Culture-independent DNA sequencing is being used to recover genetic material directly from environmental samples. This has spurred large-scale community efforts to catalogue the diversity of life and its geographic distribution using molecular data. These initiatives stand to revolutionize our understanding of the processes that shape biodiversity and may ultimately provide critical information for setting public health, environmental, and economic policies. To achieve these aims new tools are required to effectively explore these large biogeographic datasets. This thesis introduces a novel technique for visualizing hierarchically organized data in a geographic context that illustrates the influence of a geographic or environmental gradient on the phylogenetic relationships between organisms or the similarity of biological communities. This technique is incorporated into GenGIS, open-source software that supports the integration of digital map data with genetic sequences and environmental information from multiple sample sites. GenGIS addresses the need for an interactive geospatial analysis environment capable of handling large biogeographic datasets where a wealth of sequence data is available for each sample site. This is accomplished through a rich set of analysis options that produce georeferenced visualizations for data exploration and hypothesis generation. Studies conducted by myself and other research groups have used GenGIS to investigate the diversity of viruses, bacteria, plants, animals, and even language families. I then explore measures of beta diversity that aim to assess the influence of geographic or environmental gradients on the similarity of biological communities. This thesis examines phylogenetic beta-diversity measures that determine community variation by considering the relationships between organisms in a phylogenetic tree. A large comparative study is performed in order to assess specific properties and performance characteristics of these measures. Many measures of phylogenetic beta diversity were found to be robust to sequence clustering, the addition of an outlying basal lineage, root placement, and the presence of rare organisms. Additionally, performance was found to differ substantially under different models of community variation. This thesis then describes how an important class of phylogenetic beta-diversity measures can be calculated over phylogenetic networks in order to account for uncertainty and conflict in inferred ancestral relationships.

Recently there have been numerous advances in the development of numerical algorithms to solve conservation laws. Even though the analytical theory (existence-uniqueness) is complete in the case of scalar conservation laws, there are many numerically robust methods for which the question of convergence and error estimates are still open. Usually high order schemes are constructed to be Total Variation Diminishing (TVD) which only guarantees convergence of such schemes to a weak solution. The standard approach in proving convergence to the entropy solution is to try to establish cell entropy inequalities. However, this typically requires additional non-homogeneous limitations on the numerical method, which reduces the modified scheme to first order when the mesh is refined. There are only a few results on the convergence which do not impose such limitations and all of them assume some smoothness on the initial data in addition to L^infinity bound. The Nessyahu-Tadmor (NT) scheme is a typical example of a high order scheme. It is a simple yet robust second order non-oscillatory scheme, which relies on a non-linear piecewise linear reconstruction. A standard reconstruction choice is based on the so-called minmod limiter which gives a maximum principle for the scheme. Unfortunately, this limiter reduces the reconstruction to first order at local extrema. Numerical evidence suggests that this limitation is not necessary. By using MAPR-like limiters, one can allow local nonlinear reconstructions which do not reduce to first order at local extrema. However, use of such limiters requires a new approach when trying to prove a maximum principle for the scheme. It is also well known that the NT scheme does not satisfy the so-called strict cell entropy inequalities, which is the main difficulty in proving convergence to the entropy solution. In this work, the NT scheme with MAPR-like limiters is considered. A maximum principle result for a conservation law with any Lipschitz flux and also with any k-monotone flux is proven. Using this result it is also proven that in the case of strictly convex flux, the NT scheme with a properly selected MAPR-like limiter satisfies an one-sided Lipschitz stability estimate. As a result, convergence to the unique entropy solution when the initial data satisfies the so-called one-sided Lipschitz condition is obtained. Finally, compensated compactness arguments are employed to prove that for any bounded initial data, the NT scheme based on a MAPR-like limiter converges strongly on compact sets to the unique entropy solution of the conservation law with a strictly convex flux.

The issue of child soldiering continues to be a significant part of armed conflicts. The research on children in conflict has not fully been able to understand how children not only experience but also actively participate in war. This thesis is premised in the pre-condition of low civilian support which in varying rates of child soldiering are expected to explain different outcomes in rebel violence against civilians. The examination is done through the lens of socialization theory. During the 1990’s the rates of child soldiering were extreme, causing rise to groups such as the RUF, AIS and brought attention to the KNU. These three cases are compared using Mill’s method of difference and structured focused comparison. The thesis finds that low civilian support is instrumental but ultimately inefficient to explain the variation in outcomes and proposes to look further into the influence of natural resource dependency and political ideologies.

The aim of this thesis is to observe and analyze the effects of religious dimensions in armed conflict on violence against civilians. Focusing on rebel groups in intra-state conflicts, quantitative statistical analysis in form of Ordinary Least Squares multivariate regression, is utilized to examine data onreligious wars, one-sided violence, and conflict-related sexual violence. Two hypotheses are formulatedand tested; that (1) higher significance of religion in armed conflict leads to higher levels of one-sidedviolence, as well as that (2) higher significance of religion leads to higher levels of conflict-related sexual violence. The results, relying on four different datasets and 1107 observations, empirically support both hypotheses. The conclusion of this thesis suggests that civilians are found to be particularly vulnerable in religious armed conflict, pointing to the importance and urgency of further and closer examination of civilian victimization in these types of wars.

Rebel governance and rebel violence against civilians are two closely related fields within peace and conflict research that have gained increased interest amongst scholars during recent years. Still, there is a gap within current research that concerns how variation in one field may influence variation in the other. This paper aims to fill this gap by applying a theory on rebel violence in the context of rebel governance to hypothesize that a high level of rebel governance will decrease the intensity of rebel violence against civilians. The hypothesis is tested through linear regression, using data from the UCDP One-Sided Violence dataset, Rebel Governance Dataset and a replication dataset by Huang and Sullivan (2021). The findings from the regression analysis suggest a negative relationship between a high level of rebel governance and decreased intensity of rebel violence against civilians which supports the hypothesis. However, these results are not statistically significant and therefore only provides indications of a relationship. Yet, this thesis contributes by interlinking two fields that are highly relevant in modern civil wars and thereby provides a small but important building block for future research.

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While peacekeeping operations have been researched for decades, due to a lack of data there are still many aspects of peacekeeping that remain unexplored. However, with the introduction of the Peacemakers at Risk dataset a wide array of dynamics and relationships can now be researched. This thesis uses this dataset and others in order to study the risk of violence towards peacekeepers and its effects on the peacekeepers’ ability to protect civilians. My main claim is that due to a shift in priorities, peacekeepers that are exposed to risks of violence have a decreased capacity to protect civilians which leads to increased civilian casualties. The study utilizes a time-series cross-sectional quantitative approach in order to study this relationship. After the introduction of control variables, drawn from the literature, to the multivariate regression, the study finds that there is no statistical significance to the relationship supported in the existing data. However, the study can ultimately not draw a generalizable conclusion due to a lack of observations.

It is often important to detect an increase in the frequency of some event. Particular attention is given to medical events such as mortality or the incidence of a given disease, infection or birth defect. Observations are regularly taken in which either an incidence occurs or one does not. This dissertation contains the result of an investigation of prospective monitoring techniques in two distinct surveillance situations. In the first situation, the observations are assumed to be the results of independent Bernoulli trials. Some have suggested adapting the scan statistic to monitor such rates and detect a rate increase as soon as possible after it occurs. Other methods could be used in prospective surveillance, such as the Bernoulli cumulative sum (CUSUM) technique. Issues involved in selecting parameters for the scan statistic and CUSUM methods are discussed, and a method for computing the expected number of observations needed for the scan statistic method to signal a rate increase is given. A comparison of these methods shows that the Bernoulli CUSUM method tends to be more effective in detecting increases in the rate. In the second situation, the incidence information is available at multiple locations. In this case the individual sites often report a count of incidences on a regularly scheduled basis. It is assumed that the counts are Poisson random variables which are independent over time, but the counts at any given time are possibly correlated between regions. Multivariate techniques have been suggested for this situation, but many of these approaches have shortcomings which have been demonstrated in the quality control literature. In an attempt to remedy some of these shortcomings, a new control chart is recommended based on a multivariate exponentially weighted moving average. The average run-length performance of this chart is compared with that of the existing methods. / Ph. D.

Рассматриваются задачи наилучшего одностороннего приближения (снизу и сверху) в пространстве функций, суммируемых с весом на (-1,1), характеристической функции интервала (a,b) из (-1,1 ) множеством алгебраических многочленов степени не выше заданной. Приведено решение задач в случае, когда a и b - узлы положительной квадратурной формулы при некоторых условиях на ее алгебраическую точность, а также в случае симметричного интервала для четного веса. / We consider the problems of the best one-sided approximation (from below and from above) in the space of functions integrable on (-1,1) with a weight to the characteristic function of an interval (a,b) from (-1,1) by the set of algebraic polynomials of degree not exceeding a given number. We solve the problems in the case when a and b are nodes of a positive quadrature formula under some conditions on its degree of precision as well as in the case of a symmetric interval for an even weight.

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