Equivalence and Reduction of Hidden Markov Models

This report studies when and why two Hidden Markov Models (HMMs) may represent the same stochastic process. HMMs are characterized in terms of equivalence classes whose elements represent identical stochastic processes. This characterization yields polynomial time algorithms to detect equivalent HMMs. We also find fast algorithms to reduce HMMs to essentially unique and minimal canonical representations. The reduction to a canonical form leads to the definition of 'Generalized Markov Models' which are essentially HMMs without the positivity constraint on their parameters. We discuss how this generalization can yield more parsimonious representations of stochastic processes at the cost of the probabilistic interpretation of the model parameters.

Why do nominal characteristics acquire status value? A minimal explanation for status construction.

Why do beliefs that attach different amounts of status to different categories of people become consensually held by the members of a society? We show that two microlevel mechanisms, in combination, imply a system-level tendency toward consensual status beliefs about a nominal characteristic. (1) Status belief diffusion: a person who has no status belief about a characteristic can acquire a status belief about that characteristic from interacting with one or more people who have that status belief. (2) Status belief loss: a person who has a status belief about a characteristic can lose that belief from interacting with one or more people who have the opposite status belief. These mechanisms imply that opposite status beliefs will tend to be lost at equal rates and will tend to be acquired at rates proportional to their prevalence. Therefore, if a status belief ever becomes more prevalent than its opposite, it will increase in prevalence until every person holds it.

Global Sensitivity Analysis for MAP Inference in Graphical Models

We study the sensitivity of a MAP configuration of a discrete probabilistic graphical model with respect to perturbations of its parameters. These perturbations are global, in the sense that simultaneous perturbations of all the parameters (or any chosen subset of them) are allowed. Our main contribution is an exact algorithm that can check whether the MAP configuration is robust with respect to given perturbations. Its complexity is essentially the same as that of obtaining the MAP configuration itself, so it can be promptly used with minimal effort. We use our algorithm to identify the largest global perturbation that does not induce a change in the MAP configuration, and we successfully apply this robustness measure in two practical scenarios: the prediction of facial action units with posed images and the classification of multiple real public data sets. A strong correlation between the proposed robustness measure and accuracy is verified in both scenarios.

Minimal state-space realizations of 2D convolutional codes

In this thesis we consider two-dimensional (2D) convolutional codes. As happens in the one-dimensional (1D) case one of the major issues is obtaining minimal state-space realizations for these codes. It turns out that the problem of minimal realization of codes is not equivalent to the minimal realization of encoders. This is due to the fact that the same code may admit different encoders with different McMillan degrees. Here we focus on the study of minimality of the realizations of 2D convolutional codes by means of separable Roesser models. Such models can be regarded as a series connection between two 1D systems. As a first step we provide an algorithm to obtain a minimal realization of a 1D convolutional code starting from a minimal realization of an encoder of the code. Then, we restrict our study to two particular classes of 2D convolutional codes. The first class to be considered is the one of codes which admit encoders of type n 1. For these codes, minimal encoders (i.e., encoders for which a minimal realization is also minimal as a code realization) are characterized enabling the construction of minimal code realizations starting from such encoders. The second class of codes to be considered is the one constituted by what we have called composition codes. For a subclass of these codes, we propose a method to obtain minimal realizations by means of separable Roesser models.

Development of human central nervous system 3D in vitro models for preclinical research

Neurological disorders are a major concern in modern societies, with increasing prevalence mainly related with the higher life expectancy. Most of the current available therapeutic options can only control and ameliorate the patients’ symptoms, often be-coming refractory over time. Therapeutic breakthroughs and advances have been hampered by the lack of accurate central nervous system (CNS) models. The develop-ment of these models allows the study of the disease onset/progression mechanisms and the preclinical evaluation of novel therapeutics. This has traditionally relied on genetically engineered animal models that often diverge considerably from the human phenotype (developmentally, anatomically and physiologically) and 2D in vitro cell models, which fail to recapitulate the characteristics of the target tissue (cell-cell and cell-matrix interactions, cell polarity). The in vitro recapitulation of CNS phenotypic and functional features requires the implementation of advanced culture strategies that enable to mimic the in vivo struc-tural and molecular complexity. Models based on differentiation of human neural stem cells (hNSC) in 3D cultures have great potential as complementary tools in preclinical research, bridging the gap between human clinical studies and animal models. This thesis aimed at the development of novel human 3D in vitro CNS models by integrat-ing agitation-based culture systems and a wide array of characterization tools. Neural differentiation of hNSC as 3D neurospheres was explored in Chapter 2. Here, it was demonstrated that human midbrain-derived neural progenitor cells from fetal origin (hmNPC) can generate complex tissue-like structures containing functional dopaminergic neurons, as well as astrocytes and oligodendrocytes. Chapter 3 focused on the development of cellular characterization assays for cell aggregates based on light-sheet fluorescence imaging systems, which resulted in increased spatial resolu-tion both for fixed samples or live imaging. The applicability of the developed human 3D cell model for preclinical research was explored in Chapter 4, evaluating the poten-tial of a viral vector candidate for gene therapy. The efficacy and safety of helper-dependent CAV-2 (hd-CAV-2) for gene delivery in human neurons was evaluated, demonstrating increased neuronal tropism, efficient transgene expression and minimal toxicity. The potential of human 3D in vitro CNS models to mimic brain functions was further addressed in Chapter 5. Exploring the use of 13C-labeled substrates and Nucle-ar Magnetic Resonance (NMR) spectroscopy tools, neural metabolic signatures were evaluated showing lineage-specific metabolic specialization and establishment of neu-ron-astrocytic shuttles upon differentiation. Chapter 6 focused on transferring the knowledge and strategies described in the previous chapters for the implementation of a scalable and robust process for the 3D differentiation of hNSC derived from human induced pluripotent stem cells (hiPSC). Here, software-controlled perfusion stirred-tank bioreactors were used as technological system to sustain cell aggregation and dif-ferentiation. The work developed in this thesis provides practical and versatile new in vitro ap-proaches to model the human brain. Furthermore, the culture strategies described herein can be further extended to other sources of neural phenotypes, including pa-tient-derived hiPSC. The combination of this 3D culture strategy with the implemented characterization methods represents a powerful complementary tool applicable in the drug discovery, toxicology and disease modeling.

School funding and education policy-making models in Ontario /

The purpose of this thesis is to examine various policy implementation models, and to determine what use they are to a government. In order to insure that governmental proposals are created and exercised in an effective manner, there roust be some guidelines in place which will assist in resolving difficult situations. All governments face the challenge of responding to public demand, by delivering the type of policy responses that will attempt to answer those demands. The problem for those people in positions of policy-making responsibility is to balance the competitive forces that would influence policy. This thesis examines provincial government policy in two unique cases. The first is the revolutionary recommendations brought forth in the Hall -Dennis Report. The second is the question of extending full -funding to the end of high school in the separate school system. These two cases illustrate how divergent and problematic the policy-making duties of any government may be. In order to respond to these political challenges decision-makers must have a clear understanding of what they are attempting to do. They must also have an assortment of policy-making models that will insure a policy response effectively deals with the issue under examination. A government must make every effort to insure that all policymaking methods are considered, and that the data gathered is inserted into the most appropriate model. Currently, there is considerable debate over the benefits of the progressive individualistic education approach as proposed by the Hall -Dennis Committee. This debate is usually intensified during periods of economic uncertainty. Periodically, the province will also experience brief yet equally intense debate on the question of separate school funding. At one level, this debate centres around the efficiency of maintaining two parallel education systems, but the debate frequently has undertones of the religious animosity common in Ontario's history. As a result of the two policy cases under study we may ask ourselves these questions: a) did the policies in question improve the general quality of life in the province? and b) did the policies unite the province? In the cases of educational instruction and finance the debate is ongoing and unsettling. Currently, there is a widespread belief that provincial students at the elementary and secondary levels of education are not being educated adequately to meet the challenges of the twenty-first century. The perceived culprit is individual education which sees students progressing through the system at their own pace and not meeting adequate education standards. The question of the finance of Catholic education occasionally rears its head in a painful fashion within the province. Some public school supporters tend to take extension as a personal religious defeat, rather than an opportunity to demonstrate that educational diversity can be accommodated within Canada's most populated province. This thesis is an attempt to analyze how successful provincial policy-implementation models were in answering public demand. A majority of the public did not demand additional separate school funding, yet it was put into place. The same majority did insist on an examination of educational methods, and the government did put changes in place. It will also demonstrate how policy if wisely created may spread additional benefits to the public at large. Catholic students currently enjoy a much improved financial contribution from the province, yet these additional funds were taken from somewhere. The public system had it funds reduced with what would appear to be minimal impact. This impact indicates that government policy is still sensitive to the strongly held convictions of those people in opposition to a given policy.

Some Applications of Markov Additive Processes as Models in Insurance and Financial Mathematics

Cette thèse est principalement constituée de trois articles traitant des processus markoviens additifs, des processus de Lévy et d'applications en finance et en assurance. Le premier chapitre est une introduction aux processus markoviens additifs (PMA), et une présentation du problème de ruine et de notions fondamentales des mathématiques financières. Le deuxième chapitre est essentiellement l'article "Lévy Systems and the Time Value of Ruin for Markov Additive Processes" écrit en collaboration avec Manuel Morales et publié dans la revue European Actuarial Journal. Cet article étudie le problème de ruine pour un processus de risque markovien additif. Une identification de systèmes de Lévy est obtenue et utilisée pour donner une expression de l'espérance de la fonction de pénalité actualisée lorsque le PMA est un processus de Lévy avec changement de régimes. Celle-ci est une généralisation des résultats existant dans la littérature pour les processus de risque de Lévy et les processus de risque markoviens additifs avec sauts "phase-type". Le troisième chapitre contient l'article "On a Generalization of the Expected Discounted Penalty Function to Include Deficits at and Beyond Ruin" qui est soumis pour publication. Cet article présente une extension de l'espérance de la fonction de pénalité actualisée pour un processus subordinateur de risque perturbé par un mouvement brownien. Cette extension contient une série de fonctions escomptée éspérée des minima successives dus aux sauts du processus de risque après la ruine. Celle-ci a des applications importantes en gestion de risque et est utilisée pour déterminer la valeur espérée du capital d'injection actualisé. Finallement, le quatrième chapitre contient l'article "The Minimal entropy martingale measure (MEMM) for a Markov-modulated exponential Lévy model" écrit en collaboration avec Romuald Hervé Momeya et publié dans la revue Asia-Pacific Financial Market. Cet article présente de nouveaux résultats en lien avec le problème de l'incomplétude dans un marché financier où le processus de prix de l'actif risqué est décrit par un modèle exponentiel markovien additif. Ces résultats consistent à charactériser la mesure martingale satisfaisant le critère de l'entropie. Cette mesure est utilisée pour calculer le prix d'une option, ainsi que des portefeuilles de couverture dans un modèle exponentiel de Lévy avec changement de régimes.

Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

Non-intrusive monitoring of atmospheric CO2 in analogue models of terrestrial carbon cycle

1. Closed Ecological Systems (CES) are small manmade ecosystems which do not have any material exchange with the surrounding environment. Recent ecological and technological advances enable successful establishment and maintenance of CES, making them a suitable tool for detecting and measuring subtle feedbacks and mechanisms. 2. As a part of an analogue (physical) C cycle modelling experiment, we developed a non-intrusive methodology to control the internal environment and to monitor atmospheric CO2 concentration inside 16 replicated CES. Whilst maintaining an air-tight seal of all CES, this approach allowed for access to the CO2 measuring equipment for periodic re-calibration and repairs. 3. To ensure reliable cross-comparison of CO2 observations between individual CES units and to minimise the cost of the system, only one CO2 sampling unit was used. An ADC BioScientific OP-2 (open-path) analyser mounted on a swinging arm was passing over a set of 16 measuring cells. Each cell was connected to an individual CES with air continuously circulating between them. 4. Using this setup, we were able to continuously measure several environmental variables and CO2 concentration within each closed system, allowing us to study minute effects of changing temperature on C fluxes within each CES. The CES and the measuring cells showed minimal air leakage during an experimental run lasting, on average, 3 months. The CO2 analyser assembly performed reliably for over 2 years, however an early iteration of the present design proved to be sensitive to positioning errors. 5. We indicate how the methodology can be further improved and suggest possible avenues where future CES based research could be applied.

Reliable knowledge discovery with a minimal causal model inducer

This paper presents a Minimal Causal Model Inducer that can be used for the reliable knowledge discovery. The minimal-model semantics of causal discovery is an essential concept for the identification of a best fitting model in the sense of satisfactory consistent with the given data and be the simpler, less expressive model. Consistency is one of major measures of reliability in knowledge discovery. Therefore to develop an algorithm being able to derive a minimal model is an interesting topic in the are of reliable knowledge discovery. various causal induction algorithms and tools developed so far can not guarantee that the derived model is minimal and consistent. It was proved the MML induction approach introduced by Wallace, Keven and Honghua Dai is a minimal causal model learner. In this paper, we further prove that the developed minimal causal model learner is reliable in the sense of satisfactory consistency. The experimental results obtained from the tests on a number of both artificial and real models provided in this paper confirm this theoretical result.

Probing neutrino oscillations in supersymmetric models at the Large Hadron Collider

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

DYNAMICAL SYMMETRY BREAKING IN A MINIMAL 3-3-1 MODEL

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Scalar bosons in minimal and ultraminimal technicolor: Masses, trilinear couplings, and widths

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Deciphering the minimum of energy of some walking technicolor models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Anomaly-free constraints in neutrino seesaw models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)