On a Limit of Perturbed Conservation Laws with Diffusion and Non-Positive Dispersion

We consider a conservation law perturbed by a linear diffusion and a general form of non-positive dispersion. We prove the convergence of the corresponding solution to the entropy weak solution of the hyperbolic conservation law.

Detection of Glass pattern configurations by the primary visual cortex

The neurons in the primary visual cortex that respond to the orientation of visual stimuli were discovered in the late 1950s (Hubel, D.H. & Wiesel, T.N. 1959. J. Physiol. 148:574-591) but how they achieve this response is poorly understood. Recently, experiments have demonstrated that the visual cortex may use the image processing techniques of cross or auto-correlation to detect the streaks in random dot patterns (Barlow, H. & Berry, D.L. 2010. Proc. R. Soc. B. 278: 2069-2075). These experiments made use of sinusoidally modulated random dot patterns and of the so-called Glass patterns - where randomly positioned dot pairs are oriented in a parallel configuration (Glass, L. 1969. Nature. 223: 578-580). The image processing used by the visual cortex could be inferred from how the threshold of detection of these patterns in the presence of random noise varied as a function of the dot density in the patterns. In the present study, the detection thresholds have been measured for other types of patterns including circular, hyperbolic, spiral and radial Glass patterns and an indication of the type of image processing (cross or auto-correlation) by the visual cortex is presented. As a result, it is hoped that this study will contribute to an understanding of what David Marr called the ‘computational goal’ of the primary visual cortex (Marr, D. 1982. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. New York: Freeman.)

Numerical invariants for measurable cocycles

The theory of numerical invariants for representations can be generalized to measurable cocycles. This provides a natural notion of maximality for cocycles associated to complex hyperbolic lattices with values in groups of Hermitian type. Among maximal cocycles, the class of Zariski dense ones turns out to have a rigid behavior. An alternative implementation of numerical invariants can be given by using equivariant maps at the level of boundaries and by exploiting the Burger-Monod approach to bounded cohomology. Due to their crucial role in this theory, we prove existence results in two different contexts. Precisely, we construct boundary maps for non-elementary cocycles into the isometry group of CAT(0)-spaces of finite telescopic dimension and for Zariski dense cocycles into simple Lie groups. Then we approach numerical invariants. Our first goal is to study cocycles from complex hyperbolic lattices into the Hermitian group SU(p,q). Following the theory recently developed by Moraschini and Savini, we define the Toledo invariant by using the pullback along cocycles, also by involving boundary maps. For cocycles Γ × X → SU(p,q) with 1

Homological and Hodge-theoretic aspects of matroids and polymatroids

In the first part of this thesis, we study the action of the automorphism group of a matroid on the homology space of the co-independent complex. This representation turns out to be isomorphic, up to tensoring with the sign representation, with that on the homology space associated with the lattice of flats. In the case of the cographic matroid of the complete graph, this result has application in algebraic geometry: indeed De Cataldo, Heinloth and Migliorini use this outcome to study the Hitchin fibration. In the second part, on the other hand, we use ideas from algebraic geometry to prove a purely combinatorial result. We construct a Leray model for a discrete polymatroid with arbitrary building set and we prove a generalized Goresky-MacPherson formula. The first row of the model is the Chow ring of the polymatroid; we prove Poincaré duality, Hard-Lefschetz theorem and Hodge-Riemann relations for the Chow ring.

Gene expression and genome-wide association studies analysis to select heavy pigs for protected designation of origin cured meats production

The high quality of protected designation of origin (PDO) dry-cured pork products depends largely on the chemical and physical parameters of the fresh meat and their variation during the production process of the final product. The discovery of the mechanisms that regulate the variability of these parameters was aided by the reference genome of swine adjuvant to genetic analysis methods. This thesis can contribute to the discovery of genetic mechanisms that regulate the variability of some quality parameters of fresh meat for PDO dry-cured pork production. The first study is of gene expression and showed that between low and high glycolytic potential (GP) samples of Semimembranosus muscle of Italian Large White (ILW) pigs in early postmortem, the differentially expressed genes were all but one over expressed in low GP. These were involved in ATP biosynthesis processes, calcium homeostasis, and lipid metabolism including the potential master regulator gene Peroxisome Proliferator-Activated Receptor Alpha (PPARA). The second is a study in commercial hybrid pigs to evaluate correlations between carcass and fresh ham traits, including carcass and fresh ham lean meat percentages, the former, a potential predictor of the latter. In addition, a genome-wide association study allowed the identification of chromosome-wide associations with phenotypic traits for 19 SNPs, and genome-wide associations for 14 SNPs for ferrochelatase activity. The latter could be a determinant for color variation in nitrite-free dry-cured ham. The third study showed gene expression differences in the Longissimus thoracis muscle of ILW pigs by feeding diets with extruded linseed (source of polyunsaturated fatty acids) and vitamin E and selenium (diet three) or natural (diet four) antioxidants. The diet three promoted a more rapid and massive immune system response possibly determined by improvement in muscle tissue function, while the diet four promoted oxidative stability and increased the anti-inflammatory potential of muscle tissue.