This thesis investigates a gesture segmentation and recognition scheme that employs a random forest classification model. A complete gesture recognition system should localize and classify each gesture from a given gesture vocabulary, within a continuous video stream. Thus, the system must determine the start and end points of each gesture in time, as well as accurately recognize the class label of each gesture. We propose a unified approach that performs the tasks of temporal segmentation and classification simultaneously. Our method trains a random forest classification model to recognize gestures from a given vocabulary, as presented in a training dataset of video plus 3D body joint locations, as well as out-of-vocabulary (non-gesture) instances. Given an input video stream, our trained model is applied to candidate gestures using sliding windows at multiple temporal scales. The class label with the highest classifier confidence is selected, and its corresponding scale is used to determine the segmentation boundaries in time. We evaluated our formulation in segmenting and recognizing gestures from two different benchmark datasets: the NATOPS dataset of 9,600 gesture instances from a vocabulary of 24 aircraft handling signals, and the CHALEARN dataset of 7,754 gesture instances from a vocabulary of 20 Italian communication gestures. The performance of our method compares favorably with state-of-the-art methods that employ Hidden Markov Models or Hidden Conditional Random Fields on the NATOPS dataset. We conclude with a discussion of the advantages of using our model.

The pricing of options is one of the key problems in mathematical finance. In recent years, pricing models that are based on the continuous time random walk (CTRW), an anomalous diffusive random walk model widely used in physics, have been introduced. In this thesis, we investigate the pricing of European call options with CTRW and generalized CTRW models within the Black-Scholes framework. Here, the non-Markovian character of the underlying pricing model is manifest in Black-Scholes PDEs with fractional time derivatives containing memory terms. The inclusion of non-zero interest rates leads to a distinction between different types of \forward" and \backward" options, which are easily mapped onto each other in the standard Markovian framework, but exhibit significant dfferences in the non-Markovian case. The backward-type options require us in particular to include the multi-point statistics of the non-Markovian pricing model. Using a representation of the CTRW in terms of a subordination (time change) of a normal diffusive process with an inverse L evy-stable process, analytical results can be obtained. The extension of the formalism to arbitrary waiting time distributions and general payoff functions is discussed. The pricing of path-dependent Asian options leads to further distinctions between different variants of the subordination. We obtain analytical results that relate the option price to the solution of generalized Feynman-Kac equations containing non-local time derivatives such as the fractional substantial derivative. Results for L evy-stable and tempered L evy-stable subordinators, power options, arithmetic and geometric Asian options are presented.

Il est bien connu que divers solides amorphes ont de nombreuses propriétés universelles. L'une d'entre elles est la variation de la conductivité thermique en fonction de la température. Cependant, le mécanisme microscopique du transfert de chaleur dans le domaine de température supérieure à 20 K est encore mal compris. Simulations numériques récentes du silicium et de la silice amorphes montrent que les modes de vibration dans la gamme de fréquences correspondante (au-dessus de plusieurs THz) sont délocalisés. En même temps ils sont complètement différents des phonons acoustiques de basse fréquence, dits « diffusions ».Dans ce travail, nous présentons un modèle stable de matrice aléatoire d'un solide amorphe. Dans ce modèle, on peut faire varier le degré de désordre allant du cristal parfait jusqu'au milieu mou extrêmement désordonné sans rigidité macroscopique. Nous montrons que les solides amorphes réels sont proches du deuxième cas limite, et que les diffusions occupent la partie dominante du spectre de vibration. La fréquence de transition entre les phonons acoustiques et diffusons est déterminée par le critère Ioffe-Regel. Fait intéressant, cette fréquence de transition coïncide pratiquement avec la position du pic Boson. Nous montrons également que la diffusivité et la densité d'états de vibration de diffusons sont pratiquement constantes en fonction de la fréquence. Par conséquent, la conductivité thermique est une fonction linéaire de la température dans le domaine allant à des températures relativement élevées, puis elle sature. Cette conclusion est en accord avec de nombreuses données expérimentales. En outre, nous considérons un modèle numérique de matériaux de type de silicium amorphe et étudions le rôle du désordre pour les vibrations longitudinales et transverses. Nous montrons aussi que la théorie des matrices aléatoires peut être appliquée avec succès pour estimer la densité d'états vibrationnels des systèmes granulaires bloqués. / It is well known that various amorphous solids have many universal properties. One of them is the temperature dependence of the thermal conductivity. However, the microscopic mechanism of the heat transfer above 20 K is still poorly understood. Recent numerical simulations of amorphous silicon and silica show that vibrational modes in the corresponding frequency range (above several THz) are delocalized, however they are completely different from low-frequency acoustic phonons, called “diffusons”.In this work we present a stable random matrix model of an amorphous solid. In this model one can vary the strength of disorder going from a perfect crystal to extremely disordered soft medium without macroscopic rigidity. We show that real amorphous solids are close to the second limiting case, and that diffusons occupy the dominant part of the vibrational spectrum. The crossover frequency between acoustic phonons and diffusons is determined by the Ioffe-Regel criterion. Interestingly, this crossover frequency practically coincides with the Boson peak position. We also show that, as a function of frequency, the diffusivity and the vibrational density of states of diffusons are practically constant. As a result, the thermal conductivity is a linear function of temperature up to rather high temperatures and then saturates. This conclusion is in agreement with numerous experimental data.Further, we consider a numerical model of amorphous silicon-like materials and investigate the role of disorder for longitudinal and transverse vibrations. We also show that the random matrix theory can be successfully applied to estimate the vibrational density of states of granular jammed systems.

The electroencephalogram (EEG) is a commonly used tool for studying the emergent electrical rhythms of the brain. It has wide utility in psychology, as well as bringing a useful diagnostic aid for neurological conditions such as epilepsy. It is of growing importance to better understand the emergence of these electrical rhythms and, in the case of diagnosis of neurological conditions, to find mechanistic differences between healthy individuals and those with a disease. Mathematical models are an important tool that offer the potential to reveal these otherwise hidden mechanisms. In particular Neural Mass Models (NMMs), which describe the macroscopic activity of large populations of neurons, are increasingly used to uncover large-scale mechanisms of brain rhythms in both health and disease. The dynamics of these models is dependent upon the choice of parameters, and therefore it is crucial to be able to understand how dynamics change when parameters are varied. Despite they are considered low-dimensional in comparison to micro-scale neural network models, with regards to understanding the relationship between parameters and dynamics NMMs are still prohibitively high dimensional for classical approaches such as numerical continuation. We need alternative methods to characterise the dynamics of NMMs in high dimensional parameter spaces. The primary aim of this thesis is to develop a method to explore and analyse the high dimensional parameter space of these mathematical models. We develop an approach based on statistics and machine learning methods called decision tree mapping (DTM). This method is used to analyse the parameter space of a mathematical model by studying all the parameters simultaneously. With this approach, the parameter space can efficiently be mapped in high dimension. We have used measures linked with this method to determine which parameters play a key role in the output of the model. This approach recursively splits the parameter space into smaller subspaces with an increasing homogeneity of dynamics. The concepts of decision tree learning, random forest, measures of importance, statistical tests and visual tools are introduced to explore and analyse the parameter space. We introduce formally the theoretical background and the methods with examples. The DTM approach is used in three distinct studies to: • Identify the role of parameters on the dynamic model. For example, which parameters have a role in the emergence of seizure dynamics? • Constrain the parameter space, such that regions of the parameter space which give implausible dynamic are removed. • Compare the parameter sets to fit different groups. How does the thalamocortical connectivity of people with and without epilepsy differ? We demonstrate that classical studies have not taken into account the complexity of the parameter space. DTM can easily be extended to other fields using mathematical models. We advocate the use of this method in the future to constrain high dimensional parameter spaces in order to enable more efficient, person-specific model calibration.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Bibliography: leaves 364-373. / by Robert Buchanan Washburn, Jr. / Ph.D.

Neste trabalho, aplicamos o algoritmo Breadth-First Search para encontrar o tamanho de uma componente conectada no grafo aleatório de Erdos-Rényi. Uma cadeia de Markov é obtida deste procedimento. Apresentamos alguns resultados bem conhecidos sobre o comportamento dessa cadeia de Markov. Combinamos alguns destes resultados para obter uma proposição sobre a probabilidade da componente atingir um determinado tamanho e um resultado de convergência do estado da cadeia neste instante. Posteriormente, aplicamos o teorema de convergência de Darling (2002) a sequência de cadeias de Markov reescaladas e indexadas por N, o número de vértices do grafo, para mostrar que as trajetórias dessas cadeias convergem uniformemente em probabilidade para a solução de uma equação diferencial ordinária. Deste resultado segue a bem conhecida lei fraca dos grandes números para a componente gigante do grafo aleatório de Erdos-Rényi, no caso supercrítico. Além disso, obtemos o limite do fluído para um modelo epidêmico que é uma extensão daquele proposto em Kurtz et al. (2008). / In this work, we apply the Breadth-First Search algorithm to find the size of a connected component of the Erdos-Rényi random graph. A Markov chain is obtained of this procedure. We present some well-known results about the behavior of this Markov chain, and combine some of these results to obtain a proposition about the probability that the component reaches a certain size and a convergence result about the state of the chain at that time. Next, we apply the convergence theorem of Darling (2002) to the sequence of rescaled Markov chains indexed by N, the number of vertices of the graph, to show that the trajectories of these chains converge uniformly in probability to the solution of an ordinary dierential equation. From the latter result follows the well-known weak law of large numbers of the giant component of the Erdos-Renyi random graph, in the supercritical case. Moreover, we obtain the uid limit for an epidemic model which is an extension of that proposed in Kurtz et al. (2008).

The first part of this thesis considers the residual empirical process of a nearly unstable long-memory time series. Chan and Ling [8] showed that the usual limit distribution of the Kolmogorov-Smirnov test statistics does not hold when the characteristic polynomial of the unstable autoregressive model has a unit root. A key question of interest is what happens when this model has a near unit root, that is, when it is nearly non-stationary. In this thesis, it is established that the statistics proposed by Chan and Ling can be extended. The limit distribution is expressed as a functional of an Orenstein-Uhlenbeck process that is driven by a fractional Brownian motion. This result extends and generalizes Chan and Ling's results to a nearly non-stationary long-memory time series. / The second part of the thesis investigates the weak convergence of weighted sums of random variables that are functionals of moving aver- age processes. A non-central limit theorem is established in which the Wiener integrals with respect to the Hermite processes appear as the limit. As an application of the non-central limit theorem, we examine the asymptotic theory of least squares estimators (LSE) for a nearly unstable AR(1) model when the innovation sequences are functionals of moving average processes. It is shown that the limit distribution of the LSE appears as functionals of the Ornstein-Uhlenbeck processes driven by Hermite processes. / Liu, Weiwei. / Adviser: Chan Ngai Hang. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 60-67). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Complete randomized experimental design has been a popular standard in clinical trials due to its abilities to yield a smaller bias and to provide a strong foundation for statistical inferences. However, because of ethical issues, there is a growing demand for response adaptive designs which shift the allocation probabilities such that more patients receive the better treatment. The principal idea of response adaptive designs to allocate fewer patients to treatments which appears to be inferior based on the accruing response data and information collected up to the current stage. Although they are more complex than complete randomized experiments in theory and method, adaptive designs are practically more useful. The objective of this dissertation is to develop an adaptive design, the generalized drop-the-loser rule, for comparing multiple treatments in clinical trials, including the situation where the responses of patients are delayed moderately. Asymptotic properties including strong consistency and asymptotic normality of the new design are investigated through the martingale technique. Monte Carlo simulation studies are conducted to reveal the empirical performance of this design. The new design will be potentially useful in the practical context of clinical trials. / Sun Ruibo. / "July 2006." / Adviser: Siu Hung Cheung. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6488. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (p. 62-66). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

by Stephen Siu-ming Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 164-170). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Cache Memory --- p.2 / Chapter 1.2 --- System Performance --- p.3 / Chapter 1.3 --- Cache Performance --- p.3 / Chapter 1.4 --- Cache Prefetching --- p.5 / Chapter 1.5 --- Organization of Dissertation --- p.7 / Chapter 2 --- Related Work --- p.8 / Chapter 2.1 --- Memory Hierarchy --- p.8 / Chapter 2.2 --- Cache Memory Management --- p.10 / Chapter 2.2.1 --- Configuration --- p.10 / Chapter 2.2.2 --- Replacement Algorithms --- p.13 / Chapter 2.2.3 --- Write Back Policies --- p.15 / Chapter 2.2.4 --- Cache Miss Types --- p.16 / Chapter 2.2.5 --- Prefetching --- p.17 / Chapter 2.3 --- Locality --- p.18 / Chapter 2.3.1 --- Spatial vs. Temporal --- p.18 / Chapter 2.3.2 --- Instruction Cache vs. Data Cache --- p.20 / Chapter 2.4 --- Why Not a Large L1 Cache? --- p.26 / Chapter 2.4.1 --- Critical Time Path --- p.26 / Chapter 2.4.2 --- Hardware Cost --- p.27 / Chapter 2.5 --- Trend to have L2 Cache On Chip --- p.28 / Chapter 2.5.1 --- Examples --- p.29 / Chapter 2.5.2 --- Dedicated L2 Bus --- p.31 / Chapter 2.6 --- Hardware Prefetch Algorithms --- p.32 / Chapter 2.6.1 --- One Block Look-ahead --- p.33 / Chapter 2.6.2 --- Chen's RPT & similar algorithms --- p.34 / Chapter 2.7 --- Software Based Prefetch Algorithm --- p.38 / Chapter 2.7.1 --- Prefetch Instruction --- p.38 / Chapter 2.8 --- Hybrid Prefetch Algorithm --- p.40 / Chapter 2.8.1 --- Stride CAM Prefetching --- p.40 / Chapter 3 --- Simulator --- p.43 / Chapter 3.1 --- Multi-level Memory Hierarchy Simulator --- p.43 / Chapter 3.1.1 --- Multi-level Memory Support --- p.45 / Chapter 3.1.2 --- Non-blocking Cache --- p.45 / Chapter 3.1.3 --- Cycle-by-cycle Simulation --- p.47 / Chapter 3.1.4 --- Cache Prefetching Support --- p.47 / Chapter 4 --- Proposed Algorithms --- p.48 / Chapter 4.1 --- SIRPA --- p.48 / Chapter 4.1.1 --- Rationale --- p.48 / Chapter 4.1.2 --- Architecture Model --- p.50 / Chapter 4.2 --- Line Concept --- p.56 / Chapter 4.2.1 --- Rationale --- p.56 / Chapter 4.2.2 --- "Improvement Over ""Pure"" Algorithm" --- p.57 / Chapter 4.2.3 --- Architectural Model --- p.59 / Chapter 4.3 --- Combined L1-L2 Cache Management --- p.62 / Chapter 4.3.1 --- Rationale --- p.62 / Chapter 4.3.2 --- Feasibility --- p.63 / Chapter 4.4 --- Combine SIRPA with Default Prefetch --- p.66 / Chapter 4.4.1 --- Rationale --- p.67 / Chapter 4.4.2 --- Improvement Over “Pure´ح Algorithm --- p.69 / Chapter 4.4.3 --- Architectural Model --- p.70 / Chapter 5 --- Results --- p.73 / Chapter 5.1 --- Benchmarks Used --- p.73 / Chapter 5.1.1 --- SPEC92int and SPEC92fp --- p.75 / Chapter 5.2 --- Configurations Tested --- p.79 / Chapter 5.2.1 --- Prefetch Algorithms --- p.79 / Chapter 5.2.2 --- Cache Sizes --- p.80 / Chapter 5.2.3 --- Cache Block Sizes --- p.81 / Chapter 5.2.4 --- Cache Set Associativities --- p.81 / Chapter 5.2.5 --- "Bus Width, Speed and Other Parameters" --- p.81 / Chapter 5.3 --- Validity of Results --- p.83 / Chapter 5.3.1 --- Total Instructions and Cycles --- p.83 / Chapter 5.3.2 --- Total Reference to Caches --- p.84 / Chapter 5.4 --- Overall MCPI Comparison --- p.86 / Chapter 5.4.1 --- Cache Size Effect --- p.87 / Chapter 5.4.2 --- Cache Block Size Effect --- p.91 / Chapter 5.4.3 --- Set Associativity Effect --- p.101 / Chapter 5.4.4 --- Hardware Prefetch Algorithms --- p.108 / Chapter 5.4.5 --- Software Based Prefetch Algorithms --- p.119 / Chapter 5.5 --- L2 Cache & Main Memory MCPI Comparison --- p.127 / Chapter 5.5.1 --- Cache Size Effect --- p.130 / Chapter 5.5.2 --- Cache Block Size Effect --- p.130 / Chapter 5.5.3 --- Set Associativity Effect --- p.143 / Chapter 6 --- Conclusion --- p.154 / Chapter 7 --- Future Directions --- p.157 / Chapter 7.1 --- Prefetch Buffer --- p.157 / Chapter 7.2 --- Dissimilar L1-L2 Management --- p.158 / Chapter 7.3 --- Combined LRU/MRU Replacement Policy --- p.160 / Chapter 7.4 --- N Loops Look-ahead --- p.163

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