Horizontal visibility graphs generated by type-I intermittency

The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associatedHVgraphs.We showhowthe alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics.We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

Quasiperiodic graphs at the onset of chaos

We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers

UAS See-and-Avoid Strategy using a Fuzzy Logic Controller Optimized by Cross-Entropy in Scaling Factors and Membership Functions

This work aims to develop a novel Cross-Entropy (CE) optimization-based fuzzy controller for Unmanned Aerial Monocular Vision-IMU System (UAMVIS) to solve the seeand- avoid problem using its accurate autonomous localization information. The function of this fuzzy controller is regulating the heading of this system to avoid the obstacle, e.g. wall. In the Matlab Simulink-based training stages, the Scaling Factor (SF) is adjusted according to the specified task firstly, and then the Membership Function (MF) is tuned based on the optimized Scaling Factor to further improve the collison avoidance performance. After obtained the optimal SF and MF, 64% of rules has been reduced (from 125 rules to 45 rules), and a large number of real flight tests with a quadcopter have been done. The experimental results show that this approach precisely navigates the system to avoid the obstacle. To our best knowledge, this is the first work to present the optimized fuzzy controller for UAMVIS using Cross-Entropy method in Scaling Factors and Membership Functions optimization.

Hierarchical graph maps for visualization of collaborative recommender systems

In this paper we provide a method that allows the visualization of similarity relationships present between items of collaborative filtering recommender systems, as well as the relative importance of each of these. The objective is to offer visual representations of the recommender system?s set of items and of their relationships; these graphs show us where the most representative information can be found and which items are rated in a more similar way by the recommender system?s community of users. The visual representations achieved take the shape of phylogenetic trees, displaying the numerical similarity and the reliability between each pair of items considered to be similar. As a case study we provide the results obtained using the public database Movielens 1M, which contains 3900 movies.

A new label fusion method using graph cuts: application to hippocampus segmentation

The aim of this paper is to develop a probabilistic modeling framework for the segmentation of structures of interest from a collection of atlases. Given a subset of registered atlases into the target image for a particular Region of Interest (ROI), a statistical model of appearance and shape is computed for fusing the labels. Segmentations are obtained by minimizing an energy function associated with the proposed model, using a graph-cut technique. We test different label fusion methods on publicly available MR images of human brains.

Heterogeneous architecture for the optimization of large-scale graph processing data centres

Con el auge del Cloud Computing, las aplicaciones de proceso de datos han sufrido un incremento de demanda, y por ello ha cobrado importancia lograr m�ás eficiencia en los Centros de Proceso de datos. El objetivo de este trabajo es la obtenci�ón de herramientas que permitan analizar la viabilidad y rentabilidad de diseñar Centros de Datos especializados para procesamiento de datos, con una arquitectura, sistemas de refrigeraci�ón, etc. adaptados. Algunas aplicaciones de procesamiento de datos se benefician de las arquitecturas software, mientras que en otras puede ser m�ás eficiente un procesamiento con arquitectura hardware. Debido a que ya hay software con muy buenos resultados en el procesamiento de grafos, como el sistema XPregel, en este proyecto se realizará una arquitectura hardware en VHDL, implementando el algoritmo PageRank de Google de forma escalable. Se ha escogido este algoritmo ya que podr��á ser m�ás eficiente en arquitectura hardware, debido a sus características concretas que se indicaráan m�ás adelante. PageRank sirve para ordenar las p�áginas por su relevancia en la web, utilizando para ello la teorí��a de grafos, siendo cada página web un vértice de un grafo; y los enlaces entre páginas, las aristas del citado grafo. En este proyecto, primero se realizará un an�álisis del estado de la técnica. Se supone que la implementaci�ón en XPregel, un sistema de procesamiento de grafos, es una de las m�ás eficientes. Por ello se estudiará esta �ultima implementaci�ón. Sin embargo, debido a que Xpregel procesa, en general, algoritmos que trabajan con grafos; no tiene en cuenta ciertas caracterí��sticas del algoritmo PageRank, por lo que la implementaci�on no es �optima. Esto es debido a que en PageRank, almacenar todos los datos que manda un mismo v�értice es un gasto innecesario de memoria ya que todos los mensajes que manda un vértice son iguales entre sí e iguales a su PageRank. Se realizará el diseño en VHDL teniendo en cuenta esta caracter��ística del citado algoritmo,evitando almacenar varias veces los mensajes que son iguales. Se ha elegido implementar PageRank en VHDL porque actualmente las arquitecturas de los sistemas operativos no escalan adecuadamente. Se busca evaluar si con otra arquitectura se obtienen mejores resultados. Se realizará un diseño partiendo de cero, utilizando la memoria ROM de IPcore de Xillinx (Software de desarrollo en VHDL), generada autom�áticamente. Se considera hacer cuatro tipos de módulos para que as�� el procesamiento se pueda hacer en paralelo. Se simplificar�á la estructura de XPregel con el fin de intentar aprovechar la particularidad de PageRank mencionada, que hace que XPregel no le saque el m�aximo partido. Despu�és se escribirá el c�ódigo, realizando una estructura escalable, ya que en la computación intervienen millones de páginas web. A continuación, se sintetizar�á y se probará el código en una FPGA. El �ultimo paso será una evaluaci�ón de la implementaci�ón, y de posibles mejoras en cuanto al consumo.

UAS See-and-Avoid Strategy using a Fuzzy Logic Controller Optimized by Cross-Entropy in Scaling Factors and Membership Functions.

This work aims to develop a novel Cross-Entropy (CE) optimization-based fuzzy controller for Unmanned Aerial Monocular Vision-IMU System (UAMVIS) to solve the seeand-avoid problem using its accurate autonomous localization information. The function of this fuzzy controller is regulating the heading of this system to avoid the obstacle, e.g. wall. In the Matlab Simulink-based training stages, the Scaling Factor (SF) is adjusted according to the specified task firstly, and then the Membership Function (MF) is tuned based on the optimized Scaling Factor to further improve the collison avoidance performance. After obtained the optimal SF and MF, 64% of rules has been reduced (from 125 rules to 45 rules), and a large number of real flight tests with a quadcopter have been done. The experimental results show that this approach precisely navigates the system to avoid the obstacle. To our best knowledge, this is the first work to present the optimized fuzzy controller for UAMVIS using Cross-Entropy method in Scaling Factors and Membership Functions optimization.

Using the Cross-Entropy Method for Control Optimization: A Case Study of See-and-Avoid on Unmanned Aerial Vehicles

This paper presents an adaptation of the Cross-Entropy (CE) method to optimize fuzzy logic controllers. The CE is a recently developed optimization method based on a general Monte-Carlo approach to combinatorial and continuous multi-extremal optimization and importance sampling. This work shows the application of this optimization method to optimize the inputs gains, the location and size of the different membership functions' sets of each variable, as well as the weight of each rule from the rule's base of a fuzzy logic controller (FLC). The control system approach presented in this work was designed to command the orientation of an unmanned aerial vehicle (UAV) to modify its trajectory for avoiding collisions. An onboard looking forward camera was used to sense the environment of the UAV. The information extracted by the image processing algorithm is the only input of the fuzzy control approach to avoid the collision with a predefined object. Real tests with a quadrotor have been done to corroborate the improved behavior of the optimized controllers at different stages of the optimization process.

Energy-entropy-momentum time integration methods for coupled smooth dissipative problems

Esta tesis aborda la formulación, análisis e implementación de métodos numéricos de integración temporal para la solución de sistemas disipativos suaves de dimensión finita o infinita de manera que su estructura continua sea conservada. Se entiende por dichos sistemas aquellos que involucran acoplamiento termo-mecánico y/o efectos disipativos internos modelados por variables internas que siguen leyes continuas, de modo que su evolución es considerada suave. La dinámica de estos sistemas está gobernada por las leyes de la termodinámica y simetrías, las cuales constituyen la estructura que se pretende conservar de forma discreta. Para ello, los sistemas disipativos se describen geométricamente mediante estructuras metriplécticas que identifican claramente las partes reversible e irreversible de la evolución del sistema. Así, usando una de estas estructuras conocida por las siglas (en inglés) de GENERIC, la estructura disipativa de los sistemas es identificada del mismo modo que lo es la Hamiltoniana para sistemas conservativos. Con esto, métodos (EEM) con precisión de segundo orden que conservan la energía, producen entropía y conservan los impulsos lineal y angular son formulados mediante el uso del operador derivada discreta introducido para asegurar la conservación de la Hamiltoniana y las simetrías de sistemas conservativos. Siguiendo estas directrices, se formulan dos tipos de métodos EEM basados en el uso de la temperatura o de la entropía como variable de estado termodinámica, lo que presenta importantes implicaciones que se discuten a lo largo de esta tesis. Entre las cuales cabe destacar que las condiciones de contorno de Dirichlet son naturalmente impuestas con la formulación basada en la temperatura. Por último, se validan dichos métodos y se comprueban sus mejores prestaciones en términos de la estabilidad y robustez en comparación con métodos estándar. This dissertation is concerned with the formulation, analysis and implementation of structure-preserving time integration methods for the solution of the initial(-boundary) value problems describing the dynamics of smooth dissipative systems, either finite- or infinite-dimensional ones. Such systems are understood as those involving thermo-mechanical coupling and/or internal dissipative effects modeled by internal state variables considered to be smooth in the sense that their evolutions follow continuos laws. The dynamics of such systems are ruled by the laws of thermodynamics and symmetries which constitutes the structure meant to be preserved in the numerical setting. For that, dissipative systems are geometrically described by metriplectic structures which clearly identify the reversible and irreversible parts of their dynamical evolution. In particular, the framework known by the acronym GENERIC is used to reveal the systems' dissipative structure in the same way as the Hamiltonian is for conserving systems. Given that, energy-preserving, entropy-producing and momentum-preserving (EEM) second-order accurate methods are formulated using the discrete derivative operator that enabled the formulation of Energy-Momentum methods ensuring the preservation of the Hamiltonian and symmetries for conservative systems. Following these guidelines, two kind of EEM methods are formulated in terms of entropy and temperature as a thermodynamical state variable, involving important implications discussed throughout the dissertation. Remarkably, the formulation in temperature becomes central to accommodate Dirichlet boundary conditions. EEM methods are finally validated and proved to exhibit enhanced numerical stability and robustness properties compared to standard ones.

Pedestrian Motion Prediction: A Graph Based Approach

A novel pedestrian motion prediction technique is presented in this paper. Its main achievement regards to none previous observation, any knowledge of pedestrian trajectories nor the existence of possible destinations is required; hence making it useful for autonomous surveillance applications. Prediction only requires initial position of the pedestrian and a 2D representation of the scenario as occupancy grid. First, it uses the Fast Marching Method (FMM) to calculate the pedestrian arrival time for each position in the map and then, the likelihood that the pedestrian reaches those positions is estimated. The technique has been tested with synthetic and real scenarios. In all cases, accurate probability maps as well as their representative graphs were obtained with low computational cost.