We consider the computational complexity of evaluating the Tutte polynomial of three particular classes of greedoid, namely rooted graphs, rooted digraphs and binary greedoids. Furthermore we construct polynomial-time algorithms to evaluate the Tutte polynomial of these classes of greedoid when they're of bounded tree-width. We also construct a Möbius function formulation for the characteristic polynomial of a rooted graph and determine the computational complexity of computing the coefficients of the Tutte polynomial of a rooted graph.

Despite being found in all presently sequenced genomes, the evolution of tandemly repeated sequences has only just begun to be understood. We can represent the duplication history of tandemly repeated sequences with duplication trees. Most phylogenetic techniques need to be modified to be used on duplication trees. Due to gene loss, it is not always possible to reconstruct the duplication history of a tandemly repeated sequence. This thesis addresses this problem by providing a polynomial-time locally optimal algorithm to reconstruct the duplication history of a tandemly repeated sequence in the presence of gene loss. Supertree methods cannot be directly applied to duplication trees. A polynomial-time algorithm that takes a forest of ordered phylogenies and looks for a super duplication tree is presented. If such a super duplication tree is found then the algorithm constructs the super duplication tree. However, the algorithm does not always find a super duplication tree when one exists. The SPR topological rearrangement in its current form cannot be used on duplication trees. The necessary modifications are made to an agreement forest so that the SPR operation can be used on duplication trees. This operation is called the duplication rooted subtree prune and regraft operation (DrSPR). The size of the DrSPR neighbourhood is calculated for simple duplication trees and the tree shapes that maximize and minimize this are given.

C. Scott Littleton and Ann C. Thomas' assertion that the core of the Arthurian legends is ultimately rooted in a Sarmatian heroic tradition is challenged. It is argued that, at best, the Arthurian legends contain several names and motifs of possible Sarmatian origin that have been borrowed into what Arthurian scholars have long recognized as an inherently Celtic tradition. Several agencies for their introduction into the Arthurian cycle are considered. It is proposed that two names and at least one of the motifs were introduced by Iazyge cataphractarii stationed along Hadrian's Wall in 175 AD. The other motifs, however, are thought to have been introduced at a much later date --possibly by returning members of the crusader population in the East during the twelfth century. / Thesis / Master of Arts (MA)

This thesis is a study of the subgroup structure of some remarkable groups of automorphisms of rooted trees. It is divided into two parts. The main result of the first part is seemingly of an algorithmic nature, establishing that the Gupta--Sidki 3-group G has solvable membership problem. This follows the approach of Grigorchuk and Wilson who showed the same result for the Grigorchuk group. The proof, however, is not algorithmic, and it moreover shows a striking subgroup property of G: that all its infinite finitely generated subgroups are abstractly commensurable with either G or G × G. This is then used to show that G is subgroup separable which, together with some nice presentability properties of G, implies that the membership problem is solvable. The proof of the main theorem is also used to show that G satisfies a "strong fractal" property, in that every infinite finitely generated subgroup acts like G on some rooted subtree. The second part concerns the subgroup structure of branch and weakly branch groups in general. Motivated by a natural question raised in the first part, a necessary condition for direct products of branch groups to be abstractly commensurable is obtained. From this condition it follows that the Gupta--Sidki 3-group is not abstractly commensurable with its direct square. The first main result in the second part states that any (weakly) branch action of a group on a rooted tree is determined by the subgroup structure of the group. This is then applied to answer a question of Bartholdi, Siegenthaler and Zalesskii, showing that the congruence subgroup property for branch and weakly branch groups is independent of the actions on a tree. Finally, the information obtained on subgroups of branch groups is used to examine which groups have an essentially unique branch action and why this holds.

In this thesis we propose a description of the operad defining post-Lie algebras in terms of rooted trees and we discuss some applications of such a construction. In particular, we re-derive both the free post-Lie algebra defined in [22] and the main result of the paper [8]. Furthermore, a possible extension of the concept of symmetric brace algebra to the category of the post-Lie algebras is proposed. / Nessa tese propomos a descrição da operad que define as álgebras pós-Lie em termos de árvores enraizadas e discutimos algumas aplicações dessa construção. Em particular, nós obtemos novamente a álgebra pós-Lie livre definida em [22] e o resultado principal do artigo [8]. Além disso, uma possível extensão do conceito de álgebra brace simétrica à categoria de álgebras pós-Lie é apresentada.

The purpose of this thesis is to explain why China put so much emphasizes on the Taiwan issue in their relations with the U.S. This will be explored by looking at what elements are affecting the commitment to the Taiwan question in Sino-American relations and how this can be explained by using ontological terms such as "rooted identity" and "significant others". Two key elements has been identified to analyze this; victimization and legitimacy. To evaluate the subject two research questions will be used; how can legitimacy and victimization explain China’s commitment to the Taiwan question when it comes to Sino-American relations? What is the connection between legitimacy, victimization and the PRC’s rooted identity? Policy-statement and official documents will be used to sheed light on the Taiwan-questions affects on Sino-American relations from an ontological security theory perspective. The thesis will argue that the PRC’s early history has great effects on their commitment to this issue and that legitimacy and victimization is affecting China’s commitment to Taiwan to the extent that it cannot accept an independent Taiwan. Hence this issue will continue to have great impact on China’s foreign relations, especially with the U.S. However, despite strong rhetoric’s China does not necessarily need to achieve unification with Taiwan in the near future.

It has become well known that an evolutionary tree is inadequate to represent fully the history of life. Two possible ways of dealing with this are the rooted subtree prune and regraft distance between a pair of trees, which measures how different they are, and the slightly more biologically sound hybridisation number of a set of trees that attempts to determine the minimum number of hybrid events that must have occurred for a given set of evolutionary trees. When characterised via agreement forests both problems are, although NP hard, fixed parameter tractable---meaning the problem can be converted to a similar problem with a smaller input size. This thesis investigates ways of improving existing algorithms for calculating the minimum rooted subtree prune and regraft distance and hybridisation number for a pair or, in the latter case, set of trees. In both cases a technique is used that allows the problem to be rekernelised during the run of the program. Another, less effective method, is also looked at which finds the rooted subtree prune and regraft distance or hybridisation number solely on what cannot be contained within any agreement forest. Additionally the characterisation of the minimum rooted subtree prune and regraft distance via maximum agreement forests is extended to non-binary trees and the hybridisation number of a set of phylogenetic trees is extended to unrooted trees.

It has become well known that an evolutionary tree is inadequate to represent fully the history of life. Two possible ways of dealing with this are the rooted subtree prune and regraft distance between a pair of trees, which measures how different they are, and the slightly more biologically sound hybridisation number of a set of trees that attempts to determine the minimum number of hybrid events that must have occurred for a given set of evolutionary trees. When characterised via agreement forests both problems are, although NP hard, fixed parameter tractable---meaning the problem can be converted to a similar problem with a smaller input size. This thesis investigates ways of improving existing algorithms for calculating the minimum rooted subtree prune and regraft distance and hybridisation number for a pair or, in the latter case, set of trees. In both cases a technique is used that allows the problem to be rekernelised during the run of the program. Another, less effective method, is also looked at which finds the rooted subtree prune and regraft distance or hybridisation number solely on what cannot be contained within any agreement forest. Additionally the characterisation of the minimum rooted subtree prune and regraft distance via maximum agreement forests is extended to non-binary trees and the hybridisation number of a set of phylogenetic trees is extended to unrooted trees.

?rea de concentra??o: Produ??o vegetal. / Submitted by Jos? Henrique Henrique (jose.neves@ufvjm.edu.br) on 2017-01-03T16:10:54Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) debora_cintia_santos_avelar.pdf: 1075322 bytes, checksum: 956aee85f03869781bc0c12ae661e4f7 (MD5) / Approved for entry into archive by Rodrigo Martins Cruz (rodrigo.cruz@ufvjm.edu.br) on 2017-01-31T16:25:33Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) debora_cintia_santos_avelar.pdf: 1075322 bytes, checksum: 956aee85f03869781bc0c12ae661e4f7 (MD5) / Made available in DSpace on 2017-01-31T16:25:33Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) debora_cintia_santos_avelar.pdf: 1075322 bytes, checksum: 956aee85f03869781bc0c12ae661e4f7 (MD5) Previous issue date: 2016 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / A determina??o da dose de inoculante ? essencial para a obten??o de benef?cios da utiliza??o de fungos ectomicorr?zicos (FEM) em mudas de eucalipto. O objetivo deste estudo foi avaliar a melhor dose de inoculante miceliano de isolados de Pisolithus sp., encapsulados em gel de alginato de c?lcio, visando a promo??o da coloniza??o, nutri??o e do crescimento das mudas de clones de eucalipto em viveiro comercial. Em experimentos independentes e utilizando aduba??o fosfatada reduzida, foram produzidas mudas de dois clones de eucalipto (AEC 2034 e AEC 2233) inoculados com 9, 18 e 36 esferas de inoculante miceliano dos isolados f?ngicos D17, D216, D5 e D95 e um tratamento N?o-inoculado (fatorial 3x5). Al?m disso, foram feitos mais dois tratamentos adicionais com (Controle) e sem (Comercial) redu??o da aduba??o fosfatada do substrato e sem adi??o dos inoculantes. A dose de 36 esferas de inoculante, em geral, promoveu maiores ganhos para as mudas de eucalipto, como maior coloniza??o, massa seca da parte a?rea (MSPA) e de ra?zes (MSR) e teores de K, sendo algumas vezes maior que nas mudas do Controle e Comercial. A maior altura da parte a?rea e di?metro do coleto foram observados com o uso de 18 esferas. A coloniza??o ectomicorr?zica foi maior nas mudas inoculadas e considerada m?dia para os dois clones. A inocula??o pr?via nos dois clones n?o promoveu aumento nos teores de P em rela??o ao Comercial, no entanto para o clone AEC 2233 com a utiliza??o do D216, houve aumento nos teores de P em rela??o ao N?o-inoculado, sendo este isolado o mesmo que proporcionou uma das maiores porcentagens de coloniza??o, contribuindo para maior absor??o desse nutriente. Em rela??o aos isolados, a inocula??o com o D17 em geral aumentou a sobreviv?ncia, altura, MSPA, MSR e teores de K no AEC 2034 e a altura e di?metro no AEC 2233, mas isto foi dependente da dose e do clone de eucalipto. A dose de 18 esferas foi mais apropriada, pois, na maioria dos casos, os maiores benef?cios como sobreviv?ncia, altura, di?metro, MSPA, MSR, coloniza??o, teores de N e K foram obtidos com a adi??o de 18 ou mais esferas por mini-estaca e, em alguns casos, os par?metros altura e coloniza??o foram reduzidos nas maiores doses. O isolado D17 ? promissor para uso em programas de micorriza??o controlada em viveiros comerciais de mudas clonais de eucalipto e a dose de 18 esferas por mini-estaca ? a mais recomendada. / Disserta??o (Mestrado) ? Programa de P?s-Gradua??o em Produ??o Vegetal, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2016. / The determination of the inoculum dose is essential for obtaining the benefits from the utilization of ectomycorrhizal fungi (EMF) in eucalypt saplings. The aim of this study was to evaluate the best dose of inoculum consists of mycelium from isolates Pisolithus sp., encapsulated in calcium alginate gel, aiming at promoting the colonization, nutrition and growth of the eucalypt rooted cuttings in commercial nursery. In independent experiments and using reduced phosphorus fertilization, were produced rooted cuttings from two eucalypts clones (AEC 2034 e AEC 2233) inoculated with 9, 8 and 36 beads of inoculum from fungal isolates D17, D216, D5 e D95 and one Non-inoculated treatment (factorial 3x5). Furthermore, two more additional treatments were performed with (Control) and without (Commercial) reduction of phosphorus fertilization of the substrate and without the addition of the inoculum.The dose of 36 inoculum beads, in general, has promoted higher benefits for the saplings, such as greater colonization, dry mass of shoot (DMS) and of roots (DMR) and K concentrations, sometimes being higher than in the saplings from Control and Commercial. The greater height of the shoot and collar diameter were observed with the use of 18 beads of inoculum. The ectomycorrhizal colonization was higher in inoculated saplings and considered average for the two clones. The previous inoculation in both clones did not promote an increase in P concentrations in relation to Commercial, however for the AEC 2233 clone with the utilization of D216, there was an increase in the P concentrations in relation to Non-inoculated, this being the same isolate that provided one of the greatest percentages of colonization, contributing to a higher absorption of this nutrient. Regarding the isolates, the inoculation with D17 in general increased the survival, height, DMS, DMR and K concentrations in AEC 2034, and height and diameter in AEC 2233, but this was dependent on the dose and on the eucalypt clone. The dose of 18 beads of inoculum was most appropriate, because in most cases, the greatest benefits as survival, height, diameter, DMS, DMR, colonization, N and K concentrations were obtained with addition of 18 or more beads of inoculum by mini-cutting and, in some cases, the parameters height and colonization were reduced with the highest doses. The isolate D17 is promising for its use in controlled mycorrization programs in commercial nurseries of eucalypt rooted cuttings and the dose of 18 beads by mini-cutting is the most recommended.

In this thesis we propose a description of the operad defining post-Lie algebras in terms of rooted trees and we discuss some applications of such a construction. In particular, we re-derive both the free post-Lie algebra defined in [22] and the main result of the paper [8]. Furthermore, a possible extension of the concept of symmetric brace algebra to the category of the post-Lie algebras is proposed. / Nessa tese propomos a descrição da operad que define as álgebras pós-Lie em termos de árvores enraizadas e discutimos algumas aplicações dessa construção. Em particular, nós obtemos novamente a álgebra pós-Lie livre definida em [22] e o resultado principal do artigo [8]. Além disso, uma possível extensão do conceito de álgebra brace simétrica à categoria de álgebras pós-Lie é apresentada.