Geometric Study of the Weak Equilibrium in a Weighted Case for a Two-Dimensional Competition Game

In this work, an improvement of the results presented by [1] Abellanas et al. (Weak Equilibrium in a Spatial Model. International Journal of Game Theory, 40(3), 449-459) is discussed. Concretely, this paper investigates an abstract game of competition between two players that want to earn the maximum number of points from a finite set of points in the plane. It is assumed that the distribution of these points is not uniform, so an appropriate weight to each position is assigned. A definition of equilibrium which is weaker than the classical one is included in order to avoid the uniqueness of the equilibrium position typical of the Nash equilibrium in these kinds of games. The existence of this approximated equilibrium in the game is analyzed by means of computational geometry techniques.

Técnicas avanzadas de metrología dimensional indirecta mediante el empleo de máquinas de medición por visión en entornos industriales. Modelo para la estimación de incertidumbres

Esta tesis contiene una investigación detallada sobre las características y funcionamiento de las máquinas de medición por visión. El objetivo fundamental es modelar su comportamiento y dotarlas de trazabilidad metrológica bajo cualquier condición de medida. Al efecto, se ha realizado un exhaustivo análisis de los elementos que conforman su cadena de medición, a saber: sistema de iluminación, estructura, lentes y objetivos, cámara, software de tratamiento de imágenes y software de cálculo. Se han definido modelos físico-matemáticos, de desarrollo propio, capaces de simular con fiabilidad el comportamiento de los elementos citados, agrupados, a efectos de análisis numérico, en dos subsistemas denominados: de visión y mecánico. Se han implementado procedimientos de calibración genuinos para ambos subsistemas mediante el empleo de patrones ópticos. En todos los casos se ha podido determinar la incertidumbre asociada a los diferentes parámetros involucrados, garantizando la trazabilidad metrológica de los resultados. Los distintos modelos desarrollados han sido implementados en Matlab®. Se ha verificado su validez empleando valores sintéticos obtenidos a partir de simulaciones informáticas y también con imágenes reales capturadas en el laboratorio. El estudio experimental y validación definitiva de los resultados se ha realizado en el Laboratorio de Longitud del Centro Español de Metrología y en el Laboratorio de Metrología Dimensional de la ETS de Ingeniería y Diseño Industrial de la UPM. Los modelos desarrollados se han aplicado a dos máquinas de medición por visión de diferentes características constructivas y metrológicas. Empleando dichas máquinas se han medido distintas piezas, pertenecientes a los ámbitos mecánico y oftalmológico. Los resultados obtenidos han permitido la completa caracterización dimensional de dichas piezas y la determinación del cumplimiento de las especificaciones metrológicas en todos los casos, incluyendo longitudes, formas y ángulos. ABSTRACT This PhD thesis contains a detailed investigation of characteristics and performance of the optical coordinate measurement machines. The main goal is to model their behaviour and provide metrological traceability to them under any measurement conditions. In fact, a thorough analysis of the elements which form the measuring chain, i.e.: lighting system, structure, lenses and objectives, camera, image processing software and coordinate metrology software has conducted. Physical-mathematical models, of self-developed, able to simulate with reliability the behavior of the above elements, grouped, for the purpose of numerical analysis, in two subsystems called: “vision subsystem” and “mechanical subsystem”, have been defined. Genuine calibration procedures for both subsystems have been implemented by use of optical standards. In all cases, it has been possible to determine the uncertainty associated with the different parameters involved, ensuring metrological traceability of results. Different developed models have been implemented in Matlab®. Their validity has been verified using synthetic values obtained from computer simulations and also with real images captured in laboratory. The experimental study and final validation of the results was carried out in the Length Laboratory of “Centro Español de Metrología” and Dimensional Metrology Laboratory of the “Escuela Técnica Superior de Ingeniería y Diseño Industrial” of the UPM. The developed models have been applied to two optical coordinate measurement machines with different construction and metrological characteristics. Using such machines, different parts, belonging to the mechanical and ophthalmologist areas, have been measured. The obtained results allow the full dimensional characterization of such parts and determination of compliance with metrological specifications in all cases, including lengths, shapes and angles.

One-dimensional self-similar solution of the dynamics of axisymmetric slender liquid bridges

In this paper the dynamics of axisymmetric, slender, viscous liquid bridges having volume close to the cylindrical one, and subjected to a small gravitational field parallel to the axis of the liquid bridge, is considered within the context of one-dimensional theories. Although the dynamics of liquid bridges has been treated through a numerical analysis in the inviscid case, numerical methods become inappropriate to study configurations close to the static stability limit because the evolution time, and thence the computing time, increases excessively. To avoid this difficulty, the problem of the evolution of these liquid bridges has been attacked through a nonlinear analysis based on the singular perturbation method and, whenever possible, the results obtained are compared with the numerical ones.

One-dimensional linear analysis of the compound jet

The stability of an infinitely long compound liquid column is analysed by using a one-dimensional inviscid slice model. Results obtained from this one-dimensional linear analysis are applicable to the study of compound capillary jets, which are used in the ink-jet printing technique. Stability limits and the breaking regimes of such fluid configurations are established, and, whenever possible, theoretical results are compared with experimental ones.

A wind tunnel two-dimensional parametric investigation of biplane configurations

This paper presents an experimental and systematic investigation about how geometric parameters on a biplane configuration have an influence on aerodynamic parameters. This experimental investigation has been developed in a two-dimensional approach. Theoretical studies about biplanes configurations have been developed in the past, but there is not enough information about experimental wind tunnel data at low Reynolds number. This two-dimensional study is a first step to further tridimensional investigations about the box wing configuration. The main objective of the study is to find the relationships between the geometrical parameters which present the best aerodynamic behavior: the highest lift, the lowest drag and the lowest slope of the pitching moment. A tridimensional wing-box model will be designed following the pattern of the two dimensional study conclusions. It will respond to the geometrical relationships that have been considered to show the better aerodynamic behavior. This box-wing model will be studied in the aim of comparing the advantages and disadvantages between this biplane configuration and the plane configuration, looking for implementing the box-wing in the UAV?s field. Although the box wing configuration has been used in a small number of existing UAV, prestigious researchers have found it as a field of high aerodynamic and structural potential.

Three-dimensional mapping of real environments for cognitive robots navigation

Abstract The development of cognitive robots needs a strong “sensorial” support which should allow it to perceive the real world for interacting with it properly. Therefore the development of efficient visual-processing software to be equipped in effective artificial agents is a must. In this project we study and develop a visual-processing software that will work as the “eyes” of a cognitive robot. This software performs a three-dimensional mapping of the robot’s environment, providing it with the essential information required to make proper decisions during its navigation. Due to the complexity of this objective we have adopted the Scrum methodology in order to achieve an agile development process, which has allowed us to correct and improve in a fast way the successive versions of the product. The present project is structured in Sprints, which cover the different stages of the software development based on the requirements imposed by the robot and its real necessities. We have initially explored different commercial devices oriented to the acquisition of the required visual information, adopting the Kinect Sensor camera (Microsoft) as the most suitable option. Later on, we have studied the available software to manage the obtained visual information as well as its integration with the robot’s software, choosing the high-level platform Matlab as the common nexus to join the management of the camera, the management of the robot and the implementation of the behavioral algorithms. During the last stages the software has been developed to include the fundamental functionalities required to process the real environment, such as depth representation, segmentation, and clustering. Finally the software has been optimized to exhibit real-time processing and a suitable performance to fulfill the robot’s requirements during its operation in real situations.

Transverse galloping of two-dimensional bodies having a rhombic cross-section

Transverse galloping is a type of aeroelastic instability characterized by oscillations perpendicular to wind direction, large amplitude and low frequency, which appears in some elastic two-dimensional bluff bodies when they are subjected to an incident flow, provided that the flow velocity exceeds a threshold critical value. Understanding the galloping phenomenon of different cross-sectional geometries is important in a number of engineering applications: for energy harvesting applications the interest relies on strongly unstable configurations but in other cases the purpose is to avoid this type of aeroelastic phenomenon. In this paper the aim is to analyze the transverse galloping behavior of rhombic bodies to understand, on the one hand, the dependence of the instability with a geometrical parameter such as the relative thickness and, on the other hand, why this cross-section shape, that is generally unstable, shows a small range of relative thickness values where it is stable. Particularly, the non-galloping rhombus-shaped prism?s behavior is revised through wind tunnel experiments. The bodies are allowed to freely move perpendicularly to the incoming flow and the amplitude of movement and pressure distributions on the surfaces is measured.

One-dimensional linear analysis of the liquid injection or removal in a liquid bridge

The filling-withdrawal process of a long liquid bridge is analyzed using a one-dimensional linearized model for the dynamics of the liquid column. To carry out this study, a well-known standard operational method (Laplace transform) has been used, and time variation of both liquid velocity field and interface shape are obtained.

Multi-dimensional classification of GABAergic interneurons with Bayesian network-modeled label uncertainty

Abstract Interneuron classification is an important and long-debated topic in neuroscience. A recent study provided a data set of digitally reconstructed interneurons classified by 42 leading neuroscientists according to a pragmatic classification scheme composed of five categorical variables, namely, of the interneuron type and four features of axonal morphology. From this data set we now learned a model which can classify interneurons, on the basis of their axonal morphometric parameters, into these five descriptive variables simultaneously. Because of differences in opinion among the neuroscientists, especially regarding neuronal type, for many interneurons we lacked a unique, agreed-upon classification, which we could use to guide model learning. Instead, we guided model learning with a probability distribution over the neuronal type and the axonal features, obtained, for each interneuron, from the neuroscientists’ classification choices. We conveniently encoded such probability distributions with Bayesian networks, calling them label Bayesian networks (LBNs), and developed a method to predict them. This method predicts an LBN by forming a probabilistic consensus among the LBNs of the interneurons most similar to the one being classified. We used 18 axonal morphometric parameters as predictor variables, 13 of which we introduce in this paper as quantitative counterparts to the categorical axonal features. We were able to accurately predict interneuronal LBNs. Furthermore, when extracting crisp (i.e., non-probabilistic) predictions from the predicted LBNs, our method outperformed related work on interneuron classification. Our results indicate that our method is adequate for multi-dimensional classification of interneurons with probabilistic labels. Moreover, the introduced morphometric parameters are good predictors of interneuron type and the four features of axonal morphology and thus may serve as objective counterparts to the subjective, categorical axonal features.

Three-dimensional distribution of cortical synapses: a replicated point pattern-based analysis

The biggest problem when analyzing the brain is that its synaptic connections are extremely complex. Generally, the billions of neurons making up the brain exchange information through two types of highly specialized structures: chemical synapses (the vast majority) and so-called gap junctions (a substrate of one class of electrical synapse). Here we are interested in exploring the three-dimensional spatial distribution of chemical synapses in the cerebral cortex. Recent research has showed that the three-dimensional spatial distribution of synapses in layer III of the neocortex can be modeled by a random sequential adsorption (RSA) point process, i.e., synapses are distributed in space almost randomly, with the only constraint that they cannot overlap. In this study we hypothesize that RSA processes can also explain the distribution of synapses in all cortical layers. We also investigate whether there are differences in both the synaptic density and spatial distribution of synapses between layers. Using combined focused ion beam milling and scanning electron microscopy (FIB/SEM), we obtained three-dimensional samples from the six layers of the rat somatosensory cortex and identified and reconstructed the synaptic junctions. A total volume of tissue of approximately 4500μm3 and around 4000 synapses from three different animals were analyzed. Different samples, layers and/or animals were aggregated and compared using RSA replicated spatial point processes. The results showed no significant differences in the synaptic distribution across the different rats used in the study. We found that RSA processes described the spatial distribution of synapses in all samples of each layer. We also found that the synaptic distribution in layers II to VI conforms to a common underlying RSA process with different densities per layer. Interestingly, the results showed that synapses in layer I had a slightly different spatial distribution from the other layers.

Multi-dimensional classification of GABAergic interneurons with Bayesian network-modeled label uncertainty

Interneuron classification is an important and long-debated topic in neuroscience. A recent study provided a data set of digitally reconstructed interneurons classified by 42 leading neuroscientists according to a pragmatic classification scheme composed of five categorical variables, namely, of the interneuron type and four features of axonal morphology. From this data set we now learned a model which can classify interneurons, on the basis of their axonal morphometric parameters, into these five descriptive variables simultaneously. Because of differences in opinion among the neuroscientists, especially regarding neuronal type, for many interneurons we lacked a unique, agreed-upon classification, which we could use to guide model learning. Instead, we guided model learning with a probability distribution over the neuronal type and the axonal features, obtained, for each interneuron, from the neuroscientists’ classification choices. We conveniently encoded such probability distributions with Bayesian networks, calling them label Bayesian networks (LBNs), and developed a method to predict them. This method predicts an LBN by forming a probabilistic consensus among the LBNs of the interneurons most similar to the one being classified. We used 18 axonal morphometric parameters as predictor variables, 13 of which we introduce in this paper as quantitative counterparts to the categorical axonal features. We were able to accurately predict interneuronal LBNs. Furthermore, when extracting crisp (i.e., non-probabilistic) predictions from the predicted LBNs, our method outperformed related work on interneuron classification. Our results indicate that our method is adequate for multi-dimensional classification of interneurons with probabilistic labels. Moreover, the introduced morphometric parameters are good predictors of interneuron type and the four features of axonal morphology and thus may serve as objective counterparts to the subjective, categorical axonal features.

Multi-dimensional classification with super-classes

The multi-dimensional classification problem is a generalisation of the recently-popularised task of multi-label classification, where each data instance is associated with multiple class variables. There has been relatively little research carried out specific to multi-dimensional classification and, although one of the core goals is similar (modelling dependencies among classes), there are important differences; namely a higher number of possible classifications. In this paper we present method for multi-dimensional classification, drawing from the most relevant multi-label research, and combining it with important novel developments. Using a fast method to model the conditional dependence between class variables, we form super-class partitions and use them to build multi-dimensional learners, learning each super-class as an ordinary class, and thus explicitly modelling class dependencies. Additionally, we present a mechanism to deal with the many class values inherent to super-classes, and thus make learning efficient. To investigate the effectiveness of this approach we carry out an empirical evaluation on a range of multi-dimensional datasets, under different evaluation metrics, and in comparison with high-performing existing multi-dimensional approaches from the literature. Analysis of results shows that our approach offers important performance gains over competing methods, while also exhibiting tractable running time.

Predicting EQ-5D from the Parkinson's disease questionnaire PDQ-8 using multi-dimensional Bayesian network classifiers

The impact of the Parkinson's disease and its treatment on the patients' health-related quality of life can be estimated either by means of generic measures such as the european quality of Life-5 Dimensions (EQ-5D) or specific measures such as the 8-item Parkinson's disease questionnaire (PDQ-8). In clinical studies, PDQ-8 could be used in detriment of EQ-5D due to the lack of resources, time or clinical interest in generic measures. Nevertheless, PDQ-8 cannot be applied in cost-effectiveness analyses which require generic measures and quantitative utility scores, such as EQ-5D. To deal with this problem, a commonly used solution is the prediction of EQ-5D from PDQ-8. In this paper, we propose a new probabilistic method to predict EQ-5D from PDQ-8 using multi-dimensional Bayesian network classifiers. Our approach is evaluated using five-fold cross-validation experiments carried out on a Parkinson's data set containing 488 patients, and is compared with two additional Bayesian network-based approaches, two commonly used mapping methods namely, ordinary least squares and censored least absolute deviations, and a deterministic model. Experimental results are promising in terms of predictive performance as well as the identification of dependence relationships among EQ-5D and PDQ-8 items that the mapping approaches are unable to detect

Efficient Monte Carlo methods for multi-dimensional learning with classifier chains

Multi-dimensional classification (MDC) is the supervised learning problem where an instance is associated with multiple classes, rather than with a single class, as in traditional classification problems. Since these classes are often strongly correlated, modeling the dependencies between them allows MDC methods to improve their performance – at the expense of an increased computational cost. In this paper we focus on the classifier chains (CC) approach for modeling dependencies, one of the most popular and highest-performing methods for multi-label classification (MLC), a particular case of MDC which involves only binary classes (i.e., labels). The original CC algorithm makes a greedy approximation, and is fast but tends to propagate errors along the chain. Here we present novel Monte Carlo schemes, both for finding a good chain sequence and performing efficient inference. Our algorithms remain tractable for high-dimensional data sets and obtain the best predictive performance across several real data sets.

Aportación de la monitorización mediante redes de sensores y técnicas no invasivas para la conservación preventiva del Patrimonio

La presente tesis doctoral presenta una serie de estudios en el campo del patrimonio basados en metodologías de monitorización mediante redes de sensores y técnicas no invasivas con el objetivo de realizar nuevas aportaciones a la conservación preventiva mediante el seguimiento de los daños de deterioro o la prevención de los mismos. Las metodologías de monitorización mediante el despliegue de redes tridimensionales basadas en data loggers abordan estudios microclimáticos, de confort y energéticos a corto plazo, donde se establecen conclusiones relativas a la eficiencia energética de tres sistemas de calefacción muy utilizados en iglesias de la región centro de la Península Ibérica, abordando aspectos de afección de los mismos en el confort de los ocupantes o en el deterioro de los elementos patrimoniales o constructivos. Se desplegaron además distintas plataformas de redes de sensores inalámbricas procediendo a analizar en esta tesis cuál es la que presenta mejores resultados en el ámbito del patrimonio con el objetivo de una monitorización a largo plazo y considerando aspectos de comunicaciones, consumo y configuración de las redes. Una vez conocida la plataforma que presenta mejores resultados comparativos se muestra una metodología de estudio de la calidad de las comunicaciones en múltiples escenarios de patrimonio cultural y natural con la misma, que servirá para establecer una serie de aspectos a considerar en el despliegue de redes de sensores inalámbricas en futuros escenarios a monitorizar. Al igual que ocurre con las redes de sensores basadas en data loggers, las tareas de monitorización desarrolladas en esta tesis mediante el despliegue de las distintas plataformas inalámbricas ha permitido la detección de numerosos fenómenos de deterioro que son descritos a lo largo de la investigación y cuyo seguimiento supone una aportación a la prevención de daños en los distintos escenarios. Asimismo en el desarrollo de la tesis se realiza una aportación para la conservación preventiva mediante la monitorización con distintas técnicas no invasivas como la termografía infrarroja, las medidas de humedad superficial mediante protimeter, las técnicas de prospección de resistividad eléctrica de alta resolución o la prospección georradar. De este modo se desarrollan distintas aportaciones y conclusiones acerca de las ventajas y/o limitaciones de uso de las mismas analizando la idoneidad de aplicar cada una de ellas en distintas fases de análisis o con distintas capacidades de detección o caracterización de los daños. El estudio de imbricación de dichas técnicas ha sido desarrollado en un escenario real que presenta graves daños por humedad, habiendo sido posible la caracterización del origen de los mismos. ABSTRACT This doctoral dissertation discusses field research conducted to monitor heritage assets with sensor networks and other non-invasive techniques. The aim pursued was to contribute to conservation by tracking or preventing decay-induced damage. Monitoring methodologies based on three-dimensional data logger networks were used in short-term micro-climatic, comfort and energy studies to draw conclusions about the energy efficiency of three heating systems widely used in central Iberian churches. The impact of these systems on occupant comfort and decay of heritage or built elements was also explored. Different wireless sensor platforms were deployed and analysed to determine which delivered the best results in the context of long-term heritage monitoring from the standpoints of communications, energy demand and network architecture. A methodology was subsequently designed to study communication quality in a number of cultural and natural heritage scenarios and help establish the considerations to be borne in mind when deploying wireless sensor networks for heritage monitoring in future. As in data logger-based sensor networks, the monitoring conducted in this research with wireless platforms identified many instances of decay, described hereunder. Tracking those situations will help prevent damage in the respective scenarios. The research also contributes to preventive conservation based on non-invasive monitoring using techniques such as infrared thermography, protimeter-based surface damp measurements, high resolution electrical resistivity surveys and georadar analysis. The conclusions drawn address the advantages and drawbacks of each technique and its suitability for the various phases of analysis and capacity to detect or characterise damage. This dissertation also describes the intermeshed usage of these techniques that led to the identification of the origin of severe damp-induced damage in a real scenario.