No description available.

No description available.

The aetiology of common diseases is shaped by the effects of genetic and environmental factors. Big efforts have been devoted to unravel the genetic basis of disease with the hope that it will help to develop new therapeutic treatments and to achieve personalized medicine. With the development of high-throughput genotyping technologies, hundreds of association studies have described many loci associated to disease. However, the depiction of disease architecture remains incomplete. The aim of this work is to perform exhaustive comparisons across human populations to evaluate pressing questions. Our results provide new insights in the allele frequency of risk variants, their sharing across populations and the likely architecture of disease / La etiología de las enfermedades comunes está formada por factores genéticos y ambientales. Se ha puesto mucho empeño en describir sus bases genéticas. Este conocimiento será útil para desarrollar nuevas terapias y la medicina personalizada. Gracias a las técnicas de genotipado masivo, centenares de estudios de asociación han descrito una infinidad de genes asociados a enfermedad. Pese a ello, la arquitectura genética de las enfermedades no ha sido totalmente descrita. Esta tesis pretende llevar a cabo exhaustivas comparaciones entre poblaciones para responder diversas preguntas candentes. Nuestros resultados dan pistas sobre la frecuencia de los alelos de riesgo, su presencia entre poblaciones y la probable arquitectura de las enfermedades.

This research investigates existing relationships between the three apparently unrelated subjects: Markov process, Semigroups and Partial difierential equations. Markov processes define semigroups through their transition functions. Conversely particular semigroups determine transition functions and can be regarded as Markov processes. We have exploited these relationships to study some Markov chains. The infnitesimal generator of a Feller semigroup on the closure of a bounded domain of Rn; (n ^ 2), is an integro-diferential operator in the interior of the domain and verifes a boundary condition. The existence of a Feller semigroup defined by a diferential operator and a boundary condition is due to the existence of solution of a bounded value problem. From this result other existence suficient conditions on the existence of Feller semigroups have been obtained and we have applied some of them to construct Feller semigroups on the unity disk of R2. / Decision Sciences / M. Sc. (Operations Research)

<p>The study of symmetries is an essential tool in modern physics. The analysis of symmetries is often carried out in the form of Lie algebras and their representations. Knowing the representation theory of a Lie algebra includes knowing how tensor products of representations behave. In this thesis two methods to study and decompose tensor products of representations of non-compact Lie algebras are presented and applied to sl(2,R). We focus on products containing non-unitary representations, especially the product of a unitary highest weight representation and a non-unitary finite dimensional. Such products are not necessarily decomposable. Following the theory of B. Kostant we use infinitesimal characters to show that this kind of tensor product is fully reducible iff the sum of the highest weights in the two modules is not a positive integer or zero. The same result is obtained by looking for an invariant coupling between the product module and the contragredient module of some possible submodule. This is done in the formulation by Barut & Fronsdal. From the latter method we also obtain a basis for the submodules consisting of vectors from the product module. The described methods could be used to study more complicated semisimple Lie algebras.</p>

The study of symmetries is an essential tool in modern physics. The analysis of symmetries is often carried out in the form of Lie algebras and their representations. Knowing the representation theory of a Lie algebra includes knowing how tensor products of representations behave. In this thesis two methods to study and decompose tensor products of representations of non-compact Lie algebras are presented and applied to sl(2,R). We focus on products containing non-unitary representations, especially the product of a unitary highest weight representation and a non-unitary finite dimensional. Such products are not necessarily decomposable. Following the theory of B. Kostant we use infinitesimal characters to show that this kind of tensor product is fully reducible iff the sum of the highest weights in the two modules is not a positive integer or zero. The same result is obtained by looking for an invariant coupling between the product module and the contragredient module of some possible submodule. This is done in the formulation by Barut &amp; Fronsdal. From the latter method we also obtain a basis for the submodules consisting of vectors from the product module. The described methods could be used to study more complicated semisimple Lie algebras.

Stochastic hybrid dynamic systems that incorporate both continuous and discrete dynamics have been an area of great interest over the recent years. In view of applications, stochastic hybrid dynamic systems have been employed to diverse fields of studies, such as communication networks, air traffic management, and insurance risk models. The aim of the present study is to investigate properties of some classes of stochastic hybrid dynamic systems. The class of stochastic hybrid dynamic systems investigated has random jumps driven by a non-homogeneous Poisson process and deterministic jumps triggered by hitting the boundary. Its real-valued continuous dynamic between jumps is described by stochastic differential equations of the It\^o-Doob type. Existing results of piecewise deterministic models are extended to obtain the infinitesimal generator of the stochastic hybrid dynamic systems through a martingale approach. Based on results of the infinitesimal generator, some stochastic stability results are derived. The infinitesimal generator and stochastic stability results can be used to compute the higher moments of the solution process and find a bound of the solution. Next, the study focuses on a class of multidimensional stochastic hybrid dynamic systems. The continuous dynamic of the systems under investigation is described by a linear non-homogeneous systems of It\^o-Doob type of stochastic differential equations with switching coefficients. The switching takes place at random jump times which are governed by a non-homogeneous Poisson process. Closed form solutions of the stochastic hybrid dynamic systems are obtained. Two important special cases for the above systems are the geometric Brownian motion process with jumps and the Ornstein-Uhlenbeck process with jumps. Based on the closed form solutions, the probability distributions of the solution processes for these two special cases are derived. The derivation employs the use of the modal matrix and transformations. In addition, the parameter estimation problem for the one-dimensional cases of the geometric Brownian motion and Ornstein-Uhlenbeck processes with jumps are investigated. Through some existing and modified methods, the estimation procedure is presented by first estimating the parameters of the discrete dynamic and subsequently examining the continuous dynamic piecewisely. Finally, some simulated stochastic hybrid dynamic processes are presented to illustrate the aforementioned parameter-estimation methods. One simulated insurance example is given to demonstrate the use of the estimation and simulation techniques to obtain some desired quantities.

This research investigates existing relationships between the three apparently unrelated subjects: Markov process, Semigroups and Partial difierential equations. Markov processes define semigroups through their transition functions. Conversely particular semigroups determine transition functions and can be regarded as Markov processes. We have exploited these relationships to study some Markov chains. The infnitesimal generator of a Feller semigroup on the closure of a bounded domain of Rn; (n ^ 2), is an integro-diferential operator in the interior of the domain and verifes a boundary condition. The existence of a Feller semigroup defined by a diferential operator and a boundary condition is due to the existence of solution of a bounded value problem. From this result other existence suficient conditions on the existence of Feller semigroups have been obtained and we have applied some of them to construct Feller semigroups on the unity disk of R2. / Decision Sciences / M. Sc. (Operations Research)

short time scale. Four differential GPS stations were installed in the lower ablation area of Storglaciären in Sweden for one week in August 2012. The position data over the period were then compared with the environment information including temperature, precipitation, known hydrology and topography.The instantaneous velocity results show 9 acceleration events in correlation to temperature and precipitation. The increase of the meltwater inputs drive increases of the motion supposedly through water pressures and basal sliding.Strain determination using the stations geometry showed that the lower part of the survey area had an extensive behavior when the upper part was showing compressive properties. A deformation event occurring the 14th of august shows an elongation deformation along the centerline from the front of the glacier resulting in a lateral compression on the upper part due to shear stress closer to the margin.It was proposed that the force driving the elongation is due to the increase of water pressure on the front of the glacier where the internal hydrological system pass from a complex multi-branched system to a channelized output. / Syftet med detta projekt var att studera sambandet mellan en glaciärs hydrologi och isrörelse under korta tidsperioder (minuter till timmar). I augusti 2012 installerades fyra differentiella GPS-stationer under en veckas tid i nedre ablationsområdet på Storglaciären i Sverige. Positionsdata under perioden jämfördes sedan med miljöinformation inklusive temperatur, nederbörd, avrinning från glaciären och topografi.De uppskattade hastighetsresultaten visar på 9 olika accelerationshändelser som relaterar till tempe-ratur och nederbörd. En ökad införsel av smältvatten driver upp vattentrycket vid glaciärens botten som minskar friktionsmotståndet och glaciären får ökad basal glidning.Isdeformationsberäkningar mellan DGPS-stationerna visar att den nedre delen av undersök-ningsområdet hade extensionell deformation i isrörelseriktningen medan den övre delen visade kompression vinkelrätt mot denna riktning. Deformationshändelsen den 14 augusti visar det motsatta med extensionell deformation längs mittlinjen från fronten av glaciären vilket resulterar i en lateral kompression i den övre delen av det undersökta området kanske orsakade av skjuvspänning vid marginalen.Det föreslås att utsträckningen av glaciären under dessa händelser är på grund av en ökning av vattentrycket i det område där det interna subglaciala hydrologiska systemet ändras från en komplex multigrenade system högre upp i ablationsområdet till ett kanaliserat system vid fronten.

In this thesis we analyze lumpability of infinite dimensional dynamical systems. Lumping is a method to project a dynamics by a linear reduction operator onto a smaller state space on which a self-contained dynamical description exists. We consider a well-posed dynamical system defined on a Banach space X and generated by an operator F, together with a linear and bounded map M : X → Y, where Y is another Banach space. The operator M is surjective but not an isomorphism and it represents a reduction of the state space. We investigate whether the variable y = M x also satisfies a well-posed and self-contained dynamics on Y . We work in the context of strongly continuous semigroup theory. We first discuss lumpability of linear systems in Banach spaces. We give conditions for a reduced operator to exist on Y and to describe the evolution of the new variable y . We also study lumpability of nonlinear evolution equations, focusing on dissipative operators, for which some interesting results exist, concerning the existence and uniqueness of solutions, both in the classical sense of smooth solutions and in the weaker sense of strong solutions. We also investigate the regularity properties inherited by the reduced operator from the original operator F . Finally, we describe a particular kind of lumping in the context of C*-algebras. This lumping represents a different interpretation of a restriction operator. We apply this lumping to Feller semigroups, which are important because they can be associated in a unique way to Markov processes. We show that the fundamental properties of Feller semigroups are preserved by this lumping. Using these ideas, we give a short proof of the classical Tietze extension theorem based on C*-algebras and Gelfand theory.