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Alternating Euler trails has been extensively studied for its diverse applications, for example, in genetic and molecular biology, social science and channel assignment in wireless networks, as well as for theoretical reasons. We will consider the following edge-coloring. Let $H$ be a graph possibly with loops and $G$ a graph without loops. An $H$-coloring of $G$ is a function $c: E(G) \rightarrow V(H)$. We will say that $G$ is an $H$-colored graph whenever we are taking a fixed $H$-coloring of $G$. A sequence $W=(v_0,e_0^1, \ldots, e_0^{k_0},v_1,e_1^1,\ldots,e_{n-1}^{k_{n-1}},v_n)$ in $G$, where for each $i \in \{0,\ldots, n-1\}$, $k_i \geq 1$ and $e_i^j = v_iv_{i+1}$ is an edge in $G$, for every $j \in \{1,\ldots, k_i \}$, is a dynamic $H$-trail if $W$ does not repeat edges and $c(e_i^{k_i})c(e_{i+1}^1)$ is an edge in $H$, for each $i \in \{0,\ldots,n-2\}$. In particular a dynamic $H$-trail is an alternating Euler trail when $H$ is a complete graph without loops and $k_i=1$, for every $i \in \{1,\ldots,n-1\}$. In this paper, we introduce the concept of dynamic $H$-trail, which arises in a natural way in the modeling of many practical problems, in particular, in theoretical computer science. We provide necessary and sufficient conditions for the existence of closed Euler dynamic $H$-trail in $H$-colored multigraphs. Also we provide polynomial time algorithms that allows us to convert a cycle in an auxiliary graph, $L_2^H(G)$, in a closed dynamic H-trail in $G$, and vice versa, where $L_2^H(G)$ is a non-colored simple graph obtained from $G$ in a polynomial time., Comment: 14 pages, 4 figures

RESUMEN : Durante los últimos años el número de investigaciones realizadas en el campo de la microbiota intestinal y su repercusión en el organismo ha crecido exponencialmente. Además de profundizar sobre las funciones que ejerce y sus mecanismos de acción, la microbiota intestinal se ha relacionado con diversas patologías estableciéndolas como un factor importante tanto en la etiología, diagnóstico y tratamiento de ellas. De esta forma una de las implicaciones más estudias de la microbiota intestinal, es el papel que ejerce en una de las neoplasias más prevalentes, el carcinoma colorrectal (CCR). En esta revisión se aborda su grado de implicación en la patología y cómo afecta en origen, desarrollo y cómo se postula como una nueva arma el tratamiento de la enfermedad. Desde hace varias décadas la patogenia del CCR se ha descrito como una enfermedad multifactorial donde las variaciones genéticas y los factores ambientales conformaban el modelo etiopatogénico, sin embargo en los últimos años gracias al avance en el conocimiento de los microorganismos que habitan en el tracto gastrointestinal, se ha descrito un nuevo punto de vista a la hora de entender mejor la enfermedad. El conocer el papel exacto que desempeña la microbiota intestinal en el CCR ofrece un amplio abanico de posibilidades para incidir sobre la enfermedad y conocer con exactitud todos los mecanismos implicados en su desarrollo. ABSTRACT : During the last few years, the number of investigations carried out in the field of gut microbiota and its impact on the human body has grown exponentially. Furthermore, in addition to deepening on the functions and its mechanism of action, the intestinal microbiota has been related to various pathologies establishing itself as an important factor in the etiology, diagnosis and treatment of them. Thus, one of the most studied implications of the intestinal microbiota is the role it plays in one of the most prevalent neoplasms, colorectal carcinoma (CRC). This review addresses its degree of involvement in the pathology and how it affects its origin, development and how it is postulated as a new weapon in the treatment of the disease. For several decades, the pathogenesis of CRC has been described as a multifactorial disease where genetic variations and environmental factors made up the etiopathogenic model; however, in recent years, thanks to advances in the knowledge of the microorganisms that inhabit the gastrointestinal tract, a new point of view has been described when it comes to understanding the disease. Therefore, understanding the exact role of gut microbiota plays in CRC offers a wide range of possibilities to affect the disease and to know exactly all the mechanisms involved in its development. Grado en Medicina

Determinantal ideals of graphs generalize, among others, the spectrum and the Smith normal form (SNF) of integer matrices associated to graphs. In this work we investigate the relationship of the spectrum and the SNF with the determinantal ideals. We show that an eigenvalue divides the $k$-th invariant factor of its SNF if the eigenvalue belongs to a variety of the $k$-th univariate integer determinantal ideal of the matrix. This result has as a corollary a theorem of Rushanan. We also study graphs having the same determinantal ideals with at most one indeterminate; the socalled codeterminantal graphs, which generalize the concepts of cospectral and coinvariant graphs. We establish a necessary and sufficient condition for graphs to be codeterminantal on $\mathbb{R}[x]$, and we present some computational results on codeterminantal graphs up to 9 vertices. Finally, we show that complete graphs and star graphs are determined by the SNF of its distance Laplacian matrix., Comment: arXiv admin note: text overlap with arXiv:1401.1773 by other authors

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This project studies FPGA-based heterogeneous computing architectures with the objective of discovering their ability to optimize the performances of algorithms characterized by irregular memory access patterns. The example used to achieve this is a graph algorithm known as Triad Census Algorithm, whose implementation has been developed and tested. First of all, the triad census algorithm is presented, explaining the possible variants and reviewing the existing implementations upon different architectures. The analysis focuses on the parallelization techniques which have allowed to boost performance, thus reducing execution time. Besides, the study tackles the OpenCL programming model, the standard used to develop the final application. Special attention is paid to the language details that have motivated some of the most important design decisions. The dissertation continues with the description of the project implementation, including the application objectives, the system design, and the different variants developed to enhance algorithm performance. Finally, some of the experimental results are presented and discussed. All implemented versions are evaluated and compared to decide which is the best in terms of scalability and execution time.

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A linear system is a pair $(P,\mathcal{L})$ where $\mathcal{L}$ is a family of subsets on a ground finite set $P$ such that $|l\cap l^\prime|\leq 1$, for every $l,l^\prime \in \mathcal{L}$. If all elements of $\mathcal{L}$ of a linear system $(P,\mathcal{L})$, then the linear system is called $r$-uniform linear system. The transversal number of a linear system $(P,\mathcal{L})$, $\tau(P,\mathcal{L})$, is the minimum cardinality of a subset $\hat{P}\subseteq P$ satisfying $l\cap\hat{P}\neq\emptyset$, for every $l\in\mathcal{L}$. The 2-packing number of a linear system $(P,\mathcal{L})$, $\nu_2(P,\mathcal{L})$, is the maximum cardinality of a subset $R\subseteq\mathcal{L}$ such that, any three elements of $R$ don't have a common point (are triplewise disjoint), that is, if three elements are chosen in $R$, then they are not incidents in a common point. For $r\geq2$, let $(P,\mathcal{L})$ be an $r$-uniform linear system. In "{\sc M. A. Henning and A. Yeo:} {\it Hypergraphs with large transversal number,} Discrete Math. {\bf 313} (2013), no. 8, 959--966." Henning and Yeo state the following question: Is it true that if $(P,\mathcal{L})$ is an $r$-uniform linear system then $\tau(P,\mathcal{L})\leq\displaystyle\frac{|P|+|\mathcal{L}|}{r+1}$ holds for all $r\geq2$?. In this note, we give some results of $r$-uniform linear systems, whose 2-packing number is fixed, satisfying the inequality.

Foram estudados os registros de 238 vacas holandesas, variedade Preta e Branca, criadas no Campo Experimental de São Bento do Una da Empresa Pernambucana de Pesquisa Agropecuária (IPA), PE. Foram analisados os efeitos de diversos fatores como causas de variação na idade à primeira cria e período de serviço. Os resultados encontrados foram: idade à primeira cria de 941 +- 136 dias com coeficiente de variação de 14,45%, constatando-se que o ano do nascimento influencia, de forma linear a quadrática, a idade à primeira cria. O período de serviço encontrado foi 157,9 +- 87,25 dias com coeficiente de variação 55,24%, sendo influenciado pela produção de leite e período seco da lactação anterior.

En un estudio sobre los problemas de la enseñanza secundaria en Costa Rica, Azofeifa ha analizado aspectos tales como la orientación, los cursos de estudio, la organización, la metodología y la administración; ha propuesto una orientación y una organización nuevas que se adapten mejor a las necesidades y aspiraciones del país. Una comisión del Ministerio de Educación ha llevado a cabo un estudio sobre la segunda enseñanza (5) en el que se tratan los mismos problemas analizados por Azofeifa.