This set of lecture notes is the outcome of a lecture series, given in April 2000 by the author while holding the -Cattedra Galileiana- at Scuola Normale Superiore in Pisa. The purpose of the lectures was to give an overview of some recent work concerning structural properties of the evolution of the forward rate curve in an arbitrage free bond market.

During the academic year 1995/96, I was invited by the Scuola Normale Superiore to give a series of lectures. The purpose of these notes is to make the underlying economic problems and the mathematical theory of exterior differential systems accessible to a larger number of people. It is the purpose of these notes to go over these results at a more leisurely pace, keeping in mind that mathematicians are not familiar with economic theory and that very few people have read Elie Cartan.

These lecture notes contain the main topics presented in a series of lectures given at the Scuola Normale di Pisa in the academic years 1998-1999-2000. The audience was made up of students of the last two years of the Physics program and a few Ph.D. students. The lectures address selected topics in stellar dynamics, presented in a deductive approach. Completeness is by no means the final goal of this work. The course is divided into two parts. In the first part, basic mathematical concepts are introduced, with some discussion of their physical meaning. In the second part, the tools developed...

Electron gas theory is one of the broadest fields in theoretical condensed matter physics, and even its most elementary application to the study of collective excitations and screening in the simple metals poses interesting questions. Recent Electron Energy Loss and Inelastic X-Ray Scattering experiments have shown that traditional electron gas theories are unable to account for the measured plasmon dispersion relation. While it has become clear that neither correlation nor band structure alone can explain those results, the recently developed Time Dependent Density Functional Theory provides...

Sensory experience can dynamically modify both the anatomy and function of the brain. In particular, neurons can modify their connections in response to enviromental stimuli. This process, generally referred to as -neuronal plasticity-, is the basis of learning and memory processes in the brain. Which are the bases of neuronal plasticity? That is, how can environmental factors and sensory experience modify the connections between neurons? Neurotrophic factors of the Nerve Growth Factor (NGF) family are known to finely regulate the development and maintenance of synaptic connections in the...

Cp20 is a neuronal protein involved in the molecular mechanisms of synaptic plasticity. Cp20 was first identified in the CNS of the marine snail Hermissenda, which can be trained to learn an association between visual and vestibular stimuli in a Pavlovian conditioning procedure. Upon learning, cp20 is phosphorylated in a few defined neurons of Hermissenda, and inhibits the Ca2+-dependent K+ channels. This results in an increase in membrane resistence and therefore a hyperexcitability of the neuronal pathway. Similar biochemical mechanisms have been proposed to underlie memory in higher...

Presents a study on bipolaron formation in heavily doped and polar materials. This book addresses the problem of the formation and superconducting properties of real space electron (hole) pairs in these systems and their dependence on the carrier density.

The subject of this thesis is the Mu-calculus, which nowadays represents a very active research area in both theoretical and practical Computer Science. The Mu-calculus is a logic capable of expressing least and greatest solutions of fixpoint equations x=f(x), where f is a monotone function mapping some complete ordered set into itself. The thesis has two goals, one expository and one technical. The expository goal is to present some results and problems about the Mu-calculus. On the technical respect, this thesis addresses a specific expressiveness problem of the Mu-calculus, the alternation...

These notes contain my lectures on light scattering by matter presented at the Scuola Normale Superiore, Pisa during May and June 1995. I have deleted some of the topics discussed then and added a few related to my recent work. The notes are not to be regarded as exhaustive but rather as a selection of topics. In particular I have discussed, as examples, the theoretical basis for the interpretation of experiment on light scattering by photons in alpha-quartz and by electronic excitations in boron-doped diamond.

The study of shape optimization problems is a very wide field, both classical, as the isoperimetric problem and Newton problem of the best aerodynamical shape show, and modern, for all the recent results obtained in the last two, three decades. The fascinating feature is that the competing objects are shapes, i.e. domains of Rn, instead of functions, as usually occurs in problems of calculus of variations. This constraint often produces additional difficulties that lead to a lack of existence of a solution and the introduction of suitable relaxed formulations of the problem. However, in a few...