Orientador: Claudio Aguinaldo Buzzi / Banca: Marco Antônio Teixeira / Banca: Paulo Ricardo da Silva / Resumo: O objetivo principal desse trabalho é provar, sob certas hipóteses de transversalidade e sobre os autovalores, que se uma família a um-parâmetro de equações diferenciais possuindo, para um determinado valor do parâmetro, um laço homoclínico conectado a um ponto de equilíbrio do tipo sela, então existe uma variedade central invariante, de dimensão dois, que contém o laçco homoclínico, que contém todas as trajetórias que permanecem numa vizinhança do laço homoclínico e ainda é tangente ao autoespaço gerado por autovetores associados aos autovalores que determinam o laço homoclínico. / Abstract: The main goal of this work is to prove, under certain hypothesis of transversality and about the eigenvalues, that if a one-parameter family of ordinary differential equations possess, for a determined value of the parameter, a homoclinic loop connected to an equilibrium point of type saddle, then there exists an invariant center manifold, of dimension two, that contains the homoclinic loop, that contains all trajectories which stay in a small neighborhood of the homoclinic loop and that is tangent to the eigenspace spanned by the eigenvectors associated to the eigenvalues that determine the homoclinic loop. / Mestre

Abstract Automatic face recognition is a challenging problem which has received much attention during recent years due to its many applications in different fields such as law enforcement, security applications, human-machine interaction etc. Up to date there is no technique that provides a robust solution for all situations and different applications. From still gray images to face sequences (and passing through color images), this thesis provides new algorithms to learn, detect and recognize faces. It also analyzes some emerging directions such as the integration of facial dynamics in the recognition process. To recognize faces, the thesis proposes a new approach based on Local Binary Patterns (LBP) which consists of dividing the facial image into small regions from which LBP features are extracted and concatenated into a single feature histogram efficiently representing the face image. Then, face recognition is performed using a nearest neighbor classifier in the computed feature space with Chi-square as a dissimilarity metric. The extensive experiments clearly show the superiority of the proposed method over the state-of the-art algorithms on FERET tests. To detect faces, another LBP-based representation which is suitable for low-resolution images, is derived. Using the new representation, a second-degree polynomial kernel SVM classifier is trained to detect frontal faces in complex gray scale images. Experimental results using several complex images show that the proposed approach performs favorably compared to the state-of-art methods. Additionally, experiments with detecting and recognizing low-resolution faces are carried out to demonstrate that the same facial representation can be efficiently used for both the detection and recognition of faces in low-resolution images. To detect faces when the color cue is available, the thesis proposes an approach based on a robust model of skin color, called a skin locus, which is used to extract the skin-like regions. After orientation normalization and based on verifying a set of criteria (face symmetry, presence of some facial features, variance of pixel intensities and connected component arrangement), only facial regions are selected. To learn and visualize faces in video sequences, the recently proposed algorithms for unsupervised learning and dimensionality reduction (LLE and ISOMAP), as well as well known ones (PCA, SOM etc.) are considered and investigated. Some extensions are proposed and a new approach for selecting face models from video sequences is developed. The approach is based on representing the face manifold in a low-dimensional space using the Locally Linear Embedding (LLE) algorithm and then performing K-means clustering. To analyze the emerging direction in face recognition which consists of combining facial shape and dynamic personal characteristics for enhancing face recognition performance, the thesis considers two factors (face sequence length and image quality) and studies their effects on the performance of video-based systems which attempt to use a spatio-temporal representation instead of a still image based one. The extensive experimental results show that motion information enhances automatic recognition but not in a systematic way as in the human visual system. Finally, some key findings of the thesis are considered and used for building a system for access control based on detecting and recognizing faces.

Within machine learning, the problem of class imbalance refers to the scenario in which one or more classes is significantly outnumbered by the others. In the most extreme case, the minority class is not only significantly outnumbered by the majority class, but it also considered to be rare, or absolutely imbalanced. Class imbalance appears in a wide variety of important domains, ranging from oil spill and fraud detection, to text classification and medical diagnosis. Given this, it has been deemed as one of the ten most important research areas in data mining, and for more than a decade now the machine learning community has been coming together in an attempt to unequivocally solve the problem. The fundamental challenge in the induction of a classifier from imbalanced training data is in managing the prediction bias. The current state-of-the-art methods deal with this by readjusting misclassification costs or by applying resampling methods. In cases of absolute imbalance, these methods are insufficient; rather, it has been observed that we need more training examples. The nature of class imbalance, however, dictates that additional examples cannot be acquired, and thus, synthetic oversampling becomes the natural choice. We recognize the importance of selecting algorithms with assumptions and biases that are appropriate for the properties of the target data, and argue that this is of absolute importance when it comes to developing synthetic oversampling methods because a large generative leap must be made from a relatively small training set. In particular, our research into gamma-ray spectral classification has demonstrated the benefits of incorporating prior knowledge of conformance to the manifold assumption into the synthetic oversampling algorithms. We empirically demonstrate the negative impact of the manifold property on the state-of-the-art methods, and propose a framework for manifold-based synthetic oversampling. We algorithmically present the generic form of the framework and demonstrate formalizations of it with PCA and the denoising autoencoder. Through use of the helix and swiss roll datasets, which are standards in the manifold learning community, we visualize and qualitatively analyze the benefits of our proposed framework. Moreover, we unequivocally show the framework to be superior on three real-world gamma-ray spectral datasets and on sixteen benchmark UCI datasets in general. Specifically, our results demonstrate that the framework for manifold-based synthetic oversampling produces higher area under the ROC results than the current state-of-the-art and degrades less on data that conforms to the manifold assumption.

Dimensionality reduction techniques such as t-SNE and UMAP are useful both for overview of high-dimensional datasets and as part of a machine learning pipeline. These techniques create a non-parametric model of the manifold by fitting a density kernel about each data point using the distances to its k-nearest neighbors. In dense regions, this approach works well, but in sparse regions, it tends to draw unrelated points into the nearest cluster. Our work focuses on a homotopy method which imposes graph-based regularization over the manifold parameters to update the embedding. As the homotopy parameter increases, so does the cost of modeling different scales between adjacent neighborhoods. This gradually imposes a more uniform scale over the manifold, resulting in a more faithful embedding which preserves structure in dense areas while pushing sparse anomalous points outward.

京都大学 / 0048 / 新制・課程博士 / 博士(人間健康科学) / 甲第21704号 / 人健博第70号 / 新制||人健||5(附属図書館) / 京都大学大学院医学研究科人間健康科学系専攻 / (主査)教授 青山 朋樹, 教授 黒木 裕士, 教授 松田 秀一 / 学位規則第4条第1項該当 / Doctor of Human Health Sciences / Kyoto University / DFAM

Throughout the history of interplanetary space travel, the Newtonian dynamics of the two-body problem have been used to design orbital trajectories to traverse the solar system. That is, that a spacecraft orbits only one large celestial body at a time. These dynamics have produced impressive interplanetary trajectories utilizing numerous gravity assists, such as those of Voyager, Cassini, Rosetta and countless others. But these missions required large amounts of delta-v for their maneuvers and therefore large amounts of fuel mass. As we desire to travel farther and more extensively in space, these two-body dynamics lead to impossibly high delta-v values, and missions become infeasible due to the massive amounts of fuel that they would need to carry. In the last few decades a new dynamical system has been researched in order to find new ways of designing mission trajectories: the N-body problem. This utilizes the gravitational acceleration from multiple celestial bodies on a spacecraft, and can lead to unconventional, but very useful trajectories. The goal of this thesis is to use the dynamics of the Circular Restricted Three-Body Problem (CRTBP) to design interplanetary transfer trajectories. This method of modelling orbital dynamics takes into account the gravitational acceleration of two celestial bodies acting on a spacecraft, rather than just one. The invariant manifolds of halo orbits about Sun-planet Lagrange points are used to aid in the transfer from one planet to another, and can lead into orbital insertion about the destination planet or flyby trajectories to get to another planet. This work uses this method of dynamics to test transfers from Earth to both Jupiter and Saturn, and compares delta-v and time of flight values to traditional transfer methods. Using the CRTBP can lead to reduced delta-v amounts for completing the same missions as two-body dynamics would. The aim of this work is to research if using manifolds for interplanetary transfers could be superior for some high delta-v missions, as it could drastically reduce the required delta-v for maneuvers. With this method it could be possible to visit more distant destinations, or carry more mass of scientific payloads, due to the reduced fuel requirements. Results of this research showed that using manifolds to aid in interplanetary transfers can reduce the delta-v of both departure from Earth and arrival at a destination planet. For transfers to Jupiter the delta-v for the interplanetary transfer was reduced by 4.12 km/s compared to starting and ending in orbits about the planets. For a transfer to Saturn the delta-v required for the interplanetary transfer was reduced by 6.77 km/s. These delta-v savings are significant and show that utilizing manifolds can lead to lower energy interplanetary transfer trajectories, and have the potential to be useful for high delta-v missions.

In the era of Internet of Things (IoT) and big data, collecting, processing and analyzing enormous data faces unprecedented challenges even when being stored in preprocessed form. Anomaly detection, statistically viewed as identifying outliers having low probabilities from the modelling of data distribution p(x), becomes more crucial. In this Master thesis, two (supervised and unsupervised) novel deep anomaly detection frameworks are presented which can achieve state-of-art performance on a range of datasets. Capsule net is an advanced artificial neural network, being able to encode intrinsic spatial relationship between parts and a whole. This property allows it to work as both a classifier and a deep autoencoder. Taking this advantage of CapsNet, a new anomaly detection technique named AnoCapsNet is proposed and three normality score functions are designed: prediction-probability-based (PP-based) normality score function, reconstruction-error-based (RE-based) normality score function, and a normality score function that combines prediction-probability-based and reconstruction-error-based together (named as PP+RE-based normality score function) for evaluating the "outlierness" of unseen images. The results on four datasets demonstrate that the PP-based method performs consistently well, while the RE-based approach is relatively sensitive to the similarity between labeled and unlabeled images. The PP+RE-based approach effectively takes advantages of both methods and achieves state-of-the-art results. In many situations, neither the domain of anomalous samples can be fully understood, nor the domain of the normal samples is straightforward. Thus deep generative models are more suitable than supervised methods in such cases. As a variant of variational autoencoder (VAE), beta-VAE is designed for automated discovery of interpretable factorised latent representations from raw image data in a completely unsupervised manner. The t-Distributed Stochastic Neighbor Embedding (t-SNE), an unsupervised non-linear technique primarily used for data exploration and visualizing high-dimensional data, has advantages at creating a single map that reveals local and important global structure at many different scales. Taking advantages of both disentangled representation learning (using beta-VAE as an implementation) and low-dimensional neighbor embedding (using t-SNE as an implementation), another novel anomaly detection approach named AnoDM (stands for Anomaly detection based on unsupervised Disentangled representation learning and Manifold learning) is presented. A new anomaly score function is defined by combining (1) beta-VAE's reconstruction error, and (2) latent representations' distances in the t-SNE space. This is a general framework, thus any disentangled representation learning and low-dimensional embedding techniques can be applied. AnoDM is evaluated on both image and time-series data and achieves better results than models that use just one of the two measures and other existing advanced deep learning methods.

No description available.

Cubical complexes are defined in a manner analogous to that for simplicial complexes, the chief difference being that cubical complexes are unions of cubes rather than of simplices. A very natural cubical complex to consider is the complex C(k_1,...,k_n) where k_1,...,k_n are nonnegative integers. This complex has as its underlying space [0,k_1]x...x[0,k_n] subset of R^n with vertices at all points having integer coordinates and higher dimensional cubes formed by the vertices in the natural way. The genus of a cubical complex is defined to be the maximum genus of all surfaces that are subcomplexes of the cubical complex. A formula is given for determining the genus of the cubical complex C(k_1,...,k_n) when at least three of the k_i are odd integers. For the remaining cases a general solution is not known. When k_1=...=k_n=1 the genus of C(k_1,...,k_n) is shown to be (n-4)2^{n-3}+1 which is equivalent to the genus of the graph of the n-cube. Indeed, the genus of the complex and the genus of the graph of the 1-skeleton of the complex, are shown to be equal when at least three of the k_i are odd, but not equal in general.

We study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. We prove a multiplicative ergodic theorem. Then, we use this theorem to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.