Bounds of the rank of the Mordell-Weil group of jacobians of hyperelliptic curves

In this article we extend work of Shanks and Washington on cyclic extensions, and elliptic curves associated to the simplest cubic fields. In particular, we give families of examples of hyperelliptic curves $C: y^2=f(x)$ defined over $\mathbb{Q}$, with $f(x)$ of degree $p$, where $p$ is a Sophie Germain prime, such that the rank of the Mordell--Weil group of the jacobian $J/\mathbb{Q}$ of $C$ is bounded by the genus of $C$ and the $2$-rank of the class group of the (cyclic) field defined by $f(x)$, and exhibit examples where this bound is sharp.Comment: 22 pages, To appear in J. Th\'eor. Nombres Bordeau

Advanced motion system using animations and physics

Treball final de Grau en Disseny i Desenvolupament de Videojocs. Codi: VJ1241. Curs acadèmic: 2019/2020To create an animator with an extensive library of animations, giving it variety. The final result should look smooth and should work correctly and needs to be realistic. To learn about ragdoll and create one that reacts and behaves in a realistic way. To implement a smooth movement system that involves procedural animation, with interpolated transitions and real-time adjusted animations according to the environment. Discover how a complex system used in one of the most advanced games can be implemented in Unity, and if it is not possible, why

Suppressors of selection

Inspired by recent works on evolutionary graph theory, an area of growing interest in mathematical and computational biology, we present the first known examples of undirected structures acting as suppressors of selection for any fitness value $r > 1$. This means that the average fixation probability of an advantageous mutant or invader individual placed at some node is strictly less than that of this individual placed in a well-mixed population. This leads the way to study more robust structures less prone to invasion, contrary to what happens with the amplifiers of selection where the fixation probability is increased on average for advantageous invader individuals. A few families of amplifiers are known, although some effort was required to prove it. Here, we use computer aided techniques to find an exact analytical expression of the fixation probability for some graphs of small order (equal to $6$, $8$ and $10$) proving that selection is effectively reduced for $r > 1$. Some numerical experiments using Monte Carlo methods are also performed for larger graphs.Comment: New title, improved presentation, and further examples. Supporting Information is also include

Fast and asymptotic computation of the fixation probability for Moran processes on graphs

Evolutionary dynamics has been classically studied for homogeneous populations, but now there is a growing interest in the non-homogenous case. One of the most important models has been proposed by Lieberman, Hauert and Nowak, adapting to a weighted directed graph the classical process described by Moran. The Markov chain associated with the graph can be modified by erasing all non-trivial loops in its state space, obtaining the so-called Embedded Markov chain (EMC). The fixation probability remains unchanged, but the expected time to absorption (fixation or extinction) is reduced. In this paper, we shall use this idea to compute asymptotically the average fixation probability for complete bipartite graphs. To this end, we firstly review some recent results on evolutionary dynamics on graphs trying to clarify some points. We also revisit the 'Star Theorem' proved by Lieberman, Hauert and Nowak for the star graphs. Theoretically, EMC techniques allow fast computation of the fixation probability, but in practice this is not always true. Thus, in the last part of the paper, we compare this algorithm with the standard Monte Carlo method for some kind of complex networks.Comment: Corrected typo

Gasificación en gasificadores de flujo arrastrado: Simulación en ASPEN plus y comparación

El documento consta de diferentes simulaciones en ASPEN Plus de una planta IGCC con diferentes modelos de gasificador y diferentes métodos de enfriamiento del gas. Se realizan cuatro simulaciones principales, dos con carbón como combustible, una con biomasa y una última donde se estudia la co-gasificación de carbón y biomasa. Los resultados obtenidos para las diferentes plantas son estudiados y una breve valoración es expresada