Nesta dissertação trabalhamos com o Modelo de Hull-White para a Estrutura a Termo da Taxa de Juro (ETTJ), considerando o caso em que a volatilidade é uma função determinística do tempo, e duas extensões em que ela segue um processo estocástico não correlacionado com a taxa de juro: uma considerando um movimento Browniano geométrico com drift nulo, e outra considerando um processo de Ornstein-Uhlenbeck com reversão á média. Obtemos aproximações perturbativas para o preço de Zero-coupoun bonds aplicando o Metódo de Perturbação Regular quando os parâmetros envolvendo a volatilidade são pequenos, e realizamos simulações para o caso em que os coeficientes são constantes (Modelo de Vasicek). Desta forma, obtemos uma aproximação para o yield curve, ou ETTJ. Para o caso clássico comparamos a aproximação perturbativa com a solução exata do modelo, e concluímos que uma aproximação considerando correções de até quarta ordem é muito precisa. Para os modelos com volatilidade estocástica, comparamos a aproximação perturbativa de quarta ordem com simulações de Monte Carlo, e observamos um comportamento qualitativo semelhante, principalmente para maturidades menores. / In this dissertation we work with the Hull-White model for the Term-Structure of Interest Rate (TSIR), considering the situation where the volatility is a deterministic function of time, and two extensions that follow a stochastic process uncorrelated with the interest rate: the first considers a geometric Brownian motion with zero drift, and the second a Ornstein-Uhlenbeck process with mean-reversion. We obtain perturbation approximations for the Zero-coupon bond prices using the Regular Perturbation Method when the parameters involving the volatility are small, and perform simulations for the constant coefficient case (Vasicek Model). Once this is done, we obtain a perturbative approximation for the yield curve, or TSIR. For the classical case we compare this approximation with the exact solution, and conclude that a fourth order perturbative approximation is very precise. For the cases with stochastic volatility, we compared the fourth order perturbative approximation with Monte Carlo simulations, and observed essentially the same qualitative behavior, mainly for short maturities.

Nesta dissertação trabalhamos com o Modelo de Hull-White para a Estrutura a Termo da Taxa de Juro (ETTJ), considerando o caso em que a volatilidade é uma função determinística do tempo, e duas extensões em que ela segue um processo estocástico não correlacionado com a taxa de juro: uma considerando um movimento Browniano geométrico com drift nulo, e outra considerando um processo de Ornstein-Uhlenbeck com reversão á média. Obtemos aproximações perturbativas para o preço de Zero-coupoun bonds aplicando o Metódo de Perturbação Regular quando os parâmetros envolvendo a volatilidade são pequenos, e realizamos simulações para o caso em que os coeficientes são constantes (Modelo de Vasicek). Desta forma, obtemos uma aproximação para o yield curve, ou ETTJ. Para o caso clássico comparamos a aproximação perturbativa com a solução exata do modelo, e concluímos que uma aproximação considerando correções de até quarta ordem é muito precisa. Para os modelos com volatilidade estocástica, comparamos a aproximação perturbativa de quarta ordem com simulações de Monte Carlo, e observamos um comportamento qualitativo semelhante, principalmente para maturidades menores. / In this dissertation we work with the Hull-White model for the Term-Structure of Interest Rate (TSIR), considering the situation where the volatility is a deterministic function of time, and two extensions that follow a stochastic process uncorrelated with the interest rate: the first considers a geometric Brownian motion with zero drift, and the second a Ornstein-Uhlenbeck process with mean-reversion. We obtain perturbation approximations for the Zero-coupon bond prices using the Regular Perturbation Method when the parameters involving the volatility are small, and perform simulations for the constant coefficient case (Vasicek Model). Once this is done, we obtain a perturbative approximation for the yield curve, or TSIR. For the classical case we compare this approximation with the exact solution, and conclude that a fourth order perturbative approximation is very precise. For the cases with stochastic volatility, we compared the fourth order perturbative approximation with Monte Carlo simulations, and observed essentially the same qualitative behavior, mainly for short maturities.

En el presente artículo el autor realiza un reexamen del “ejercicio regular de un derecho” de cara a su consideración como presunta causal absoluta de exclusión de responsabilidad civil. Al respecto, el autor da una mirada más allá de lo evidente y nos presenta una postura interesante al sostener que es posible que el ejercicio regular de un derecho active la tutela resarcitoria. Así, se propone que el análisis de la responsabilidad civil se efectúe tomando en cuenta dos supuestos: el abuso del derecho y la colisión de derechos. Finalmente, dando énfasis al escenario de colisión de derechos, el autor insta a la realización de una ponderación de intereses o, como él lo denomina, un “juicio de resarcibilidad” de los intereses tanto de la víctima como del autor del daño. This article analyzes the regular exercise of a right in relation to its consideration as a cause of exclusion from civil responsibility. Campos García goes beyond the obvious and presents an interesting approach, arguing that it is possible that the exercise of a right activates this responsibility. Thus, it is proposed that the determination of civil responsibility be carried out taking into account two suppositions: the abuse of a right and the collision of rights. Finally, emphasizing the latter, the author urges that an assessment of interests be carried out or, as the author calls it, a process of compensability of the interests both of the victim and the author of the damages.

The Generalised Star-Height Problem is an open question in the field of formal language theory that concerns a measure of complexity on the class of regular languages; specifically, it asks whether or not there exists an algorithm to determine the generalised star-height of a given regular language. Rather surprisingly, it is not yet known whether there exists a regular language of generalised star-height greater than one. Motivated by a theorem of Thérien, we first take a combinatorial approach to the problem and consider the languages in which every word features a fixed contiguous subword an exact number of times. We show that these languages are all of generalised star-height zero. Similarly, we consider the languages in which every word features a fixed contiguous subword a prescribed number of times modulo a fixed number and show that these languages are all of generalised star-height at most one. Using these combinatorial results, we initiate work on identifying the generalised star-height of the languages that are recognised by finite semigroups. To do this, we establish the generalised star-height of languages recognised by Rees zero-matrix semigroups over nilpotent groups of classes zero and one before considering Rees zero-matrix semigroups over monogenic semigroups. Finally, we explore the generalised star-height of languages recognised by finite groups of a given order. We do this through the use of finite state automata and 'count arrows' to examine semidirect products of the form A x Zr where A is an abelian group and Zr is the cyclic group of order r.

FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico / A popularizaÃÃo de dispositivos mÃveis equipados com serviÃos de localizaÃÃo geogrÃfica (e.g. GPS) està permitindo a coleta de dados de trajetÃrias de objetos mÃveis de forma rÃpida e barata. O armazenamento destes dados vem possibilitando o desenvolvimento de novos tipos de aplicaÃÃes que podem utilizar esses dados para realizar anÃlise sobre o comportamento de objetos mÃveis. PorÃm, realizar tais anÃlises a partir de dados brutos, gerados pelo dispositivo de localizaÃÃo geogrÃfica, à um grande desafio, visto que tais dispositivos apenas coletam as informaÃÃes sobre as coordenadas e o instante de tempo, por onde o objeto mÃvel se deslocou. Apesar dos diversos esforÃos empreendidos na busca de soluÃÃes para enriquecer dados de trajetÃrias de objetos mÃveis com informaÃÃes semÃnticas da aplicaÃÃo, pouco foi realizado no sentido de prover mecanismos para consultar tais trajetÃrias enriquecidas. Foi percebido, entÃo, que a falta de mÃtodos para processamento de consultas sobre trajetÃrias semÃnticas, em especial, consulta sobre padrÃes de movimento, sÃo um obstÃculo para a realizaÃÃo de anÃlises de interesse de uma grande parte das aplicaÃÃes deste domÃnio. Desta forma, as principais contribuiÃÃes deste trabalho sÃo: (1) um mÃtodo para processar e realizar consultas que descrevem um padrÃo de movimento constituÃdo de uma sequÃncia de conjuntos de predicados que podem ocorrer em uma trajetÃria semÃntica armazenada em um banco de dados e (2) definiÃÃo de uma linguagem para expressar padrÃes de movimento sobre trajetÃrias semÃnticas. Com objetivo de validar a proposta apresentada, desenvolvemos um sistema que permite a especificaÃÃo de uma consulta para expressar um padrÃo de movimento na linguagem definida. AlÃm disso, utilizamos tal ferramenta para realizar testes sobre um banco de dados de trajetÃrias de carros da cidade de MilÃo, semanticamente enriquecidas com informaÃÃes do aplicativo Foursquare. Os resultados obtidos mostraram que a complexidade para processar as consultas à linear com relaÃÃo ao nÃmero de trajetÃrias semÃnticas e o nÃmero de predicados na consulta, considerando poucas trajetÃrias com muitos episÃdios e muitas trajetÃrias com poucos episÃdios. A abordagem proposta superou outras abordagens existentes, tanto no que concerne a performance do processamento de consultas, quanto na expressividade das consultas que podem ser escritas na linguagem proposta.

Nesta dissertação trabalhamos com o Modelo de Hull-White para a Estrutura a Termo da Taxa de Juro (ETTJ), considerando o caso em que a volatilidade é uma função determinística do tempo, e duas extensões em que ela segue um processo estocástico não correlacionado com a taxa de juro: uma considerando um movimento Browniano geométrico com drift nulo, e outra considerando um processo de Ornstein-Uhlenbeck com reversão á média. Obtemos aproximações perturbativas para o preço de Zero-coupoun bonds aplicando o Metódo de Perturbação Regular quando os parâmetros envolvendo a volatilidade são pequenos, e realizamos simulações para o caso em que os coeficientes são constantes (Modelo de Vasicek). Desta forma, obtemos uma aproximação para o yield curve, ou ETTJ. Para o caso clássico comparamos a aproximação perturbativa com a solução exata do modelo, e concluímos que uma aproximação considerando correções de até quarta ordem é muito precisa. Para os modelos com volatilidade estocástica, comparamos a aproximação perturbativa de quarta ordem com simulações de Monte Carlo, e observamos um comportamento qualitativo semelhante, principalmente para maturidades menores. / In this dissertation we work with the Hull-White model for the Term-Structure of Interest Rate (TSIR), considering the situation where the volatility is a deterministic function of time, and two extensions that follow a stochastic process uncorrelated with the interest rate: the first considers a geometric Brownian motion with zero drift, and the second a Ornstein-Uhlenbeck process with mean-reversion. We obtain perturbation approximations for the Zero-coupon bond prices using the Regular Perturbation Method when the parameters involving the volatility are small, and perform simulations for the constant coefficient case (Vasicek Model). Once this is done, we obtain a perturbative approximation for the yield curve, or TSIR. For the classical case we compare this approximation with the exact solution, and conclude that a fourth order perturbative approximation is very precise. For the cases with stochastic volatility, we compared the fourth order perturbative approximation with Monte Carlo simulations, and observed essentially the same qualitative behavior, mainly for short maturities.

When needing to search for data in multiple datasets there is a risk that not all da-tasets are of the same type. Some might be in XML-format; others might use a re-lational database. This could frighten developers from using two separate datasets to search for the data in, because of the fact that crafting different search methods for different datasets can be time consuming. One option that is greatly overlooked is the usage of regular expressions. If a search expression is created it can be used in a majority of database engines as a “WHERE” statement and also in other form of data sources such as XML. This option is however, at best, poorly documented and few tests have been made in how it performs against traditional search methods in databases such as “LIKE”. Multiple experiments comparing “LIKE” and “REGEXP” in MySQL have been performed for this paper. The results of these experiments show that the possible overhead by using regular expressions can be motivated when considering the gain of only using one search phrase over several data sources. / När behovet att söka over flertalet typer av datakällor finns det alltid en risk att inte alla datakällor är av samma typ. Några kan vara i XML-format; andra kan vara i form av en relationsdatabas. Detta kan avskräcka utvecklare ifrån att använda två oberoende datakällor för att söka efter data, detta för att det kan vara väldigt tidskrävande att utveckla två olika vis att skapa sökmetoderna. Ett alternativ som ofta är förbisett är att använda sig av reguljära uttryck. Om ett sökuttryck är skapat i reguljära uttryck så kan det användas i en majoritet av data-basmotorerna på marknaden som ett ”WHERE” påstående, men det kan även an-vändas i andra typer av datakällor så som XML. Detta alternativ är allt som ofta dåligt dokumenterat och väldigt få tester har ut-förts på prestandan i jämförelse med ”LIKE”. Som grund för denna uppsats har flertalet experiment utförs där ”LIKE” och ”REGEXP” jämförs i en MySQL databas. Försöken visar på att den eventuella försämringen i prestanda kan betala sig vid användande av multipla datatyper.

Security policy specification languages are a response to today's complex and vulnerable software climate. These languages allow an individual or organization to restrict and modify the behavior of third-party applications such that they adhere to the rules specified in the policy. As software grows in complexity, so do the security policies that govern them. Existing policy specification languages have not adapted to the growing complexity of the software they govern and as a result do not scale well, often resulting in code that is overly complex or unreadable. Writing small, isolated policies as separate modules and combining them is known as policy composition, and is an area in which existing policy specification languages have a number of drawbacks. Policy composition is unpredictable and nonstandard with existing languages. PoCo is a new policy specification language that uses signed regular expressions to return sets of allowed and denied actions as output from its policies, allowing policies to be combined with standard set operations in an algebraic way. This thesis covers my contribution to the PoCo project in creating a formal grammar for the language, developing a static analysis tool for policy designers, and implementation of the first PoCo language compiler and runtime for the Java platform.

This thesis is concerned with the quantum Dirac magnetic monopole and two classes of its generalisations. The first of these are certain analogues of the Dirac magnetic monopole on coadjoint orbits of compact Lie groups, equipped with the normal metric. The original Dirac magnetic monopole on the unit sphere S^2 corresponds to the particular case of the coadjoint orbits of SU(2). The main idea is that the Hilbert space of the problem, which is the space of L^2-sections of a line bundle over the orbit, can be interpreted algebraically as an induced representation. The spectrum of the corresponding Schodinger operator is described explicitly using tools of representation theory, including the Frobenius reciprocity and Kostant's branching formula. In the second part some discrete versions of Dirac magnetic monopoles on S^2 are introduced and studied. The corresponding quantum Hamiltonian is a magnetic Schodinger operator on a regular polyhedral graph. The construction is based on interpreting the vertices of the graph as points of a discrete homogeneous space G/H, where G is a binary polyhedral subgroup of SU(2). The edges are constructed using a specially selected central element from the group algebra, which is used also in the definition of the magnetic Schrodinger operator together with a character of H. The spectrum is computed explicitly using representation theory by interpreting the Hilbert space as an induced representation.

In this thesis we examine properties and constructions of graph automatic semigroups, a generalisation of both automatic semigroups and finitely generated FA-presentable semigroups. We consider the properties of graph automatic semigroups, showing that they are independent of the choice of generating set, have decidable word problem, and that if we have a graph automatic structure for a semigroup then we can find one with uniqueness. Semigroup constructions and their effect on graph automaticity are considered. We show that finitely generated direct products, free products, finitely generated Rees matrix semigroup constructions, zero unions, and ordinal sums all preserve unary graph automaticity, and examine when the converse also holds. We also demonstrate situations where semidirect products, Bruck-Reilly extensions, and semilattice constructions preserve graph automaticity, and consider the conditions we may impose on such constructions in order to ensure that graph automaticity is preserved. Unary graph automatic semigroups, that is semigroups which have graph automatic structures over a single letter alphabet, are also examined. We consider the form of an automaton recognising multiplication by generators in such a semigroup, and use this to demonstrate various properties of unary graph automatic semigroups. We show that infinite periodic semigroups are not unary graph automatic, and show that we may always find a uniform set of normal forms for a unary graph automatic semigroup. We also determine some necessary conditions for a semigroup to be unary graph automatic, and use this to provide examples of semigroups which are not unary graph automatic. Finally we consider semigroup constructions for unary graph automatic semigroups. We show that the free product of two semigroups is unary graph automatic if and only if both semigroups are trivial; that direct products do not always preserve unary graph automaticity; and that Bruck-Reilly extensions are never unary graph automatic.