Huntington’s disease is a neurodegenerative disorder caused by expansion of the CAG repeat in huntingtin exon 1. Early studies demonstrated the huntingtin gene is transcribed into two 3′UTR isoforms in normal human tissue. Decades later, researchers identified a truncated huntingtin mRNA isoform in disease but not control human brain. We speculated the amount of huntingtin 3′UTR isoforms might also vary between control and Huntington’s disease brains. We provide evidence that the abundance of huntingtin 3′UTR isoforms, including a novel mid-3′UTR isoform, differs between patient and control neural stem cells, fibroblasts, motor cortex, and cerebellum. Both alleles of huntingtin contribute to isoform changes. We show huntingtin 3′UTR isoforms are metabolized differently. The long and mid isoforms have shorter half-lives, shorter polyA tails, and more microRNA and RNA binding protein sites than the short isoform. 3′UTR Isoform changes are not limited to huntingtin. Isoforms from 11% of genes change abundance in Huntington’s motor cortex. Only 17% of genes with isoform alterations are differentially expressed in disease tissue. However, gene ontology analysis suggests they share common pathways with differentially expressed genes. We demonstrate knockdown of the RNA binding protein CNOT6 in control fibroblasts results in huntingtin isoform changes similar to those in disease fibroblasts. This study further characterizes Huntington’s disease molecular pathology and suggests RNA binding protein expression may influence mRNA isoform expression in the Huntington’s disease brain.

Induced graphs are used to describe the structure of a graph, one such type of induced graph that has been studied are long paths. In this thesis we show a way to represent such graphs in terms of an array with two colors and a labeled graph. Using this representation and the techniques of Polya counting we will then be able to get upper and lower bounds for graphs containing a long path as an induced subgraph. In particular, if we let P(n,k) be the number of graphs on n+k vertices which contains P_n, a path on n vertices, as an induced subgraph then using our upper and lower bounds for P(n,k) we will show that for any fixed value of k that P(n,k)~2^(nk+k_C_2)/(2k!).

The goal of this paper is to develop extensions of Polya enumeration methods which count orbits of functions. De Bruijn, Harary, and Palmer all worked on this problem and created generalizations which involve permuting the codomain and domain of functions simultaneously. We cover their results and specifically extend them to the case where the group of permutations need not be a direct product of groups. In this situation, we develop a way of breaking the orbits into subclasses based on a characteristic of the functions involved. Additionally, we develop a formula for the number of orbits made up of bijective functions. As a final extension, we also expand the set we are acting on to be the set of all relations between finite sets. Then we show how to count the orbits of relations.

<p> An investigation into the impact of the Reynolds Bauxite Company, a decentralized industry in north-central Jamaica, on the spatial pattern of employment in the surrounding area. The spatial impact is simulated using the Polya-Eggenberger distribution. </p> / Thesis / Master of Arts (MA)

Quantum trajectories are investigated within the complex quantum Hamilton-Jacobi formalism. A unified description is presented for complex quantum trajectories for one-dimensional time-dependent and time-independent problems. Complex quantum trajectories are examined for the free Gaussian wave packet, the coherent state in the harmonic potential, and the the barrier scattering problems. We analyze the variations of the complex-valued kinetic energy, the classical potential, and the quantum potential along the complex quantum trajectories. For one-dimensional time-independent scattering problems, we demonstrate general properties and similar structures of the complex quantum trajectories and the quantum potentials. In addition, it is shown that a quantum vortex forms around a node in the wave function in complex space, and the quantized circulation integral originates from the discontinuity in the real part of the complex action. Although the quantum momentum field displays hyperbolic flow around a node, the corresponding Polya vector field displays circular flow. Moreover, local topologies of the quantum momentum function and the Polya vector field are thoroughly analyzed near a stagnation point or a pole (including circular, hyperbolic, and attractive or repulsive structures). The local structure of the quantum momentum function and the Polya vector field around a stagnation point are related to the first derivative of the quantum momentum function. However, the magnitude of the asymptotic structures for these two fields near a pole depends only on the order of the node in the wave function. Finally, quantum interference is investigated and it leads to the formation of the topological structure of quantum caves in space-time Argand plots. These caves consist of the vortical and stagnation tubes originating from the isosurfaces of the amplitude of the wave function and its first derivative. Complex quantum trajectories display helical wrapping around the stagnation tubes and hyperbolic deflection near the vortical tubes. Moreover, the wrapping time for a specific trajectory is determined by the divergence and vorticity of the quantum momentum field. The lifetime for interference features is determined by the rotational dynamics of the nodal line in the complex plane. Therefore, these results demonstrate that the complex quantum trajectory method provides a novel perspective for analysis and interpretation of quantum phenomena. / text

For centuries, scientists have dreamed of creating materials by design. Rather than discovery by accident, bespoke materials could be tailored to fulfill specific technological needs. Quantum theory and computational methods are essentially equal to the task, and computational power is the new bottleneck. Machine learning has the potential to solve that problem by approximating material behavior at multiple length scales. A full end-to-end solution must allow us to approximate the quantum mechanics, microstructure and engineering tasks well enough to be predictive in the real world. In this dissertation, I present algorithms and methodology to address some of these problems at various length scales. In the realm of enumeration, systems with many degrees of freedom such as high-entropy alloys may contain prohibitively many unique possibilities so that enumerating all of them would exhaust available compute memory. One possible way to address this problem is to know in advance how many possibilities there are so that the user can reduce their search space by restricting the occupation of certain lattice sites. Although tools to calculate this number were available, none performed well for very large systems and none could easily be integrated into low-level languages for use in existing scientific codes. I present an algorithm to solve these problems. Testing the robustness of machine-learned models is an essential component in any materials discovery or optimization application. While it is customary to perform a small number of system-specific tests to validate an approach, this may be insufficient in many cases. In particular, for Cluster Expansion models, the expansion may not converge quickly enough to be useful and reliable. Although the method has been used for decades, a rigorous investigation across many systems to determine when CE "breaks" was still lacking. This dissertation includes this investigation along with heuristics that use only a small training database to predict whether a model is worth pursuing in detail. To be useful, computational materials discovery must lead to experimental validation. However, experiments are difficult due to sample purity, environmental effects and a host of other considerations. In many cases, it is difficult to connect theory to experiment because computation is deterministic. By combining advanced group theory with machine learning, we created a new tool that bridges the gap between experiment and theory so that experimental and computed phase diagrams can be harmonized. Grain boundaries in real materials control many important material properties such as corrosion, thermal conductivity, and creep. Because of their high dimensionality, learning the underlying physics to optimizing grain boundaries is extremely complex. By leveraging a mathematically rigorous representation for local atomic environments, machine learning becomes a powerful tool to approximate properties for grain boundaries. But it also goes beyond predicting properties by highlighting those atomic environments that are most important for influencing the boundary properties. This provides an immense dimensionality reduction that empowers grain boundary scientists to know where to look for deeper physical insights.

This thesis explores stochastic modeling and Bayesian inference strategies in the context of the following three problems: 1) Modeling the complex interactions between and within molecules; 2) Extracting information from stepwise signals that are commonly found in biophysical experiments; 3) Improving the computational efficiency of a non-parametric Bayesian inference algorithm. Chapter 1 studies the data from a recent single-molecule biophysical experiment on enzyme kinetics. Using a stochastic network model, we analyze the autocorrelation of experimental fluorescence intensity and the autocorrelation of enzymatic reaction times. This chapter shows that the stochastic network model is capable of explaining the experimental data in depth and further explains why the enzyme molecules behave fundamentally differently from what the classical model predicts. The modern knowledge on the molecular kinetics is often learned through the information extracted from stepwise signals in experiments utilizing fluorescence spectroscopy. Chapter 2 proposes a new Bayesian method to estimate the change-points in stepwise signals. This approach utilizes marginal likelihood as the tool of inference. This chapter illustrates the impact of the choice of prior on the estimator and provides guidelines for setting the prior. Based on the results of simulation study, this method outperforms several existing change-points estimators under certain settings. Furthermore, DNA array CGH data and single molecule data are analyzed with this approach. Chapter 3 focuses on the optional Polya tree, a newly established non-parametric Bayesian approach (Wong and Li 2010). While the existing study shows that the optional Polya tree is promising in analyzing high dimensional data, its applications are hindered by the high computational costs. A heuristic algorithm is proposed in this chapter, with an attempt to speed up the optional Polya tree inference. This study demonstrates that the new algorithm can reduce the running time significantly with a negligible loss of precision. / Statistics

This PhD thesis consists of a summary and four papers which deal with stochastic approximation algorithms and first-passage percolation. Paper I deals with the a.s. limiting properties of bounded stochastic approximation algorithms in relation to the equilibrium points of the drift function. Applications are given to some generalized Pólya urn processes. Paper II continues the work of Paper I and investigates under what circumstances one gets asymptotic normality from a properly scaled algorithm. The algorithms are shown to converge in some other circumstances, although the limiting distribution is not identified. Paper III deals with the asymptotic speed of first-passage percolation on a graph called the ladder when the times associated to the edges are independent, exponentially distributed with the same intensity. Paper IV generalizes the work of Paper III in allowing more edges in the graph as well as not having all intensities equal.

Linear programming (LP) decoding of low-density parity-check codes was introduced by Feldman et al. in [1]. In his formulation it is assumed that communication takes place over a memoryless channel and that the source is uniform. Here, we extend the LP decoding paradigm by studying its application to scenarios with source non-uniformity and to decoding over channels with memory. We develop two decoders for the scenario of non-uniform memoryless sources transmitted over memoryless channels. The first decoder uses a modified linear cost function which incorporates the a-priori source information and works with systematic codes. The second decoder differs by using non-systematic codes obtained by puncturing lower rate systematic codes and using an “extended decoding polytope.” Simulations show that the modified decoders yield gains over the standard LP decoder. Next, LP decoding is considered for two channels with memory: the binary additive Markov noise channel and the infinite-memory non-ergodic Polya-contagion channel. For the Markov channel, no linear cost function corresponding to maximum likelihood (ML) decoding could be obtained and hence it is unclear how to proceed. For the Polya channel, two LP-based decoders are developed. The first is derived in a straightforward manner from the ML decoding rule of [2]. The second decoder relies on a simplification of the same ML decoding rule which holds for codes containing the all-ones codeword. Simulations are performed for both decoders with regular and irregular LDPC codes and demonstrate relatively good performance with respect to the channel epsilon-capacity. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2008-12-08 16:24:43.358

Made available in DSpace on 2014-06-11T19:31:42Z (GMT). No. of bitstreams: 0 Previous issue date: 2004-04-14Bitstream added on 2014-06-13T20:22:45Z : No. of bitstreams: 1 balieirofilho_if_dr_rcla.pdf: 975143 bytes, checksum: c638314fd6a38782767ef440acd3aa67 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O presente trabalho apresenta uma análise e discussão de indícios heurísticos presentes nas obras O Método de Arquimedes, A Coleção Matemática de Pappus e Regras para a Direção do Espírito de Descartes, buscando estabelecer relações com a sistematização da atividade heurística apresentada nas obras A arte de Resolver Problemas e Matemática e Raciocínio Plausível de George Polya. Através de uma metodologia de pesquisa em História da Matemática, foi consultado o original da obra de Arquimedes e traduções das demais obras citadas. Considerando que O Método é a mais antiga obra de heurística de que tem-se conhecimento, foi feita a primeira tradução do original em Grego Clássico para o Português desse texto de Arquimedes. A atividade heurística, definida como um esquema psíquico através do qual o homem cria, elabora e descobre a resolução de um problema, é o eixo central dos estudos sobre .como pensamos., estabelecidos por Polya, e que fundamentam a Resolução de Problemas, linha de pesquisa em Educação Matemática. / This work presents an analysis and discussion of heuristic traces contained in the works The Method of Archimedes, The Mathematical Collection by Pappus and Rules for the Direction of the Mind by Descartes, trying to establish relationships with the systematization of heuristic activity in the works How to solve it and Mathematics and Plausible Reasoning by George Polya. Through a research methodology in History of Mathematics, the Archimedes.s original work and translation of the other mentioned works were consulted. Considering that The Method is the oldest heurist work for all we know, it was made the first translation from the original classic Greek to Portuguese language of that Archimedes.s text. The heuristic activity, defined as a psychic outline through which the man creates, elaborates and discovers the resolution of a problem, is the central axis of the studies about .as we thing., established by Polya, and that have founded the Resolution of Problems, a field of research in Mathematical Education.