76 research outputs found

    Effets de la dimension des réseaux hyperboliques sur la modélisation de la structure communautaire

    Get PDF
    Le cadre théorique de la géométrie des réseaux consiste à placer des points, les nœuds, dans un espace métrique, puis les connecter par des liens par paires selon la distance qui les sépare. Lorsque la géométrie sous-jacente est hyperbolique, de nombreuses propriétés de réseaux qui proviennent de données empiriques peuvent être élégamment expliquées à l'aide de la proximité entre les nœuds et des caractéristiques de ces espaces si particuliers, dont la courbure est négative. Le modèle de réseaux hyperboliques le plus couramment utilisé attribue à chaque nœud une coordonnée radiale associée à son nombre total de liens et une coordonnée angulaire. Avec celle-ci, les nœuds peuvent être envoyés à un cercle, et à plus petite distance angulaire ils ont plus de chances d'être connectés, ce qui encode la similarité avec les autres nœuds. Or, dans de nombreux systèmes réels, il existe plus d'un facteur poussant les éléments à s'associer, et donc plusieurs manières d'être similaires ou pas. Cela se reflète dans les modèles de réseaux hyperboliques de plus grande dimension, où plus d'une coordonnée angulaire est associée à chaque nœud, qui est alors envoyé à une sphère de plus grande dimension à la place du cercle. Dans ce mémoire, on étudie les effets de la dimension des modèles de réseaux hyperboliques aléatoires. En particulier, la distribution des distances angulaires entre les nœuds connectés change selon la dimension. Or, la coordonnée angulaire des nœuds est aussi utilisée pour modéliser la structure communautaire, c'est-à-dire lorsque des sous-groupes de nœuds, les communautés, sont reliés plus densément entre eux qu'au reste du réseau. Par conséquent, augmenter le nombre de coordonnées angulaires affecte naturellement comment les communautés peuvent être générées et la manière dont elles sont reliées entre elles. Ces effets sont quantifiés en simulant des réseaux hyperboliques qui possèdent de la structure communautaire. Une différence marquée est observée entre le cas le plus simple et l'ajout d'une seule dimension, où la structure communautaire générée est plus diversifiée et réaliste.The framework of network geometry involves placing points, nodes of a network, in a metric space and then creating pairwise connections, the edges, according to the distance between them. When the underlying geometry is hyperbolic, many network properties are elegantly explained by the closeness between nodes through properties of these negatively curved spaces. The flagship model of this framework assigns to each node one radial coordinate related to its total number of connections and one angular coordinate related to its similarity to other nodes. Nodes can thus be mapped to a circle where a smaller angular distance increases the chances to be connected, hence the idea of similarity. However, in many systems, there is more than one factors that drives relationships between elements, and thus more than one way in which they can be similar or not. This is captured by higher dimensional hyperbolic network models, where each node has more angular coordinates that maps it to a higher dimensional sphere instead of the circle. In this master's thesis, we study the effects of the dimension of hyperbolic network models. In particular, the distribution of angular distances between connected nodes changes with dimension. Yet, nodes' angular coordinates are also used to model hyperbolic networks' community structure, when some subgroups of nodes, the communities, are more densely connected than to the rest of the network. Hence, increasing the number of angular coordinates naturally affects how communities can be created and how they are related to one another. These effects are quantified through simulations of hyperbolic networks possessing community structure. A significant difference is observed between the simplest case and the addition of a single dimension, in which case the community structure generated is more diverse and realistic

    [Activity of Institute for Computer Applications in Science and Engineering]

    Get PDF
    This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science

    Computational studies of genome evolution and regulation

    Get PDF
    This thesis takes on the challenge of extracting information from large volumes of biological data produced with newly established experimental techniques. The different types of information present in a particular dataset have been carefully identified to maximise the information gained from the data. This also precludes the attempts to infer the types of information that are not present in the data. In the first part of the thesis I examined the evolutionary origins of de novo taxonomically restricted genes (TRGs) in Drosophila subgenus. De novo TRGs are genes that have originated after the speciation of a particular clade from previously non-coding regions - functional ncRNA, within introns or alternative frames of older protein-coding genes, or from intergenic sequences. TRGs are clade-specific tool-kits that are likely to contain proteins with yet undocumented functions and new protein folds that are yet to be discovered. One of the main challenges in studying de novo TRGs is the trade-off between false positives (non-functional open reading frames) and false negatives (true TRGs that have properties distinct from well established genes). Here I identified two de novo TRG families in Drosophila subgenus that have not been previously reported as de novo originated genes, and to our knowledge they are the best candidates identified so far for experimental studies aimed at elucidating the properties of de novo genes. In the second part of the thesis I examined the information contained in single cell RNA sequencing (scRNA-seq) data and propose a method for extracting biological knowledge from this data using generative neural networks. The main challenge is the noisiness of scRNA-seq data - the number of transcripts sequenced is not proportional to the number of mRNAs present in the cell. I used an autoencoder to reduce the dimensionality of the data without making untestable assumptions about the data. This embedding into lower dimensional space alongside the features learned by an autoencoder contains information about the cell populations, differentiation trajectories and the regulatory relationships between the genes. Unlike most methods currently used, an autoencoder does not assume that these regulatory relationships are the same in all cells in the data set. The main advantages of our approach is that it makes minimal assumptions about the data, it is robust to noise and it is possible to assess its performance. In the final part of the thesis I summarise lessons learnt from analysing various types of biological data and make suggestions for the future direction of similar computational studies

    Advanced Biometrics with Deep Learning

    Get PDF
    Biometrics, such as fingerprint, iris, face, hand print, hand vein, speech and gait recognition, etc., as a means of identity management have become commonplace nowadays for various applications. Biometric systems follow a typical pipeline, that is composed of separate preprocessing, feature extraction and classification. Deep learning as a data-driven representation learning approach has been shown to be a promising alternative to conventional data-agnostic and handcrafted pre-processing and feature extraction for biometric systems. Furthermore, deep learning offers an end-to-end learning paradigm to unify preprocessing, feature extraction, and recognition, based solely on biometric data. This Special Issue has collected 12 high-quality, state-of-the-art research papers that deal with challenging issues in advanced biometric systems based on deep learning. The 12 papers can be divided into 4 categories according to biometric modality; namely, face biometrics, medical electronic signals (EEG and ECG), voice print, and others

    Recent Advances in Signal Processing

    Get PDF
    The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

    New Directions for Contact Integrators

    Get PDF
    Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

    Applications

    Get PDF
    • …
    corecore