In this paper we propose an algorithm for solving systems of coupled monotone inclusions in Hilbert spaces. The operators arising in each of the inclusions of the system are processed in each iteration separately, namely, the single-valued are evaluated explicitly (forward steps), while the set-valued ones via their resolvents (backward steps). In addition, most of the steps in the iterative scheme can be executed simultaneously, this making the method applicable to a variety of convex minimization problems. The numerical performances of the proposed splitting algorithm are emphasized through applications in average consensus on colored networks and image classification via support vector machines.

Although the study of the interaction of acoustic and elastic waves with periodic surfaces and structures has a rich history dating back to Lord Rayleigh, it has recently been attracting new research efforts due to its value in the study of phononic crystals and in methods for ultrasonic non-destructive evaluation (NDE). The objective of the research described in this thesis is to provide new numerical and experimental tools capable of capturing important features that occur due to the diffraction of ultrasound on periodic solid surfaces. This thesis is divided into four main parts. First, the Rayleigh-Fourier (R-F) method will be used to simulate diffracted fields generated by structures containing multiple periodic surfaces and/or multiple solid layers. The second part of this thesis examines diffraction effects and compares ultrasonic NDE techniques for surfaces with imperfect periodicities. The third portion of this thesis focuses on one unusual phenomenon that has been observed on periodic surfaces, namely the lateral backward displacement of a bounded ultrasonic beam along the surface. This effect is currently understood to occur due to backward propagating surface waves that result from diffraction and mode conversion on the surface. The fourth and final part of this thesis describes the diffraction of bulk ultrasonic waves that can occur on the surfaces of phononic crystals.

As Aristotle wrote, rhetoric is an art or faculty of finding the available means of persuasion in a given circumstance, and the late nineteenth century was a time in American history when many authors used utopian fiction as the best available means of persuasion. For a few years, the utopian novel became a widespread, versatile and common rhetorical trope. Edward Bellamy was the most popular of these writers. Bellamy’s utopian novel Looking Backward was not only the third best-selling book of nineteenth century America, it inspired over a hundred other utopian novels and helped create a mass movement of “Bellamy clubs” along with a political party (Nationalism). During the latter part of the nineteenth century, American public discourse underwent a general shift from a focus on communal values to a focus on individuals as the source of truth. Utopian fiction of the era helps illuminate why and how this shift occurred. In nineteenth century America, literature was generally not considered to be rhetorical. At most, critics treated fiction as a form of epideictic rhetoric, aiming only to delight, educate, or create discussion. When fiction was used to promote legislative agendas and thus entered into the realm of deliberative rhetoric, critics argued that its transgression of rhetorical boundaries supposedly ruined its appeal. Utopian literature came the closest to breaking down the barriers between literature and rhetoric, as hundreds of utopian novels were published, most of them in response to Edward Bellamy. A close rhetorical reading of Looking Backward details its rhetorical nature and helps account for its rhetorical success. I treat each of the novels as participants in the larger cultural conversation, and detail the ways in which they address Bellamy, each other, and issues such as the temperance movement and the decline of classical languages in higher education. In modern times, though Bellamy has faded from the public memory, he has proven useful in a variety of contexts, from a political punching bag to a way to lend an air of erudition to various types of popular fiction. / text

Nano-devices are molecular machines synthesized from molecular subcomponents whose functions are combined in order to perform the func- tion of the machine. It frequently results of relative motions of subcomponents triggered by chemical events such as excitement induced by light, acidity or tem- perature changes. Thus the function consists in the transformation of a chemical event into a mechanical event. An important and characteristic feature of these devices is their intrinsic compositional nature. Therefore process-algebra for- malisms are natural candidates for their modeling. To this aim we introduce a dialect of the -calculus, the nano calculus. It is a rule-based language, the basic agents are molecules, with explicit representa- tion of molecular complexations and internal states. Its stochastic semantics is governed by rules which correspond to chemical reactions. The stochastic rate of the rule, possibly in nite, corresponds to the kinetic rate of the reaction. We illustrated its relevance for the modeling and simulation of nano-devices with an example stemming from the collaboration with the chemistry department of bologna: the [2]RaH rotaxane. We modeled it in nano and simulated its behaviour under various conditions of concentration: rst we validate our model by checking its correspondance with the experimental data and then we investi- gate extreme conditions not observable in practice. We were able to show that some classical assumption about kinetic rates were not correct any longer in this setting. The calculus has many advantages for the modelling of biochemical sys- tems. It is in particular compact, easily reusable and modi able and maybe more importantly much biological-like and thus easier to learn for biochemists. On the other hand the -calculus, also often used to model biochemical sys- tems, has a much more developed theory and more available tools. We present an encoding from the nano calculus to the stochastic -calculus. It satis es a very strong correctness property: S ! T , [[S]] ! [[T]], where S and T are nano terms, is the rate of the reaction and [[:]] is the encoding. Thus it permits to use nano as a front-end formalism and still get the bene ts of the theory and tools of the -calculus. We carry on with a study of the chemical master equation. It probabilisti- cally describes the possible behaviours of the system over time as a di erential equation on the probability to be in a given state at a given instant. It is a key notion in chemistry. There have been many e orts to solve it, and methods such as the Gillespie's algorithm has been developed to simulate its solution. We introduce and motivate a notion of equivalence based on the chemical master equation. It equates state with similar stochastic behavior. Then we prove that this equivalence corresponds exactly to the notion backward stochastic bisimu- lation. This bisimulation di ers from the usual ones because it considers ingoing transitions instead of outgoing transitions. This results is worth in itself since it establishes a bridge between a chemical semantics and a computer semantics, but it is also the rst step towards a metrics for biochemistry. Finally we present an unexpected consequence of our study of the nano calculus. We study the relative expressiveness of the synchronous and asyn- chronous -calculus. In the classical setting the latter is known to be strictly less expressive than the former. We prove that the separation also holds in the stochastic setting. We then extend the result to the -calculi with in nite rates. We also show that under a small restriction the asynchronous -calculus with in nite rates can encode the synchronous -calculus without in nite rates. In- terestingly the separation results are proved using the encodability of the nano calculus. We also propose and motivate a stochastic -calculus with rates of di erent orders of magnitude: the multi-scale -calculus to which we generalize our results. Finally we prove that in the probabilistic settings the asynchronous -calculus can be encoded into the asynchronous one.

The thesis is based on using dynamical systems theories and techniques to study the qualitative dynamics of herpes simplex virus type 2 (HSV-2), a sexually-transmitted disease of major public health significance. A deterministic model for the interaction of the virus with the immune system in the body of an infected individual (in vivo) is designed first of all. It is shown, using Lyapunov function and LaSalle's Invariance Principle, that the virus-free equilibrium of the model is globally-asymptotically stable whenever a certain biological threshold, known as the reproduction number, is less than unity. Furthermore, the model has at least one virus-present equilibrium when the threshold quantity exceeds unity. Using persistence theory, it is shown that the virus will always be present in vivo whenever the reproduction threshold exceeds unity. The analyses (theoretical and numerical) of this model show that a future HSV-2 vaccine that enhances cell-mediated immune response will be effective in curtailling HSV-2 burden in vivo. A new single-group model for the spread of HSV-2 in a homogenously-mixed sexually-active population is also designed. The disease-free equilibrium of the model is globally-asymptotically stable when its associated reproduction number is less than unity. The model has a unique endemic equilibrium, which is shown to be globally-stable for a special case, when the reproduction number exceeds unity. The model is extended to incorporate an imperfect vaccine with some therapeutic benefits. Using centre manifold theory, it is shown that the resulting vaccination model undergoes a vaccine-induced backward bifurcation (the epidemiological importance of the phenomenon of backward bifurcation is that the classical requirement of having the reproduction threshold less than unity is, although necessary, no longer sufficient for disease elimination. In such a case, disease elimination depends upon the initial sizes of the sub-populations of the model). Furthermore, it is shown that the use of such an imperfect vaccine could lead to a positive or detrimental population-level impact (depending on the sign of a certain threshold quantity). The model is extended to incorporate the effect of variability in HSV-2 susceptibility due to gender differences. The resulting two-group (sex-structured) model is shown to have essentially the same qualitative dynamics as the single-group model. Furthermore, it is shown that adding periodicity to the corresponding autonomous two-group model does not alter the dynamics of the autonomous two-group model (with respect to the elimination of the disease). The model is used to evaluate the impact of various anti-HSV control strategies. Finally, the two-group model is further extended to address the effect of risk structure (i.e., risk of acquiring or transmitting HSV-2). Unlike the two-group model described above, it is shown that the risk-structured model undergoes backward bifurcation under certain conditions (the backward bifurcation property can be removed if the susceptible population is not stratified according to the risk of acquiring infection). Thus, one of the main findings of this thesis is that risk structure can induce the phenomenon of backward bifurcation in the transmission dynamics of HSV-2 in a population.

The thesis is based on using dynamical systems theories and techniques to study the qualitative dynamics of herpes simplex virus type 2 (HSV-2), a sexually-transmitted disease of major public health significance. A deterministic model for the interaction of the virus with the immune system in the body of an infected individual (in vivo) is designed first of all. It is shown, using Lyapunov function and LaSalle's Invariance Principle, that the virus-free equilibrium of the model is globally-asymptotically stable whenever a certain biological threshold, known as the reproduction number, is less than unity. Furthermore, the model has at least one virus-present equilibrium when the threshold quantity exceeds unity. Using persistence theory, it is shown that the virus will always be present in vivo whenever the reproduction threshold exceeds unity. The analyses (theoretical and numerical) of this model show that a future HSV-2 vaccine that enhances cell-mediated immune response will be effective in curtailling HSV-2 burden in vivo. A new single-group model for the spread of HSV-2 in a homogenously-mixed sexually-active population is also designed. The disease-free equilibrium of the model is globally-asymptotically stable when its associated reproduction number is less than unity. The model has a unique endemic equilibrium, which is shown to be globally-stable for a special case, when the reproduction number exceeds unity. The model is extended to incorporate an imperfect vaccine with some therapeutic benefits. Using centre manifold theory, it is shown that the resulting vaccination model undergoes a vaccine-induced backward bifurcation (the epidemiological importance of the phenomenon of backward bifurcation is that the classical requirement of having the reproduction threshold less than unity is, although necessary, no longer sufficient for disease elimination. In such a case, disease elimination depends upon the initial sizes of the sub-populations of the model). Furthermore, it is shown that the use of such an imperfect vaccine could lead to a positive or detrimental population-level impact (depending on the sign of a certain threshold quantity). The model is extended to incorporate the effect of variability in HSV-2 susceptibility due to gender differences. The resulting two-group (sex-structured) model is shown to have essentially the same qualitative dynamics as the single-group model. Furthermore, it is shown that adding periodicity to the corresponding autonomous two-group model does not alter the dynamics of the autonomous two-group model (with respect to the elimination of the disease). The model is used to evaluate the impact of various anti-HSV control strategies. Finally, the two-group model is further extended to address the effect of risk structure (i.e., risk of acquiring or transmitting HSV-2). Unlike the two-group model described above, it is shown that the risk-structured model undergoes backward bifurcation under certain conditions (the backward bifurcation property can be removed if the susceptible population is not stratified according to the risk of acquiring infection). Thus, one of the main findings of this thesis is that risk structure can induce the phenomenon of backward bifurcation in the transmission dynamics of HSV-2 in a population.

This thesis is done in the framework of the ILC. The determination of the electroweak couplings of the top quark, is one of the tasks at the ILC. The thesis is dedicated to the measurement of the Forward-backward asymmetry in top quark pairs, at 500 GeV, using two beam polarization configurations, in the fully hadronic decay channel. The top quark almost exclusively decays to a b quark and a W boson. The 6 jet final state is analyzed using full detector simulation. Two jets with highest b-tag are taken as b jets and the remaining four jets are used to reconstruct the W s. The identification of the top and anti-top quarks is done by using the vertex charge of the b quark. Precisions on the production cross sections are also calculated. This thesis also includes a chapter on the optimization of the Si-W Electromagnetic calorimeter of the International Large Detector (ILD), one of the two detectors at the ILC. The ECAL of ILD, will consist of alternate layers of Silicon and Tungsten, where Silicon layers are active layers, while Tungsten is passive material. The Silicon layers are divided into wafers, surrounded by guard rings, to avoid the leakage currents. The analysis is focused to optimize the guard ring size. The thesis is divided into 6 chapters. The first chapter gives a brief over view of the Standard Model. The second chapter is dedicated to the theoretical aspects of the top quark physics at the ILC. A detailed description of the ILD and its sub-detectors is given in the 3rd chapter. The 4th chapter presents the studies of the optimization of Si-W ECAL guard ring size. The 5th chapter contains the details of analysis of tt production at ILC, and measurement of the AFBt . The last chapter contains the summary of the results.

A method to solve the Navier-Stokes equations for incompressible viscous flows is proposed. This method is SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm to iteratively solve the two-dimensional laminar steady momentum equations and based upon finite volume method on staggered grids. Numerical tests are performed on several cases of the flow in the lid-driven cavity, as well as of the flow after a backward-facing step with SIMPLE and SIMPLER (SIMPLE Revised) methods. Finally, results are compared qualitatively and quantitatively with numerical and experimental results available in the literature for different Reynolds numbers to validate the methods.

A new method is developed to determine a set of informative and refined interface assertions satisfied by functions that are represented by feed-forward neural networks. Neural networks have often been criticized for their low degree of comprehensibility.It is difficult to have confidence in software components if they have no clear and valid interface description. Precise and understandable interface assertions for a neural network based software component are required for safety critical applications and for theintegration into larger software systems. The interface assertions we are considering are of the form &quote if the input x of the neural network is in a region (alpha symbol) of the input space then the output f(x) of the neural network will be in the region (beta symbol) of the output space &quote and vice versa. We are interested in computing refined interface assertions, which can be viewed as the computation of the strongest pre- and postconditions a feed-forward neural network fulfills. Unions ofpolyhedra (polyhedra are the generalization of convex polygons in higher dimensional spaces) are well suited for describing arbitrary regions of higher dimensional vector spaces. Additionally, polyhedra are closed under affine transformations. Given a feed-forward neural network, our method produces an annotated neural network, where each layer is annotated with a set of valid linear inequality predicates. The main challenges for the computation of these assertions is to compute the solution of a non-linear optimization problem and the projection of a polyhedron onto a lower-dimensional subspace.

Cette thèse traite des équations différentielles stochastiques rétrogrades réfléchies du second ordre dans une filtration générale . Nous avons traité tout d'abord la réflexion à une barrière inférieure puis nous avons étendu le résultat dans le cas d'une barrière supérieure. Notre contribution consiste à démontrer l'existence et l'unicité de la solution de ces équations dans le cadre d'une filtration générale sous des hypothèses faibles. Nous remplaçons la régularité uniforme par la régularité de type Borel. Le principe de programmation dynamique pour le problème de contrôle stochastique robuste est donc démontré sous les hypothèses faibles c'est à dire sans régularité sur le générateur, la condition terminal et la barrière. Dans le cadre des Équations Différentielles Stochastiques Rétrogrades (EDSRs ) standard, les problèmes de réflexions à barrières inférieures et supérieures sont symétriques. Par contre dans le cadre des EDSRs de second ordre, cette symétrie n'est plus valable à cause des la non linéarité de l'espérance sous laquelle est définie notre problème de contrôle stochastique robuste non dominé. Ensuite nous un schéma d'approximation numérique d'une classe d'EDSR de second ordre réfléchies. En particulier nous montrons la convergence de schéma et nous testons numériquement les résultats obtenus. / This thesis deals with the second-order reflected backward stochastic differential equations (2RBSDEs) in general filtration. In the first part , we consider the reflection with a lower obstacle and then extended the result in the case of an upper obstacle . Our main contribution consists in demonstrating the existence and the uniqueness of the solution of these equations defined in the general filtration under weak assumptions. We replace the uniform regularity by the Borel regularity(through analytic measurability). The dynamic programming principle for the robust stochastic control problem is thus demonstrated under weak assumptions, that is to say without regularity on the generator, the terminal condition and the obstacle. In the standard Backward Stochastic Differential Equations (BSDEs) framework, there is a symmetry between lower and upper obstacles reflection problem. On the contrary, in the context of second order BSDEs, this symmetry is no longer satisfy because of the nonlinearity of the expectation under which our robust stochastic non-dominated stochastic control problem is defined. In the second part , we get a numerical approximation scheme of a class of second-order reflected BSDEs. In particular we show the convergence of our scheme and we test numerically the results.