Nonbipartite Dulmage-Mendelsohn Decomposition for Berge Duality

The Dulmage-Mendelsohn decomposition is a classical canonical decomposition in matching theory applicable for bipartite graphs, and is famous not only for its application in the field of matrix computation, but also for providing a prototypal structure in matroidal optimization theory. The Dulmage-Mendelsohn decomposition is stated and proved using the two color classes, and therefore generalizing this decomposition for nonbipartite graphs has been a difficult task. In this paper, we obtain a new canonical decomposition that is a generalization of the Dulmage-Mendelsohn decomposition for arbitrary graphs, using a recently introduced tool in matching theory, the basilica decomposition. Our result enables us to understand all known canonical decompositions in a unified way. Furthermore, we apply our result to derive a new theorem regarding barriers. The duality theorem for the maximum matching problem is the celebrated Berge formula, in which dual optimizers are known as barriers. Several results regarding maximal barriers have been derived by known canonical decompositions, however no characterization has been known for general graphs. In this paper, we provide a characterization of the family of maximal barriers in general graphs, in which the known results are developed and unified

Cyclic cycle systems of the complete multipartite graph

In this paper, we study the existence problem for cyclic $\ell$-cycle decompositions of the graph $K_m[n]$, the complete multipartite graph with $m$ parts of size $n$, and give necessary and sufficient conditions for their existence in the case that $2\ell \mid (m-1)n$

Reconstructing cancer genomes from paired-end sequencing data

<p>Abstract</p> <p>Background</p> <p>A cancer genome is derived from the germline genome through a series of somatic mutations. Somatic structural variants - including duplications, deletions, inversions, translocations, and other rearrangements - result in a cancer genome that is a scrambling of intervals, or "blocks" of the germline genome sequence. We present an efficient algorithm for reconstructing the block organization of a cancer genome from paired-end DNA sequencing data.</p> <p>Results</p> <p>By aligning paired reads from a cancer genome - and a matched germline genome, if available - to the human reference genome, we derive: (i) a partition of the reference genome into intervals; (ii) adjacencies between these intervals in the cancer genome; (iii) an estimated copy number for each interval. We formulate the Copy Number and Adjacency Genome Reconstruction Problem of determining the cancer genome as a sequence of the derived intervals that is consistent with the measured adjacencies and copy numbers. We design an efficient algorithm, called Paired-end Reconstruction of Genome Organization (PREGO), to solve this problem by reducing it to an optimization problem on an interval-adjacency graph constructed from the data. The solution to the optimization problem results in an Eulerian graph, containing an alternating Eulerian tour that corresponds to a cancer genome that is consistent with the sequencing data. We apply our algorithm to five ovarian cancer genomes that were sequenced as part of The Cancer Genome Atlas. We identify numerous rearrangements, or structural variants, in these genomes, analyze reciprocal vs. non-reciprocal rearrangements, and identify rearrangements consistent with known mechanisms of duplication such as tandem duplications and breakage/fusion/bridge (B/F/B) cycles.</p> <p>Conclusions</p> <p>We demonstrate that PREGO efficiently identifies complex and biologically relevant rearrangements in cancer genome sequencing data. An implementation of the PREGO algorithm is available at <url>http://compbio.cs.brown.edu/software/</url>.</p

O direito ao lazer no estado socioambiental

Made available in DSpace on 2015-04-14T14:33:50Z (GMT). No. of bitstreams: 1 437488.pdf: 292746 bytes, checksum: c0073dabbdf0894d70f6352aaa9808bf (MD5) Previous issue date: 2011-12-14El presente estudio tiene como objetivo reflexionar sobre el derecho al ocio en el Estado del Medio Ambiente. Al definir el objeto de estudio identifica la importancia del ocio en la vida humana y caracterizan las actividades que pueden ser identificadas como actividades de ocio. Se presenta la historia de la relaci?n entre tiempo, trabajo y ocio. Se identifica el ocio como derecho social fundamental. Analiza el derecho al ocio en el medio ambiente natural, artificial, del trabajo y cultural. Elabora una investigaci?n documental a efectos de presentaci?n de los marcos normativos del derecho al ocio. Se determina el alcance de la protecci?n, a quien se destinan los derechos, y los deberes de protecci?n del Estado al ocio. Se refiere a la calidad de vida y medio ambiente ecol?gicamente equilibrado. Reconoce el derecho al ocio como un derecho de volumen multidimensional , con un tratamiento jur?dico espec?fico para cada una de sus dimensiones.O presente estudo tem por objetivo refletir sobre o direito ao lazer no Estado Socioambiental. Atrav?s da delimita??o do objeto de estudo, identifica-se a import?ncia do lazer na vida humana e caracterizam-se quais atividades podem ser identificadas como atividades de lazer. Apresenta-se a historicidade da rela??o entre tempo, trabalho e lazer. Identifica-se o lazer como direito fundamental social. Discute-se o direito ao lazer no meio ambiente natural, artificial, do trabalho e cultural. Elabora-se pesquisa documental com finalidade de apresenta??o dos marcos regulat?rios do direito ao lazer. Delimitam-se o ?mbito de prote??o, as titularidades, os destinat?rios, bem como os deveres de prote??o estatais do direito fundamental ao lazer. Relaciona-se o lazer ? qualidade de vida e ao ambiente ecologicamente equilibrado. Reconhece-se o direito ao lazer como direito de volumetria multidimensional, com tratamento jur?dico distinto para cada uma de suas dimens?es