The divisor theories on finite graphs and metric graphs were introduced systematically as analogues to the divisor theory on algebraic curves, and all these theories are deeply connected to each other via tropical geometry and non-archimedean geometry. In particular, rational functions, divisors and linear systems on algebraic curves can be specialized to those on finite graphs and metric graphs. Important results and interesting problems, including a graph-theoretic Riemann-Roch theorem, tropical proofs of conventional Brill-Noether theorem and Gieseker-Petri theorem, limit linear series on metrized complexes, and relations among moduli spaces of algebraic curves, non-archimedean analytic curves, and metric graphs are discovered or under intense investigations. The content in this thesis is divided into three main subjects, all of which are based on my research and are essentially related to the divisor theory of linear systems on metric graphs and its application to tropical geometry and non-archimedean geometry. Chapter 1 gives an overview of the background and a general introduction of the main results. Chapter 2 is on the theory of rank-determining sets, which are subsets of a metric graph that can be used for the computation of the rank function. A general criterion is provided for rank-determining sets and certain specific examples of finite rank-determining sets are presented. Chapter 3 is on the subject of a tropical convexity theory on linear systems on metric graphs. In particular, the notion of general reduced divisors is introduced as the main tool used to study this tropical convexity theory. Chapter 4 is on the subject of smoothing of limit linear series of rank one on re_ned metrized complexes. A general criterion for smoothable limit linear series of rank 1 is presented and the relations between limit linear series of rank 1 and possible harmonic morphisms to genus 0 metrized complexes are studied.

At the present time it is unknown how the U(1)A anomaly of Quantum Chromodynamics behaves at high temperatures. We therefore want to look for thermal changes of the effects of the anomaly. For example, by studying the properties of the η' meson at high temperatures it would be possible to deduce important information on the axial anomaly, thanks to the deep connection between them. In this thesis the width of the η' as a function of the temperature is studied in the framework of large-Nc Chiral Perturbation Theory, at next-to-leading order, and in the corresponding Resonance Chiral Theory. We calculate the width increase due to scattering with particles from the heat bath, which we assume to consist of a pion gas. We compare the results obtained in both frameworks and as expected we find a smaller, but still consistent width increase when the more realistic resonance exchange is taken into account. The results suggest that the in-medium width of the η' may increase up to ΔΓ<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Capprox" /> 10 MeV at a temperature of T<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Capprox" /> 120 MeV. We find therefore a width increase of considerable size, comparable to the inverse lifetime of the fireball created in relativistic heavy-ion collisions. In other words, our results suggest that it may be possible to study experimentally how the properties of the η' change at high temperatures.

Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 332–350, July–September, 2006.

Stochastic fluctuations can have profound impacts on engineered systems. Nonetheless, we can achieve significant benefits such as cost reduction based upon expanding our fundamental knowledge of stochastic systems. The primary goal of this thesis is to contribute to our understanding by developing and analyzing stochastic models for specific types of engineered systems. The knowledge gained can help management to optimize decision making under uncertainty. This thesis has three parts. In Part I, we study many-server queues that model large-scale service systems such as call centers. We focus on the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) processes and the validity of using these processes to predict the steady-state performance of the corresponding many-server queues. In Part II, we investigate diffusion processes constrained to the positive orthant under infinitesimal changes in the drift. This sensitivity analysis on the drift helps us understand how changes in service capacities at individual stations in a stochastic network would affect the steady-state queue-length distributions. In Part III, we study the trading mechanism known as limit order book. We are motivated by a desire to better understand the interplay among order flow rates, liquidity fluctuation, and optimal executions. The goal is to characterize the temporal evolution of order book shape on the “macroscopic” time scale.

Limit-setting in publicly funded healthcare is unavoidable, and increasingly important in the governance and management of the demand for health services. The work of limit-setting takes place in the organising of the provision of health services, where various health workers (professionals, administrators, unit managers, politicians) collectively exercise their skills. Limit-setting often creates tensions which impose the quest for legitimacy; it involves norms and values which are related to the interests of the health workers, and moreover to society at large. In that sense, limit-setting is related to internal processes of legitimacy within the healthcare organisation, i.e. internal legitimacy, and external processes of legitimacy where citizens are legitimating the activities in the healthcare organisation, i.e. external legitimacy. The purpose of this thesis was to discover, and increase the understanding of the dilemma associated with sustaining, generating and designing internal legitimacy, when working with a policy of limit-setting in healthcare, in relation to the provision of Assistive Technologies (AT). It has explored what health workers do when they are working with a policy, and in particular how they work out what they should be doing. Finally the role of mediating institutions in supporting and designing internal legitimacy, was explored in the thesis. Following a case-study design and a qualitative approach, where fifty-seven semi-structured open-ended interviews were conducted, data allowed the exploration of internal legitimacy in a context of complex interaction and construction of policy work in two Swedish county councils. This research produced a number of key findings; in an environment of finite resources health workers encountered situations that were characterised by conflicting pressures, and handled these by way of interaction, sense making, presenting arguments, negotiating and seeking support for an appropriate course of action and practices. The policy work with limit-setting can therefore be regarded as a dynamic interactive process, which incorporates several actors in different situations and locations, together negotiating and institutionalising the policy. Various policy sites, which had the role of mediating institutions, were identified, and were important in the interactive processes of forming a shared collective meaning in order to reach an appropriate act. Hence, designing legitimacy has to acknowledge the interactive policy work, and its contextual character, taking place at the different levels of a healthcare system.

Most of existing North American bridge infrastructure is reported to be deficient. Present infrastructure management mainly relies on qualitative evaluation, where bridge safety and serviceability are judged through routine visual inspection. With the successive increase in the number of severely deficient bridges and the limited available resources, it is crucial to develop a performance-based quantitative assessment evaluation approach that enables an accurate estimation of aging bridges ultimate and seismic capacities and ensures their serviceability. Reinforcement corrosion is the main cause of most of North American concrete infrastructure deterioration. Experimental investigations prove that reinforcement corrosion results in reduction of the steel reinforcement cross sectional area, localized (or global in very extreme cases) loss of bond action, concrete spalling, loss of core concrete confinement, and structural collapse. Field observations show that damage due to reinforcement corrosion in reinforced concrete (RC) bridge columns is localized in highly affected zones by splash of deicing water. In this thesis, an innovative performance-based semi-quantitative assessment framework is developed using newly developed simplified nonlinear static and dynamic finite element analysis approaches. The framework integrates the bridge’s available design and after-construction information with enhanced inspection and additional material testing as sources for accurate input data. In order to evaluate the structural performance and the capacity of the corrosion-damaged bridge columns, four nonlinear static and dynamic analysis approaches have been developed: (i) simplified nonlinear sectional analysis (NLSA) approach that presents the basis of the analysis approaches to estimate the ultimate and seismic capacities, and serviceability of bridge columns; (ii) simplified nonlinear finite element analysis (NLFEA) approach, which enables estimating the ultimate structural capacity of corrosion-damaged RC columns; (iii) simplified hybrid linear/nonlinear dynamic finite element analysis (SHDFEA) approach to evaluate the serviceability of the bridge; and, (iv) simplified non-linear seismic analysis (SNLSA) approach to evaluate the seismic capacity of the bridge columns. The four analysis approaches are verified by comprehensive comparisons with available test experimental and analytical results. The proposed semi-quantitative assessment framework suggests three thresholds for each performance measure of the evaluation limit states to be decided by the bridge management system team. Case studies are presented to show the integrity and the consistency of using the proposed assessment framework. The proposed assessment framework together with the analysis approaches provide bridge owners, practicing engineers, and management teams with simplified and accurate evaluation tools, which lead to reduce the maintenance/rehabilitation cost and provide better safety, and reduce the variation in the data collected using only traditional inspection methods.

This thesis explores the 'theories of Bataille and Baudrillard' in relation to the problem of extreme violence. The particular events of concern are the death of James Bulger, the Dunblane massacre and the 'serial killers' Frederick and Rosemary West. The thesis argues that dominant traditions in the social sciences are unable to engage with the horror of such events with anything approaching adequate terminology and that alternatives are urgently required. The study is theoretical not empirical and these cases act as crucial reference points throughout the theoretical discussions. Such events seem to disable reason and are frequently referred to as 'inexplicable' or 'evil'. They appear to be 'in excess' of the established explanatory paradigms. The thesis investigates the possibility of 'thinking excess' in new and alternative ways, more commensurate with the intensity of such events. The importance of Bataille notions of the sacred, sacrificial expenditure and non-dialectical negativity in approaching changing forms of extreme violence are emphasised. Bataille specifies a fundamental 'need' for violent expenditure or sacrifice that persists in a contemporary age no longer equipped to recognise these principles. Baudrillard's approach is related but departs from Bataille's thought. Baudrillard's emphasis on symbolic exchange, seduction and the fatal denies the existenceo f fundamental 'needs' yet also emphasisesth e cultural and ritual nature of extreme violence. These themes are developed into a detailed reading of 'deathevents'. They are theorised as distinctively contemporary, occupying a postdialectical cultural space characterised by the elimination of sacred and symbolic principles, which nevertheless endure in fragmentary, displaced and deracinated form. These are conditions in which new forms of 'evil' may emerge. In emphasising the theoretical differences between the readings of violence offered by Bataille, and by Baudrillard, the thesis rey-eals shifts in the nature of radical theory from the middle to the late twentieth century. The notions of utility, limit and excess are central to this shift and to alternative ways of thinking the excessive nature of contemporary violence.

We consider a general class of finite dimensional deterministic dynamical systems with finitely many local attractors each of which supports a unique ergodic probability measure, which includes in particular the class of Morse–Smale systems in any finite dimension. The dynamical system is perturbed by a multiplicative non-Gaussian heavytailed Lévy type noise of small intensity ε > 0. Specifically we consider perturbations leading to a Itô, Stratonovich and canonical (Marcus) stochastic differential equation. The respective asymptotic first exit time and location problem from each of the domains of attractions in case of inward pointing vector fields in the limit of ε-> 0 has been investigated by the authors. We extend these results to domains with characteristic boundaries and show that the perturbed system exhibits a metastable behavior in the sense that there exits a unique ε-dependent time scale on which the random system converges to a continuous time Markov chain switching between the invariant measures. As examples we consider α-stable perturbations of the Duffing equation and a chemical system exhibiting a birhythmic behavior.

The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is a general alpha-stable process. It is proved that extremal solutions are selected and the probability of selection is computed. Detailed analysis of the characteristic function of an exit time form on the half-line is performed, with a suitable decomposition in small and large jumps adapted to the singular drift.

Flowering plants display diverse reproductive systems, including a variety of gender strategies and mechanisms of clonal propagation. Here, I investigate gender strategies, sex-ratio evolution, and sexual dimorphism in the North American clonal aquatic, Sagittaria latifolia (Alismataceae), which exhibits three sex phenotypes (hermaphrodites, females, males) and two modal sexual systems (monoecy, dioecy). This provides an outstanding opportunity to examine the costs and benefits of combined versus separate sexes. My research focused on the northern range limit in eastern N. America, and on disjunct populations in western N. America. I developed microsatellite (SSR) markers to investigate population genetic structure at several spatial scales, including the clonal structure of local populations to continental patterns. These analyses provided insights on the roles of historical, ecological and reproductive factors in the evolution and maintenance of sexual system diversity. Phenotypic sex ratios varied near continuously from monoecy through subdioecy (three sex phenotypes) to dioecy. A comparison of phenotypic and genotypic sex ratios in dioecious populations demonstrated close correspondence. The northern range limit was characterized by a decline in female frequency and an increased incidence of subdioecy. I evaluated two hypotheses to explain this pattern: (1) increased sex inconstancy in dioecious populations; (2) hybridization between monoecious and dioecious populations. I found support for both hypotheses, although hybridization appears to be the more common pathway to subdioecy. I parameterized a model predicting female frequency and hermaphrodite sex allocation; observed and predicted values were correlated suggesting that subdioecious populations are closer to equilibrium than expected for a clonal perennial. A comparison of eastern and western populations indicated genetic differentiation between monoecy and dioecy in the east, but in the west, due to habitat isolation, geography plays a more important role in genetic differentiation. Evidence from cpDNA haplotype variation indicated that the western range was established following long-distance colonization from the east involving a genetic bottleneck. The discovery of gynodioecious populations of S. latifolia in the west, and the absence of ecological and genetic differentiation between monoecious and dioecious populations, raise the possibility that dioecy may have evolved autochthonously in the west, and more recently than in the eastern range.