This dissertation explores two themes central to the field of non-equilibrium statistical physics. The first is centered around the use of random walks, first-passage processes, and Brownian motion to model basic stochastic search processes found in biology and ecological systems. The second is centered around clustered networks: how clustering modifies the nature of transition in the appearance of various graph motifs and their use in modeling social networks. In the first part of this dissertation, we start by investigating properties of intermediate crossings of Brownian paths. We develop simple analytical tools to obtain probability distributions of intermediate crossing positions and intermediate crossing times of Brownian paths. We find that the distribution of intermediate crossing times can be unimodal or bimodal. Next, we develop analytical and numerical methods to solve a system of 𝑁 diffusive searchers which are reset to the origin at stochastic or periodic intervals. We obtain the optimal criteria to search for a fixed target in one, two and three dimensions. For these two systems, we also develop efficient ways to simulate Brownian paths, where the simulation kernel makes maximal use of first-passage ideas. Finally we develop a model to understand foraging in a resource-rich environment. Specifically, we investigate the role of greed on the lifetime of a diffusive forager. This lifetime shows non-monotonic dependence on greed in one and two dimensions, and surprisingly, a peak for negative greed in 1d. In the second part of this dissertation, we develop simple models to capture the non-tree-like (clustering) aspects of random networks that arise in the real world. By 'clustered networks', we specifically mean networks where the probability of links between neighbors of a node (i.e., 'friends of friends') is positive. We discuss three simple and related models. We find a series of transitions in the density of graph motifs such as triangles (3-cliques), 4-cliques etc as a function of the clustering probability. We also find that giant 3-cores emerge through first- or second-order, or even mixed transitions in clustered networks.

Context. In this thesis, a GPU-based light culling technique performed with conservative rasterization is presented. Accurate lighting calculations are expensive in real-time applications and the number of lights used in a typical virtual scene increases as real-time applications become more advanced. Performing light culling prior to shading a scene has in recent years become a vital part of any high-end rendering pipeline. Existing light culling techniques suffer from a variety of problems which clustered shading tries to address. Objectives. The main goal of this thesis is to explore the use of the rasterizer to efficiently assign convex light shapes to clusters. Being able to accurately represent and assign light volumes to clusters is a key objective in this thesis. Methods. This method is designed for real-time applications that use large amounts of dynamic and arbitrarily shaped convex lights. By using using conservative rasterization to assign convex light volumes to a 3D cluster structure, a more suitable light volume approximation can be used. This thesis implements a novel light culling technique in DirectX 12 by taking advantage of the hardware conservative rasterization provided by the latest consumer grade Nvidia GPUs. Experiments are conducted to prove the efficiency of the implementation and comparisons with AMD´s Forward+ tiled light culling are provided to relate the implementation to existing techniques. Results. The results from analyzing the algorithm shows that most problems with existing light culling techniques are addressed and the light assignment is of high quality and allows for easy integration of new convex light types. Assigning the lights and shading the CryTek Sponza scene with 2000 point lights and 2000 spot lights takes 2.92ms on a GTX970. Conclusions. The conclusion shows that the main goal of the thesis has been reached to the extent that all existing problems with current light culling techniques have been solved, at the cost of using more memory. The technique is novel and a lot of future work is outlined and would benefit the validity of the implementation if further researched.

One area of forest biometrics that continues to progress is the development of statistical models as tools to describe tree taper. Taper models allow for the prediction of multiple tree level attributes including: diameter at any height, total tree stem volume, merchantable volume and height to any upper stem diameter from any lower stem height, individual log volumes, and subsequently total tree value. In this work, we generalize segmented regression taper models to include multiple segments and compare it to the traditional 3-Segment (2-Knot) models commonly observed in the forestry literature. We then focus on predicting a future realization of diameter given previously observed data. This is accomplished by comparing a segmented taper model under both the Generalized Algebraic Difference Approach (GADA) and Nonlinear Mixed Effects Models (NLMM) methodologies. Both the GADA and NLMM allow for predictions at the individual tree level of a future realization diameter given a differing number of observed height-diameter pairs. Finally, we explore the prediction and cost/benefit of total tree volume obtained from an integrated taper equation with the incorporation of tree specific random effects given differing observed height-diameter pairs.

The effects of pore density and distribution were investigated on the fatigue crack initiation behavior in an A713 sand cast aluminum alloy plate of 12 mm thickness. The applied stress- the number of cycles to failure (S-N) curves of the samples taken from 2 mm and 5 mm from the free surface were obtained using four-point bend fatigue testing at room temperature, frequency of 20 Hz, stress ratio of 0.1, sinusoidal waveform, and in ambient air. The fatigue strengths of both, the 2 mm and 5 mm samples were 60% of the yield strength (σy=171.9 MPa) of the alloy. Optical microscopy, SEM, and EDS mapping were used to characterize pores and particles in 2 mm and 5 mm samples. The average pore sizes of the 2 mm and 5 mm samples were measured to be 10 to 14 μm, and 14 to 32 μm, respectively. The pore number densities in 5 mm and 2 mm samples were comparable, but higher number densities of non-clustered coarse pores (gas pores) were observed in 5 mm samples. The crack population found after fatigue testing showed a Weibull function of stress level. The peaks of strength distributions of fatigue weak link density of 5 mm and 2 mm samples were measured to be 0.017 mm-2 at 67.6 % σy, and 0.01027 mm-2 at 69.5% σy. Crack populations, when normalized by number densities of gas pores (non-clustered) and number densities of shrinkage pores (clustered), giving crack nucleation rate (crack/pore, mm-2), showed a good fit with the Weibull function in 2 mm and 5 mm samples. Shrinkage and gas pores could both become the main crack initiation sites (i.e. fatigue weak links) in this alloy. Higher nucleation rates of gas pores and shrinkage pores were observed in 5 mm samples compared to those rates in 2 mm samples. At high applied stresses, the 2 mm samples showed better fatigue lives than those of 5 mm samples. Fractured surfaces were analyzed using SEM and found that the main crack initiation were predominately from pores. The pores on the fractured surfaces were counted and their depth and width were measured. It was found that the cracks may not necessarily initiate from coarse pores, but sometimes from shrinkage pores (i.e. group of pores). The depth from the free surface, the width, the size, and the orientation of pores are key factors in increasing the driving force for crack initiation and subsequently those pores turn into long cracks. Moreover, the aspect ratios of pores on the main cracks were measured and found that in 5 mm samples, some pores have an aspect ratios of less than 0.7, which means that these pores are elongated in depth and have a narrow width which increase the stress concentration on the surface, thus, increasing the driving force for crack nucleation.

No description available.

Text in English / Submitted in partial fulfillment of a Master's Degree at the University of South Africa / Our main goal is to collate into a single document what is presently known regarding pointfree convergence. This will be done by exposing some well-known results on pointfree convergence in a much more simpler way. We will start to study the convergence and clustering of filters in frames in terms of covers and use this to characterise compact frames and some type of uniform frames. We will extend this study to a more general type of filters. We will then discuss convergence and clustering of filters on a locale, where a filter on a locale L is just a filter in the sublattice of all the sublocales of L. This convergence has many applications like characterising compact locales and also characterising sharp points which will also be studied. Finally, the latter concepts of convergence and clustering will be reconciled with the previous one. / Mathematical Sciences

No description available.

No description available.

This dissertation presents a novel methodology based on test summaries, which characterize desired tests as constraints written in a mixed imperative and declarative notation, for automated systematic testing of relational applications, such as relational database engines. The methodology has at its basis two novel techniques for effective and efficient testing: (1) mixed-constraint solving, which provides systematic generation of inputs characterized by mixed-constraints using translations among different data domains; and (2) clustered test execution, which optimizes execution of test suites by leveraging similarities in execution traces of different tests using abstract-level undo operations, which allow common segments of partial traces to be executed only once and the execution results to be shared across those tests. A prototype embodiment of the methodology enables a novel approach for systematic testing of commonly used database engines, where test summaries describe (1) input SQL queries, (2) input database tables, and (3) expected output of query execution. An experimental evaluation using the prototype demonstrates its efficacy in systematic testing of relational applications, including Oracle 11g, and finding bugs in them. / text

Multivariate generalized linear mixed models (MGLMM) are used for jointly modeling the clustered mixed outcomes obtained when there are two or more responses repeatedly measured on each individual in scientific studies. The relationship among these responses is often of interest. In the clustered mixed data, the correlation could be present between repeated measurements either within the same observer or between different observers on the same subjects. This study proposes a series of in- dices, namely, intra, inter and total correlation coefficients, to measure the correlation under various circumstances of observations from a multivariate generalized linear model, especially for joint modeling of clustered count and continuous outcomes. Bayesian methods are widely used techniques for analyzing MGLMM. The need for noninformative priors arises when there is insufficient prior information on the model parameters. Another aim of this study is to propose an approximate uniform shrinkage prior for the random effect variance components in the Bayesian analysis for the MGLMM. This prior is an extension of the approximate uniform shrinkage prior. This prior is easy to apply and is shown to possess several nice properties. The methods are illustrated in terms of both a simulation study and a case example.