcations et des formes normales, nous procédons à une étude systématique des solutions stationnaires de cette équation, et prouvons l'existence de solutions périodiques et localisées. Dans le Chapitre 2, nous présentons un critère simple d'instabilité linéaire pour des ondes non linéaires. Nous appliquons ce résultat aux équations de Lugiato-Lefever, de Kadomtsev-Petviashvili-I et de Davey-Stewartson. Ces deux dernières équations sont des équations modèles dérivées en mécanique des fluides. Dans le Chapitre 3, nous montrons un critère d'instabilité linéaire pour des solutions périodiques de petite amplitude, par rapport à certaines perturbations quasipériodiques. Ce résultat est ensuite appliqué à l'équation de Lugiato-Lefever. / In this thesis we present several contributions to qualitative study of solutions of nonlinear partial differential equations in optics and fluid mechanics models. More precisely, we focus on the existence of solutions and their stability properties. In Chapter 1, we study the Lugiato-lefever equation, which is a variant of the nonlinear Schrödinger equation arising in sereval contexts in nonlinear optics. Using tools from bifurcation and normal forms theory, we perfom a systematic analysis of stationary solutions of this equation and prove the existence of periodic and localized solutions. In Chapter 2, we present a simple criterion for linear instability of nonlinear waves. We then apply this result to the Lugiato-Lefever equation, to the Kadomtsev-Petviashvili-I equation and the Davey-Stewartson equations. These last two equations are model equations arising in fluid mechanics. In Chapter 3, we prove a criterion for linear instability of periodic solutions with small amplitude, with respect to certain quasiperiodic perturbations. This result is then applied to the Lugiato-Lefever equation.

Este trabalho apresenta um estudo sobre o método da continuação aplicado ao problema de fluxo de potência. Definições e conceitos de estabilidade de tensão são descritos de forma a explicitar as diferenças e semelhanças existentes com relação ao estudo de máximo carregamento em sistemas de energia elétrica. Uma síntese da teoria da bifurcação aborda sua importância em estudos de colapso de tensão. É proposta uma técnica de controle do tamanho do passo para o método da continuação com o objetivo de determinar o ponto de máximo carregamento (PMC) sem a necessidade de especificar, por meio do usuário, um valor para o tamanho inicial do passo. Os resultados dos estudos realizados em sistemas testes do IEEE (14, 30, 57 e 118 barras) mostram a aplicação do método da continuação convencional e de sua associação à técnica de controle do tamanho do passo. / This work presents a research about the continuation method applied to the power flow problem. Voltage stability definitions and concepts are described in a way to highlight and point out the differences and the similarities among several methods used to determine the maximum loading of electrical power systems. A short description of the bifurcation theory is also presented in order to show its importance to the voltage collapse studies. A technique based on automatically controlling the step size is proposed as an innovation of the continuation method. The objective of this technique is to determine the maximum loading point without the traditional need of asking the user for the initial step size. The results compare the performance between the conventional and the new method. These methods are analyzed using IEEE test systems (14, 30, 57 and 118-bus).

Prédire la statistique des grandes échelles des écoulements turbulents constitue un enjeu important. Pour l'équation d'Euler 2D et des modèles analogues d'écoulements géophysiques, une auto-organisation est observée (formation de cyclones/anticyclones, jets intenses). La mécanique statistique d'équilibre des écoulements bidimensionnels s'est avérée fondamentale et pertinente même en présence de forçage et dissipation, dans la limite inertielle. La thèse est motivée par le phénomène de transitions aléatoires entre deux topologies différentes, lié à une bistabilité. Il s'agit de prédire la multiplicité des équilibres d'un écoulement (quasi) bidimensionnel. On développe une classification des transitions de phase, pour des équilibres (statistiques et/ou dynamiques) d'un tel écoulement. Les diagrammes de phase font apparaître la présence générique de points critiques et tricritiques, et des domaines d'inéquivalence d'ensembles statistiques. Dans le cas d'une géométrie annulaire, on décrit les effets de la topographie et de la conservation de deux circulations. Des analogies avec la bistabilité du courant océanique Kuroshio sont proposées à partir de cette étude académique. Enfin, pour le système Euler 2D, on détaille un résultat de mécanique statistique dans l'ensemble énergie-enstrophie : la distribution microcanonique, construite à partir du théorème de Liouville en dimension finie, correspond à la maximisation d'une entropie de mélange de la vorticité. / A most challenging problem in turbulence is to predict the statistics of flows at the large scales. In the case of the 2D Euler equation and analogous models for geophysical flows, the flow is observed to self-organize: cyclones/anticyclones and intense jets form. Equilibrium statistical mechanics has proven to be fundamental and relevant even in the presence of forcing and dissipation, in the inertial limit. The thesis is motivated by the phenomenon of random transitions between two different topologies. This phenomenon implies bistability. The goal is to predict the multiplicity of equilibria for a (quasi) two-dimensional flow. We develop a classification of phase transitions for the (statistical and/or dynamical) equilibria of this flow. Phase diagrams show critical and tricritical points as well as domains of statistical ensemble inequivalence, all this generically. In the case of an annular geometry, the effects of topography and of conserving two circulations are described. Analogies between the bistability of the ocean current Kuroshio and this academic study are suggested. Lastly, for the 2D Euler system, a statistical-mechanical result in the energy-enstrophy ensemble is detailed: the microcanonical distribution, constructed from Liouville's theorem in finite dimension, corresponds to the maximization of a vorticity-mixing entropy.

The purpose of this thesis was to examine a partial differential equation to model the Tacoma Narrows bridge failure. This thesis will examine the equation developed by Lazer and McKenna to model a suspension bridge in no wind.