Rearranjo de genomas : algoritmos e complexidade

This thesis discusses events of genome rearrangements problems: transposition, breakpoint, block interchange, short block move, and the restricted multi break. We consider problems of sorting, closest permutation, and the diameter. We develop approximation algorithms, NP-completeness and properties about these problems. Regarding the sorting by transpositions, which is an NP-complete problem, several approximation algorithms were proposed based on the graph called the reality and desire diagram. Through a case analyses of the cycles of this graph, we propose a new one which achieves so far the best 1.375 ratio and O(n log n) running time complexity. Although sorting by transpositions is NP-complete, there are several metrics whose sorting problems are polynomial or are open. In such cases, an interesting problem arises to find a permutation with maximum distance of an input permutation set at most some value, this is the closest permutation problem. We show that with respect to the polynomial distance problems of breakpoint and of block interchange, both problems are NP-complete. In order to explore properties on operations that are restriction or generalization of others, we deal with the operation of short block move and we propose the operation of restricted multi break. Regarding the short block move, we show tractable classes of permutations, properties on the permutation graph, and we show that the closest permutation problem is NP-complete. Regarding the restricted multi break, we study two versions: one where the number of non reversible blocks is bounded by a constant, and another one whose number of non reversible blocks is arbitrary. We prove tight bounds on the distance and the diameter problems for both versions.Esta tese trata de rearranjo de genomas nos eventos de: transposição, pontos de quebra, movimento de blocos, movimento de blocos curtos, e de multi corte restritos. Abordamos os problemas de ordenação, permutação mais próxima, e de diâmetro. Apresentamos algoritmos aproximativos, NP-completudes e propriedades. Sobre o problema de ordenação por transposições, provado ser NP-completo, alguns algoritmos aproximativos foram propostos baseados no grafo chamado diagrama de realidade e desejo. Através da análise dos ciclos deste grafo, propomos um novo algoritmo que atinge melhores resultados correntes, tanto de razão de aproximação de 1,375 quanto de complexidade de tempo de O(n log n). Embora ordenação por transposições seja NP-completo, há outros problemas polinomiais ou em aberto. Nestes casos, surge o desafio de encontrar uma permutação que esteja a uma distância máxima limitada por algum valor em relação a um conjunto de permutações dadas de entrada. Este é o problema de encontrar a permutação mais próxima. Mostramos que, em relação `as operações de pontos de quebra e de movimento de blocos, tais problemas são NP-completos. Com o objetivo de obter propriedades sobre operações que restingem ou generalizam outras, tratamos da operação de movimento de blocos curtos e propomos a operação de multi corte restritos. Sobre movimento de blocos curtos, mostramos classes com distâncias exatas, propriedades sobre o grafo de permutação, e mostramos que o problema de permutação mais próxima é NP-completo. Sobre multi corte restritos, tratamos de duas variações: uma cujo número de blocos não reversíveis é limitado por constante, e outra cujo número de blocos não reversíveis é arbitrário. Mostramos limites justos de distância e de diâmetro para ambas as versões

Bridge between worlds: relating position and disposition in the mathematical field

Using ethnographic observations and interview based research I document the production of research mathematics in four European research institutes, interviewing 45 mathematicians from three areas of pure mathematics: topology, algebraic geometry and differential geometry. I use Bourdieu's notions of habitus, field and practice to explore how mathematicians come to perceive and interact with abstract mathematical spaces and constructions. Perception of mathematical reality, I explain, depends upon enculturation within a mathematical discipline. This process of socialisation involves positioning an individual within a field of production. Within a field mathematicians acquire certain structured sets of dispositions which constitute habitus, and these habitus then provide both perspectives and perceptual lenses through which to construe mathematical objects and spaces. I describe how mathematical perception is built up through interactions within three domains of experience: physical spaces, conceptual spaces and discourse spaces. These domains share analogous structuring schemas, which are related through Lakoff and Johnson's notions of metaphorical mappings and image schemas. Such schemas are mobilised during problem solving and proof construction, in order to guide mathematicians' intuitions; and are utilised during communicative acts, in order to create common ground and common reference frames. However, different structuring principles are utilised according to the contexts in which the act of knowledge production or communication take place. The degree of formality, privacy or competitiveness of environments affects the presentation of mathematicians' selves and ideas. Goffman's concept of interaction frame, front-stage and backstage are therefore used to explain how certain positions in the field shape dispositions, and lead to the realisation of different structuring schemas or scripts. I use Sewell's qualifications of Bourdieu's theories to explore the multiplicity of schemas present within mathematicians' habitus, and detail how they are given expression through craftwork and bricolage. I argue that mathematicians' perception of mathematical phenomena are dependent upon their positions and relations. I develop the notion of social space, providing definitions of such spaces and how they are generated, how positions are determined, and how individuals reposition within space through acquisition of capital

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Handbook of Stemmatology

Stemmatology studies aspects of textual criticism that use genealogical methods. This handbook is the first to cover the entire field, encompassing both theoretical and practical aspects, ranging from traditional to digital methods. Authors from all the disciplines involved examine topics such as the material aspects of text traditions, methods of traditional textual criticism and their genesis, and modern digital approaches used in the field

URI Undergraduate and Graduate Course Catalog 2007-2008

This is a digitized, downloadable version of the University of Rhode Island course catalog.https://digitalcommons.uri.edu/course-catalogs/1059/thumbnail.jp

URI Undergraduate and Graduate Studies Catalog 1995-1997

This is a digitized, downloadable version of the 1995-97 Bulletin of the University of Rhode Island: Undergraduate and Graduate Studies.https://digitalcommons.uri.edu/course-catalogs/1048/thumbnail.jp

URI Undergraduate and Graduate Course Catalog 2011-2012

This is a digitized, downloadable version of the University of Rhode Island course catalog.https://digitalcommons.uri.edu/course-catalogs/1063/thumbnail.jp

URI Undergraduate and Graduate Course Catalog 2004-2005

https://digitalcommons.uri.edu/course-catalogs/1056/thumbnail.jp

URI Undergraduate and Graduate Course Catalog 2005-2006

This is a digitized, downloadable version of the University of Rhode Island course catalog.https://digitalcommons.uri.edu/course-catalogs/1057/thumbnail.jp