Essays on Applied Network Theory.

Network economics is a fast growing area of study, with a lot of potential for addressing a wide variety of socio-economic phenomena. Networks literally permeate our social and economic lives. The unemployed find jobs using the information and assistance of their friends and relatives. Consumers benefit from the research of friends and family into new products. In medicine and other technical fields, professional networks shape research patterns. In all these settings, the well-being of participants depends on social, geographic, or trading relationships. The countless ways in which network structures affect our well-being make it critical to understand: (i) how network structures impact behavior, (ii) what can be done, in the way of design by policymakers, to improve systemic outcomes. This area of study, broadly called network economics, is at the heart of my research interests. In my dissertation I focus on three specific applications of network theory. The first application concerns networks in trade, where network structure represents the organization of trade agreements between countries. The second application deals with networks in financial market, and the network is used to model the structure of interbank exposures. Lastly, for the third application, I consider networks in labor markets and migration. In this context, the network represents the structure of social relations between people. Each of these applications of network analysis is addressed by one of three chapters in the thesis.Network analysis (Planning); Social networks -- Mathematical models; Social sciences -- Network analysis; Economics, Mathematical;

Homogenization of some degenerate pseudoparabolic variational inequalities

Multiscale analysis of a degenerate pseudoparabolic variational inequality, modelling the two-phase flow with dynamical capillary pressure in a perforated domain, is the main topic of this work. Regularisation and penalty operator methods are applied to show the existence of a solution of the nonlinear degenerate pseudoparabolic variational inequality defined in a domain with microscopic perforations, as well as to derive a priori estimates for solutions of the microscopic problem. The main challenge is the derivation of a priori estimates for solutions of the variational inequality, uniformly with respect to the regularisation parameter and to the small parameter defining the scale of the microstructure. The method of two-scale convergence is used to derive the corresponding macroscopic obstacle problem