Title: Solving Endgames in Large Imperfect-Information Games such as Poker Author: Bc. Karel Ha Department: Department of Applied Mathematics Supervisor: doc. Mgr. Milan Hladík, Ph.D., Department of Applied Mathematics Abstract: Endgames have a distinctive role for players. At the late stage of games, many aspects are finally clearly defined, deeming exhaustive analysis tractable. Specialised endgame handling is rewarding for games with perfect information (e.g., Chess databases pre-computed for entire classes of endings, or dividing Go board into separate independent subgames). An appealing idea would be to extend this approach to imperfect-information games such as the famous Poker: play the early parts of the game, and once the subgame becomes feasible, calculate an ending solution. However, the problem is much more complex for imperfect information. Subgames need to be generalized to account for information sets. Unfortunately, such a generalization cannot be solved straightaway, as it does not generally preserve optimality. As a consequence, we may end up with a far more exploitable strategy. There are currently three techniques to deal with this challenge: (a) disregard the problem entirely; (b) use a decomposition technique, which sadly retains only the same quality; (c) or formalize improvements of...

This qualitative study explores daily environmental sustainable attitudes and behaviours of Gauteng’s urban youth. A social constructivist paradigm underlines the views, challenges and activities expressed. The Reasonable Person Model (RPM) and Social Networking Theory ensure that the content, as well as methodological elements and results herein adhere to a psychological framework. Focus groups and online interviews were utilised to explore the link between community well-being and the state of the natural environment and the sample was drawn using purposive and snowball sampling. The literature reviewed focuses on existing climate change concerns, pro-environmental attitudes and behaviours, and emerging local and international practices, including the importance of expanding local practices. A thematic analysis, ensured for a broad variety of responses, and hence detailed discussion -of and dissemination of results. Using common threads in the results, recommendations and suggestions were made, to improve future studies and research practices concerning Environmental Responsible Behaviours (ERBs).

Magister Artium - MA / This study aims to explore the family environment of non-admitting sex offenders in order to gain insight into the family characteristics that could be contributing factors towards the behaviour of denial. However, the focus will not be on the families of the sex offenders, but rather on the non-admitting sex offenders’ views of their family environment. The theoretical framework used is the Social Learning Theory, because it supports the fact that most behaviour is learned through modelling the behaviour of others. The researcher used a qualitative approach and the aim of the study was to generate information that would describe the family environment of non-admitting sex offenders. The population of this study was incarcerated, sentenced sex offenders with specific focus on the non-admitting sex offender as the unit of analysis. Ten (10) participants were purposively selected for the study and semi-structured interviews were conducted with each one in order to generate the needed information for the study

The essentiality for waste reduction in society is prompted by the depletion of natural resources. Internationally, five waste management strategies have been identified, namely reduction of waste (waste prevention), re-use of waste, recycling of waste, recovery of energy and disposal to landfill. In Polokwane Declaration of September 2001, South Africa’s Department of Environmental Affairs and Tourism committed itself to achieve a 50 percent reduction in the volume of waste generated by 2012 and to be landfilled and have a zero waste plan implemented by 2022. Through the National Waste Management Act, No. 59 of 2008, the South African government also committed itself to provide protection of health, well-being and the environment through measures to avoid and minimise the generation of waste. Even though several policies and legislative documents are available that address waste minimisation and recycling, individual community members are however still reluctant to participate in these activities. This study therefore investigated the current levels of understanding, education and commitment to recycling and waste minimisation in a selected South African community. The target respondents of the study were members of a local church who are representative of the various peoples that reside in the communities serviced by the selected municipality. A convenience sample of 70 participants from that church was selected to complete the questionnaires. Seventy (70) questionnaires were distributed, and all 70 questionnaires were returned. Interviews were also conducted with two managers from the Waste Management Department of the selected municipality. The data analyses conducted, included descriptive statistics and content analysis of the interview transcripts. The empirical results revealed among others that: (1) recycling removal service is limited to pre-selected recyclables; (2) the municipality contributes to local entrepreneurial opportunities; (3) public participation is a pre-requisite in the success of the programmes; (4) participation is determined by convenience; (5) enforcement of legislation assists with compliance; (6) environmental sustainability is supported by environmental concerned consumers; (7) mismatch of opinions around separation at source of generation and (8) continuous education is instrumental in waste management. The main recommendations of the study include: (1) municipalities need to provide exciting and innovative recycling and waste minimisation programmes, continuously; (2) positive attitude and behaviour of all the stakeholders determines the success of waste minimisation and recycling; and (3) society, industry and government need to join forces in ensuring success in waste management. By implementing these recommendations, stakeholders in this field of interest will go a long way in improving waste management in South Africa communities.

This paper is an investigation into the role of the Nelson Mandela Bay Metropolitan Municipality (NMBMM) in the up-keep and management of open spaces, in Zwide Township. The study examines the manner in which the legislative framework for waste management is being implemented as prescribed in legislative directives. The Constitution of the Republic of South Africa Act, 1996 (Act 108 of 1996), envisions the transformation of the local government system. Subsequently, policy frameworks and principles have been developed to support the new vision of local government. The Batho Pele Principles and the white paper were passed in March 1998. Both documents spelt out the implementation of the principle and the framework in which the local government system should operate as set out in the developmental local government concept. The developmental local government system’s core ethos lies in working with local citizenry to find ways of meeting their needs, thereby improving their quality of life. It also makes provision for public participation. Ward councillors and ward committees are an indispensable backbone of community participation. It is assumed in this study that a number of environmental, social, economic and health challenges are associated with waste disposal in open spaces. Such hazards range from health risks to the abuse of open spaces by antisocial individuals and groups. The situation is exacerbated by poor implementation of constitutional and legislative directives regarding waste management and disposal to ensure a humane and environmentally friendly atmosphere. The research assumes that the problem cannot be overcome by the NMBMM alone. Well-orchestrated community awareness education programmes such as projects like “trash is cash “and innovative ways of managing waste, including waste recycling, need to be drawn upon. The strategic placement of waste stations and the timeous collection of waste could improve the situation. The observation is that the level of service delivery varies within residential areas and in socioeconomic strata. The previously disadvantaged areas seem to have borne the brunt in terms of poor waste management services until now. The municipality has been accustomed to a situation whereby it removes the waste on an ad hoc basis in selected areas in the townships. The situation is exacerbated by little foresight into the ever growing population, specifically amongst the lower socioeconomic sector of the population. As a result, the ecology and environment is impacted in a negative way. Amidst the challenges of dumping in open spaces, a sense of determination appears within the community to want to prevent the situation; to illustrate: There is an organized group of youths who have cleaned up open spaces at along Qeqe Street in Zwide. They developed a car wash bay as a venture to generate an income. The Green Township Movement is another scheme which is mobilising the community, street by street, to keep their neighbourhood environmentally clean and green. Potentially, the Waste Management Directorate could collaborate with these groupings to halt waste dumping in open spaces. In so doing they could contribute to establishing an environmentally friendly neighbourhood. The NMBMM needs therefore to take advantage of the situation and reengineer its waste management strategy, policies and directives and augment the initiatives that the community have taken upon themselves. The study will endeavour to ultimately advise on viable strategies in an attempt to unravel barriers that have been identified, while simultaneously addressing the challenges to improving the quality of life in the township. This will be done by analysing a legislative framework and thereafter replicating the best practice used locally, nationally and internationally.. It also seeks to associate with individuals within local government in addition to groups that are like minded in combating the concern. The existing environmental regulations and the present economic situation are sound starting points. Together they present an opportunity to change the prevailing attitudes towards recycling. Finally, a number of conclusions that were arrived at during the study will be followed by recommendations. These will be based on the literature review and observations.

Une approche efficace pour la résolution de problèmes inverses consiste à définir le signal (ou l'image) recherché(e) par minimisation d'un critère pénalisé. Ce dernier s'écrit souvent sous la forme d'une somme de fonctions composées avec des opérateurs linéaires. En pratique, ces fonctions peuvent n'être ni convexes ni différentiables. De plus, les problèmes auxquels on doit faire face sont souvent de grande dimension. L'objectif de cette thèse est de concevoir de nouvelles méthodes pour résoudre de tels problèmes de minimisation, tout en accordant une attention particulière aux coûts de calculs ainsi qu'aux résultats théoriques de convergence. Une première idée pour construire des algorithmes rapides d'optimisation est d'employer une stratégie de préconditionnement, la métrique sous-jacente étant adaptée à chaque itération. Nous appliquons cette technique à l'algorithme explicite-implicite et proposons une méthode, fondée sur le principe de majoration-minimisation, afin de choisir automatiquement les matrices de préconditionnement. L'analyse de la convergence de cet algorithme repose sur l'inégalité de Kurdyka-L ojasiewicz. Une seconde stratégie consiste à découper les données traitées en différents blocs de dimension réduite. Cette approche nous permet de contrôler à la fois le nombre d'opérations s'effectuant à chaque itération de l'algorithme, ainsi que les besoins en mémoire, lors de son implémentation. Nous proposons ainsi des méthodes alternées par bloc dans les contextes de l'optimisation non convexe et convexe. Dans le cadre non convexe, une version alternée par bloc de l'algorithme explicite-implicite préconditionné est proposée. Les blocs sont alors mis à jour suivant une règle déterministe acyclique. Lorsque des hypothèses supplémentaires de convexité peuvent être faites, nous obtenons divers algorithmes proximaux primaux-duaux alternés, permettant l'usage d'une règle aléatoire arbitraire de balayage des blocs. L'analyse théorique de ces algorithmes stochastiques d'optimisation convexe se base sur la théorie des opérateurs monotones. Un élément clé permettant de résoudre des problèmes d'optimisation de grande dimension réside dans la possibilité de mettre en oeuvre en parallèle certaines étapes de calculs. Cette parallélisation est possible pour les algorithmes proximaux primaux-duaux alternés par bloc que nous proposons: les variables primales, ainsi que celles duales, peuvent être mises à jour en parallèle, de manière tout à fait flexible. A partir de ces résultats, nous déduisons de nouvelles méthodes distribuées, où les calculs sont répartis sur différents agents communiquant entre eux suivant une topologie d'hypergraphe. Finalement, nos contributions méthodologiques sont validées sur différentes applications en traitement du signal et des images. Nous nous intéressons dans un premier temps à divers problèmes d'optimisation faisant intervenir des critères non convexes, en particulier en restauration d'images lorsque l'image originale est dégradée par un bruit gaussien dépendant du signal, en démélange spectral, en reconstruction de phase en tomographie, et en déconvolution aveugle pour la reconstruction de signaux sismiques parcimonieux. Puis, dans un second temps, nous abordons des problèmes convexes intervenant dans la reconstruction de maillages 3D et dans l'optimisation de requêtes pour la gestion de bases de données / An efficient approach for solving an inverse problem is to define the recovered signal/image as a minimizer of a penalized criterion which is often split in a sum of simpler functions composed with linear operators. In the situations of practical interest, these functions may be neither convex nor smooth. In addition, large scale optimization problems often have to be faced. This thesis is devoted to the design of new methods to solve such difficult minimization problems, while paying attention to computational issues and theoretical convergence properties. A first idea to build fast minimization algorithms is to make use of a preconditioning strategy by adapting, at each iteration, the underlying metric. We incorporate this technique in the forward-backward algorithm and provide an automatic method for choosing the preconditioning matrices, based on a majorization-minimization principle. The convergence proofs rely on the Kurdyka-L ojasiewicz inequality. A second strategy consists of splitting the involved data in different blocks of reduced dimension. This approach allows us to control the number of operations performed at each iteration of the algorithms, as well as the required memory. For this purpose, block alternating methods are developed in the context of both non-convex and convex optimization problems. In the non-convex case, a block alternating version of the preconditioned forward-backward algorithm is proposed, where the blocks are updated according to an acyclic deterministic rule. When additional convexity assumptions can be made, various alternating proximal primal-dual algorithms are obtained by using an arbitrary random sweeping rule. The theoretical analysis of these stochastic convex optimization algorithms is grounded on the theory of monotone operators. A key ingredient in the solution of high dimensional optimization problems lies in the possibility of performing some of the computation steps in a parallel manner. This parallelization is made possible in the proposed block alternating primal-dual methods where the primal variables, as well as the dual ones, can be updated in a quite flexible way. As an offspring of these results, new distributed algorithms are derived, where the computations are spread over a set of agents connected through a general hyper graph topology. Finally, our methodological contributions are validated on a number of applications in signal and image processing. First, we focus on optimization problems involving non-convex criteria, in particular image restoration when the original image is corrupted with a signal dependent Gaussian noise, spectral unmixing, phase reconstruction in tomography, and blind deconvolution in seismic sparse signal reconstruction. Then, we address convex minimization problems arising in the context of 3D mesh denoising and in query optimization for database management

Sous l'hypothèse gaussienne, la relation entre indépendance conditionnelle et parcimonie permet de justifier la construction d'estimateurs de l'inverse de la matrice de covariance -- également appelée matrice de précision -- à partir d'approches régularisées. Cette thèse, motivée à l'origine par la problématique de classification d'images, vise à développer une méthode d'estimation de la matrice de précision en grande dimension, lorsque le nombre $n$ d'observations est petit devant la dimension $p$ du modèle. Notre approche repose essentiellement sur les liens qu'entretiennent la matrice de précision et le modèle de régression linéaire. Elle consiste à estimer la matrice de précision en deux temps. Les éléments non diagonaux sont tout d'abord estimés en considérant $p$ problèmes de minimisation du type racine carrée des moindres carrés pénalisés par la norme $ell_1$.Les éléments diagonaux sont ensuite obtenus à partir du résultat de l'étape précédente, par analyse résiduelle ou maximum de vraisemblance. Nous comparons ces différents estimateurs des termes diagonaux en fonction de leur risque d'estimation. De plus, nous proposons un nouvel estimateur, conçu de sorte à tenir compte de la possible contamination des données par des {em outliers}, grâce à l'ajout d'un terme de régularisation en norme mixte $ell_2/ell_1$. L'analyse non-asymptotique de la convergence de notre estimateur souligne la pertinence de notre méthode / Under the Gaussian assumption, the relationship between conditional independence and sparsity allows to justify the construction of estimators of the inverse of the covariance matrix -- also called precision matrix -- from regularized approaches. This thesis, originally motivated by the problem of image classification, aims at developing a method to estimate the precision matrix in high dimension, that is when the sample size $n$ is small compared to the dimension $p$ of the model. Our approach relies basically on the connection of the precision matrix to the linear regression model. It consists of estimating the precision matrix in two steps. The off-diagonal elements are first estimated by solving $p$ minimization problems of the type $ell_1$-penalized square-root of least-squares. The diagonal entries are then obtained from the result of the previous step, by residual analysis of likelihood maximization. This various estimators of the diagonal entries are compared in terms of estimation risk. Moreover, we propose a new estimator, designed to consider the possible contamination of data by outliers, thanks to the addition of a $ell_2/ell_1$ mixed norm regularization term. The nonasymptotic analysis of the consistency of our estimator points out the relevance of our method

A reciclagem de resíduos de construção e demolição (RCD) é uma prática utilizada desde a Antigüidade, quando cidades destruídas pela guerra e por catástrofes naturais eram reerguidas dos próprios escombros. Hoje, ela é utilizada em larga escala em vários países da Europa e nos EUA. No Brasil, onde a preocupação com o destino desses resíduos é bem mais recente, poucos municípios se preocupam com o gerenciamento dos RCD. Os efeitos disso são visíveis: os resíduos ainda são depositados irregularmente em terrenos baldios, vias públicas, várzeas, córregos e até mesmo em áreas de proteção ambiental, causando a proliferação de vetores nocivos à saúde, enchentes e diversos prejuízos ao meio-ambiente. Assim, este trabalho tem como objetivo propor soluções que busquem a minimização desse impacto ambiental por meio da utilização dos RCD como agregados na fabricação de blocos de concreto. Os testes em laboratório e a comparação dos resultados obtidos com os das práticas convencionais provam a viabilidade da utilização dos resíduos, tanto em termos ambientais quanto econômicos, além de garantir que o emprego dos RCD atenda a todas as normas vigentes. Com isso, reafirmou-se o compromisso com a preservação ambiental, pois a reciclagem desse tipo de entulho, além de ajudar a removê-lo da paisagem urbana, ainda gera diferenciais consideráveis em termos de economia de energia e de recursos naturais não-renováveis que seriam utilizados como matérias-primas, reduzindo a poluição do ar, da água, do solo, desafogando aterros sanitários, e visando atingir o desenvolvimento sustentável. / Recycling of construction and demolition refuses (CDR) is a has been practiced since ancient history, when cities that were destroyed by war and natural disasters were rebuilt from their own ruins. Today, it is used in large scale in many countries in Europe and in the USA. In Brazil, where the concern with the destination of this kind of refuses is much more recent, few cities have planned and executed CDR management to this day. The side effects of this situation are plainly visible: the refuses have been continually and irregularly deposed in unused areas, thoroughfares, riversides, creeks and even in environmental protection areas, causing the proliferation of health-affecting problems, flooding and many other damages to the environment. Therefore, this study has the main goal of proposing solutions that can lessen the environmental impact by using CDR as aggregate in the manufacturing of concrete blocks. The lab tests and the comparing of the results obtained with those measured with the conventional techniques prove the viability of reutilizing these refuses, both in environmental and economical terms, as well as assuring that the use of CDR follows all the current regulations. With this, the compromise with environmental preservation is reinforced, since the recycling this type of refuse, beside helping to remove it from the urban landscape, generates considerable gains in saving energy and the non-renewable natural resources that would be used as raw material, lessening air, water and soil pollution, releasing the burden on landfills, always aiming at achieving sustainable development.

Problemas reais em áreas como aprendizado de máquina têm chamado atenção pela enorme quantidade de variáveis (> 10^6) e volume de dados. Em problemas dessa escala o custo para se obter e trabalhar com informações de segunda ordem são proibitivos. Tais problemas apresentam características que podem ser aproveitadas por métodos de busca em coordenada. Essa classe de métodos é caracterizada pela alteração de apenas uma ou poucas variáveis a cada iteração. A variante do método comumente descrita na literatura é a minimização cíclica de variáveis. Porém, resultados recentes sugerem que variantes aleatórias do método possuem melhores garantias de convergência. Nessa variante, a cada iteração, a variável a ser alterada é sorteada com uma probabilidade preestabelecida não necessariamente uniforme. Neste trabalho estudamos algumas variações do método de busca em coordenada. São apresentados aspectos teóricos desses métodos, porém focamos nos aspectos práticos de implementação e na comparação experimental entre variações do método de busca em coordenada aplicados a diferentes problemas com aplicações reais. / Real world problemas in areas such as machine learning are known for the huge number of decision variables (> 10^6) and data volume. For such problems working with second order derivatives is prohibitive. These problems have properties that benefits the application of coordinate descent/minimization methods. These kind of methods are defined by the change of a single, or small number of, decision variable at each iteration. In the literature, the commonly found description of this type of method is based on the cyclic change of variables. Recent papers have shown that randomized versions of this method have better convergence properties. This version is based on the change of a single variable chosen randomly at each iteration, based on a fixed, but not necessarily uniform, distribution. In this work we present some theoretical aspects of such methods, but we focus on practical aspects.

<div> <div> <div> <p>Real-time pricing (RTP) of electricity for consumers has long been argued to be crucial for realizing the many envisioned benefits of demand flexibility in a smart grid. However, many details of how to actually implement a RTP scheme are still under debate. Since most of the organized wholesale electricity markets in the US implement a two-settlement mechanism, with day-ahead electricity price forecasts guiding financial and physical transactions in the next day and real-time ex post prices settling any real-time imbalances, it is a natural idea to let consumers respond to the day-ahead prices in real-time. However, if such an idea is not controlled properly, the inherent closed-loop operation may lead consumers to all respond in the same fashion, causing large swings of real-time demand and prices, which may jeopardize system stability and increase consumers’ financial risks. </p><p><br></p> <p>To overcome the potential uncertainties and undesired demand peak caused by “selfish” behaviors by individual consumers under RTP, in this research, we develop a fully decentralized price-driven demand response (DR) approach under game- theoretical frameworks. In game theory, agents usually make decisions based on their belief about competitors’ states, which needs to maintain a large amount of knowledge and thus can be intractable and implausible for a large population. Instead, we propose using regret-based learning in games by focusing on each agent’s own history and utility received. We study two learning mechanisms: bandit learning with incomplete information feedback, and low regret learning with full information feedback. With the learning in games, we establish performance guarantees for each individual agent (i.e., regret minimization) and the overall system (i.e., bounds on price of anarchy).</p><p><br></p></div></div></div><div><div><div> <p>In addition to the game-theoretical framework for price-driven demand response, we also apply such a framework for peer-to-peer energy trading auctions. The market- based approach can better incentivize the development of distributed energy resources (DERs) on demand side. However, the complexity of double-sided auctions in an energy market and agents’ bounded rationality may invalidate many well-established theories in auction design, and consequently, hinder market development. To address these issues, we propose an automated bidding framework based on multi-armed bandit learning through repeated auctions, and is aimed to minimize each bidder’s cumulative regret. We also use such a framework to compare market outcomes of three different auction designs. </p> </div> </div> </div>