<p> The object of this dissertation is to investigate the properties, associated boundary conditions and generalized resolvents of symmetric ordinary differential operators associated with formally self-adjoint nth order ordinary differential expressions with complex coefficients. </p> <p> While symmetric differential operators with equal deficiency indices have been studied in some detail, expecially the particular case when the underlying differential expression has real coefficients, little research has been done on the properties of symmetric differential operators with unequal deficiency indices which are associated with a differential expression with complex coefficients. </p> <p> By extending the symmetric differential operators with unequal deficiency indices to suitable operators with equal deficiency indices in larger Hilbert spaces and introducing a new type of boundary conditions to these extensions, we obtain important information about the original symmetric differential operators with unequal deficiency indices. We are able to generate some well-known theorems of I. M. Glazman (1950) and E. A. Coddington (1954) dealing with the characterization of self-adjoint extensions of symmetric operators in terms of boundary conditions, the relation between the deficiency indices of operators on the whole real line and on the half-line, and the resolvent of self-adjoint extensions, from the theory of symmetric, in particular real, differential operators with equal deficiency indices. We also generalize the result of W. N. Everitt (1959) concerning the number of integrable-square solutions of differential equations with one particular and one singular end-point to the case in which both end-points are singular. Finally, under certain assumptions, we extend some of the fundamental results of K. Kodaira (1950) based upon the methods of algebraic geometry, concerning Green's functions and the minimal symmetric differential operator associated with an even-order formally self-adjoint ordinary differential expansion with real coefficients to the case of Green's functions and the minimal symmetric differential operator associated with an even-order formally self-adjoint ordinary differential expression with complex coefficients. </p> / Thesis / Doctor of Philosophy (PhD)

In 2007 and 2008 more than 100 million dollars of fresh market tomatoes were grown in Virginia, with the majority of production occurring on the Eastern Shore of Virginia (ESV), according to the National Agricultural Statistics Service. Bacterial wilt of tomato, caused by Ralstonia solanacearum (Smith) and Yabucchi et al., is the most devastating disease of tomato on the ESV. Four 'observational trials' were conducted on the ESV over three growing seasons to determine the temporal and spatial distribution of this disease in commercial tomato fields. Plants were assessed at approximately one-week intervals throughout the growing seasons and the incidence of bacterial wilt for each individual plant was recorded. A steady increase in both disease incidence and clustered distribution of the disease within rows was observed as the growing season progressed. Positive correlations between disease incidence and percentage of rows exhibiting a significant clustered distribution occurred in all trials, which indicated an increase in clustered distribution as disease incidence increased. Research trials were conducted over three years, beginning in the summer of 2007, to investigate the effects of tomato bacterial wilt resistant cultivars on the ESV. In 2008 and 2009, the selective, systemic compound which induces host plant resistance, acibenzolar-S-methyl (ASM) was incorporated into resistant cultivar trials. Results from the 2007 trial revealed significant resistance in some of the breeding lines, CRA 66 and PI 126408. The 2008 and 2009 trials revealed that ASM was not effective at reducing levels of bacterial wilt. Grafted transplants in the spring trials of 2008 and 2009 had varied results in resistance and yield. Results revealed the tomato cultivar BHN 669 was an excellent resistant cultivar with promising yield potential and fruit quality. / Master of Science

Cell cycle models used in biology can be very complex. These models have parameters with initially unknown values. The values of the parameters vastly aect the accuracy of the models in representing real biological cells. Typically people search for the best parameters to these models using computers only as tools to run simulations. In this thesis methods and results are described for a computer program that searches for parameters to a series of related models using well tested algorithms. The code for this program uses ODRPACK for parameter estimation and LSODAR to solve the dierential equations that comprise the model. / Master of Science

This thesis on the project Anti-age takes an interest in the passing of time, the different ways in which we have historically measured it and its respective effects on how we view the subject. Time as a theme came about from reading about the period prior to us having a wide availability to clocks. There is an old practise in Sweden were you sing a psalm when boiling an egg, as to keep time. The psalm in turn becomes a clock, a time-keeper. The abstractness of time takes another form.  Because of the climate crise which we start seeing unravel, this project turns its attention to objects which exist in the realm of the ordinary and therefore is invisible or uninteresting to us. Here, a regular tin can, the official office chair of Konstfack and a balcony table that we’ve seen one too many times are being turned into pre-historic clocks. With their rather unprecise measuring of time, the clocks designed in this project works as sort of vessels. The objects become a sundial, clepsydra and what we know to be the oldest clocks in the world. Sand, sun and shadow are visible units of time which remind us and grant acess to a sense of something bigger, other and further away from ourselves.

Determining the dynamics and parameter values that drive tumor growth is of great interest to mathematical modelers, experimentalists and practitioners alike. We provide a basis on which to estimate the growth dynamics of ten different tumors by fitting growth parameters to at least five sets of published experimental data per type of tumor. These timescale tumor growth data are also used to determine which of the most common tumor growth models (exponential, power law, logistic, Gompertz, or von Bertalanffy) provides the best fit for each type of tumor. In order to compute the best-fit parameters, we implemented a hybrid local-global least squares minimization algorithm based on a combination of Nelder-Mead simplex direct search and Monte Carlo Markov Chain methods.

This thesis contributes towards understanding of how ‘ordinary’ Christians, who have little or no experience of academic biblical study or theological training, might be enabled to engage more deeply with the Bible. I propose that attempts to cultivate the skills of biblical engagement among ordinary Christians might be shaped around lectio divina, this ancient practice being adapted for the situation of contemporary readers. The adaptations would involve use of a range of modern media with which to encounter the texts, working in small groups in order to make space for a more intentional engagement between the voices of multiple ordinary interpreters, and employment of strategies to enable readers to navigate a perceived tension when approaching the Bible: one between head and heart, academic learning and spiritual growth. More specifically, I propose that the promotion of biblical engagement among ordinary Christians should be undertaken as a planned programme with a suite of different resources, which complement one another in both style and aim, together with a sign-posted framework to show participants what each stage is designed to achieve. It should begin with a widely accessible introduction to the whole Bible that conveys the overall narrative and historical setting while communicating the sense that the reader is a participant in the ongoing biblical story. This and subsequent resources should be selected in order to attempt to integrate cognitive and emotive approaches to the texts and, where possible, straightforward terminology would be employed to maximise accessibility. These proposals emerged from my evaluation of an experiment in promoting biblical engagement among ordinary Christians (Bible Society’s ‘Pathfinder’). Analysis of, and reflection upon, the rich qualitative data generated there led to my examining the process of developing biblical engagement in the context of the lectio divina tradition and in the light of contemporary theological reflection across a wide range of theological hermeneutics.

In modern mining industry, new resource efficient and climate resilient methods have been gaining traction. Commissioned efforts to improve the efficiency of European mining is further helping us to such goals. Orexplore AB's X-ray technology for analyzing drill cores is currently involved in two such project. Orexplore AB wishes to incorporate geostatistics (spatial statistics) into their analyzing process in order to further extend the information gained from the mineral data. The geostatistical method implemented here is ordinary kriging which is an interpolation method that, given measured data, predicts intermediate values governed by prior covariance models. Ordinary kriging facilitates prediction of mineral concentrations on a continuous grid in 1-D up to 3-D. Intermediate values are predicted on a Gaussian process regression line, governed by prior covariances. The covariance is modeled by fitting a model to a calculated experimental variogram. Mineral concentrations are available along the lateral surface of the drill core. Ordinary kriging is implemented to sequentially predict mineral concentrations on shorter sections of the drill core, one mineral at a time. Interpolation of mineral concentrations is performed on the data considered in 1-D and 3-D. The validation is performed by calculating the corresponding density at each section that concentrations are predicted on and compare each such value to measured densities. The performance of the model is evaluated by subjective visual evaluation of the fit of the interpolation line, its smoothness, together with the variance. Moreover, the fit is tested through cross-validation using different metrics that evaluates the variance and prediction errors of different models. The results concluded that this method accurately reproduces the measured concentrations while performing well according to the above mentioned metrics, but does not outperform the measured concentrations when evaluated against the measured densities. However, the method was successful in providing information of the minerals in the drill core by producing mineral concentrations on a continuous grid. The method also produced mineral concentrations in 3-D that reproduced the measured densities well. It can be concluded that ordinary kriging implemented according to the methodology described in this report efficiently produces mineral concentrations that can be used to obtain information of the distribution of concentrations in the interior of the drill core. / I den moderna gruvindustrin har nya resurseffektiva och klimatbeständiga metoder ökat i efterfråga. Beställda projekt för att förbättra effektiviteten gällande den europeiska gruvdriften bidrar till denna effekt ytterligare. Orexplore AB:s röntgenteknologi för analys av borrkärnor är för närvarande involverad i två sådana projekt. Orexplore AB vill integrera geostatistik (spatial statistik) i sin analysprocess för att ytterligare vidga informationen från mineraldatan. Den geostatistiska metoden som implementeras här är ordinary kriging, som är en interpolationsmetod som, givet uppmätta data, skattar mellanliggande värden betingade av kovariansmodeller. Ordinary kriging tillåter skattning av mineralkoncentrationer på ett kontinuerligt nät i 1-D upp till 3-D. Mellanliggande värden skattas enligt en Gaussisk process-regressionslinje. Kovariansen modelleras genom att passa en modell till ett beräknat experimentellt variogram. Mineralkoncentrationer är tillgängliga längs borrkärnans mantelyta. Ordinary kriging implementeras för att sekventiellt skatta mineralkoncentrationer på kortare delar av borrkärnan, ett mineral i taget. Interpolering av mineralkoncentrationer utförs på datan betraktad i 1-D och 3-D. Valideringen utförs genom att utifrån de skattade koncentrationerna beräkna den motsvarande densiteten vid varje sektion som koncentrationer skattas på och jämföra varje sådant värde med uppmätta densiteter. Undersökning av modellen utförs genom subjektiv visuell utvärdering av interpolationslinjens passning av datan, dess mjukhet, tillsammans med variansen. Dessutom testas passformen genom korsvalidering med olika mätvärden som utvärderar varians- och skattningsfel för olika modeller. Slutsatsen från resultaten är att denna metod reproducerar de uppmätta koncentrationerna väl samtidigt som den presterar bra enligt de mätvärden som utvärderas, men överträffar ej de uppmätta koncentrationerna vid utvärdering mot de uppmätta densiteterna. Metoden var emellertid framgångsrik med att tillhandahålla information om mineralerna i borrkärnan genom att producera mineralkoncentrationer på ett kontinuerligt rutnät. Metoden producerade också mineralkoncentrationer i 3-D som reproducerade de uppmätta densiteterna väl. Slutsatsen dras att ordinary kriging, implementerad enligt den metod som beskrivs i denna rapport, effektivt skattar mineralkoncentrationer som kan användas för att få information om fördelningen av koncentrationer i det inre av borrkärnan.

Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a new method, the MCR method, which is unique to stochastic models and provides significantly better estimates and smaller confidence intervals for parameter values. Initial analysis of the new MCR method indicates that this method might be a viable method for parameter estimation for continuous time Markov chain models.

Due to the inherently hierarchical nature of many natural phenomena, data collected rests in nested entities. As an example, students are nested in schools, school are nested in districts, districts are nested in counties, and counties are nested within states. Multilevel models provide a statistical framework for investigating and drawing conclusions regarding the influence of factors at differing hierarchical levels of analysis. The work in this paper serves as an introduction to multilevel models and their comparison to Ordinary Least Squares (OLS) regression. We overview three basic model structures: variable intercept model, variable slope model, and hierarchical linear model and illustrate each model with an example of student data. Then, we contrast the three multilevel models with the OLS model and present a method for producing confidence intervals for the regression coefficients. / text

The dissertation addresses the research topics of machine learning outlined below. We developed the theory about traditional first-order algorithms from convex opti- mization and provide new insights in nonconvex objective functions from machine learning. Based on the theory analysis, we designed and developed new algorithms to overcome the difficulty of nonconvex objective and to accelerate the speed to obtain the desired result. In this thesis, we answer the two questions: (1) How to design a step size for gradient descent with random initialization? (2) Can we accelerate the current convex optimization algorithms and improve them into nonconvex objective? For application, we apply the optimization algorithms in sparse subspace clustering. A new algorithm, CoCoSSC, is proposed to improve the current sample complexity under the condition of the existence of noise and missing entries. Gradient-based optimization methods have been increasingly modeled and inter- preted by ordinary differential equations (ODEs). Existing ODEs in the literature are, however, inadequate to distinguish between two fundamentally different meth- ods, Nesterov’s acceleration gradient method for strongly convex functions (NAG-SC) and Polyak’s heavy-ball method. In this paper, we derive high-resolution ODEs as more accurate surrogates for the two methods in addition to Nesterov’s acceleration gradient method for general convex functions (NAG-C), respectively. These novel ODEs can be integrated into a general framework that allows for a fine-grained anal- ysis of the discrete optimization algorithms through translating properties of the amenable ODEs into those of their discrete counterparts. As a first application of this framework, we identify the effect of a term referred to as gradient correction in NAG-SC but not in the heavy-ball method, shedding deep insight into why the for- mer achieves acceleration while the latter does not. Moreover, in this high-resolution ODE framework, NAG-C is shown to boost the squared gradient norm minimization at the inverse cubic rate, which is the sharpest known rate concerning NAG-C itself. Finally, by modifying the high-resolution ODE of NAG-C, we obtain a family of new optimization methods that are shown to maintain the accelerated convergence rates as NAG-C for minimizing convex functions.