Optimal management of natural resources. Accounting for heterogeneity

Dynamic optimization methods have become increasingly important over the last years in economics. Within the dynamic optimization techniques employed, optimal control has emerged as the most powerful tool for the theoretical economic analysis. However, there is the need to advance further and take account that many dynamic economic processes are, in addition, dependent on some other parameter different than time. One can think of relaxing the assumption of a representative (homogeneous) agent in macro- and micro-economic applications allowing for heterogeneity among the agents. For instance, the optimal adaptation and diffusion of a new technology over time, may depend on the age of the person that adopted the new technology. Therefore, the economic models must take account of heterogeneity conditions within the dynamic framework. This thesis intends to accomplish two goals. The first goal is to analyze and revise existing environmental policies that focus on defining the optimal management of natural resources over time, by taking account of the heterogeneity of environmental conditions. Thus, the thesis makes a policy orientated contribution in the field of environmental policy by defining the necessary changes to transform an environmental policy based on the assumption of homogeneity into an environmental policy which takes account of heterogeneity. As a result the newly defined environmental policy will be more efficient and likely also politically more acceptable since it is tailored more specifically to the heterogeneous environmental conditions. Additionally to its policy orientated contribution, this thesis aims making a methodological contribution by applying a new optimization technique for solving problems where the control variables depend on two or more arguments --- the so-called two-stage solution approach ---, and by applying a numerical method --- the Escalator Boxcar Train Method --- for solving distributed optimal control problems, i.e., problems where the state variables, in addition to the control variables, depend on two or more arguments. Chapter 2 presents a theoretical framework to determine optimal resource allocation over time for the production of a good by heterogeneous producers, who generate a stock externalit and derives government policies to modify the behavior of competitive producers in order to achieve optimality. Chapter 3 illustrates the method in a more specific context, and integrates the aspects of quality and time, presenting a theoretical model that allows to determine the socially optimal outcome over time and space for the problem of waterlogging in irrigated agricultural production. Chapter 4 of this thesis concentrates on forestry resources and analyses the optimal selective-logging regime of a size-distributed forest.

Synthesis of unusual alpha-amino acids and study of the effect of their incorporation into antimicrobial peptides. Total synthesis of biactive marine natural products and analogues thereof

The principle theme of this thesis was the synthesis of bioactive compounds. To this end, this work was focus on two main projects. The first one, which was carried out in the Department of Chemistry of the University of Girona under the supervision of Dr Montserrat Heras, concerned the synthesis of new unnatural amino acids bearing a pyrimidine ring within their side chain for incorporation into the antimicrobial peptide BP100 following a rational design in order to improve its biological profile. On the other hand, the second chapter of this thesis was developed in collaboration with the Laboratoire de Chimie Organique (ESPCI-ParisTech, Paris, France) under the guidance of Pr Janine Cossy and Dr Arseniyadis. This chapter was centered on the total synthesis of three marine natural products with complex structures and interesting biological activities: acremolide B, (–) bitungolide F and lyngbouilloside.