La modélisation du transport cytosquelettique contribue d'une part à la compréhension de phénomènes biologiques complexes associés à des fonctionnalités cellulaires vitales.D'autre part, cette approche adresse de nouvelles réflexions en physique fondamentale du transport dirigé d'un gaz de particules, en interactions de volume exclu, et hors équilibre thermodynamique.L'étude proposée est basée sur le modèle Totally Asymmetric Simple Exclusion Process (TASEP), traité en champ moyen, et dont les résultats sont comparés à des simulations de type Monte Carlo.En considérant que le transport sur l'ensemble du réseau cytosquelettique peut être régulé aux jonctions, on se focalise sur des motifs architecturaux simples, autour d'une jonction, à laquelle on s'intéresse à la régulation du transport par des effets cinétiques et topologiques.Ainsi, on construit une méthodologie de calcul analytique et numérique, motivée par des configurations de transport observées expérimentalement.L'analyse des caractéristiques cinétiques et topologiques aux croisements des filaments du cytosquelette, pour des situations de transport pourtant très différentes, conduit à formuler les mêmes modèles génériques.Notre travail apporte également un éclairage sur l'effet des moyennes sur les protofilaments au croisement de deux microtubules, qui est inhérent aux limites de résolution de l'imagerie expérimentale actuelle.La double approche, analytique et numérique, sur des modèles génériques ouvre de nombreuses perspectives, nous disposons notamment de tous les outils pour aborder le transport à un croisement plus réaliste de deux microtubules, en prenant en compte la connectivité à la jonction des treize protofilaments typiques, et la cinétique particulière des protéines motrices sur chacun d'eux. / Cytoskeletal transport modeling contributes to the understanding of complex biological phenomena that are associated to vital cell functions.In addition, this approach addresses new questions in fundamental physics related to the transport of a gas of particles, interacting by excluded volume, and out of equilibrium transport.The study is based on the Totally Asymmetric Simple Exclusion Process (TASEP) model, treated in a mean field approach, and the results are compared to Monte Carlo simulations.Considering that the transport on the whole network can be regulated at junctions, we focus on simple patterns with one junction, and we investigate the regulation of transport due to the local kinetics and topology.We build up an analytical and numerical methodology of calculation motivated by experimentally observed structures.The analysis of kinetic and topological characteristics at the crossings of filaments, even in very distinct situations, can lead to the same generic models.Our work also provides insights into the effects of averaging on protofilaments at crossing microtubules, as it is inherent to current imaging experiments.The double approach, analytical and numerical, on generic models, opens many prospects.Notably, we have at our disposal the tools to investigate transport through a more realistic crossing of two typical microtubules with thirteen protofilaments each, and to deal with the particular kinetics of motor proteins on these filaments.

Dans cette thèse, nous discutons l'influence d'un réseau qui possède une topologie non triviale sur les propriétés collectives d'un modèle hamiltonien pour spins,le modèle $XY$, défini sur ces réseaux.Nous nous concentrons d'abord sur la topologie des chaînes régulières et du réseau Petit Monde (Small World), créé avec le modèle Watt- Strogatz.Nous contrôlons ces réseaux par deux paramètres $\gamma$, pour le nombre d' interactions et $p$, la probabilité de ré-attacher un lien aléatoirement.On définit deux mesures, le chemin moyen $\ell$ et la connectivité $C$ et nous analysons leur dépendance de $(\gamma,p)$.Ensuite,nous considérons le comportement du modèle $XY$ sur la chaîne régulière et nous trouvons deux régimes: un pour $\gamma<1,5$,qui ne présente pas d'ordre longue portée et un pour $\gamma>1,5$ où une transition de phase du second ordre apparaît.Nous observons l'existence d'un état ​​métastable pour $\gamma_ {c} = 1,5$. Sur les réseaux Petit Monde,nous illustrons les conditions pour avoir une transition et comment son énergie critique $\varepsilon_{c}(\gamma,p)$ dépend des paramètres $(\gammap$).Enfin,nous proposons un modèle de réseau où les liens d'une chaîne régulière sont ré-attachés aléatoirement avec une probabilité $p$ dans un rayon spécifique $r$. Nous identifions la dimension du réseau $d(p,r)$ comme un paramètre crucial:en le variant,il nous est possible de passer de réseaux avec $d<2$ qui ne présentent pas de transition de phase à des configurations avec $d>2$ présentant une transition de phase du second ordre, en passant par des régimes de dimension $d=2$ qui présentent des états caractérisés par une susceptibilité infinie et une dynamique chaotique. / In this thesis we discuss the influence of a non trivial network topology on the collective properties of an Hamiltonian model defined on it, the $XY$ -rotors model. We first focus on networks topology analysis, considering the regular chain and a Small World network, created with the Watt-Strogatz model. We parametrize these topologies via $\gamma$, giving the vertex degree and $p$, the probability of rewiring. We then define two topological parameters, the average path length $\ell$and the connectivity $C$ and we analize their dependence on $\gamma$ and $p$. Secondly, we consider the behavior of the $XY$- model on the regular chain and we find two regimes: one for $\gamma<1.5$, which does not display any long-range order and one for $\gamma>1.5$ in which a second order phase transition of the magnetization arises. Moreover we observe the existence of a metastable state appearing for $\gamma_{c}=1.5$. Finally we illustrate in what conditions we retrieve the phase transition on Small World networks and how its critical energy $\varepsilon_{c}(\gamma,p)$ depends on the topological parameters $\gamma$ and $p$. In the last part, we propose a network model in which links of a regular chain are rewired according to a probability $p$ within a specific range $r$. We identify a quantity, the network dimension $d(p,r)$ as a crucial parameter. Varying this dimension we are able to cross over from topologies with $d<2$ exhibiting no phase transitions to ones with $d>2$ displaying a second order phase transition, passing by topologies with dimension $d=2$ which exhibit states characterized by infinite susceptibility and macroscopic chaotic dynamical behavior.

A emergência de fenômenos coletivos e correlações de longo alcance impossibilitam a inferência de propriedades de sistemas como um todo a partir de suas partes componentes. A modelagem destes sistemas frequentemente ocorre mediante emprego de operadores de spin localizados em grafos com topologias não-triviais. Aqui, mostramos que o operador de momento angular de muitos corpos une o estudo de diversos sistemas complexos, desde a sistemas epidêmicos até cadeias magnéticas de spin. Para o modelo epidêmico SIS, determinamos a matriz de transição do processo estocástico correspondente e mostramos suas soluções para grafos regulares e aleatórios, por meio de técnicas geralmente empregadas em sistemas fortemente correlacionados. Já no modelo de Dicke, identificamos o vínculo que explica a relevância e o efeito finito de operadores anti-girantes para duas espécies atômicas confinadas numa cavidade óptica que interagem com radiação eletromagnética. Por fim, o papel do momento angular também é identificado para duas cadeias quânticas de spin 1/2 acopladas, as quais modelam nanoestruturas magnéticas heterogêneas. A estrutura de bandas é calculada, enquanto efeitos espúrios de superfície são removidos pela introdução de quasipartículas dotadas de grau de liberdade de spin adicional / The emergence of collective phenomena and long range correlations makes it impossible to infer the properties of whole systems from their components. Their modeling often occurs through the use of localized spin operators, taking place within graphs with non-trivial topologies. Here, we show that the many-body angular momentum operator connects the study of several complex systems, ranging from epidemic systems to magnetic spinchains. For the SIS epidemic model, we calculate the transition matrix of the corresponding stochastic process and show the corresponding solutions for regular and random graphs, using techniques generally employed in strongly correlated systems. For the Dicke model we identify the constraint that explains the relevance and finite size effect of anti-rotating operators, for two atomic species, confined within an optical cavity, and interacting with electromagnetic radiation. Finally, the role of angular momentum is also identified for two coupled quantum spinchains 1/2 which model heterogeneous magnetic nanostructures. The band structure is calculated, while spurious surface effects are removed due to the introduction of quasiparticles with an additional spin degree of freedom.

Este estudo tem como finalidade principal a análise termodinâmica e estatística de proteínas através de modelos mínimos. Uma proteína é um polímero de aminoácidos, cuja função está essencialmente relacionada às conformações espaciais que ela adota em solução aquosa. Na forma funcional (dita nativa), essas conformações flutuam levemente em torno de um mínimo de energia-livre. O processo pelo qual uma cadeia protéica transita de estados não-nativos para a estrutura nativa é chamado de enovelamento, ou dobramento. Uma questão em aberto no campo de estudo de proteínas consiste justamente em entender a fundo o processo de enovelamento, cujo avanço tem um vasto potencial de aplicação, desde a predição de estruturas a partir de sequências de aminoácidos até o planejamento de fármacos e moléculas bioativas. Nossa investigação teórica procura abordar aspectos do enovelamento expressos através de grandezas termodinâmicas (energia média, calor específico, número de ligações de hidrogênio, entre outras) derivadas de modelos estatísticos na rede. Assim, num primeiro momento, analisamos o chamado modelo HP, ora por meio de enumeração exata, para cadeias curtas, ora por simulações de Monte Carlo, para cadeias maiores. No primeiro caso, propusemos a existência de uma relação entre a ocorrência de um segundo pico no calor específico associado na literatura à transição de congelamento com uma drástica redução no número de configurações entre os primeiros estados excitados e aqueles de menor energia. Observamos, também, que esse pico pode aparecer tanto para homopolímeros quanto para heteropolímeros, em ambas as redes quadrada e triangular. Num segundo momento, nosso enfoque se voltou para a inclusão de um solvente aquoso (dado pelo modelo de Bell-Lavis) ao sistema inicial. Isso nos possibilitou verificar, usando exclusivamente simulações de Monte Carlo e o algoritmo de Metropolis, o comportamento e a competição das ligações de hidrogênio água-água, água-proteína, proteína-proteína e na primeira camada de solvatação. O modelo acoplado exibiu algumas características do enovelamento, como o colapso hidrofóbico e a separação de monômeros (apolares no núcleo e polares na superfície), embora não capture a desnaturação fria. No apêndice, adicionamos algumas propostas para realização do cálculo numérico da pressão no ensemble canônico, desenvolvidas em paralelo ao projeto principal desta dissertação, mas que, numa primeira análise, verificamos serem consistentes e passíveis de futuros desdobramentos. / The finality of this study is to analyse proteins thermodynamics and statistics through minimal models. A protein is a polymer of amino acids, whose spatial conformations in aqueous solution determine its function. In the functional form (said native), those conformations fluctuates slightly around a free-energy minimum. The process by which a protein chain passes from non-native states to a stable native structure is called protein folding. An open question in the field of protein studies is to understand more deeply the folding process, whose advance can find a wide range of potential applications, since ab initio structure prediction from the amino acids sequence to biomolecules design. The theoretical approaches used here focus on aspects of protein folding given by some thermodynamic quantities (as mean energy, specific heat, number of hydrogen bonds and so on) obtained from statistical lattice models. Initially, we analyse the so-called HP model, at first using exact enumeration for short chains, then by Monte Carlo simulations for longer chains. In the first case, we propose a correlation between the occurrence of a second peak in the specific heat associated in the literature with a freezing transition and a sharp reduction on the number of configurations from the first excited states to the lowest energy states. In addition, we observe that this peak may appear to both homopolymers and heteropolymers on square and triangular lattices. At a second moment, our focus turned to the introduction of a water-like solvent (Bell-Lavis model) to the initial system. This allowed us to verify, exclusively by means of Monte Carlo simulations with Metropolis algorithm, the behavior and competition of hydrogen bonds between water-water molecules, water-protein, and protein-protein monomers and at the first hydration layer. The combined model showed some classical folding properties, as hydrophobic collapse and monomers segregation (apolar residues at the core and polar residues at the surface), although it did not capture cold denaturation. We have included in the appendix some proposals to perform numerical calculations of the canonical pressure, which were developed alongside the main subject of this thesis and a first analysis has proved to be consistent and susceptible to further developments.

Computer simulations of the growth of binary alloy thin films in two and three dimensions were performed using an extension of the Solid on Solid model. Snapshots for a range of interactions and diffusion rates are presented and critically compared to experiment. A wide variety of distinct phases is identified and their growth conditions analyzed. These findings are summarized in a phase diagram. In addition, a fractal analysis of the domains is performed. It is found that for negative interactions the islands are two-dimensional, while for positive interactions, regardless of diffusion rate, a fractal dimension of 1.78 is obtained. / by Mark R. Bouwens. / Thesis (Ph.D.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.

The main objective of this thesis is to simulate, evaluate and discuss several methods for pricing European-style options. The Black-Scholes model has long been considered the standard method for pricing options. One of the downfalls of the Black-Scholes model is that it is strictly continuous and does not incorporate discrete jumps. This thesis will consider two alternate Levy models that include discretized jumps; The Merton Jump Diffusion and Kou's Double Exponential Jump Diffusion. We will use each of the three models to price real world stock data through software simulations and explore the results.Keywords: Levy Processes, Brownian motion, Option pricing, Simulation, Black-Scholes, Merton Jump Diffusion, Kou, Kou's Double Exponential Jump Diffusion. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2013.

Complex communities of microbes act collectively to regulate human health, provide sources of clean energy, and ripen aromatic cheese. The efficient functioning of these communities can be directly related to competitive and cooperative interactions between species. Physical constraints and local environment affect the stability of these interactions. Here we explore the role of spatial habitat and interaction networks in microbial ecology and human disease. In the first part of the dissertation, we model mutualism to understand how spatial microbial communities survive number fluctuations in physical habitats. We explicitly account for the production, consumption, and diffusion of public goods in a two-species microbial community. We show that increased sharing of nutrients breaks down coexistence, and that species may benefit from making slower-diffusing nutrients. In multi-species communities, indirect and higher order interactions may affect community function. We find that the requirement for spatial proximity severely restricts the network of possible microbial interactions. While cooperation between two species is stable, higher-order mutualism requiring three or more species succumbs easily to number fluctuations. Additional cyclic or reciprocal interactions between pairs can stabilize multi-species communities. Inter-species interactions also affect human health via the human microbiome: microbial communities in the gut, lungs and skin. In the second part of the dissertation, we use machine learning and statistics to establish links between microbiota abundance and composition, and the incidence of chronic diseases. We study the gut fungal profile to probe the effects of diet and fungal dysbiosis in a cohort of Saudi children with Crohn's disease. While statistical microbiome studies established that each disease phenotype is associated with a distinct state of intestinal dysbiosis, they often produced conflicting results and identified a very large number of microbes associated with disease. We show that a handful of taxa could drive the dynamics of ecosystem-level abundance changes due to strong inter-species interactions. Using maximum entropy methods, we propose a simple statistical approach (Direct Association Analysis or DAA) to account for interspecific interactions. When applied to the largest dataset on IBD, DAA detects a small subset of associations directly linked to the disease, avoids p-value inflation and identifies most predictive features of the microbiome.

Wong Yuk Chun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 71-74). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgments --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.2 / Chapter 1.2 --- The Scope of the Project --- p.2 / Chapter 1.3 --- An Outline of the Thesis --- p.3 / Chapter 2 --- Related Work --- p.5 / Chapter 2.1 --- Percolation Effect --- p.5 / Chapter 2.2 --- Percolation Models --- p.6 / Chapter 2.2.1 --- Site Percolation --- p.6 / Chapter 2.2.2 --- Bond Percolation --- p.8 / Chapter 2.3 --- Simulated Annealing --- p.8 / Chapter 3 --- Electrical Property --- p.11 / Chapter 3.1 --- Electrical Conductivity --- p.11 / Chapter 3.2 --- Physical Model --- p.13 / Chapter 3.3 --- Algorithm --- p.16 / Chapter 3.3.1 --- Simulated Annealing --- p.18 / Chapter 3.3.2 --- Neighborhood Relation and Objective Function --- p.19 / Chapter 3.3.3 --- Configuration Space --- p.21 / Chapter 3.3.4 --- Annealing Schedule --- p.22 / Chapter 3.3.5 --- Expected Time Bound --- p.23 / Chapter 3.4 --- Results --- p.26 / Chapter 3.5 --- Discussion --- p.27 / Chapter 4 --- Thermal Properties --- p.30 / Chapter 4.1 --- Thermal Expansivity --- p.31 / Chapter 4.2 --- Physical Model --- p.32 / Chapter 4.2.1 --- The Physical Properties --- p.32 / Chapter 4.2.2 --- Objective Function and Neighborhood Relation --- p.37 / Chapter 4.3 --- Algorithm --- p.38 / Chapter 4.3.1 --- Parallel Simulated Annealing --- p.39 / Chapter 4.3.2 --- The Physical Annealing Schedule --- p.42 / Chapter 4.4 --- Results --- p.43 / Chapter 4.5 --- Discussion --- p.47 / Chapter 5 --- Scaling Properties --- p.48 / Chapter 5.1 --- Problem Define --- p.49 / Chapter 5.2 --- Physical Model --- p.50 / Chapter 5.2.1 --- The Physical Properties --- p.50 / Chapter 5.2.2 --- Bond Stretching Force --- p.50 / Chapter 5.2.3 --- Objective Function and Configuration Space --- p.51 / Chapter 5.3 --- Algorithm --- p.52 / Chapter 5.3.1 --- Simulated Annealing --- p.52 / Chapter 5.3.2 --- The Conjectural Method --- p.54 / Chapter 5.3.3 --- The Physical Annealing Schedule --- p.56 / Chapter 5.4 --- Results --- p.57 / Chapter 5.4.1 --- Case I --- p.59 / Chapter 5.4.2 --- Case II --- p.60 / Chapter 5.4.3 --- Case III --- p.60 / Chapter 5.5 --- Discussion --- p.61 / Chapter 6 --- Conclusion --- p.62 / Chapter A --- An Example on Studying Electrical Resistivity --- p.64 / Chapter B --- Theory of Elasticity --- p.67 / Chapter C --- Random Number Generator --- p.69 / Bibliography

by Lo Ting Shek = 複雜適應系統中的個體為本模型 / 盧庭碩. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 105-107). / Text in English; abstracts in English and Chinese. / by Lo Ting Shek = Fu za shi ying xi tong zhong de ge ti wei ben mo xing / Lu Tingshuo. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Minority game --- p.9 / Chapter 2.1 --- The model --- p.9 / Chapter 2.2 --- Review on selected work on MG --- p.13 / Chapter 2.2.1 --- Market efficiency and Phase transition --- p.13 / Chapter 2.2.2 --- Crowd effect in MG --- p.17 / Chapter 2.2.3 --- Hamming distance between strategies --- p.19 / Chapter 2.2.4 --- Statistical mechanics of systems with heterogeneous agents --- p.21 / Chapter 3 --- Theory of the minority game --- p.23 / Chapter 3.1 --- Formalism --- p.23 / Chapter 3.2 --- Discussion --- p.31 / Chapter 4 --- Evolutionary Minority Game --- p.33 / Chapter 4.1 --- Model --- p.33 / Chapter 4.2 --- Results --- p.36 / Chapter 4.3 --- Discussion --- p.38 / Chapter 5 --- Theory of the Evolutionary Minority game --- p.43 / Chapter 5.1 --- The theory of D'hulst and Rodgers [1] --- p.44 / Chapter 5.1.1 --- Discussion on the D'hulst and Rodgers's theory --- p.51 / Chapter 5.2 --- Theory of EMG [2] --- p.54 / Chapter 5.2.1 --- Formalism --- p.55 / Chapter 5.2.2 --- Results --- p.60 / Chapter 5.2.3 --- Discussion --- p.66 / Chapter 6 --- Evolutionary Minority Game with arbitrary cutoffs --- p.68 / Chapter 6.1 --- Model --- p.68 / Chapter 6.2 --- Results --- p.69 / Chapter 6.3 --- Theory --- p.76 / Chapter 6.4 --- Discussion --- p.85 / Chapter 7 --- Evolutionary minority game with heterogeneous strategy distribution --- p.88 / Chapter 7.1 --- Model --- p.89 / Chapter 7.2 --- Results --- p.90 / Chapter 7.3 --- Discussion --- p.99 / Chapter 8 --- Conclusion --- p.103

Thesis. 1978. Sc.D.--Massachusetts Institute of Technology. Dept. of Materials Science and Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Includes bibliographical references. / Sc.D.