This thesis consists of four papers, all concerning random iteration of isometries. The papers are: I. Ambroladze A, Ådahl M, Random iteration of isometries in unbounded metric spaces. Nonlinearity 16 (2003) 1107-1117. II. Ådahl M, Random iteration of isometries controlled by a Markov chain. Manuscript. III. Ådahl M, Melbourne I, Nicol M, Random iteration of Euclidean isometries. Nonlinearity 16 (2003) 977-987. IV. Johansson A, Ådahl M, Recurrence of a perturbed random walk and an iterated function system depending on a parameter. Manuscript. In the first paper we consider an iterated function system consisting of isometries on an unbounded metric space. Under suitable conditions it is proved that the random orbit {Zn} ∞n=0, of the iterations corresponding to an initial point Z0, “escapes to infinity" in the sense that P(Zn Є K) → 0, as n → ∞ for every bounded set K. As an application we prove the corresponding result in the Euclidean and hyperbolic spaces under the condition that the isometries do not have a common fixed point. In the second paper we let a Markov chain control the random orbit of an iterated function system of isometries on an unbounded metric space. We prove under necessary conditions that the random orbit \escapes to infinity" and we also give a simple geometric description of these conditions in the Euclidean and hyperbolic spaces. The results generalises the results of Paper I. In the third paper we consider the statistical behaviour of the reversed random orbit corresponding to an iterated function system consisting of a finite number of Euclidean isometries of <b>R</b>n. We give a new proof of the central limit theorem and weak invariance principles, and we obtain the law of the iterated logarithm. Our results generalise immediately to Markov chains. Our proofs are based on dynamical systems theory rather than a purely probabilistic approach. In the fourth paper we obtain a suficient condition for the recurrence of a perturbed (one-sided) random walk on the real line. We apply this result to the study of an iterated function system depending on a parameter and defined on the open unit disk in the complex plane.

For high-voltage direct-current (HVDC) transmission, the strength of the ac system is important for normal operation. An ac system can be considered as weak either because its impedance is high or its inertia is low. A typical high-impedance systemis when an HVDC link is terminated at a weak point of a large ac system where the short-circuit capacity of the ac system is low. Low-inertia systems are considered to have limited number of rotating machines, or no machines at all. Examples of such applications can be found when an HVDC link is powering an isand system, or if it is connected to a wind farm. One of the advantages of applying a voltage-source converter (VSC) based HVDC systemis its potential to be connected to very weak ac systems where the conventional linecommutated converter (LCC) based HVDC system has difficulties. In this thesis, the modeling and control issues for VSC-HVDC links connected to weak ac systems are investigated. In order to fully utilize the potential of the VSC-HVDC system for weak-ac-system connections, a novel control method, i.e., powersynchronization control, is proposed. By using power-synchronization control, the VSC resembles the dynamic behavior of a synchronous machine. Several additional functions, such as high-pass current control, current limitation, etc. are proposed to deal with  issues during operation. For modeling of ac/dc systems, the Jacobian transfer matrix is proposed as a unified modeling approach. With the ac Jacobian transfer matrix concept, a synchronous ac system is viewed upon as one multivariable feedback system. In the thesis, it is shown that the transmission zeros and poles of the Jacobian transfer matrix are closely related to several power-system stability phenomena. The similar modeling concept is extended to model a dc system with multiple VSCs. It is mathematically proven that the dc system is an inherently unstable process, which requires feedback controllers to be stabilized. For VSC-HVDC links using power-synchronization control, the short-circuit ratio (SCR) of the ac system is no longer a limiting factor, but rather the load angles. The righthalf plane (RHP) transmission zero of the ac Jacobian transfer matrix moves closer to the origin with larger load angles, which imposes a fundamental limitation on the achievable bandwidth of the VSC. As an example, it is shown that a VSC-HVDC link using powersynchronization control enables a power transmission of 0.86 p.u. from a system with an SCR of 1.2 to a system with an SCR of 1.0. For low-inertia systemconnections, simulation studies show that power-synchronization control is flexible for various operation modes related to island operation and handles the mode shifts seamlessly. / QC20100607

<p>Evolutionary dynamics can be notoriously complex and difficult to analyze. In this dissertation I describe a population genetic regime where the dynamics are simple enough to allow a relatively complete and elegant treatment. Consider a haploid, asexual population, where each possible genotype has been assigned a fitness. When mutations enter a population sufficiently rarely, we can model the evolution of this population as a Markov chain where the population jumps from one genotype to another at the birth of each new mutant destined for fixation. Furthermore, if the mutation rates are assigned in such a manner that the Markov chain is reversible when all genotypes are assigned the same fitness, then it is still reversible when genotypes are assigned differing fitnesses. </p><p>The key insight is that this Markov chain can be analyzed using the spectral theory of finite-state, reversible Markov chains. I describe the spectral decomposition of the transition matrix and use it to build a general framework with which I address a variety of both classical and novel topics. These topics include a method for creating low-dimensional visualizations of fitness landscapes; a measure of how easy it is for the evolutionary process to `find' a specific genotype or phenotype; the index of dispersion of the molecular clock and its generalizations; a definition for the neighborhood of a genotype based on evolutionary dynamics; and the expected fitness and number of substitutions that have occurred given that a population has been evolving on the fitness landscape for a given period of time. I apply these various analyses to both a simple one-codon fitness landscape and to a large neutral network derived from computational RNA secondary structure predictions.</p> / Dissertation

Weak Affinity Chromatography (WAC) is a technology that was developed to analyse weak (KD &gt; 10-5 M) although selective interactions between biomolecules. The focus of this thesis was to develop this method for various applications in the drug development process.   Fragment Based Drug Discovery is a new approach in finding new small molecular drugs. Here, relatively small libraries (a few hundreds to a few thousands of compounds) of fragments (150 – 300 Da) are screened against the target. Fragment hits are then developed into lead molecules by linking, growing or merging fragments binding to different locations of the protein’s active site. However, due to the weakly binding nature of fragments, methods that are able to detect very weak binding events are needed. In this thesis, WAC is presented as a new robust and highly reproducible technology for fragment screening. The technology is demonstrated against a number of different protein targets – proteases, kinases, chaperones and protein-protein interaction (PPI) targets. Comparison of data from fragment screening of 111 fragments by WAC and other more established technologies for fragment screening, such as surface plasmon resonance (SPR) and nuclear magnetic resonance (NMR), validates WAC as a screening technology. It also points at the importance of performing fragment screening by multiple methods as they complement each other.   Other applications of WAC in drug development are also presented. The method can be used for chiral separations of racemic mixtures during fragment screening, which enables affinity measurements of individual enantiomers binding to the target of interest. Further, analysis of crude reaction mixtures is shown. By these procedures, the affinity of the product can be assessed directly after synthesis without any time-consuming purification steps. In addition, a high performance liquid chromatography (HPLC) system for highly efficient drug partition studies was developed by stable immobilization of lipid bilayer disks – lipodisks – on a high performance silica support material. These lipodisks are recognized model membranes for drug partition studies. A WAC system with incorporated membrane proteins into immobilized lipodisks has also been produced and evaluated with the ultimate objective to study affinity interactions between ligands and membrane proteins. / Ett läkemedel utövar sin funktion genom att påverka aktiviteten hos ett protein i kroppen då det binder till dess aktiva säte. Förändringen i aktivitet leder till fysiologiska förändringar i kroppen beroende på vilken funktion proteinet har. Med läkemedelsmolekyl avses här en liten organisk molekyl. Fragment-baserad läkemedelsutveckling är en ny metod for att ta fram nya läkemedel. Metoden fungerar genom att man bygger läkemedelsmolekyler utifrån mindre fragment som binder till målproteinet. Fragmenten hittar man genom att screena hela bibliotek av olika fragment mot samma målprotein för att urskilja de som binder till proteinets aktiva säte. Fördelen med den här metoden är bl. a. att med mindre molekyler som utgångspunkt kan en större del av antalet möjliga kombinationer av atomer representeras med ett mindre antal fragment än för större molekyler. Normalt utgörs ett fragmentbibliotek enbart av några hundra till några tusen substanser. Eftersom fragmenten är små har de få interaktionspunker och binder relativt svagt. De svaga bindningarna är svåra att se och mycket känsliga metoder behövs.   Svagaffinitetskromatografi är en vätskekromatografisk metod som utvecklades för att studera svaga men mycket selektiva bindningar mellan biomolekyler. Den här avhandlingen syftar till att utveckla metoden för olika användningsområden inom läkemedelsutveckling, främst som en ny metod för fragment-screening. Här mäter man interaktionen mellan ett protein och ett fragment. Proteinet kopplas till ett material som sedan packas i en kolonn i formen av en cylinder. När provet pumpas igenom kolonnen kommer de analyter med affinitet till proteinets aktiva säte att fördröjas på kolonnen i relation till hur starkt de interagerar med målproteinet.   I den här avhandlingen presenteras fragment-screening med svagaffinitetskromatografi gentemot ett antal olika typer av målproteiner. Resultatet överensstämmer väl med andra metoder för fragment-screening. Analys av reaktionsblandningar med svagaffinitetskromatografi demonstreras också. Därmed kan bindningen mellan en produkt i en reaktionsblandning och ett målprotein mätas direkt utan föregående uppreningssteg av reaktionsblandningen. Lipodiskar är små diskformade modellmembran som kan användas för att bl. a. mäta hur effektivt läkemedlet tas upp i kroppen vid behandling. Ett system med immobiliserade lipodiskar i en kolonn utvecklades med det framtida målet att kunna arbeta med membranproteiner med svagaffinitetskromatografi.   Detta arbete utgör en del i att utveckla svagaffinitetskromatografi som en lättillgänglig och relativt billig metod för användning inom industrin och akademin för läkemedelsutveckling.

A rapid and accurate quantitative method was developed and validated for the analysis of four urinary organic acids with nitrogen containing functional groups, formiminoglutamic acid (FIGLU), pyroglutamic acid (PYRGLU), 5-hydroxyindoleacetic acid (5-HIAA), and 2-methylhippuric acid (2-METHIP) by liquid chromatography tandem mass spectrometry (LC/MS/MS). The chromatography was developed using a weak anion-exchange amino column that provided mixed-mode retention of the analytes. The elution gradient relied on changes in mobile phase pH over a concave gradient, without the use of counter-ions or concentrated salt buffers. A simple sample preparation was used, only requiring the dilution of urine prior to instrumental analysis. The method was validated based on linearity (r2 ¡Ý 0.995), accuracy (85¨C115%), precision (C.V. < 12%), sample preparation stability (¡Ü 5%, 72h), and established patient ranges. The method was found to be both efficient and accurate for the analysis of urinary zwitterionic organic acids.

In the field of cognitive science, as well as the area of Artificial Intelligence (AI), the role of context has been investigated in many forms, and for many purposes. It is clear in both areas that consideration of contextual information is important. However, the significance of context has not been emphasized in the Bayesian networks literature. We suggest that consideration of context is necessary for acquiring knowledge about a situation and for refining current representational models that are potentially erroneous due to hidden independencies in the data.<p>In this thesis, we make several contributions towards the automation of contextual consideration by discovering useful contexts from probability distributions. We show how context-specific independencies in Bayesian networks and discovery algorithms, traditionally used for efficient probabilistic inference can contribute to the identification of contexts, and in turn can provide insight on otherwise puzzling situations. Also, consideration of context can help clarify otherwise counter intuitive puzzles, such as those that result in instances of Simpson's paradox. In the social sciences, the branch of attribution theory is context-sensitive. We suggest a method to distinguish between <i>dispositional causes</i> and <i>situational factors</i> by means of contextual models. Finally, we address the work of Cheng and Novick dealing with causal attribution by human adults. Their <i>probabilistic contrast model</i> makes use of contextual information, called focal sets, that must be determined by a human expert. We suggest a method for discovering complete <i>focal sets</i> from probabilistic distributions, without the human expert.

The literature on the capabilities of weak states to withstand pressure from strong states suggests that more often than not, weaker states tend to give into the stronger power. What are the motivating factors that enable weak states to withstand pressure from strong states? To ensure that the International Criminal Court (ICC) does not gain jurisdiction over its nationals, the United States is currently seeking to sign Bilateral Immunity Agreements (BIAs) with all countries under the rubric of the American Servicemembers' Protection Act. This thesis examines through a comparative case study analysis how a number of African Countries are able to withstand the pressure to sign a BIA by taking advantage of internal and external institutional structures and mechanisms. It also fills a gap in the literature by examining one regions response to the BIAs relative to the U.S. position concerning the ICC.

In the field of cognitive science, as well as the area of Artificial Intelligence (AI), the role of context has been investigated in many forms, and for many purposes. It is clear in both areas that consideration of contextual information is important. However, the significance of context has not been emphasized in the Bayesian networks literature. We suggest that consideration of context is necessary for acquiring knowledge about a situation and for refining current representational models that are potentially erroneous due to hidden independencies in the data.<p>In this thesis, we make several contributions towards the automation of contextual consideration by discovering useful contexts from probability distributions. We show how context-specific independencies in Bayesian networks and discovery algorithms, traditionally used for efficient probabilistic inference can contribute to the identification of contexts, and in turn can provide insight on otherwise puzzling situations. Also, consideration of context can help clarify otherwise counter intuitive puzzles, such as those that result in instances of Simpson's paradox. In the social sciences, the branch of attribution theory is context-sensitive. We suggest a method to distinguish between <i>dispositional causes</i> and <i>situational factors</i> by means of contextual models. Finally, we address the work of Cheng and Novick dealing with causal attribution by human adults. Their <i>probabilistic contrast model</i> makes use of contextual information, called focal sets, that must be determined by a human expert. We suggest a method for discovering complete <i>focal sets</i> from probabilistic distributions, without the human expert.

A sequence fxng generates by the formula x_{n+1} =(1- £\\_n)x_n+ £\\_nT_nx_n is called the Krasnosel'skii-Mann algorithm, where {£\\_n} is a sequence in (0,1) and {T_n} is a sequence of nonexpansive mappings. We introduce KM algorithm and prove that the sequence fxng generated by KM algorithm converges weakly. This result is used to solve the split feasibility problem which is to find a point x with the property that x ∈ C and Ax ∈ Q, where C and Q are closed convex subsets form H1 to H2, respectively, and A is a bounded linear operator form H1 to H2. The purpose of this paper is to present some results which apply KM algorithm to solve the split feasibility problem, the multiple-set split feasibility problem and other applications.

In recent years, new approaches to the problem of Automated Target Recognition using techniques of shape theory and algebraic geometry have been explored. The power of this shape theoretic approach is that it allows one to develop tests for object/image matching that do not require knowledge of the object’s position in relation to the sensor nor the internal parameters of the sensor. Furthermore, these methods do not depend on the choice of coordinate systems in which the objects and images are represented. In this dissertation, we will expand on existing shape theoretic techniques and adapt these techniques to new sensor models. In each model, we develop an appropriate notion of shape for our objects and images and define the spaces of such shapes. The goal in each case is to develop tests for matching object and image shapes under an appropriate class of projections. The first tests we develop take the form of systems of polynomial equations (the so-called object/image relations) that check for exact matches of object/image pairs. Later, a more robust approach to matching is obtained by defining metrics on the shape spaces. This allows us in each model to develop a measure of “how close” an object is to being able to produce a given image. We conclude this dissertation by computing a number of examples using these tests for object/image matching.