16p11.2 600 kb Duplications confer risk for typical and atypical Rolandic epilepsy

Rolandic epilepsy (RE) is the most common idiopathic focal childhood epilepsy. Its molecular basis is largely unknown and a complex genetic etiology is assumed in the majority of affected individuals. The present study tested whether six large recurrent copy number variants at 1q21, 15q11.2, 15q13.3, 16p11.2, 16p13.11 and 22q11.2 previously associated with neurodevelopmental disorders also increase risk of RE. Our association analyses revealed a significant excess of the 600 kb genomic duplication at the 16p11.2 locus (chr16: 29.5-30.1 Mb) in 393 unrelated patients with typical (n = 339) and atypical (ARE; n = 54) RE compared with the prevalence in 65 046 European population controls (5/393 cases versus 32/65 046 controls; Fisher's exact test P = 2.83 × 10−6, odds ratio = 26.2, 95% confidence interval: 7.9-68.2). In contrast, the 16p11.2 duplication was not detected in 1738 European epilepsy patients with either temporal lobe epilepsy (n = 330) and genetic generalized epilepsies (n = 1408), suggesting a selective enrichment of the 16p11.2 duplication in idiopathic focal childhood epilepsies (Fisher's exact test P = 2.1 × 10−4). In a subsequent screen among children carrying the 16p11.2 600 kb rearrangement we identified three patients with RE-spectrum epilepsies in 117 duplication carriers (2.6%) but none in 202 carriers of the reciprocal deletion. Our results suggest that the 16p11.2 duplication represents a significant genetic risk factor for typical and atypical R

Approximation Theory in Combinatorial Optimization. Application to the generalized minimum spanning tree problem

We present an overview of the approximation theory in combinatorial optimization. As an application we consider the Generalized Minimum Spanning Tree (GMST) problem which is defined on an undirected complete graph with the nodes partitioned into clusters and non-negative costs are associated to the edges. This problem is NP-hard and it is known that a polynomial approximation algorithm cannot exist. We present an in-approximability result for the GMST problem and under special assumptions: cost function satisfying the triangle inequality and with cluster sizes bounded by $\rho$, we give an approximation algorithm with ratio $2 \rho$

Relaxation methods for the Generalized Minimum Spanning Tree Problem

Given an undirected graph whose nodes are partitioned into a number of clusters, the Generalized Minimum Spanning Tree problem (denoted GMSTP) is then to find a minimum-cost tree which includes exactly one node from each cluster. We present several integer programming formulations of the problem and compare the polyhedra defined by the LP relaxations of these formulations. Based on a new formulation of the GMSTP we give an heuristic solution, a lower bound procedure and discuss the advantages of our approach in comparison with an erlier method

Genetic characterization of egg weight, egg production and age at first egg in quails Caracterização genética da idade ao primeiro ovo, da produção e do peso dos ovos em linhagens de codornas

The objective of this research was to estimate genetic parameters for the traits egg weight, egg production in 189 days and age at first egg in three laying quails and one meat line of quails. Data was analyzed by Bayesian procedures using Gibbs sampling. The heritability estimates for egg weight, egg production in 189 days and age at first egg, were, respectively, for yellow line, 0.31, 0.84 and 0.53; for blue line, 0.14, 0.82 and 0.60; for red line, 0.70, 0.96 and 0.75; and for meat line, 0.73, 0.96 and 0.72. Genetic correlation between egg weight and egg production in 189 days, egg weight and day at first egg and egg production in 189 days and day at first egg were for yellow line, 0.58, -0.77 and -0.90; for blue line, 0.09, -0.01 and -0.95; for red line, 0.09, 0.03 and -0.76 and for meat line, -0.18, 0.19 and -0.91, respectively. Based on the probabilities of posterior parameter distribution overlap, the lines are divided in two different groups: one group with the yellow and blue lines and another with the red and meat lines.<br>O objetivo neste estudo foi obter estimativas de parâmetros genéticos para as características peso do ovo, produção de ovos em 189 dias de postura e dia do primeiro ovo em codornas de três linhagens de postura e uma de corte. Os dados foram analisados por meio de procedimentos bayesianos usando amostragem de Gibbs. As estimativas de herdabilidade para peso do ovo, produção de ovos em 189 dias de postura e dia do primeiro ovo foram, respectivamente, para a linhagem amarela, 0,31; 0,84 e 0,53; azul, 0,14; 0,82 e 0,60; vermelha, 0,70; 0,96 e 0,75; e de corte, 0,73; 0,96 e 0,72. As correlações genéticas entre peso do ovo e produção de ovos em 189 dias de postura, peso do ovo e dia do primeiro ovo e, produção de ovos em 189 dias de postura e dia do primeiro ovo foram, para amarela, 0,58; -0,77; e -0,90; azul, 0,09; -0,01; e -0,95; vermelha, 0,09; 0,03; e -0,76; e de corte, -0,18; 0,19 e -0,91. A partir das probabilidades de superposição das distribuições posteriories dos parâmetros, as linhagens dividem-se em dois grupos distintos: um com as linhagens amarela e azul e outro com as linhagens vermelha e de corte