O propósito deste trabalho é estudar a dinâmica assintótica de problemas parabólicos em domínios tipo dumbbell. Para isto primeiro estudaremos a semi-continuidade superior de atratores para problemas parabólicos com condição de fronteira do tipo Neumann homogênea e depois estudaremos a existência de equilíbrios estáveis não-constantes para problemas de reação-difusão com condições de fronteira tipo Neumann não-lineares. / The aim of this work is to study the asymptotic dynamics of parabolic problems in dumbbell type domains. To that end firstly, we study upper semicontinuity of attractors for parabolic problems with homogeneous Neumann boundary conditions and afterwards we study the existence of stable nonconstant equilibria for reaction-diffusion problems with nonlinear Neumann boundary conditions.

Les cellules de lieu de l’hippocampe sont des neurones aux propriétés intrigantes, commele fait que leur activité soit corrélée à la position spatiale de l’animal. Il est généralementconsidéré que ces propriétés peuvent être expliquées en grande partie par les comporte-ments collectifs de modèles schématiques de neurones en interaction. La physique statis-tique fournit des outils permettant l’étude analytique et numérique de ces comportementscollectifs.Nous abordons ici le problème de l’utilisation de ces outils dans le cadre du paradigmedu “réseau attracteur”, une hypothèse théorique sur la nature de la mémoire. La questionest de savoir comment ces méthodes et ce cadre théorique peuvent aider à comprendrel’activité des cellules de lieu. Dans un premier temps, nous proposons un modèle de cellulesde lieu dans lequel la localisation spatiale de l’activité neuronale est le résultat d’unedynamique d’attracteur. Plusieurs aspects des propriétés collectives de ce modèle sontétudiés. La simplicité du modèle permet de les comprendre en profondeur. Le diagrammede phase du modèle est calculé et discuté en comparaison avec des travaux précedents.Du point de vue dynamique, l’évolution du système présente des motifs particulièrementriches. La seconde partie de cette thèse est à propos du décodage de l’activité des cellulesde lieu. Nous nous demandons quelle est l’implication de l’hypothèse des attracteurs surce problème. Nous comparons plusieurs méthodes de décodage et leurs résultats sur letraitement de données expérimentales. / Place cells in the hippocampus are neurons with interesting properties such as the corre-lation between their activity and the animal’s position in space. It is believed that theseproperties can be for the most part understood by collective behaviours of models of inter-acting simplified neurons. Statistical mechanics provides tools permitting to study thesecollective behaviours, both analytically and numerically.Here, we address how these tools can be used to understand place-cell activity withinthe attractor neural network paradigm, a theory for memory. We first propose a modelfor place cells in which the formation of a localized bump of activity is accounted for byattractor dynamics. Several aspects of the collective properties of this model are studied.Thanks to the simplicity of the model, they can be understood in great detail. The phasediagram of the model is computed and discussed in relation with previous works on at-tractor neural networks. The dynamical evolution of the system displays particularly richpatterns. The second part of this thesis deals with decoding place-cell activity, and theimplications of the attractor hypothesis on this problem. We compare several decodingmethods and their results on the processing of experimental recordings of place cells in afreely behaving rat.

The development of drug resistance during treatment is possibly the most important factor hampering the success of cancer therapy. In order to survive in the presence of chemotherapeutic drugs cells must quickly adapt to their altered environment. This may involve a collective stress response of interacting cells, whose mechanism is not yet clear. In the course of this work we interrogated the conceptual framework used to describe cancer and examined different aspects of drug resistance. While the main focus was on the role of ABC transporters in the rapid acquisition of drug resistance following a short period of drug treatment, the long-term adaptation to continuous drug treatment was also studied. As a tangent to this subject, the possible role of endocytosis in the process of adaptation to continuous presence of drug and subsequent resistance was also assessed. Cancer cell populations inexorably develop resistance to therapeutic treatment. In addition to selection of genetic variants, resistance may arise through two possible non-genetic mechanisms, (1) Darwinian selection of cells occupying (non-genetic) resistant microstates, or (2) Lamarckian instruction, in which cells adopt a resistant (treatment) induced phenotype. To examine the relative contribution of these two mechanisms we studied the population dynamics of leukemic cells (HL60 cell line) following treatment with the mitotic inhibitor vincristine. Single-cell analysis and mathematical modelling of state transition kinetics demonstrated that the appearance of multi-drug resistance phenotype within 24h was overwhelmingly the result of instruction. Transcriptome dynamics pointed towards a genome-wide state transition into a stress response state. Resistance induction correlated with Wnt pathway upregulation and was suppressed by beta-catenin knockdown, revealing a new opportunity for early therapeutic intervention against the development of drug resistance. By addressing the adaptation of the cell culture to prolonged drug treatment we observed that the survivor cells mounted a cellular response that neutralised the cytotoxic stress. That response involved the stabilisation of a transcriptome state that confers drug resistance. Our results suggested that the positive correlation between Wnt signalling and ABC transporters expression is important not only for the short-term survival but also for the enduring MDR phenotype. As we explored population heterogeneity we realised that the dead cells might also help the rest of the population to survive. Thus, our results support the need for examining the role of each population fraction, and ultimately each individual cell, in the overall story of cancer adaptation towards multidrug resistance. Subsequently we examined the differential endocytic behaviour between drug-sensitive and drug-resistant cells. By combining confocal time-lapse microscopy with flow cytometry we demonstrated that fluid-phase endocytosis was reduced in the resistant cells. The differences in the endocytic pathway only became noticeable after MDR1 expression has become constitutive, suggesting another protective role of the ABC transporters. All the results obtained support the idea that acquired drug resistance is not simply the passive selection of pre-existing mutants but can be accelerated by active adaptation. Cancer treatment is a double-edge sword: while the weakest cells die, the survivors cope cell-autonomously with the therapeutic perturbation.

In this thesis I present novel mechanisms for certain computational capabilities of the cerebral cortex, building on the established notion of attractor memory. A sparse binary coding network for generating efficient representation of sensory input is presented. It is demonstrated that this network model well reproduces receptive field shapes seen in primary visual cortex and that its representations are efficient with respect to storage in associative memory. I show how an autoassociative memory, augmented with dynamical synapses, can function as a general sequence learning network. I demonstrate how an abstract attractor memory system may be realized on the microcircuit level -- and how it may be analyzed using similar tools as used experimentally. I demonstrate some predictions from the hypothesis that the macroscopic connectivity of the cortex is optimized for attractor memory function. I also discuss methodological aspects of modelling in computational neuroscience. / QC 20101220

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20375号 / 工博第4312号 / 新制||工||1668(附属図書館) / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 山川 宏, 教授 引原 隆士, 准教授 海老原 祐輔 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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Cette thèse est une étude théorique d’un système d’équations de Cahn-Hilliard/Allen-Cahn couplées qui représente un mélange binaire en séparation de phase. Le but principal de l’étude est le comportement asymptotique des solutions en termes d’attracteurs exponentiels/globaux. Pour cette raison, l’existence et l’unicité de la solution sont étudiées tout d’abord. Une des principales applications de ce modèle d’équations est la cristallographie.Dans la première partie de la thèse, on examine le modèle proposé avec des conditions de type Dirichlet sur le bord et une non linéarité régulière de type polynomial : on réussit à trouver un attracteur exponentiel et par conséquence un attracteur global de dimension finie. Une non linéarité singulière de type logarithmique est ensuite prise dans la deuxième partie, cette fonction étant approchée par une suite de fonctions régulières et l’existence d’un attracteur global est démontrée sous des conditions au bord de type Dirichlet.Enfin, dans la dernière partie, le système est couplé avec une équation pour la température: suivant la loi de Fourrier premièrement, puis la loi de type III de la thermo-élasticité. Dans les deux cas, la dynamique de l’équation est étudiée et un attracteur exponentiel est trouvé malgré la difficulté créée par l’équation hyperbolique dans le deuxième cas. / This thesis is a theoretical study of a coupled system of equations of Cahn-Hilliard and Allen-Cahn that represents phase separation of binary alloys. The main goal of this study is to investigate the asymptotic behavior of the solution in terms of exponential/global attractors. For this reason, the existence and unicity of the solution are first studied. One of the most important applications of this proposed model of equations is crystallography. In the first part of the thesis, the system is studied with boundary conditions of Dirichlet type and a regular nonlinearity (a polynomial). There, we prove the existence of an exponential attractor that leads to the existence of a global attractor of finite dimension. Then, a singular nonlinearity (a logarithmic potential) is considered in the second part. This function is approximated by a sequence of regular ones and a global attractor is found.At the end, the system of equations is coupled with temperature: with the Fourrier law in the first case, then with the type III law (in the context of thermoelasticity) in the second case. The dynamics of the equations are studied and the existence of an exponential attractor is obtained.

Cette thèse se situe dans le cadre de l'analyse théorique et numérique de quelques généralisations de l'équation de Cahn-Hilliard. On étudie l'existence, l'unicité et la régularité de la solution de ces modèles ainsi que son comportement asymptotique en terme d'existence d'un attracteur global de dimension fractale finie. La première partie de la thèse concerne des modèles appliqués à la retouche d'images. D'abord, on étudie la dynamique de l'équation de Bertozzi-Esedoglu-Gillette-Cahn-Hilliard avec des conditions de type Neumann sur le bord et une nonlinéarité régulière de type polynomial et on propose un schéma numérique avec une méthode de seuil efficace pour le problème de la retouche et très rapide en terme de temps de convergence. Ensuite, on étudie ce modèle avec des conditions de type Neumann sur le bord et une nonlinéarité singulière de type logarithmique et on donne des simulations numériques avec seuil qui confirment que les résultats obtenus avec une nonlinéarité de type logarithmique sont meilleurs que ceux obtenus avec une nonlinéarité de type polynomial. Finalement, on propose un modèle basé sur le système de Cahn-Hilliard pour la retouche d'images colorées. La deuxième partie de la thèse est consacrée à des applications en biologie et en chimie. On étudie la convergence de la solution d'une généralisation de l'équation de Cahn-Hilliard avec un terme de prolifération, associée à des conditions aux limites de type Neumann et une nonlinéarité régulière. Dans ce cas, on démontre que soit la solution explose en temps fini soit elle existe globalement en temps. Par ailleurs, on donne des simulations numériques qui confirment les résultats théoriques obtenus. On termine par l'étude de l'équation de Cahn-Hilliard avec un terme source et une nonlinéarité régulière. Dans cette étude, on considère le modèle à la fois avec des conditions aux limites de type Neumann et de type Dirichlet. / This thesis is situated in the context of the theoretical and numerical analysis of some generalizations of the Cahn-Hilliard equation. We study the well-possedness of these models, as well as the asymptotic behavior in terms of the existence of finite-dimenstional (in the sense of the fractal dimension) attractors. The first part of this thesis is devoted to some models which, in particular, have applications in image inpainting. We start by the study of the dynamics of the Bertozzi-Esedoglu-Gillette-Cahn-Hilliard equation with Neumann boundary conditions and a regular nonlinearity. We give numerical simulations with a fast numerical scheme with threshold which is sufficient to obtain good inpainting results. Furthermore, we study this model with Neumann boundary conditions and a logarithmic nonlinearity and we also give numerical simulations which confirm that the results obtained with a logarithmic nonlinearity are better than the ones obtained with a polynomial nonlinearity. Finally, we propose a model based on the Cahn-Hilliard system which has applications in color image inpainting. The second part of this thesis is devoted to some models which, in particular, have applications in biology and chemistry. We study the convergence of the solution of a Cahn-Hilliard equation with a proliferation term and associated with Neumann boundary conditions and a regular nonlinearity. In that case, we prove that the solutions blow up in finite time or exist globally in time. Furthermore, we give numericial simulations which confirm the theoritical results. We end with the study of the Cahn-Hilliard equation with a mass source and a regular nonlinearity. In this study, we consider both Neumann and Dirichlet boundary conditions.

In this thesis we will discuss the well-posedness and long-time dynamics of curved beam and thermoelastic plates. First, we considered the Bresse system with nonlinear damping and forcing terms. For this model we show the Timoshenko system as a singular limit of the Bresse system as the arch curvature l goes to 0 and under suitable assumptions on the nonlinearity we prove the existence of a smooth global attractor with finite fractal dimension and exponential attractors as well. We also compare the Bresse system with the Timoshenko system, in the sense of upper-semicontinuity of their attractors as l → 0. Second, we study a full von Karman system, this model accounts for vertical and in plane displacements. For this system we add a nonlinear thermal coupling and free boundary conditions. It is shown that the system, without any mechanical dissipation imposed on vertical displacements, admits a global attractor which is also smooth and of finite fractal dimension. / Neste trabalho iremos discutir a existência, unicidade, dependência contínua e a dinâmica a longo prazo das soluções de um sistema de equações que modela a vibração de vigas curvas e um modelo de placas termoelásticas. Primeiro consideramos o modelo de Bresse com dissipação não linear e forças externas. Provamos que o sistema de Timoshenko pode ser obtido como limite do sistema de Bresse quando o arco de curvatura l tende para zero e sob algumas hipóteses, mostramos a existência de um atrator global com dimensão fractal finita. Também comparamos o sistema de Bresse com o sistema de Timoshenko no sentido da semicontinuidade de seus atratores quando o parâmetro l → 0. Na segunda parte estudamos o sistema de full Von Karmam. Neste modelo adicionamos efeitos térmicos e condições de fronteira do tipo livre. Mostramos que esse problema, sem dissipação mecânica no deslocamento vertical, também possui um atrator global regular com dimensão infinita.