Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for [formula]

"Vegeu el resum a l'inici del document del fitxer adjunt."

The optimal behaviour of firms facing stochastic costs

This paper aims at assessing the optimal behavior of a firm facing stochastic costs of production. In an imperfectly competitive setting, we evaluate to what extent a firm may decide to locate part of its production in other markets different from which it is actually settled. This decision is taken in a stochastic environment. Portfolio theory is used to derive the optimal solution for the intertemporal profit maximization problem. In such a framework, splitting production between different locations may be optimal when a firm is able to charge different prices in the different local markets.

Sources of Competitiveness in Tourist Local Systems

At the end of the XIX Century, Marshall described the existence of some concentrations of small and medium enterprises specialised in a specific production activity in certain districts of some industrial English cities. Starting from his contribute, Italian scholars have paid particular attention to this local system of production coined by Marshall under the term industrial district. In other countries, different but related territorial models have played a central role as the milieu or the geographical industrial clusters. Recently, these models have been extended to non-industrial fields like culture, rural activities and tourism. In this text, we explore the extension of these territorial models to the study of tourist activities in Italy, using a framework that can be easily applied to other countries or regions. The paper is divided in five sections. In the first one, we propose a review of the territorial models applied to tourism industry. In the second part, we construct a tourist filiere and we apply a methodology for the identification of local systems through GIS tools. Thus, taxonomy of the Italian Tourist Local Systems is presented. In the third part, we discuss about the sources of competitiveness of these Tourist Local Systems. In the forth section, we test a spatial econometrics model regarding different kinds of Italian Tourist Local Systems (rural systems, arts cities, tourist districts) in order to measure external economies and territorial networks. Finally, conclusions and policy implications are exposed.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Numerical schemes of diffusion asymptotics and moment closures for kinetic equations

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.

Epireflections and supercompact cardinals

We prove that, under suitable assumptions on a category C, the existence of supercompact cardinals implies that every absolute epireflective class of objects of C is a small-orthogonality class. More precisely, if L is a localization functor on an accessible category C such that the unit morphism X→LX is an extremal epimorphism for all X, and the class of L-local objects is defined by an absolute formula with parameters, then the existence of a supercompact cardinal above the cardinalities of the parameters implies that L is a localization with respect to some set of morphisms.

Do creative industries cluster? mapping creative local production systems in Italy

An important debate on the role of creativity and culture as factors of local economic development is distinctly emerging. Despite the emphasis put on the theoretical definition of these concepts, it is necessary to strengthen comparative research for the identification and analysis of the kind of creativity embedded in the territory as well as its determinants. Creative local production systems are identified in Italy and Spain departing from local labour markets as territorial units, and focusing on two different kinds of creative

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Estudi neurofisiològic del control executiu de l'atenció en l'esquizofrènia

Report for the scientific sojourn carried out at the Departament de Psicologia de la Universitat de les Illes Balears, Spain, from May until July 2006. Abnormalities in executive functions, including set shifting ability, represent a cardinal feature in schizophrenia. This ability to adapt behavior to changing environmental events or contingencies requires a mechanism for switching attention between learned stimulus-response associations, or task-sets. This project aimed at gaining further knowledge on the brain mechanisms related to the executive control of attention in schizophrenia during the performace of a task switching paradigm. Furthermore, a secondary goal was to further examine the interrelationships between endogenous and exogenous control processes in task set switching.

Conjugacy in Thompson's groups

We give a unified solution the conjugacy problem in Thompson’s groups F, V , and T using strand diagrams, and we analyze the complexity of the resulting algorithms.

Dynamics in Thompson's group F

We describe an explicit relationship between strand diagrams and piecewise-linear functions for elements of Thompson’s group F. Using this correspondence, we investigate the dynamics of elements of F, and we show that conjugacy of one-bump functions can be described by a Mather-type invariant.

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

Obesity and smoking: can we catch two birds with one tax?

The debate on tobacco and fat taxes often treats smoking and eating as independent behaviors. However, the available evidence shows that they are interdependent, which implies that policies against smoking or obesity may have larger scope than expected. To address this issue, we propose a dynamic rational model where eating and smoking are simultaneous choices that jointly affect body weight and addiction to smoking. Focusing on direct and cross-price effects, we compare tobacco taxes and food taxes and we show that a single policy tool can reduce both smoking and body weight. In particular, food taxes can be more effective than tobacco taxes at simultaneously fighting obesity and smoking.

Aid and Development: Issues and Reflections

The paper has three main sections. The first is a review of two particular propositions which appear in Dambisa Moyo’s 2009 book Dead Aid which were not subjected to rigorous analysis in the reviews which appeared following its publication. The finding is that neither proposition survives serious scrutiny – that aid is responsible for most of sub-Saharan Africa’s economic woes and that the international bond market represents a viable alternative to foreign aid for the finance of development-oriented investment. The second questions some of the characteristics and uses of the World Bank’s Country Policy and Institutional Assessment (CPIA), particularly focussing on the use of an essentially ordinal measure in cardinal applications. The third subjects the UK Department for International Development’s Needs-Effectiveness Index to critical review, concluding that further consideration of its attributes is necessary.