An equilibrium approach to modelling social interaction

The aim of this work is to put forward a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. After showing the formal equivalence linking econometric multinomial logit models to equilibrium statical mechanics, a multi- population generalization of the Curie-Weiss model for ferromagnets is considered as a starting point in developing a model capable of describing sudden shifts in aggregate human behaviour. Existence of the thermodynamic limit for the model is shown by an asymptotic sub-additivity method and factorization of correlation functions is proved almost everywhere. The exact solution for the model is provided in the thermodynamical limit by nding converging upper and lower bounds for the system's pressure, and the solution is used to prove an analytic result regarding the number of possible equilibrium states of a two-population system. The work stresses the importance of linking regimes predicted by the model to real phenomena, and to this end it proposes two possible procedures to estimate the model's parameters starting from micro-level data. These are applied to three case studies based on census type data: though these studies are found to be ultimately inconclusive on an empirical level, considerations are drawn that encourage further refinements of the chosen modelling approach, to be considered in future work.

Ottimizzazione delle reti di distribuzione idrica tramite algoritmi genetici multi-obiettivo

Water distribution networks optimization is a challenging problem due to the dimension and the complexity of these systems. Since the last half of the twentieth century this field has been investigated by many authors. Recently, to overcome discrete nature of variables and non linearity of equations, the research has been focused on the development of heuristic algorithms. This algorithms do not require continuity and linearity of the problem functions because they are linked to an external hydraulic simulator that solve equations of mass continuity and of energy conservation of the network. In this work, a NSGA-II (Non-dominating Sorting Genetic Algorithm) has been used. This is a heuristic multi-objective genetic algorithm based on the analogy of evolution in nature. Starting from an initial random set of solutions, called population, it evolves them towards a front of solutions that minimize, separately and contemporaneously, all the objectives. This can be very useful in practical problems where multiple and discordant goals are common. Usually, one of the main drawback of these algorithms is related to time consuming: being a stochastic research, a lot of solutions must be analized before good ones are found. Results of this thesis about the classical optimal design problem shows that is possible to improve results modifying the mathematical definition of objective functions and the survival criterion, inserting good solutions created by a Cellular Automata and using rules created by classifier algorithm (C4.5). This part has been tested using the version of NSGA-II supplied by Centre for Water Systems (University of Exeter, UK) in MATLAB® environment. Even if orientating the research can constrain the algorithm with the risk of not finding the optimal set of solutions, it can greatly improve the results. Subsequently, thanks to CINECA help, a version of NSGA-II has been implemented in C language and parallelized: results about the global parallelization show the speed up, while results about the island parallelization show that communication among islands can improve the optimization. Finally, some tests about the optimization of pump scheduling have been carried out. In this case, good results are found for a small network, while the solutions of a big problem are affected by the lack of constraints on the number of pump switches. Possible future research is about the insertion of further constraints and the evolution guide. In the end, the optimization of water distribution systems is still far from a definitive solution, but the improvement in this field can be very useful in reducing the solutions cost of practical problems, where the high number of variables makes their management very difficult from human point of view.

A multiparental cross population for mapping QTL for relevant agronomic traits in durum wheat (Triticum durum Desf.)

Multiparental cross designs for mapping quantitative trait loci (QTL) in crops are efficient alternatives to conventional biparental experimental populations because they exploit a broader genetic basis and higher mapping resolution. We describe the development and deployment of a multiparental recombinant inbred line (RIL) population in durum wheat (Triticum durum Desf.) obtained by crossing four elite cultivars characterized by different traits of agronomic value. A linkage map spanning 2,663 cM and including 7,594 single nucleotide polymorphisms (SNPs) was produced by genotyping 338 RILs with a wheat-dedicated 90k SNP chip. A cluster file was developed for correct allele calling in the framework of the tetraploid durum wheat genome. Based on phenotypic data collected over four field experiments, a multi-trait quantitative trait loci (QTL) analysis was carried out for 18 traits of agronomic relevance (including yield, yield-components, morpho-physiological and seed quality traits). Across environments, a total of 63 QTL were identified and characterized in terms of the four founder haplotypes. We mapped two QTL for grain yield across environments and 23 QTL for grain yield components. A novel major QTL for number of grain per spikelet/ear was mapped on chr 2A and shown to control up to 39% of phenotypic variance in this cross. Functionally different QTL alleles, in terms of direction and size of genetic effect, were distributed among the four parents. Based on the occurrence of QTL-clusters, we characterized the breeding values (in terms of effects on yield) of most of QTL for heading and maturity as well as yield component and quality QTL. This multiparental RIL population provides the wheat community with a highly informative QTL mapping resource enabling the dissection of the genetic architecture of multiple agronomic relevant traits in durum wheat.