Dissertations / Theses on the topic 'Determinist theories'

Philosophiae Doctor - PhD
This thesis deals with some fundamental aspects of groundwater models. Deterministic mathematical models of groundwater are usually used to simulate flow and transport processes in aquifer systems by means of partial differential equations. Analytical solutions for the deterministic mathematical models of the Theis problem and the transient confined-unconfined flow in a confined aquifer are investigated in the thesis. The Theis equation is a most commonly applied solution for the deterministic mathematical model of the Theis problem. In the thesis, a most simplified similarity transformation method for derivation of the Theis equation is proposed by using the Boltzmann transform. To investigate the transient confined-unconfined flow towards a fully penetrating well in a confined aquifer, a new analytical solution for the deterministic mathematical models of interest is proposed in the thesis. The proposed analytical solution considers a change of hydraulic properties (transmissivity and storativity) during the confined-unconfined conversion. Based on the proposed analytical solution, a practical method to determine distance of the conversion interface from pumping well and diffusivity of the unconfined region is developed by using a constant rate test. Applicability of the proposed analytical solution is demonstrated by a comparison with previous solutions, namely the MP and the Chen models. The results show that the proposed analytical solution can be used to assess the effect of the change of diffusivity on the transient confined-unconfined flow. The MP model is only accepted if the transmissivity during the confined-unconfined conversion is constant. The Chen model, given as a special case of the proposed analytical solution, is limited to the analysis of the transient confined-unconfined flow with a fixed diffusivity. An important application of groundwater models is to estimate parameters, such as hydraulic properties and flow dynamics, of groundwater systems by assessing and analysing field data. For instance, the pumping and the hydrochemistry and environmental tracer tests are two effective ways to obtain such data. To evaluate hydraulic properties of aquifer systems by derivative interpretation of drawdown data from pumping tests, a new diagnostic analysis method is proposed based on a lg-lg drawdown derivative, dlgs/dlgt, and the differentiation algorithm namely Lagrange Interpolation Regression (LIR) in the thesis. Use of a combined plot of dlgs/dlgt and a semi-lg drawdown derivative (ds/dlgt) is made to identify various flow segments during variable discharge tests with infinite conditions, constant rate tests in bounded aquifers and tests involving double-porosity behaviours. These can be applied to further characterize pumped aquifers. Compared to traditional diagnostic analysis method using plot of ds/dlgt alone, the combined drawdown derivative plot possesses certain advantages identified as: (1) the plot of dlgs/dlgt is strikingly sensitive for use in unveiling differences between pumping and its following recovery periods in intermittent variable discharge tests; (2) storativity (S) of pumped aquifers can be evaluated by using the combined plot; and (3) quantitative assessments of double-porosity behaviours can also be achieved. Based on two case studies, advantages and disadvantages of uses of the LIR and other existing differentiation methods in calculations of numerical drawdown derivative are demonstrated in practice. The results suggest that the LIR is a preferred method for numerical differentiation of drawdown data as it can be used to effectively minimise noisy effects. The proposed derivative approach provides hydrologists with an additional tool for characterizing pumped aquifers. Use of hydrochemistry and environmental tracer tests to assess flow dynamics of groundwater systems is demonstrated via a case study in the dolomite aquifer of South Africa. An emphasis is on determining mean residence times (MRTs) of the dolomite aquifer by means of an appropriate box model with time series of 14C values of dissolved inorganic carbon (14C-DIC) and initial 14C activities of spring samples during 1970s and 2010s. To obtain the calibrated 14C MRTs, 13C values of dissolved inorganic carbon (δ13C-DIC) of the spring samples are applied to estimate mineral dissolution in the dolomite aquifer and calculate the initial 14C activities. The results indicate that the spring samples have about 50%-80% initial 14C activities. By using the appropriate box model, the calibrated 14C MRTs of the spring system are given within a range from ≤ 10 to 50 years. Additionally, the flow dynamics, including the recharge source and area, the effect of climate change on the temporal trend of the groundwater MRTs and the groundwater flow circulation, of the dolomitic spring system are also discussed for further possible management interventions in the dolomite aquifer.

Three methods are developed to study the response of nonlinear systems to combined deterministic and stochastic excitations. They are a second-order closure method, a generalized method of equivalent linearization, and a reduced non-Gaussian closure scheme. Primary resonances of single- and two-degree-of-freedom systems in the presence of different internal (autoparametric) resonances are investigated. We propose these methods to overcome some of the limitations of the existing methods of solution and explain some observed experimental results in the context of the response of randomly excited nonlinear systems. These include non-Gaussian responses, broadening effects, and shift in the resonant frequency. When available, the results of these methods are compared with those obtained by using the exact stationary solutions of the Fokker-Planck-Kolmogorov equation. It is found that the presence of the nonlinearities bend the frequency-response curves and this causes multi-valued regions for the mean-square responses. The multi-valuedness is responsible for a jump phenomenon. The results show that for some range of parameters, noise can expand the stability region of the mean response. As applications, we study the response of a shallow arch, a string, and a hinged-clamped beam to random excitations.
Ph. D.

This thesis argues that the Islamic finance industry has its ideological foundations in the business ethics and stakeholder theory since the Islamic jurisprudence supports the ethical foundation of business and financial intermediations. These ethical practices can be traced back to jurisprudential concepts of Maqasid Al Sharia and Maslaha in Islamic law. The current practices of IFI however fails to follow the ethically sound (and in line with the Maqasid and Maslaha ideals) stakeholder model because of competitive pressures from the conventional financial industry and is thus modelled more on the Neo liberal shareholder profit maximisation ideology, focusing mainly on ensuring that the shareholders and certain investments account holders get maximum returns, thereby foregoing the interest of other stakeholders. It is thus argued that due to the incompatibility of the Neo liberal ethos with the Islamic finance ideals (the Maqasid of Financial intermediation), the Islamic finance industry needs to focus on more stakeholder oriented practices. The major reason for the failure of the current regulatory framework for the Islamic finance industry is the lack of any compliance and enforcement mechanism to ensure that uniform sharia governance mechanisms can be applied across the jurisdictions. This it is argued can best be achieved by international principle based Meta regulatory framework focusing on the stakeholder nature of the Islamic finance involving the IFSB and the AAOIFI and giving these bodies the authority to issue certificates of sharia compliance whereby the IFI’s would be required to obtain these certificates to function as ‘Islamic’ institutions.

A theorem by Kurtz on convergence of Markov jump processes is presented as it relates to the use of the chemical master equation. Necessary mathematical background in the theory of stochastic processes is developed, as well as requirements of the mathematical model necessitated by results in the physical sciences. Applicability and usefulness of the master equation for this type of combinatorial model in chemistry is discussed, as well as analytical connections and modern applications in multiple research fields.

The main proponent of management of any animal species is habitat management. The ability of habitats to maintain species communities will depend on the variation in both habitat structure and composition. While spatial variation in habitat resources plays a critical role in determining the distribution of species, an equally important consideration that must be accounted for is temporal variation in the needs of the target species. Nutritional requirements, and thus the habitats used to fulfil those nutritional needs, will be different depending on if the individual is breeding, migrating, molting, enduring winter, or establishing a new range. For waterfowl, we currently assume that winter and migration are nutritionally stressful and are consequently the periods most limiting to populations. The theory of ideal free distribution assumes that animals distribute themselves according to the factor most limiting to their fitness. In the case of non-breeding waterfowl, this factor is believed to be food. We assume if habitats with abundant food resources are provided, waterfowl will make use of those habitats. Deviations from an ideal free distribution based on food become problematic for managers since these deviations will keep some areas from being exploited to their potential, while other areas may become over-exploited. Recent observations have made it clear that this assumption may need to be reconsidered for effective waterfowl management. In this dissertation I quantitatively examine the degree to which spring migrating waterfowl conform to, or deviate from, an ideal free distribution based on food. Since food availability was not expected to account for 100% of waterfowl distribution, I further investigated what other potential habitat components influence the distribution of spring migrating waterfowl. In the first chapter of this dissertation, I explicitly tested the influence of food availability on waterfowl distribution. A series of paired 0.42 ha (1 acre) plots were established in various habitat types. One plot in each pair was treated with corn to a density of 2000 kg/ha, while the remaining plot was used as a control. Background food availability was controlled for by taking core samples from each plot, and estimating the natural seed and invertebrate biomass. The abundance each species of waterfowl using the plots was recorded during morning and afternoon observation periods. Linear mixed models were used to assess how variations in food availability influenced distribution of waterfowl. Although the waterfowl community showed a significant preference for treatment plots, our ability to influence abundance was low. Food availability accounted for minimal variation in abundance of the waterfowl community as a whole or for each focal species. Since the results of the first chapter showed food availability to be a poor predictor of waterfowl distribution, in the second chapter I set out to determine other potential habitat variables could be responsible for driving waterfowl distribution during spring migration. After each observation period, a series of habitat structural measurements were made within each paired plot. Habitat measurements included water characteristics, vegetation structure, vegetation type, habitat type, and weather conditions. Linear mixed models and model selection were employed to determine which of the habitat characteristics showed the greatest ability to predict waterfowl abundance on study plots. Models containing precipitation and Wabash River flood stage predictor variables were the best performing, and were the best predictors of waterfowl abundance on study plots. The results from this chapter encouraged investigation into how environmental factors shape the formation of local duck communities are structured from regional pools. In the third chapter of this dissertation I investigate the relationship between local and regional waterfowl community structure and how this relationship is mediated through environmental filters which dictate what proportion of the regional species pool exists at local scales. To address this relationship, I tested three hypotheses: 1) resource availability drives species diversity at local scales; 2) similarity between local and regional habitats will result in a similar species community occurring at both scales, and; 3) increased heterogeneity of local habitat structure will result in more diverse waterfowl communities at local scales. I used Mahalanobis distance and cumulative standard deviation of habitat variables in conjunction with mixed models and model selection to compare hypotheses and determine which had the greatest potential for mediating local community structure from regional pools. Increasing resource abundance appeared to have the greatest influence over local duck diversity, but the model indicated that although species diversity could be increased by increasing food abundance, diversity at local scales would become saturated before becoming representative of the regional community.

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Os Sert?es of Euclides da Cunha is one of the most studied books of Brazilian social thought, with approaches ranging from literature to geology, mobilizing concepts and theoretical and disciplinary perspectives the most diverse. This work aims to identify the process of building the concept of race by Euclides da Cunha in this work. To achieve this goal, will be studied, at first, the process of intellectual and political formation of Euclides da Cunha in the years prior to his trip to Canudos, in order to identify the presence of themes and authors in their thinking, using for this purpose, as the main source, your correspondence and press articles, which are expressed in the basic references of his training and dialogue on topics and authors that permeated their way of thinking about the Brazilian reality in the late nineteenth century and early twentieth century. In the second stage of labor, with reference to the study of the presence of several theories that explain human behavior from racial lines, with a strong Brazilian influence in the intellectual environment of the late nineteenth century, an analytical effort will be made in order to understand the synthesis made specific by Euclides da Cunha in the preparation of his work, to identify the main authors based their thinking on this aspect of the changes in your way of thinking about the man of the interior in an attempt to understand how the concept this race is in the interpretation of the conflict happened in Canudos and action of some of her protagonists
Os Sert?es de Euclides da Cunha ? um dos mais estudados livros do pensamento social brasileiro, com abordagens que v?o da literatura a geologia, mobilizando conceitos e perspectivas te?ricas e disciplinares as mais diversas. Neste trabalho, pretende-se identificar o processo de constru??o do conceito de ra?a por Euclides da Cunha nessa obra. Para atingir esse objetivo, ser? estudado, num primeiro momento, o processo de forma??o intelectual e pol?tica de Euclides da Cunha nos anos anteriores ? sua ida a Canudos, com o prop?sito de identificar a presen?a de temas e autores no seu pensamento, utilizando-se, para essa finalidade, como fonte principal o seu epistol?rio e os artigos publicados na imprensa, nos quais est?o expressas as refer?ncias b?sicas da sua forma??o e o di?logo sobre temas e autores que permearam a sua forma de pensar a realidade brasileira no final do s?culo XIX e in?cio do s?culo XX. No segundo momento do trabalho, tomando como refer?ncia o estudo da presen?a das diversas teorias que explicavam o comportamento humano a partir de crit?rios raciais, com forte influ?ncia no ambiente intelectual brasileiro do final do s?culo XIX, ser? realizado um esfor?o anal?tico no sentido de compreender s?ntese espec?fica realizada por Euclides da Cunha no processo de elabora??o de sua obra, no sentido de identificar os principais autores que fundamentaram o seu pensamento nesse aspecto, as mudan?as na sua de forma de pensar sobre o homem do sert?o, na tentativa de compreender como o conceito de ra?a est? presente na interpreta??o do conflito acontecido em Canudos e na a??o de alguns dos seus protagonistas

Ce travail a pour objectif d'elaborer, de valider et de qualifier un schema de calcul pour un reacteur thermique d'irradiation. Il s'agit de la pile universitaire de strasbourg presentant les principales caracteristiques de ce type de reacteur : coeur compact et heterogene, combustible en plaques avec un fort enrichissement en uranium 235. Ce schema s'appuie sur l'utilisation inedite de deux methodes modernes du transport : la methode tdt programmee dans le code apollo 2 et la methode de monte carlo utilisee par le code tripoli 4. La premiere est une methode deterministe a deux dimensions basee sur la methode des probabilites de collision. La deuxieme est une methode stochastique. Toutes deux sont capables de traiter des geometries complexes. Apres quelques rappels theoriques sur les codes du transport, nous presentons un ensemble d'experiences integrales qui se sont deroulees dans le reacteur universitaire de strasbourg. Nous avons realise une d'entre elles. Au cours de notre etude theorique, nous montrons d'abord les erreurs importantes que peut entrainer l'utilisation d'un schema base sur l'homogeneisation, la condensation et l'approximation de la diffusion. Nous realisons ensuite une comparaison approfondie entre la methode des ordonnees discretes et la methode tdt. Ceci nous conduit a constater la pertinence de l'utilisation de la methode tdt dans le cas du reacteur etudie. Le traitement des fuites axiales par cette derniere methode apparait alors comme son seul veritable point faible. Ainsi, nous sommes amenes a recommander l'utilisation du code tripoli 4 pour une etude plus precise des fuites dans un reflecteur. Les donnees experimentales precedemment obtenues, nous permettent de qualifier notre schema pour des questions aussi importantes que la determination de la masse critique, la distribution de puissance ou la gestion du combustible.

Das Hauptresultat dieser Arbeit ist ein regularisierter arithmetischer Satz von Riemann-Roch für ein hermitesches Geradenbündel, die isometrisch zum Geradenbündel den Spitzenformen vom geraden Gewicht ist, auf eine arithmetische Fläche, deren komplexe Faser isometrisch zu einer hyperbolischen Riemannschen Fläche ohne elliptische Punkte ist. Der Beweis des Resultats erfolgt durch metrische Degeneration: Wir regularisieren die betreffenden Metriken in einer Umgebung der Singularitäten, wenden dann den arithmetischen Riemann-Roch-Satz von Gillet und Soulé an und lassen schließlich den Parameter gegen Null gehen. Durch die metrische Degeneration entsteht auf beiden Seiten der Formel ein divergenter Term. Die asymptotische Entwicklung der Divergenz berechnet sich auf der einen Seite direkt aus der Definition der glatten arithmetischen Selbstschnittzahlen. Der divergente Term auf der anderen Seite ist die zeta-regularisierte Determinante des zu den regularisierten Metriken assoziierten Laplace-Operators, der auf den 1-Formen mit Werten in dem betrachteten hermitischen Geradenbündel operiert. Wir definieren und berechnen zuerst eine Regularisiereung des entsprechenden zu den singulären Metriken assoziierten Laplace-Operators; diese wird später im regularisierten Riemann-Roch-Satz auftauchen. Zu diesem Zweck passen wir Ideen von Jorgenson-Lundelius, D'Hoker-Phong und Sarnak auf die vorliegende Situation an und verallgemeinern diese. Schließlich beweisen wir eine Formel für den zum betrachteten hermitischen Geradenbündel assoziierten Wärmeleitungskern auf der Diagonalen bei einer Modellspitze. Diese Darstellung steht im Zusammenhang mit einer Entwicklung nach zur Whittaker-Gleichung assoziierten Eigenfunktionen, die im Anhang bewiesen wird. Weitere Abschätzungen des zum betrachteten hermitischen Geradenbündel gehörigen Wärmeleitungskern auf der komplexe Faser der arithmetischen Fläche schließen den Beweis des Hauptresultats ab.
The main result of the dissertation is an arithmetic Riemann-Roch theorem for the hermitian line bundle of cusp form of given even integer weights on an arithmetic surface whose complex fiber is isometric to an hyperbolic Riemann surface without elliptic points. The proof proceeds by metric degeneration: We regularize the metric under consideration in a neighborhood of the singularities, then we apply the arithmetic Riemann-Roch theorem of Gillet and Soulé, and finally we let the parameter go to zero. Both sides of the formula blow up through metric degeneration. On one side the exact asymptotic expansion is computed from the definition of the smooth arithmetic intersection numbers. The divergent term on the other side is the zeta-regularized determinant of the Laplacian acting on 1-forms with values in the chosen hermitian line bundle associated to the regularized metrics. We first define and compute a regularization of the determinant of the corresponding Laplacian associated to the singular metrics, which will later occur int he regularized arithmetic Riemann-Roch theorem. To do so we adapt and generalize ideas od Jorgenson-Lundelius, D'Hoker-Phong, and Sarnak. Then, we prove a formula for the on-diagonal heat kernel associated to the chosen hermitian line bundle on a model cusp, from which its behavior close to a cusp is transparent. This expression is related to an expansion in terms of eigenfunctions associated to the Whittaker equation, which we prove in an appendix. Further estimates on the heat kernel associated to the chosen hermitian line bundle on the complex fiber of the arithmetic surface prove the main theorem.

In geotechnical engineering, the uncertainties such as the variability and uncertainty inherent in the geotechnical properties have caught more and more attentions from researchers and engineers. They have found that a single “Factor of Safety” calculated by traditional deterministic analyses methods can not represent the slope stability exactly. Recently in order to provide a more rational mathematical framework to incorporate different types of uncertainties in the slope stability estimation, reliability analyses and non-deterministic methods, which include probabilistic and non probabilistic (imprecise methods) methods, have been applied widely. In short, the slope non-deterministic analysis is to combine the probabilistic analysis or non probabilistic analysis with the deterministic slope stability analysis. It cannot be regarded as a completely new slope stability analysis method, but just an extension of the slope deterministic analysis. The slope failure probability calculated by slope non-deterministic analysis is a kind of complement of safety factor. Therefore, the accuracy of non deterministic analysis is not only depended on a suitable probabilistic or non probabilistic analysis method selected, but also on a more rigorous deterministic analysis method or geological model adopted. In this thesis, reliability concepts have been reviewed first, and some typical non-deterministic methods, including Monte Carlo Simulation (MCS), First Order Reliability Method (FORM), Point Estimate Method (PEM) and Random Set Theory (RSM), have been described and successfully applied to the slope stability analysis based on a numerical simulation method-Strength Reduction Method (SRM). All of the processes have been performed in a commercial finite difference code FLAC and a distinct element code UDEC. First of all, as the fundamental of slope reliability analysis, the deterministic numerical simulation method has been improved. This method has a higher accuracy than the conventional limit equilibrium methods, because of the reason that the constitutive relationship of soil is considered, and fewer assumptions on boundary conditions of slope model are necessary. However, the construction of slope numerical models, particularly for the large and complicated models has always been very difficult and it has become an obstacle for application of numerical simulation method. In this study, the excellent spatial analysis function of Geographic Information System (GIS) technique has been introduced to help numerical modeling of the slope. In the process of modeling, the topographic map of slope has been gridded using GIS software, and then the GIS data was transformed into FLAC smoothly through the program built-in language FISH. At last, the feasibility and high efficiency of this technique has been illustrated through a case study-Xuecheng slope, and both 2D and 3D models have been investigated. Subsequently, three most widely used probabilistic analyses methods, Monte Carlo Simulation, First Order Reliability Method and Point Estimate Method applied with Strength Reduction Method have been studied. Monte Carlo Simulation which needs to repeat thousands of deterministic analysis is the most accurate probabilistic method. However it is too time consuming for practical applications, especially when it is combined with numerical simulation method. For reducing the computation effort, a simplified Monte Carlo Simulation-Strength Reduction Method (MCS-SRM) has been developed in this study. This method has estimated the probable failure of slope and calculated the mean value of safety factor by means of soil parameters first, and then calculated the variance of safety factor and reliability of slope according to the assumed probability density function of safety factor. Case studies have confirmed that this method can reduce about 4/5 of time compared with traditional MCS-SRM, and maintain almost the same accuracy. First Order Reliability Method is an approximate method which is based on the Taylor\'s series expansion of performance function. The closed form solution of the partial derivatives of the performance function is necessary to calculate the mean and standard deviation of safety factor. However, there is no explicit performance function in numerical simulation method, so the derivative expressions have been replaced with equivalent difference quotients to solve the differential quotients approximately in this study. Point Estimate Method is also an approximate method involved even fewer calculations than FORM. In the present study, it has been integrated with Strength Reduction Method directly. Another important observation referred to the correlation between the soil parameters cohesion and friction angle. Some authors have found a negative correlation between cohesion and friction angle of soil on the basis of experimental data. However, few slope probabilistic studies are found to consider this negative correlation between soil parameters in literatures. In this thesis, the influence of this correlation on slope probability of failure has been investigated based on numerical simulation method. It was found that a negative correlation considered in the cohesion and friction angle of soil can reduce the variability of safety factor and failure probability of slope, thus increasing the reliability of results. Besides inter-correlation of soil parameters, these are always auto-correlated in space, which is described as spatial variability. For the reason that knowledge on this character is rather limited in literature, it is ignored in geotechnical engineering by most researchers and engineers. In this thesis, the random field method has been introduced in slope numerical simulation to simulate the spatial variability structure, and a numerical procedure for a probabilistic slope stability analysis based on Monte Carlo simulation was presented. The soil properties such as cohesion and friction angle were discretized to continuous random fields based on local averaging method. In the case study, both stationary and non-stationary random fields have been investigated, and the influence of spatial variability and averaging domain on the convergence of numerical simulation and probability of failure was studied. In rock medium, the structure faces have very important influence on the slope stability, and the rock material can be modeled as the combination of rigid or deformable blocks with joints in distinct element method. Therefore, much more input parameters like strength of joints are required to input the rock slope model, which increase the uncertainty of the results of numerical model. Furthermore, because of the limitations of the current laboratory and in-site testes, there is always lack of exact values of geotechnical parameters from rock material, even the probability distribution of these variables. Most of time, engineers can only estimate the interval of these variables from the limit testes or the expertise’s experience. In this study, to assess the reliability of the rock slope, a Random Set Distinct Element Method (RS-DEM) has been developed through coupling of Random Set Theory and Distinct Element Method, and applied in a rock slope in Sichuan province China.

Developpement d'un reseau local a insertion de registres proposant une strategie deterministe d'acces a la voie et pour l'etablissement des liaisons de donnees. Le determinisme d'acces au support de communication est assure par la technique d'insertion de registre. Le retrait du registre se fait au retour de la trame emise. La circonference de l'anneau varie selon sa charge. La fiabilite est garantie par un protocole gerant deux redondances: l'une globale porte sur l'ensemble des informations echangees, l'autre est reservee aux adresses vehiculees par la trame. Le temps de transit de l'information est connu des communicateurs grace a la circulation d'une trame "reference temporelle" sur l'anneau; ceci permet une gestion dynamique des delais

L'etude presente deux objectifs essentiels: definir un reseau garantissant le determinisme d'acces a la voie et d'etablissement d'une liaison de donnees entre deux stations et presenter a des stations heterogenes une interface unique d'acces au reseau. En associant une seule liaison physique a une communication, il s'est agi de definir un algorithme distribue operant sur sa propre liste d'attente et permettant l'etablissement d'une communication dans un temps borne et d'evaluer une borne superieure finie par le delai d'etablissement d'une liaison. L'algorithme presente les caracteristiques suivantes: controle entierement reparti (les communications sont etablies en respectant l'anciennete des requetes), equite d'etablissement de liaisons de donnees, absence d'interblocage

This dissertation is concerned with the potential multistability of protein concentrations in the cell that can arise in biochemical networks. That is, situations where one, or a family of, proteins may sit at one of two or more different steady state concentrations in otherwise identical cells, and in spite of them being in the same environment. Models of multisite protein phosphorylation have shown that this mechanism is able to exhibit unlimited multistability. Nevertheless, these models have not considered enzyme docking, the binding of the enzymes to one or more substrate docking sites, which are separate from the motif that is chemically modified. Enzyme docking is, however, increasingly being recognised as a method to achieve specificity in protein phosphorylation and dephosphorylation cycles. Most models in the literature for these systems are deterministic i.e. based on Ordinary Differential Equations, despite the fact that these are accurate only in the limit of large molecule numbers. For small molecule numbers, a discrete probabilistic, stochastic, approach is more suitable. However, when compared to the tools available in the deterministic framework, the tools available for stochastic analysis offer inadequate visualisation and intuition. We firstly try to bridge that gap, by developing three tools: a) a discrete `nullclines' construct applicable to stochastic systems - an analogue to the ODE nullcines, b) a stochastic tool based on a Weakly Chained Diagonally Dominant M-matrix formulation of the Chemical Master Equation and c) an algorithm that is able to construct non-reversible Markov chains with desired stationary probability distributions. We subsequently prove that, for multisite protein phosphorylation and similar models, in the deterministic domain, enzyme docking and the consequent substrate enzyme-sequestration must inevitably limit the extent of multistability, ultimately to one steady state. In contrast, bimodality can be obtained in the stochastic domain even in situations where bistability is not possible for large molecule numbers. We finally extend our results to cases where we have an autophosphorylating kinase, as for example is the case with $Ca^{2+}$/calmodulin-dependent protein kinase II (CaMKII), a key enzyme in synaptic plasticity.

Les calculs de précision dans les théories de jauge jouent un rôle très important pour l’étude de la physique du Modèle Standard et au-delà dans les super-collisionneurs de particules comme le LHC, TeVatron et ILC. Par conséquent, il est extrêmement important de fournir des outils du calcul d’amplitudes à une boucle stables, rapides, efficaces et hautement automatisés. Cette thèse a pour but de développer la bibliothèque d’intégrales Golem95. Cette bibliothèque est un programme écrit en Fortran95, qui contient tous les ingrédients nécessaires pour calculer une intégrale scalaire ou tensorielle à une boucle avec jusqu’à six pattes externes. Golem95 utilise une méthode traditionnelle de réduction (réduction à la Golem) qui réduit les facteurs de forme en des intégrales de base redondantes qui peuvent être scalaires (sans paramètres de Feynman au numérateur) ou tensorielles (avec des paramètres de Feynman au numérateur); ce formalisme permet d’éviter les problèmes de l’instabilité numérique engendrés par des singularités factices dues à l’annulation des déterminants de Gram. En plus, cette bibliothèque peut être interfacée avec des programmes du calcul automatique basés sur les méthodes d’unitarité comme GoSam par exemple. Les versions antérieures de Golem95 ont été conçues pour le calcul des amplitudes sans masses internes. Le but de ce travail de thèse est de généraliser cette bibliothèque pour les configurations les plus générales (les masses complexes sont incluses), et de fournir un calcul numériquement stable dans les régions problématique en donnant une représentation intégrale unidimensionnelle stable pour chaque intégrale de base de Golem95
Higher order corrections in gauge theories play a crucial role in studying physics within the standard model and beyond at TeV colliders, like LHC, TeVatron and ILC. Therefore, it is of extreme importance to provide tools for next-to-leading order amplitude computation which are fast, stable, efficient and highly automatized. This thesis aims at developing the library of integrals Golem95. This library is a program written in Fortran95, it contains all the necessary ingredients to calculate any one-loop scalar or tensorial integral with up to six external legs. Golem95 uses the traditional reduction method (Golem reduction) to reduce the form factors into redundant basic integrals, which can be scalar (without Feynman parameters in the numerator) or tensorial (with Feynman parameter in the numerator); this formalism allows us to avoid the problems of numerical instabilities generated by the spurious singularities induced by the vanishing of the Gram determinants. In addition, this library can be interfaced with automatic programs of NLO calculation based on the unitarity inspired reduction methods as GoSam for example. Earlierversions of Golem95 were designed for the calculation of amplitudes without internal masses. The purpose of this thesis is to extend this library for more general configurations (complex masses are supported); and to provide numerically stable calculation in the problematic regions (det(G) → 0), by providing a stable one-dimensional integral representation for each Golem95 basic integral

Le but de cette thèse est d'étudier les modèles stochastiques d'épidémies en tenant compte de la structure spatiale de l'environnement. Dans un premier temps, nous considérons un modèle déterministe et stochastique SIR sur une grille de [0,1]^d, d=1,2 ou 3. D'une part, on prouve qu'en fixant le pas de la grille et en faisant tendre la taille de la population en chaque point de la grille vers l'infini, le modèle stochastique converge vers le modèle déterministe sur la grille. Ce système déterministe d'équations différentielles ordinaires converge vers un système d'équations aux dérivées partielles quand le pas de la maille tend vers zéro. D'autre part, on fait tendre en même temps la taille de la population en chaque point vers l'infini et le pas de maillage vers zéro, avec une restriction sur la vitesse de convergence entre les deux paramètres. Dans ce cas le modèle stochastique converge vers le modèle déterministe en espace continu. Le chapitre 2 étudie dans le cas d=1 les fluctuations du modèle stochastique autour de sa limite loi des grands nombres, à l'aide d'un théorème central limite. Dans le chapitre 3, nous étudions la dynamique de maladie infectieuse au sein d'une population répartie sur un nombre fini d'îlots interconnectés, dans le cadre d'un modèle SIS. A l'aide du théorème central limite, des déviations modérées et des grandes déviations, on donne une estimation du temps mis par les perturbations aléatoires pour éteindre une situation endémique. Nous calculons numériquement le quasi-potentiel qui apparaît dans l'expression du temps d'extinction, que l'on compare avec celui du cas homogène
The aim of this thesis is to study stochastic epidemic models taking into account the spatial structure of the environment. Firstly, we consider a deterministic and a stochastic SIR model on a regular grid of [0,1]^d, d=1, 2 or 3. On the one hand, by letting first the size of the population on each node go to infinity and the mesh size of the grid is kept fixed, we prove that the stochastic model converges to the deterministic model on the spatial grid. This system of ordinary differential equations converges to a system of partial differential equations as the mesh size of the grid goes to zero. On the other hand, we let both the population size go to infinity and the mesh size of the grid go to zero with a restriction on the the speed of convergence between the two parameters. In this case, we show that the stochastic model converges to the deterministic model in the continuous space. Next, we study, in the case d=1, the fluctuations of the stochastic model around its deterministic law of large numbers limit, by using a cental limit theorem. Finally, we study the dynamic of infectious disease within a population distribued on a finite number of interconnected patches. We place ourselves in the context of an SIS model. By using the central limit theorem, the moderate deviations and the large deviations, we give an approximation of the time taken by the random pertubations to extinct an endemic situation. We make numerical calculus for the quasi-potential which appear in the expression of the time of extinction. Comparisons are made with that of the homogeneous model

Die vorliegende Arbeit befasst sich mit einer Vermutung von Sarnak aus dem Jahre 2010 über die Orthogonalität von durch deterministische dynamische Systeme induzierte Folgen zur Möbiusschen μ-Funktion. Ihre Hauptresultate sind zum einen der Ergodensatz mit Möbiusgewichten, welcher eine maßtheoretische (schwächere) Version von Sarnaks Vermutung darstellt, und zum anderen die bereits gesicherte Gültigkeit der genannten Vermutung in Spezialfällen, wobei hier exemplarisch unter anderem der Thue–Morse Shift und Schiefprodukterweiterungen von rationalen Rotationen auf dem Kreis gewählt worden sind. Zum Zwecke der Motivation zeigen wir, dass eine gewisse Wachstumsabschätzung für die Mertensfunktion äquivalent ist zum Primzahlsatz und skizzieren ein Resultat, welches die Äquivalenz einer weiteren solchen Abschätzung zur Riemannschen Vermutung liefert, um auf diese Weise die Bedeutung der Möbiusfunktion für die Zahlentheorie herauszustellen. Da sie für das Verständnis von Sarnaks Vermutung unerlässlich ist, geben wir eine Einführung in die Theorie der Entropie dynamischer Systeme auf Grundlage der Definitionen von Adler–Konheim–McAndrew, Bowen–Dinaburg und Kolmogorov–Sinai. Ferner berechnen wir die topologische Entropie des Thue–Morse Shifts und von Schiefprodukterweiterungen von Rotatione auf dem Kreis. Wir studieren die ergodische Zerlegung T-invarianter Maße auf kompakten metrischen Räumen mit stetiger Transformation T, welche wir für den Beweis des Ergodensatzes mit Möbiusgewichten benötigen. Sodann beweisen wir den genannten gewichteten Ergodensatz. Wir geben eine hinreichende Bedingung an für das Erfülltsein von Sarnaks Vermutung in einem gegebenen dynamischen System, welche im anschließenden Kapitel Anwendung findet. So wird nachgewiesen, dass Sarnaks Vermutung im Falle des Thue–Morse Shifts und von Schiefprodukterweiterungen von rationalen Rotationen auf dem Kreis erfüllt ist. Abschließend wird gezeigt, dass Sarnaks Vermutung sich als Konsequenz aus einer Vermutung von Chowla ergibt.
The thesis in hand deals with a conjecture of Sarnak from 2010 about the orthogonality of sequences induced by deterministic dynamical systems to the Möbius μ-function. Its main results are the ergodic theorem with Möbius weights, which is a measure theoretic (weaker) version of Sarnak’s conjecture, and the already assured validity of Sarnak’s conjecture in special cases, where we have exemplarily chosen the Thue–Morse shift and skew product extensions of rational rotations on the significance of the Möbius function for number theory. Since it is essential for the understanding of Sarnak’s conjecture we give an introduction to the theory of entropy of dynamical systems based on the definitions of Adler–Konheim–McAndrew, Bowen–Dinaburg and Kolmogorov–Sinai. Furthermore, we calculate the topological entropy of the Thue–Morse shift and of skew product extensions of rotations on the circle. We study the ergodic decomposition for T-invariant measures on compact metric spaces with continuous transformations T, which we will need for the proof of the ergodic theorem with Möbius weights. Thereafter, we prove the namely weighted ergodic theorem. We give a sufficient condition for Sarnak’s conjecture to hold for a given dynamical system, which we make use of in the following chapter. Thereupon, it is varified that Sarnak’s conjecture holds for the Thue–Morse shift and for skew product extensions of rational rotations on the circle. Lastly, it is shown that Sarnak’s conjecture from one of Chowla.

Dans cette thèse l’ancienne question philosophique “tout événement a-t-il une cause ?” sera examinée à la lumière de la mécanique quantique et de la théorie des probabilités. Aussi bien en physique qu’en philosophie des sciences la position orthodoxe maintient que le monde physique est indéterministe. Au niveau fondamental de la réalité physique – au niveau quantique – les événements se passeraient sans causes, mais par chance, par hasard ‘irréductible’. Le théorème physique le plus précis qui mène à cette conclusion est le théorème de Bell. Ici les prémisses de ce théorème seront réexaminées. Il sera rappelé que d’autres solutions au théorème que l’indéterminisme sont envisageables, dont certaines sont connues mais négligées, comme le ‘superdéterminisme’. Mais il sera argué que d’autres solutions compatibles avec le déterminisme existent, notamment en étudiant des systèmes physiques modèles. Une des conclusions générales de cette thèse est que l’interprétation du théorème de Bell et de la mécanique quantique dépend crucialement des prémisses philosophiques desquelles on part. Par exemple, au sein de la vision d’un Spinoza, le monde quantique peut bien être compris comme étant déterministe. Mais il est argué qu’aussi un déterminisme nettement moins radical que celui de Spinoza n’est pas éliminé par les expériences physiques. Si cela est vrai, le débat ‘déterminisme – indéterminisme’ n’est pas décidé au laboratoire : il reste philosophique et ouvert – contrairement à ce que l’on pense souvent. Dans la deuxième partie de cette thèse un modèle pour l’interprétation de la probabilité sera proposé. Une étude conceptuelle de la notion de probabilité indique que l’hypothèse du déterminisme aide à mieux comprendre ce que c’est qu’un ‘système probabiliste’. Il semble que le déterminisme peut répondre à certaines questions pour lesquelles l’indéterminisme n’a pas de réponses. Pour cette raison nous conclurons que la conjecture de Laplace – à savoir que la théorie des probabilités présuppose une réalité déterministe sous-jacente – garde toute sa légitimité. Dans cette thèse aussi bien les méthodes de la philosophie que de la physique seront utilisées. Il apparaît que les deux domaines sont ici solidement reliés, et qu’ils offrent un vaste potentiel de fertilisation croisée – donc bidirectionnelle.
In this thesis the ancient philosophical question whether ‘everything has a cause’ will be examined in the light of quantum mechanics and probability theory. In the physics and philosophy of science communities the orthodox position states that the physical world is indeterministic. On the deepest level of physical reality – the quantum level – things or events would have no causes but happen by chance, by irreducible hazard. Arguably the clearest and most convincing theorem that led to this conclusion is Bell’s theorem. Here the premises of this theorem will be re-evaluated, notably by investigating physical model systems. It will be recalled that other solutions to the theorem than indeterminism exist, some of which are known but neglected, such as ‘superdeterminism’. But it will be argued that also other solutions compatible with determinism exist. One general conclusion will be that the interpretation of Bell’s theorem and quantum mechanics hinges on the philosophical premises from which one starts. For instance, within a worldview à la Spinoza the quantum world may well be seen as deterministic. But it is argued that also much ‘softer’ determinism than Spinoza’s is not excluded by the existing experiments. If that is true the ‘determinism – indeterminism’ is not decided in the laboratory: it remains philosophical and open-ended – contrary to what is often believed. In the second part of the thesis a model for the interpretation of probability will be proposed. A conceptual study of the notion of probability indicates that the hypothesis of determinism is instrumental for understanding what ‘probabilistic systems’ are. It seems that determinism answers certain questions that cannot be answered by indeterminism. Therefore we believe there is room for the conjecture that probability theory cannot not do without a deterministic reality underneath probability – as Laplace claimed. Throughout the thesis the methods of philosophy and physics will be used. Both fields appear to be solidly intertwined here, and to offer a large potential for cross-fertilization – in both directions.