Genome reconstruction and combinatoric analyses of rearrangement evolution

Cancer is often associated with a high number of large-scale, structural rearrangements. In a highly selective environment, some `driver' mutations conferring clonal growth advantage will be positively selected, accounting for further cancer development. Clarifying their nature, as well as their contribution to the pathology is a major current focus of biomedical research. Next generation sequencing technologies can be used nowadays to generate high-resolution data-sets of these alterations in cancer genomes. This project has been developed along two main lines: 1) the reconstruction of cancer aberrant karyotypes, together with their underlying evolutionary history; 2) the elucidation of some combinatorial properties associated with gene duplications. We applied graph theory to the problem of reconstructing the final cancer genome sequence; additionally, we developed an algorithmic approach for the reconstruction of a multi-step evolution consistent with read coverage and paired end data, giving insights on the possible molecular mechanisms underlying rearrangements. Looking at the combinatorics of both tandem and inverted duplication, we developed an algebraic formalism for the representation of these processes. This allowed us to both explore the geometric properties of sequences arising by Tandem Duplication (TD), and obtain a recursion for the number of tandem duplications evolutions after n events. Such results are missing for inverted duplications, whose combinatorial properties have been nevertheless deeply elucidated. Our results have allowed: 1) the identification, through an original approach, of potential rearrangement mechanisms associated with cancer development, and 2) the definition and mathematical description of the complete evolutionary space of specific rearrangement classes

Localization of Deformations in Finite Elastoplasticity

In this paper the guidelines for constructing a geometrical model for the localization of deformations during elastic-plastic deformations are given. A geometrical object, namely the physical metric, introduced to take into account the internal disarrangement during the plastic flow. A number of very general thermomechanical relations are obtained. Constitutive relations giving the conditions for the absence of localization phenomena are also obtained for the two different cases of decomposition of the total deformation gradient into the elastic and the plastic part (Lee, 1969; Nemat-Nasser, 1.979)

Genomic Evidence for an African Expansion of Anatomically Modern Humans by a Southern Route

There is general agreement among scientists about a recent (less than 200,000 yrs ago) African origin of anatomically modern humans, whereas there is still uncertainty about whether, and to what extent, they admixed with archaic populations, which thus may have contributed to the modern populations’ gene pools. Data on cranial morphology have been interpreted as suggesting that, before the main expansion from Africa through the Near East, anatomically modern humans may also have taken a Southern route from the Horn of Africa through the Arabian peninsula to India, Melanesia and Australia, about 100,000 yrs ago. This view was recently supported by archaeological findings demonstrating human presence in Eastern Arabia 90,000 yrs ago. In this study we analyzed genetic variation at 111,197 nuclear SNPs in nine populations (Kurumba, Chenchu, Kamsali, Madiga, Mala, Irula, Dalit, Chinese, Japanese), chosen because their genealogical relationships are expected to differ under the alternative models of expansion (single vs. multiple dispersals). We calculated correlations between genomic distances, and geographic distances estimated under the alternative assumptions of a single dispersal, or multiple dispersals, and found a significantly stronger association for the multiple dispersal model. If confirmed, this result would cast doubts on the possibility that some non-African populations (i.e., those whose ancestors expanded through the Southern route) may have had any contacts with Neandertals

Thermodynamics of Deformable Dielectrics with a Non-Euclidean Structure as Internal Variable

In this paper we apply the geometrical theory of thermodynamics with vectorial and tensorial internal variables to a model of deformable dielectrics (which include ferro-electric crystals) due to Maugin. We explicitly consider an internal (non-Euclidean) metric as a thermodynamical non-equilibrium variable, together with polarization and temperature gradients. With the aid of Clausius-Duhem inequality we obtain the extra entropy flux and the relevant thermodynamical restrictions on entropy and free energy

The Combinatorics of Tandem Duplication

Tandem duplication is an evolutionary process whereby a segment of DNA is replicated and proximally inserted. The different configurations that can arise from this process give rise to some interesting combinatorial questions. Firstly, we introduce an algebraic formalism to represent this process as a word producing automaton. The number of words arising from n tandem duplications can then be recursively derived. Secondly, each single word accounts for multiple evolutions. With the aid of a bi-coloured 2d- tree, a Hasse diagram corresponding to a partially ordered set is constructed, from which we can count the number of evolutions corresponding to a given word. Thirdly, we implement some subtree prune and graft operations on this structure to show that the total number of possible evolutions arising from n tandem duplications is $\prod_{k=1}^n(4^k - (2k + 1))$. The space of structures arising from tandem duplication thus grows at a super-exponential rate with leading order term $\mathcal{O}(4^{\frac{1}{2}n^2})$

Credit risk contagion and systemic risk on networks

This paper proposes a model of the dynamics of credit contagion through non-performing loans on financial networks. Credit risk contagion is modeled in the context of the classical SIS (Susceptibles-Infected-Susceptibles) epidemic processes on networks but with a fundamental novelty. In fact, we assume the presence of two different classes of infected agents, and then we differentiate the dynamics of assets subject to idiosyncratic risk from those affected by systemic risk by adopting a SIIS (Susceptible-Infected1-Infected2-Susceptible) model. In the recent literature in this field, the effect of systemic credit risk on the performance of the financial network is a hot topic. We perform numerical simulations intended to explore the roles played by two different network structures on the long-term behavior of assets affected by systemic risk in order to analyze the effect of the topology of the underlying network structure on the spreading of systemic risk on the structure. Random graphs, i.e., the Erdös-Rényi model, are considered "benchmark" network structures while core-periphery structures are often indicated in the literature as idealized structures, although they are able to capture interesting, specific features of real-world financial networks. Moreover, as a matter of comparison, we also perform numerical experiments on small-world networks.Fil: Dolfin, Marina. University Of Messina. Department of Engineering; ItaliaFil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Limosani, Michele. University Of Messina. Department Of Economics; ItaliaFil: Xibilia, Maria Gabriella. University Of Messina. Department Of Engineering; Itali