Estendemos para a teria de campos o método variacional de Kleinert. Este método foi primeiramente usado na mecânica quântica e fornece uma expansão em cumulantes convergente. Sua extensão para a teoria de campos não é trivial devido às divergências ultravioletas que aparecem quando a dimensão do espaço é maior que 2. Devido a estas divergências, a teoria deve ser regularizada e normalizada. Além das dificuldades usuais associadas com a renormalização, devemos decidir se calculamos o valor ótimo do parâmetro variacional antes ou depois da renormalização. Nesta tese abordamos o problema da renormalização do potencial efetivo variacional. Primeiramente, mostramos que o potencial efetivo variacional em temperatura zero coincide com o \"potencial efetivo pós-gaussiano\" introduzido por Stancu e Stevenson. Em seguida, apresentamos um esquema de renormalização que permite que renormalizemos a teoria antes de calcular o parâmetro variacional ótimo. Usando este esquema mostramos que o potencial efetivo usual, calculado em ordem 1-loop, pode ser obtido a partir do esquema variacional de Kleinert inteirando uma única vez a equação que determina o parâmetro variacional. Para o potencial efetivo em ordem 2-loops esta aproximação não é tão boa. A renormalização da teoria antes do cálculo do parâmetro variacional permite que estudemos o potencial efetivo variacional numericamente e de forma não-perturbativa, como foi feito por Kleinert para a mecânica quântica. / We have extended the Kleinert variational technique to field theory. This method was first used in quantum mechanics and provides a convergent cumulate expansion that is extremely accurate. Its extension to field theory is non-trivial because of the ultraviolet divergences that appear when the space dimension is greater than 2. Due to these divergences the theory has to be regularized and renormalized. In addition to the usual difficulties associated with renormalization, one has to decide whether one calculates the optimum value of the variational parameter before or after renormalization. In this thesis we deal with the renormalization of the variational effective potential. Firstly, we show that the zero temperature regularized variational potential coincides with the post-Gaussian effective potential introduced by Stancu and Stenvenson. Secondly, we present a renormalization scheme that enables one to renormalize the theory before calculating the optimum variational parameter. Using this scheme we show that the usual 1-loop effective potential can be obtained from the Kleinert variational scheme by interacting only once the equation that determines the variational parameter. In this sense, the 1-loop expansion is contained within the variational scheme. For the 2-loop effective potential the same approximation is not so good. The renormalization of the theory before the calculation of the variational parameter allows one to study the variational effective potential numerically and in a non-pertubative way, as it was done in quantum mechanics by Kleinert.

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Electrical and electronic equipment waste (e-waste) is growing fast. Due to its potential economic value as well as its possible negative impacts on the environment, tracing e-waste flow is a major concern for stakeholders of e-waste management. Especially, whether or not adequate amounts of electrical and electronic equipment waste (WEEE) flow into the designed recycling systems is a fundamental issue for sustainable operations. In this paper, we analyze how technical, market, and legislative factors influence the total amount of e-waste that is collected, recycled, exported and (legally and illegally) disposed off. We formulate the e-waste network flow model as a variational inequality problem. The results of the numerical examples highlight the importance of considering the interaction between the supply and the demand side for precious materials in policy-decisions. Low collection rates of e-waste lead to low profits for stakeholders and make it difficult to establish sustainable recycling operations. Increasing WEEE collection rates increases recyclers' profits; however, it only increases smelters' profits up to a certain limit, after which smelters cannot benefit further due to limited demand for precious materials. Furthermore, the results emphasize the importance of establishing international control regimes for WEEE flows and reveal possible negative consequences of the recent trend of dematerialization. More precisely, product dematerialization tends to decrease recyles' and smelters' profits as well as to increase the outflow of e-waste from the designated recycling system. (authors' abstract)

The extension of the CJS model to include individual, continuous, time-varying covariates relies on the estimation of covariate values on occasions on which individuals were not captured. Fitting this model in a Bayesian framework typically involves the implementation of a Markov chain Monte Carlo (MCMC) algorithm, such as a Gibbs sampler, to sample from the posterior distribution. For large data sets with many missing covariate values that must be estimated, this creates a computational issue, as each iteration of the MCMC algorithm requires sampling from the full conditional distributions of each missing covariate value. This dissertation examines two solutions to address this problem. First, I explore variational Bayesian algorithms, which derive inference from an approximation to the posterior distribution that can be fit quickly in many complex problems. Second, I consider an alternative approximation to the posterior distribution derived by truncating the individual capture histories in order to reduce the number of missing covariates that must be updated during the MCMC sampling algorithm. In both cases, the increased computational efficiency comes at the cost of producing approximate inferences. The variational Bayesian algorithms generally do not estimate the posterior variance very accurately and do not directly address the issues with estimating many missing covariate values. Meanwhile, the truncated CJS model provides a more significant improvement in computational efficiency while inflating the posterior variance as a result of discarding some of the data. Both approaches are evaluated via simulation studies and a large mark-recapture data set consisting of cliff swallow weights and capture histories.

People detection has been an attractive technology in computer vision. There are many useful applications in our daily life, for instance, intelligent surveillance and driver assistance system. People detection is a challenging matter as people adopt a wide range of poses, wear diverse clothes, and are visible in different kind of backgrounds with significant changes in illumination. In this thesis, some advanced techniques and powerful tools are presented in order to design a robust people detection system. First a baseline model is implemented by combining the Histogram of Oriented Gradients descriptor and linear Support Vector Machines. This baseline model obtains a good performance on the well-known INRIA dataset. Second an advanced model is proposed which has a two-layer cascade framework that achieves both accurate detection and lower computational complexity. For the first layer, the baseline model is used as a filter to generate several candidates. In this procedure, most positive samples survived and the majority of negative samples are rejected according to a preset threshold. The second layer uses a more discriminative model. We combine the Variational Local Binary Patterns descriptor, and the Histogram of Oriented Gradients descriptor as a new discriminative feature. Furthermore multi-scale feature descriptors are used to improve the discriminative power of the Variational Local Binary Patterns feature. Then we perform Feature Selection using the Feature Generating Machine in order to generate a concise descriptor based on this concatenated feature. Moreover Histogram Intersection Kernel Support Vector Machines is employed as an efficient tool of classification. The bootstrapping algorithm is used in the training procedure to exploit the information of the dataset. Finally our approach has a good performance on the INRIA dataset, with results superior to the baseline model.

Variational principles in classical fluid mechanics and electromagnetism have sprinkled the literature since the eighteenth century. Even so, no adequate variational principle in the Eulerian description of matter was had until 1968 when an Eulerian variational principle was introduced which reproduces Euler's equation of fluid dynamics. Although it successfully produces the appropriate equation of motion for a perfect fluid, the variational principle requires imposition of a constraint which was not fully understood at the time the variational principle was introduced. That constraint is the Lin constraint. The Lin constraint has subsequently been utilized by a number of authors who have sought to develop Eulerian variational principles in both fluid mechanics and electromagnetics (or plasmadynamics). How-ever, few have sought to fully understand the constraint. This dissertation first reviews the work of earlier authors concerning the development of variational principles in both the Eulerian and Lagrangian nomenclatures. In the process, it is shown rigorously whether or not the Euler-Lagrange equations which result from the variational principles are equivalent to the generally accepted equations of motion. In particular, it is shown in the case of several Eulerian variational principles that imposition of the Lin constraint results in Euler-Lagrange equations which are equivalent to the generally accepted equations of motion. On the other hand, it is shown that neglect of the Lin constraint results in Euler-Lagrange equations restrictive of the generally accepted equations of motion. In an effort to improve the physical motivation behind introduction of the Lin constraint a new variational constraint is developed based on the concept of surface forces within a fluid. The new constraint has the advantage of producing Euler-Lagrange equations which are globally correct whereas the Lin constraint itself allows only local equivalence to the standard classical equations of fluid motion. Several additional items of interest regarding variational principles are presented. It is shown that a quantity often referred to as "the canonical momentum" of a charged fluid is not always a constant of the motion of the fluid. This corrects an error which has previously appeared in the literature. In addition, it is demonstrated that there does not exist an unconstrained Eulerian variational principle giving rise to the generally accepted equations of motion for both a perfect fluid and a cold, electromagnetic fluid.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第21208号 / 情博第661号 / 新制||情||114(附属図書館) / 京都大学大学院情報学研究科知能情報学専攻 / (主査)教授 美濃 導彦, 教授 河原 達也, 教授 中村 裕一 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Recent developments in AI is changing our world. It already governs our digital life. In my thesis I take the position that AI involvement in the field of architecture is inevitable, and indeed already here. AI is neither something we can simply accept, nor wholly ignore. Rather, we should try to understand and work with it. These algorithms should not be seen as mere tools with predictable, repeatable outcomes, they are something more complex. I’ve explored the world of AI by means of teaching a machine to design diverse, typologically similar objects: residential doorways from Stockholm. By instructing the machine to read and recreate these objects it has learned to design objects similar to them. While the machine does not know what it has designed, it has nevertheless reinterpreted the residential gate, thus offering an opportunity to glimpse into to the “mind” of AI, a world equally as unknown as omnipresent.

Facial expressions play an important role in such areas as human communication or medical state evaluation. For machine learning tasks in those areas, it would be beneficial to have a representation of facial expressions which corresponds to human similarity perception. In this work, the data-driven approach to representation learning of facial expressions is taken. The methodology is built upon Variational Autoencoders and eliminates the appearance-related features from the latent space by using neutral facial expressions as additional inputs. In order to improve the quality of the learned representation, we modify the prior distribution of the latent variable to impose the structure on the latent space that is consistent with human perception of facial expressions. We conduct the experiments on two datasets and the additionally collected similarity data, show that the human-like topology in the latent representation helps to improve the performance on the stereotypical emotion classification task and demonstrate the benefits of using a probabilistic generative model in exploring the roles of latent dimensions through the generative process. / Ansiktsuttryck spelar en viktig roll i områden som mänsklig kommunikation eller vid utvärdering av medicinska tillstånd. För att tillämpa maskininlärning i dessa områden skulle det vara fördelaktigt att ha en representation av ansiktsuttryck som bevarar människors uppfattning av likhet. I det här arbetet används ett data-drivet angreppssätt till representationsinlärning av ansiktsuttryck. Metodologin bygger på s. k. Variational Autoencoders och eliminerar utseende-relaterade drag från den latenta rymden genom att använda neutrala ansiktsuttryck som extra input-data. För att förbättra kvaliteten på den inlärda representationen så modifierar vi a priori-distributionen för den latenta variabeln för att ålägga den struktur på den latenta rymden som är överensstämmande med mänsklig perception av ansiktsuttryck. Vi utför experiment på två dataset och även insamlad likhets-data och visar att den människolika topologin i den latenta representationen hjälper till att förbättra prestandan på en typisk emotionsklassificeringsuppgift samt fördelarna med att använda en probabilistisk generativ modell när man undersöker latenta dimensioners roll i den generativa processen.

Broadly speaking, cluster analysis is the organization of a data set into meaningful groups and mixture model-based clustering is recently receiving a wide interest in statistics. Historically, the Gaussian mixture model has dominated the model-based clustering literature. When model-based clustering is performed on a large number of observed variables, it is well known that Gaussian mixture models can represent an over-parameterized solution. To this end, this thesis focuses on the development of novel non-Gaussian mixture models for high-dimensional continuous and categorical data. We developed a mixture of joint generalized hyperbolic models (JGHM), which exhibits different marginal amounts of tail-weight. Moreover, it takes into account the cluster specific subspace and, therefore, limits the number of parameters to estimate. This is a novel approach, which is applicable to high, and potentially very- high, dimensional spaces and with arbitrary correlation between dimensions. Three different mixture models are developed using forms of the mixture of latent trait models to realize model-based clustering of high-dimensional binary data. A family of mixture of latent trait models with common slope parameters are developed to reduce the number of parameters to be estimated. This approach facilitates a low-dimensional visual representation of the clusters. We further developed the penalized latent trait models to facilitate ultra high dimensional binary data which performs automatic variable selection as well. For all models and families of models developed in this thesis, the algorithms used for model-fitting and parameter estimation are presented. Real and simulated data sets are used to assess the clustering ability of the models. / Thesis / Doctor of Philosophy (PhD)