Master of Science / Department of Computing and Information Sciences / Doina Caragea / The vast amount of data present on the internet calls for ways to label and organize this data according to specific categories, in order to facilitate search and browsing activities. This can be easily accomplished by making use of folksonomies and user provided tags. However, it can be difficult for users to provide meaningful tags. Tag recommendation systems can guide the users towards informative tags for online resources such as websites, pictures, etc. The aim of this thesis is to build a system for recommending tags to URLs available through a bookmark sharing service, called BibSonomy. We assume that the URLs for which we recommend tags do not have any prior tags assigned to them. Two approaches are proposed to address the tagging problem, both of them based on Latent Dirichlet Allocation (LDA) Blei et al. [2003]. LDA is a generative and probabilistic topic model which aims to infer the hidden topical structure in a collection of documents. According to LDA, documents can be seen as mixtures of topics, while topics can be seen as mixtures of words (in our case, tags). The first approach that we propose, called topic words based approach, recommends the top words in the top topics representing a resource as tags for that particular resource. The second approach, called topic distance based approach, uses the tags of the most similar training resources (identified using the KL-divergence Kullback and Liebler [1951]) to recommend tags for a test untagged resource. The dataset used in this work was made available through the ECML/PKDD Discovery Challenge 2009. We construct the documents that are provided as input to LDA in two ways, thus producing two different datasets. In the first dataset, we use only the description and the tags (when available) corresponding to a URL. In the second dataset, we crawl the URL content and use it to construct the document. Experimental results show that the LDA approach is not very effective at recommending tags for new untagged resources. However, using the resource content gives better results than using the description only. Furthermore, the topic distance based approach is better than the topic words based approach, when only the descriptions are used to construct documents, while the topic words based approach works better when the contents are used to construct documents.

Doctor of Philosophy / Department of Mathematics / Christopher G. Pinner

A vast amount of usable electronic data is in the form of unstructured text. The relation extraction task aims to identify useful information in text (e.g., PersonW works for OrganisationX, GeneY encodes ProteinZ) and recode it in a format such as a relational database that can be more effectively used for querying and automated reasoning. However, adapting conventional relation extraction systems to new domains or tasks requires significant effort from annotators and developers. Furthermore, previous adaptation approaches based on bootstrapping start from example instances of the target relations, thus requiring that the correct relation type schema be known in advance. Generic relation extraction (GRE) addresses the adaptation problem by applying generic techniques that achieve comparable accuracy when transferred, without modification of model parameters, across domains and tasks. Previous work on GRE has relied extensively on various lexical and shallow syntactic indicators. I present new state-of-the-art models for GRE that incorporate governordependency information. I also introduce a dimensionality reduction step into the GRE relation characterisation sub-task, which serves to capture latent semantic information and leads to significant improvements over an unreduced model. Comparison of dimensionality reduction techniques suggests that latent Dirichlet allocation (LDA) – a probabilistic generative approach – successfully incorporates a larger and more interdependent feature set than a model based on singular value decomposition (SVD) and performs as well as or better than SVD on all experimental settings. Finally, I will introduce multi-document summarisation as an extrinsic test bed for GRE and present results which demonstrate that the relative performance of GRE models is consistent across tasks and that the GRE-based representation leads to significant improvements over a standard baseline from the literature. Taken together, the experimental results 1) show that GRE can be improved using dependency parsing and dimensionality reduction, 2) demonstrate the utility of GRE for the content selection step of extractive summarisation and 3) validate the GRE claim of modification-free adaptation for the first time with respect to both domain and task. This thesis also introduces data sets derived from publicly available corpora for the purpose of rigorous intrinsic evaluation in the news and biomedical domains.

In mathematical physics, Laplace's equation plays an especially significant role. It is fundamental to the solution of problems in electrostatics, thermodynamics, potential theory and other branches of mathematical physics. It is for this reason that this investigation concerns the development of some general properties of continuous solutions of this equation.

<p>Bayesian nonparametric models, such as the Gaussian process and the Dirichlet process, have been extensively applied for target kinematics modeling in various applications including environmental monitoring, traffic planning, endangered species tracking, dynamic scene analysis, autonomous robot navigation, and human motion modeling. As shown by these successful applications, Bayesian nonparametric models are able to adjust their complexities adaptively from data as necessary, and are resistant to overfitting or underfitting. However, most existing works assume that the sensor measurements used to learn the Bayesian nonparametric target kinematics models are obtained a priori or that the target kinematics can be measured by the sensor at any given time throughout the task. Little work has been done for controlling the sensor with bounded field of view to obtain measurements of mobile targets that are most informative for reducing the uncertainty of the Bayesian nonparametric models. To present the systematic sensor planning approach to leaning Bayesian nonparametric models, the Gaussian process target kinematics model is introduced at first, which is capable of describing time-invariant spatial phenomena, such as ocean currents, temperature distributions and wind velocity fields. The Dirichlet process-Gaussian process target kinematics model is subsequently discussed for modeling mixture of mobile targets, such as pedestrian motion patterns. </p><p>Novel information theoretic functions are developed for these introduced Bayesian nonparametric target kinematics models to represent the expected utility of measurements as a function of sensor control inputs and random environmental variables. A Gaussian process expected Kullback Leibler divergence is developed as the expectation of the KL divergence between the current (prior) and posterior Gaussian process target kinematics models with respect to the future measurements. Then, this approach is extended to develop a new information value function that can be used to estimate target kinematics described by a Dirichlet process-Gaussian process mixture model. A theorem is proposed that shows the novel information theoretic functions are bounded. Based on this theorem, efficient estimators of the new information theoretic functions are designed, which are proved to be unbiased with the variance of the resultant approximation error decreasing linearly as the number of samples increases. Computational complexities for optimizing the novel information theoretic functions under sensor dynamics constraints are studied, and are proved to be NP-hard. A cumulative lower bound is then proposed to reduce the computational complexity to polynomial time.</p><p>Three sensor planning algorithms are developed according to the assumptions on the target kinematics and the sensor dynamics. For problems where the control space of the sensor is discrete, a greedy algorithm is proposed. The efficiency of the greedy algorithm is demonstrated by a numerical experiment with data of ocean currents obtained by moored buoys. A sweep line algorithm is developed for applications where the sensor control space is continuous and unconstrained. Synthetic simulations as well as physical experiments with ground robots and a surveillance camera are conducted to evaluate the performance of the sweep line algorithm. Moreover, a lexicographic algorithm is designed based on the cumulative lower bound of the novel information theoretic functions, for the scenario where the sensor dynamics are constrained. Numerical experiments with real data collected from indoor pedestrians by a commercial pan-tilt camera are performed to examine the lexicographic algorithm. Results from both the numerical simulations and the physical experiments show that the three sensor planning algorithms proposed in this dissertation based on the novel information theoretic functions are superior at learning the target kinematics with</p><p>little or no prior knowledge</p> / Dissertation

In a multiple choice test, examinees gain points based on how many correct responses they got. However, in this traditional grading, it is assumed that questions in the test are replications of each other. We apply an item response theory model to estimate students' abilities characterized by item's feature in a midterm test. Our Bayesian logistic Item response theory model studies the relation between the probability of getting a correct response and the three parameters. One parameter measures the student's ability and the other two measure an item's difficulty and its discriminatory feature. In this model the ability and the discrimination parameters are not identifiable. To address this issue, we construct a hierarchical Bayesian model to nullify the effects of non-identifiability. A Gibbs sampler is used to make inference and to obtain posterior distributions of the three parameters. For a "nonparametric" approach, we implement the item response theory model using a Dirichlet process mixture model. This new approach enables us to grade and cluster students based on their "ability" automatically. Although Dirichlet process mixture model has very good clustering property, it suffers from expensive and complicated computations. A slice sampling algorithm has been proposed to accommodate this issue. We apply our methodology to a real dataset obtained on a multiple choice test from WPI’s Applied Statistics I (Spring 2012) that illustrates how a student's ability relates to the observed scores.

O objetivo desta dissertação é estudar o problema de autovalor de Dirichlet para variedades riemannianas completas. Mais precisamente, pretendemos estudar uma cota por baixo para o -ésimo autovalor de um domínio limitado em uma variedade riemanniana completa. Tal cota é obtida fazendo-se uso de uma fórmula de recorrência de Cheng e Yang e um teorema de Nash. Ademais, pretendemos estudar uma desigualdade universal para os autovalores no espaço hiperbólico. / The goal of this dissertation is to study the Dirichlet eigenvalue problem for a complete riemannian manifold. More accurately, we intend to investigate a lower-bound for the -ℎ eigenvalue on a bounded domain in a complete riemannian manifold. Such a bound is obtained by making use of a recursion formula of Cheng and Yang and Nash’s Theorem. Furthermore, we study a universal inequality for eigenvalues of the Dirichlet eigenvalue problem on a bounded domain in a hyperbolic space (−1).

分形分析的主題是研究分形上的Dirichlet形式和Laplacian. 壓縮的自相似群有一個與之關聯的極限空間,此空間通常具備分形結構，因而引發了分形分析和自相似群兩個分支的結合. / 我們回顧了自相似群和它們的極限空間極限空間可以用Schreier 圖來逼近,事實上其可以看成由Schreier圖構造出來的雙曲圖的雙曲邊界.我們探究了迭代單值群. 通過增加專門的條件我們可以得到迭代單值群的極限空間同胚於某個Julia集. / 通過運用[31] 中的想法和[47] 中自相似隨機游動的方法，我們闡明了極限空間上Laplacian和Dirichlet形式的構造步驟我們介紹了加法器， Basilica群以及Hanoi塔群的極限空間(在第三種情況下是Sierpiríski墊片)上的Laplacian 這裡得到的Dirichlet形式是局部且正則的. / 通過採用[53] 的設置, 我們描述了加法器的極限空間上的誘發型Dirichlet形式在構造了加法器的自相似圖上的嚴格可逆隨機游動後，我們可以得到一個非局部的Dirichlet形式. / The major theme of fractal analysis is studying Dirichlet forms and Laplacians on fractals. For a contracting self-similar group there is an associated limit space, which usually exhibits a fractal structure, thereby triggering the combination of fractal analysis and self-similar groups. / We give reviews of self-similar groups and their limit spaces. Limit space can be approximated by Schreier graphs, and it is in fact identied as a hyperbolic boundary of a hyperbolic graph constructed from Schreier graphs. We explore the iterated monodromy groups. By adding technical conditions, we have that the limit space of an iterated monodromy group is homeomorphic to a Julia set. / We show the construction process of Laplacians and Dirichlet forms on limit spaces using the idea of [31] and the method of self-similar random walks from [47]. We present examples of Laplacians of the limit spaces of adding machine, the Basilica group and the Hanoi Tower group (it is Sierpi´nski gasket in this case). In this context these forms are local and regular. / We describe the induced Dirichlet forms on limit space of the adding machine by adopting the settings of [53] . By constructing strictly reversible random walks on self-similarity graph of the adding machine, we can obtain a non-local Dirichlet form. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Lin, Dateng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 71-76). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Review of fractal analysis --- p.6 / Chapter 1.2 --- Applications to self-similar groups --- p.7 / Chapter 1.3 --- Boundary theory method --- p.8 / Chapter 1.4 --- Summary of the thesis --- p.9 / Chapter 2 --- Self-similar groups --- p.11 / Chapter 2.1 --- Basic definitions --- p.11 / Chapter 2.2 --- Limit spaces of self-similar groups --- p.18 / Chapter 2.3 --- Schreier graphs approximations --- p.24 / Chapter 2.4 --- Iterated monodromy groups --- p.28 / Chapter 3 --- Construction of Laplacians on limit spaces --- p.35 / Chapter 3.1 --- Dirichlet forms, Laplacians and resistance forms --- p.35 / Chapter 3.2 --- Representations of groups and functions --- p.42 / Chapter 3.3 --- Laplacians on limit spaces --- p.45 / Chapter 4 --- Induced Dirichlet form on limit space of the adding machine --- p.53 / Chapter 4.1 --- Martin boundary and hyperbolic boundary --- p.53 / Chapter 4.2 --- Graph energy and the induced form --- p.62 / Chapter 4.3 --- Induced Dirichlet form of the adding machine --- p.65 / Bibliography --- p.71

Orientador: Ilma Aparecida Marques Silva / Dissertação (mestrado) - Universidade Federal do ABC. Programa de Pós-Graduação em Matemática, 2012

Submitted by JOSIANE DE CARVALHO REZENDE null (josiane.carvalho.rezende@gmail.com) on 2017-02-20T22:45:59Z No. of bitstreams: 1 COMFICHACATALOGRAFICAdissertacaoJOSIANE2017.pdf: 1131643 bytes, checksum: 9fc3ec5860776cf6c5bd4a8267a39302 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2017-02-23T17:45:13Z (GMT) No. of bitstreams: 1 rezende_jc_me_rcla.pdf: 1131643 bytes, checksum: 9fc3ec5860776cf6c5bd4a8267a39302 (MD5) / Made available in DSpace on 2017-02-23T17:45:13Z (GMT). No. of bitstreams: 1 rezende_jc_me_rcla.pdf: 1131643 bytes, checksum: 9fc3ec5860776cf6c5bd4a8267a39302 (MD5) Previous issue date: 2017-02-03 / A procura pela solução de alguns problemas relevantes, ou ainda, de equações, têm sido uma fonte de inspiração para ampliar os conjuntos numéricos. Quanto ao conjunto dos números complexos, um importante resultado é que todo polinômio de grau n (maior ou igual a 1) e com coeficientes complexos tem n raízes complexas. De modo geral, o presente trabalho tem o objetivo de contextualizar algumas aplicações das raízes da unidade na matemática. Apresentamos sua aplicação em um caso particular do Teorema de Dirichlet, na construção de reticulados, cuja utilidade está ligada a problemas de transmissão de sinal, e na história da resolução do Último Teorema de Fermat. / The search for the solution of some relevant problems, or even of equations, has been a source of inspiration to extend the numerical sets. As for the set of complex numbers, an important result is that every polynomial of degree n (bigger or equal 1) and with complex coefficients has n complex roots. In general, the present work aims to contextualize some applications of the roots of unit in mathematics. We present its application in a particular case of the Dirichlet Theorem, in the construction of lattices, whose utility is linked to signal transmission problems, and in the history of the resolution of the Fermat's Last Theorem.