Thesis (Ph. D.)--Rutgers University, 2007. / "Graduate Program in Computer Science." Includes bibliographical references (p. 94-100).

Thesis (B.S.)--Butler University, 2007. / Includes bibliographical references (leaf 52).

In this thesis, I investigate quantum walks in quantum computing from three aspects: the insights, the implementation, and the applications. Quantum walks are the quantum analogue of classical random walks. For the insights of quantum walks, I list and explain the required components for quantizing a classical random walk into a quantum walk. The components are, for instance, Markov chains, quantum phase estimation, and quantum spectrum theorem. I then demonstrate how the product of two reflections in the walk operator provides a quadratic speed-up, in comparison to the classical counterpart. For the implementation of quantum walks, I show the construction of an efficient circuit for realizing one single step of the quantum walk operator. Furthermore, I devise a more succinct circuit to approximately implement quantum phase estimation with constant precision controlled phase shift operators. From an implementation perspective, efficient circuits are always desirable because the realization of a phase shift operator with high precision would be a costly task and a critical obstacle. For the applications of quantum walks, I apply the quantum walk technique along with other fundamental quantum techniques, such as phase estimation, to solve the partition function problem. However, there might be some scenario in which the speed-up of spectral gap is insignificant. In a situation like that that, I provide an amplitude amplification-based iii approach to prepare the thermal Gibbs state. Such an approach is useful when the spectral gap is extremely small. Finally, I further investigate and explore the effect of noise (perturbation) on the performance of quantum walks

Current Question Answering (QA) systems have been significantly advanced in demonstrating finer abilities to answer simple factoid and list questions. Such questions are easier to process as they require small snippets of texts as the answers. However, there is a category of questions that represents a more complex information need, which cannot be satisfied easily by simply extracting a single entity or a single sentence. For example, the question: “How was Japan affected by the earthquake?” suggests that the inquirer is looking for information in the context of a wider perspective. We call these “complex questions” and focus on the task of answering them with the intention to minimize the existing gaps in the literature. The major limitation of the available search and QA systems is that they lack a way of measuring whether a user is satisfied with the information provided. This was our motivation to propose a reinforcement learning formulation to the complex question answering problem. Next, we presented an integer linear programming formulation where sentence compression models were applied for the query-focused multi-document summarization task in order to investigate if sentence compression improves the overall performance. Both compression and summarization were considered as global optimization problems. We also investigated the impact of syntactic and semantic information in a graph-based random walk method for answering complex questions. Decomposing a complex question into a series of simple questions and then reusing the techniques developed for answering simple questions is an effective means of answering complex questions. We proposed a supervised approach for automatically learning good decompositions of complex questions in this work. A complex question often asks about a topic of user’s interest. Therefore, the problem of complex question decomposition closely relates to the problem of topic to question generation. We addressed this challenge and proposed a topic to question generation approach to enhance the scope of our problem domain. / xi, 192 leaves : ill. ; 29 cm

Epidemiologists rely on human interaction networks for determining states and dynamics of disease propagations in populations. However, such networks are empirical snapshots of the past. It will greatly benefit if human interaction networks are statistically predicted and dynamically created while an epidemic is in progress. We develop an application framework for the generation of human interaction networks and running epidemiological processes utilizing research on human mobility patterns and agent-based modeling. The interaction networks are dynamically constructed by incorporating different types of Random Walks and human rules of engagements. We explore the characteristics of the created network and compare them with the known theoretical and empirical graphs. The dependencies of epidemic dynamics and their outcomes on patterns and parameters of human motion and motives are encountered and presented through this research. This work specifically describes how the types and parameters of random walks define properties of generated graphs. We show that some configurations of the system of agents in random walk can produce network topologies with properties similar to small-world networks. Our goal is to find sets of mobility patterns that lead to empirical-like networks. The possibility of phase transitions in the graphs due to changes in the parameterization of agent walks is the focus of this research as this knowledge can lead to the possibility of disruptions to disease diffusions in populations. This research shall facilitate work of public health researchers to predict the magnitude of an epidemic and estimate resources required for mitigation.

Mass transfer processes in food systems, such as solute infusion, are poorly understood because of their complex nature. Food systems contain porous matrices and a variety of continuous phases within cellular tissues. Mass transfer processes are generally not pure diffusion: often convection, binding and obstructing diffusion will occur. Monte Carlo (MC) simulation has been increasingly used in life science and engineering to elucidate molecular transport in biological systems. However, there are few articles available discussing MC simulation in food processing, especially mass transfer. The main goal of this study was to show the inherent simplicity of the MC approach and its potential when combined with traditional experimental and theoretical approaches to better describe and understand mass transfer processes. A basic framework for MC random walk - simulation applied to a diffusion problem - is developed in this project. Infusion of two sizes of dextran macromolecules in fish muscle cells is used to apply the MC framework in combination with Fluorescence Recovery After Photobleaching experiments. Effective diffusivity coefficients within cells, considering the degree of obstruction due to the myofibrilar matrix, are assessed. Then, the results are used as input in a mathematical model that was developed for theoretical simulation of mass transfer in the multi-cellular tissue. Diffusivity values obtained by the MC framework had an SD of ±0.02 [µm²/s] around the true value of 0.25 [µm²/s]. MC results for degree of obstruction were 0.29 and 0.34 for dextran FD1OS and FD2OS, respectively, and the Devalues were 23.7 and 11.2 [µm2/s]. The statistical error in the estimation of D was estimated to be [22.8-24.6] and [9.7-12.7] (95% CI), where average experimental values of 24.3 [µm²/s] for FD1OS and 11.4 [µm²/s] for FD2OS were captured by the respective interval. The theoretical model showed a significant influence of the cell membrane characteristics and tissue porosity in both the degree of solute penetration and the solute distribution between intra- and extra-cellular space. The combined approach was successfully applied to a diffusion problem. Overall, it is expected that the present work will contribute towards the application of MC simulation in the field of Food Science and Engineering. / Graduation date: 2006

This thesis conducts a comprehensive examination on the random walk behavior of 29 foreign exchange rates over the period of floating exchange regime, using variance-ratio tests. The cross-country and time-series test show that random walk model cannot be rejected on majority, and the random walk behavior is quite volatile across the whole floating exchange regime period. It then goes further to explore possible factors that can explain the probability of rejection/ non-rejections on random walk model using linear as well as nonlinear probability models, and find that the factors such as capital openness and investment-to-trade ratio significantly increases the chance of its exchange rate exhibiting random walk behavior.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 79-81). Also available on the Internet.

Orientador: Serguei Popov / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-25T09:42:00Z (GMT). No. of bitstreams: 1 Costa_MarceloRocha_M.pdf: 576974 bytes, checksum: 3b01a9f15e6e0f9fdd98631dc69cd202 (MD5) Previous issue date: 2014 / Resumo: O problema considerado no presente trabalho cumpre o papel de reforçar a eficácia dos métodos apresentados nos capítulos introdutórios, bem como investiga a resposta de um problema até então não publicado na literatura especializada. Introduzimos uma partícula realizando um passeio aleatório simples no espaço, ou seja, uma partícula que a cada passo escolhe uniformemente um de seus vizinhos para onde irá saltar. Fixando sua posição inicial ao longo da fronteira do cubo, pergunta-se: qual é a probabilidade de que a trajetória de tal partícula nunca mais retorne ao cubo? Em outras palavras, se T é o tempo de primeiro retorno ao cubo, estamos interessados em descrever o comportamento assintótico da probabilidade de que T seja infinito / Abstract: It has been considered in this work a problem which play a role of showing the effectiveness of the content covered in the introductory chapters, as well as it is a unsolved problem across the specialized literature. We introduce a particle performing a simple random walk in space, i.e., a particle which at each step choose uniformly one of its neighbourhood sites to which it then jumps into. Fixed its initial position along the boundary of a cube, we are interested in answering the following question: what is the probability that such particle's trajectory will never reach the cube again. In other words, if T is the first return time to the cube, we aim to analyse the asymptotic behaviour of the probability that T is infinite / Mestrado / Estatistica / Mestre em Estatística

Orientador: Serguei Popov / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-25T10:22:43Z (GMT). No. of bitstreams: 1 Bernardini_DiegoFernandode_D.pdf: 1410086 bytes, checksum: b77a17aefd06d547f1c5db3c5cc1a8f7 (MD5) Previous issue date: 2014 / Resumo: O modelo de entrelaçamentos aleatórios foi introduzido no sentido de se investigar originalmente o traço deixado por passeios aleatórios em grandes grafos e, basicamente, tal processo é descrito por um processo pontual de Poisson em um espaço de trajetórias duplamente infinitas de passeios aleatórios simples no reticulado d-dimensional, com dimensão d pelo menos igual a três. Neste sentido, o processo é caracterizado por um emaranhado aleatório de trajetórias deste tipo. Tal modelo possui ainda um parâmetro de intensidade, que controla, de certa forma, a quantidade de trajetórias que constituem o processo. Um problema relevante no contexto deste processo, e que tem sido amplamente estudado na literatura, diz respeito à caracterização da relação de dependência (através da covariância) entre os eventos denominados como crescentes neste modelo e suportados em subconjuntos disjuntos do reticulado, e é justamente este o problema no qual nos concentramos. Em uma primeira etapa neste trabalho, determinamos expressões explícitas para a derivada, com respeito ao parâmetro de intensidade, da probabilidade de um evento crescente e suportado em um subconjunto finito do reticulado, estabelecendo assim aquilo que denominamos como a fórmula de Russo para os entrelaçamentos aleatórios. A utilização desta denominação é justificada e motivada pelo amplamente conhecido termo original, que no contexto do modelo usual de percolação estabelece uma expressão para a derivada da probabilidade dos eventos definidos como crescentes naquele modelo. Em seguida, tentamos utilizar este resultado no sentido de estabelecer uma primeira abordagem para o problema da covariância entre os eventos crescentes, e esta investigação é baseada essencialmente em uma observação sobre o número esperado das trajetórias então denominadas como pivotais positivas para o evento de interesse. Por fim, estabelecemos uma nova abordagem para o mesmo problema, utilizando uma construção alternativa do processo de entrelaçamentos baseada na técnica dos soft local times, e investigando uma espécie de pivotalidade conjunta de coleções de excursões das trajetórias dos passeios aleatórios pelos conjuntos nos quais estão suportados os eventos de interesse. Justamente a partir desta abordagem obtemos nosso último resultado sobre a covariância. De forma geral, acreditamos que a investigação e a tentativa de obter uma caracterização cada vez mais precisa para a relação de dependência que mencionamos deve ajudar a entender o processo de entrelaçamentos e suas propriedades de forma cada vez mais clara / Abstract: The random interlacements model was originally introduced in order to investigate the trace left by random walks in large graphs and, basically, such process is described by a Poisson point process in a space of doubly infinite simple random walk trajectories in the d-dimensional lattice, with dimension d at least equal to three. In this sense, the process is characterized by a random tangle of trajectories of this kind. Such model also has an intensity parameter, which controls, in a certain sense, the quantity of trajectories that constitutes the process. A relevant issue in the context of this process, which has been largely studied in the literature, concerns the characterization of the dependence relation (through the covariance) between the so-called increasing events in this model, which are supported on disjoint subsets of the lattice, and this is precisely the issue on which we focus. In a first step in this work, we determine explicit expressions for the derivative, with respect to the intensity parameter, of the probability of an increasing event which is supported in a finite subset of the lattice, thus establishing what we call as Russo¿s formula for random interlacements. The use of this term is justified and motivated by the widely known original term, which, in the context of the usual percolation model, provides an expression for the derivative of the probability of events defined as increasing in that model. Then, we try to use this result to establish a first approach to the problem of the covariance between increasing events, and such investigation is essentially based in a fact about the expected number of the so-called positive pivotal (or plus pivotal) trajectories for the event of interest. Finally, we establish a new approach to the same problem by using an alternative construction of the interlacements process based on the technique of soft local times, and investigating a kind of joint "pivotality" of collections of excursions of the random walk trajectories, through the sets on which the events of interest are supported. From this approach we obtain our last result on the covariance. Overall, we believe that the investigation and the attempt to get an increasingly accurate characterization of the above mentioned dependence relation should help to understand the interlacements process and its properties in an increasingly clear way / Doutorado / Estatistica / Doutor em Estatística