Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Design, development and first evaluation of a client/server system for managing and querying linguistic corpora

This thesis is concerned with the role played by software tools in the analysis and dissemination of linguistic corpora and their contribution to a more widespread adoption of corpora in different fields. Chapter 1 contains an overview of some of the most relevant corpus analysis tools available today, presenting their most interesting features and some of their drawbacks. Chapter 2 begins with an explanation of the reasons why none of the available tools appear to satisfy the requirements of the user community and then continues with technical overview of the current status of the new system developed as part of this work. This presentation is followed by highlights of features that make the system appealing to users and corpus builders (i.e. scholars willing to make their corpora available to the public). The chapter concludes with an indication of future directions for the projects and information on the current availability of the software. Chapter 3 describes the design of an experiment devised to evaluate the usability of the new system in comparison to another corpus tool. Usage of the tool was tested in the context of a documentation task performed on a real assignment during a translation class in a master's degree course. In chapter 4 the findings of the experiment are presented on two levels of analysis: firstly a discussion on how participants interacted with and evaluated the two corpus tools in terms of interface and interaction design, usability and perceived ease of use. Then an analysis follows of how users interacted with corpora to complete the task and what kind of queries they submitted. Finally, some general conclusions are drawn and areas for future work are outlined.