Geometric diagnostics of complex patterns: Spiral defect chaos

Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biological systems, we present an automated approach that aims at characterizing quantitatively spiral-like elements in complex stripelike patterns. The approach provides the location of the spiral tip and the size of the spiral arms in terms of their arc length and their winding number. In addition, it yields the number of pattern components (Betti number of order 1), as well as their size and certain aspects of their shape. We apply the method to spiral defect chaos in thermally driven Rayleigh- Bénard convection and find that the arc length of spirals decreases monotonically with decreasing Prandtl number of the fluid and increasing heating. By contrast, the winding number of the spirals is nonmonotonic in the heating. The distribution function for the number of spirals is significantly narrower than a Poisson distribution. The distribution function for the winding number shows approximately an exponential decay. It depends only weakly on the heating, but strongly on the Prandtl number. Large spirals arise only for larger Prandtl numbers. In this regime the joint distribution for the spiral length and the winding number exhibits a three-peak structure, indicating the dominance of Archimedean spirals of opposite sign and relatively straight sections. For small Prandtl numbers the distribution function reveals a large number of small compact pattern components.

Correlation Dimension of Complex Networks

We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synthetic networks and real-world networks such as the world air-transportation network or urban networks, and provides a computationally fast way for estimating the dimensionality of networks which only relies on the local information provided by the walkers.

Development of a method of assessment of the problem-solving competence at the technical University of Madrid.

The competence evaluation promoted by the European High Education Area entails a very important methodological change that requires guiding support to help lecturers carry out this new and complex task. In this regard, the Technical University of Madrid (UPM, by its Spanish acronym) has financed a series of coordinated projects with the objective of developing a model for teaching and evaluating core competences and providing support to lecturers. This paper deals with the problem-solving competence. The first step has been to elaborate a guide for teachers to provide a homogeneous way to asses this competence. This guide considers several levels of acquisition of the competence and provides the rubrics to be applied for each one. The guide has been subsequently validated with several pilot experiences. In this paper we will explain the problem-solving assessment guide for teachers and will show the pilot experiences that has been carried out. We will finally justify the validity of the method to assess the problem-solving competence.

Development of a method of assessment of the problem-solving competency at the Technical University of Madrid

The competence evaluation promoted by the European High Education Area entails a very important methodological change that requires guiding support to help lecturers carry out this new and complex task. In this regard, the Technical University of Madrid (UPM, by its Spanish acronym) has financed a series of coordinated projects with the objective of developing a model for teaching and evaluating core competences and providing support to lecturers. This paper deals with the problem solving competence. The first step has been to elaborate a guide for teachers to provide an homogeneous way to asses this competence. This guide considers several levels of acquisition of the competence and provided the rubrics to be applied for each one. The guide has been subsequently validated with several pilot experiences. In this paper we will explain the problem-solving assessment guide for teachers and will show the pilot experiences that has been carried out. We will finally justify the validity of the method to assess the problem solving competence.

3D simulation of complex shading affecting PV systems taking benefit from the power of graphics cards developed for the video game industry

Shading reduces the power output of a photovoltaic (PV) system. The design engineering of PV systems requires modeling and evaluating shading losses. Some PV systems are affected by complex shading scenes whose resulting PV energy losses are very difficult to evaluate with current modeling tools. Several specialized PV design and simulation software include the possibility to evaluate shading losses. They generally possess a Graphical User Interface (GUI) through which the user can draw a 3D shading scene, and then evaluate its corresponding PV energy losses. The complexity of the objects that these tools can handle is relatively limited. We have created a software solution, 3DPV, which allows evaluating the energy losses induced by complex 3D scenes on PV generators. The 3D objects can be imported from specialized 3D modeling software or from a 3D object library. The shadows cast by this 3D scene on the PV generator are then directly evaluated from the Graphics Processing Unit (GPU). Thanks to the recent development of GPUs for the video game industry, the shadows can be evaluated with a very high spatial resolution that reaches well beyond the PV cell level, in very short calculation times. A PV simulation model then translates the geometrical shading into PV energy output losses. 3DPV has been implemented using WebGL, which allows it to run directly from a Web browser, without requiring any local installation from the user. This also allows taken full benefits from the information already available from Internet, such as the 3D object libraries. This contribution describes, step by step, the method that allows 3DPV to evaluate the PV energy losses caused by complex shading. We then illustrate the results of this methodology to several application cases that are encountered in the world of PV systems design. Keywords: 3D, modeling, simulation, GPU, shading, losses, shadow mapping, solar, photovoltaic, PV, WebGL

Effect of the curing conditions of concrete on the behaviour under freeze-thaw cycles*

The aim of this work is to relate the curing conditions of concrete and the addition of an air-entraining admixture with the damage caused by freeze–thaw cycles. In countries with a continental climate, the curing of concrete in summer is performed under climatic conditions of high temperature and low humidity, and during the winter the concrete suffers conditions of freeze–thaw, often accompanied by the use of de-icing salts. This paper shows the experimental results of the behaviour of concrete specimens cured under climatic summer conditions (high temperature and low humidity) and then subjected to freeze–thaw cycles. Curing of the specimens includes conditions of good and bad practice in relation to wetting and protection of the concrete. It also examines the effectiveness of using an air-entraining admixture in both cases. The experimental programme includes an evaluation of the mechanical properties of the concrete, the study of the cement hydration and the measurement of the volume and pore sizes of the concrete. These tests were performed before and after the application of the freeze–thaw cycles. The results obtained showed that the specimens without air-entraining admixture show a deterioration of mechanical properties after the freeze–thaw test. However, the inclusion of air bubbles benefits the behaviour of concrete against freeze–thaw cycles so even better mechanical properties after the test were observed. This anomalous behaviour is because the cement hydration process continues over the freeze–thaw tests, closing the pore structure. This aspect has been confirmed with the DTA and TG tests performed

Knowledge Discovery in Spectral Data by Means of Complex Networks

In the last decade, complex networks have widely been applied to the study of many natural and man-made systems, and to the extraction of meaningful information from the interaction structures created by genes and proteins. Nevertheless, less attention has been devoted to metabonomics, due to the lack of a natural network representation of spectral data. Here we define a technique for reconstructing networks from spectral data sets, where nodes represent spectral bins, and pairs of them are connected when their intensities follow a pattern associated with a disease. The structural analysis of the resulting network can then be used to feed standard data-mining algorithms, for instance for the classification of new (unlabeled) subjects. Furthermore, we show how the structure of the network is resilient to the presence of external additive noise, and how it can be used to extract relevant knowledge about the development of the disease.

Feature selection in the reconstruction of complex network representations of spectral data

Complex networks have been extensively used in the last decade to characterize and analyze complex systems, and they have been recently proposed as a novel instrument for the analysis of spectra extracted from biological samples. Yet, the high number of measurements composing spectra, and the consequent high computational cost, make a direct network analysis unfeasible. We here present a comparative analysis of three customary feature selection algorithms, including the binning of spectral data and the use of information theory metrics. Such algorithms are compared by assessing the score obtained in a classification task, where healthy subjects and people suffering from different types of cancers should be discriminated. Results indicate that a feature selection strategy based on Mutual Information outperforms the more classical data binning, while allowing a reduction of the dimensionality of the data set in two orders of magnitude

Collective Organization of Complex Networks: Emergent Scales, Vulnerability, and Targeting of Desired Dynamics

Cuando una colectividad de sistemas dinámicos acoplados mediante una estructura irregular de interacciones evoluciona, se observan dinámicas de gran complejidad y fenómenos emergentes imposibles de predecir a partir de las propiedades de los sistemas individuales. El objetivo principal de esta tesis es precisamente avanzar en nuestra comprensión de la relación existente entre la topología de interacciones y las dinámicas colectivas que una red compleja es capaz de mantener. Siendo este un tema amplio que se puede abordar desde distintos puntos de vista, en esta tesis se han estudiado tres problemas importantes dentro del mismo que están relacionados entre sí. Por un lado, en numerosos sistemas naturales y artificiales que se pueden describir mediante una red compleja la topología no es estática, sino que depende de la dinámica que se desarrolla en la red: un ejemplo son las redes de neuronas del cerebro. En estas redes adaptativas la propia topología emerge como consecuencia de una autoorganización del sistema. Para conocer mejor cómo pueden emerger espontáneamente las propiedades comúnmente observadas en redes reales, hemos estudiado el comportamiento de sistemas que evolucionan según reglas adaptativas locales con base empírica. Nuestros resultados numéricos y analíticos muestran que la autoorganización del sistema da lugar a dos de las propiedades más universales de las redes complejas: a escala mesoscópica, la aparición de una estructura de comunidades, y, a escala macroscópica, la existencia de una ley de potencias en la distribución de las interacciones en la red. El hecho de que estas propiedades aparecen en dos modelos con leyes de evolución cuantitativamente distintas que siguen unos mismos principios adaptativos sugiere que estamos ante un fenómeno que puede ser muy general, y estar en el origen de estas propiedades en sistemas reales. En segundo lugar, proponemos una medida que permite clasificar los elementos de una red compleja en función de su relevancia para el mantenimiento de dinámicas colectivas. En concreto, estudiamos la vulnerabilidad de los distintos elementos de una red frente a perturbaciones o grandes fluctuaciones, entendida como una medida del impacto que estos acontecimientos externos tienen en la interrupción de una dinámica colectiva. Los resultados que se obtienen indican que la vulnerabilidad dinámica es sobre todo dependiente de propiedades locales, por tanto nuestras conclusiones abarcan diferentes topologías, y muestran la existencia de una dependencia no trivial entre la vulnerabilidad y la conectividad de los elementos de una red. Finalmente, proponemos una estrategia de imposición de una dinámica objetivo genérica en una red dada e investigamos su validez en redes con diversas topologías que mantienen regímenes dinámicos turbulentos. Se obtiene como resultado que las redes heterogéneas (y la amplia mayora de las redes reales estudiadas lo son) son las más adecuadas para nuestra estrategia de targeting de dinámicas deseadas, siendo la estrategia muy efectiva incluso en caso de disponer de un conocimiento muy imperfecto de la topología de la red. Aparte de la relevancia teórica para la comprensión de fenómenos colectivos en sistemas complejos, los métodos y resultados propuestos podrán dar lugar a aplicaciones en sistemas experimentales y tecnológicos, como por ejemplo los sistemas neuronales in vitro, el sistema nervioso central (en el estudio de actividades síncronas de carácter patológico), las redes eléctricas o los sistemas de comunicaciones. ABSTRACT The time evolution of an ensemble of dynamical systems coupled through an irregular interaction scheme gives rise to dynamics of great of complexity and emergent phenomena that cannot be predicted from the properties of the individual systems. The main objective of this thesis is precisely to increase our understanding of the interplay between the interaction topology and the collective dynamics that a complex network can support. This is a very broad subject, so in this thesis we will limit ourselves to the study of three relevant problems that have strong connections among them. First, it is a well-known fact that in many natural and manmade systems that can be represented as complex networks the topology is not static; rather, it depends on the dynamics taking place on the network (as it happens, for instance, in the neuronal networks in the brain). In these adaptive networks the topology itself emerges from the self-organization in the system. To better understand how the properties that are commonly observed in real networks spontaneously emerge, we have studied the behavior of systems that evolve according to local adaptive rules that are empirically motivated. Our numerical and analytical results show that self-organization brings about two of the most universally found properties in complex networks: at the mesoscopic scale, the appearance of a community structure, and, at the macroscopic scale, the existence of a power law in the weight distribution of the network interactions. The fact that these properties show up in two models with quantitatively different mechanisms that follow the same general adaptive principles suggests that our results may be generalized to other systems as well, and they may be behind the origin of these properties in some real systems. We also propose a new measure that provides a ranking of the elements in a network in terms of their relevance for the maintenance of collective dynamics. Specifically, we study the vulnerability of the elements under perturbations or large fluctuations, interpreted as a measure of the impact these external events have on the disruption of collective motion. Our results suggest that the dynamic vulnerability measure depends largely on local properties (our conclusions thus being valid for different topologies) and they show a non-trivial dependence of the vulnerability on the connectivity of the network elements. Finally, we propose a strategy for the imposition of generic goal dynamics on a given network, and we explore its performance in networks with different topologies that support turbulent dynamical regimes. It turns out that heterogeneous networks (and most real networks that have been studied belong in this category) are the most suitable for our strategy for the targeting of desired dynamics, the strategy being very effective even when the knowledge on the network topology is far from accurate. Aside from their theoretical relevance for the understanding of collective phenomena in complex systems, the methods and results here discussed might lead to applications in experimental and technological systems, such as in vitro neuronal systems, the central nervous system (where pathological synchronous activity sometimes occurs), communication systems or power grids.

An interactive method of fuzzy probability elicitation in risk analysis

Expert knowledge is used to assign probabilities to events in many risk analysis models. However, experts sometimes find it hard to provide specific values for these probabilities, preferring to express vague or imprecise terms that are mapped using a previously defined fuzzy number scale. The rigidity of these scales generates bias in the probability elicitation process and does not allow experts to adequately express their probabilistic judgments. We present an interactive method for extracting a fuzzy number from experts that represents their probabilistic judgments for a given event, along with a quality measure of the probabilistic judgments, useful in a final information filtering and analysis sensitivity process.

Teaching based on the case method of building collective protection

One of the fundamental aspects in the adaptation of the teaching to the European higher education is changing based models of teacher education to models based on student learning. In this work we present an educational experience developed with the teaching method based on the case method, with a clearly multidisciplinary. The experience has been developed in the teaching of analysis and verification of safety rails. This is a multidisciplinary field that presents great difficulties during their teaching. The use of the case method has given good results in the competences achieved by students

A combined algorithm for analyzing structural controllability and observability of complex networks

In this paper a combined algorithm for analyzing structural controllability and observability of complex networks is presented. The algorithm addresses the two fundamental properties to guarantee structural controllability of a system: the absence of dilations and the accessibility of all nodes. The first problem is reformulated as a Maximum Matching search and it is addressed via the Hopcroft- Karp algorithm; the second problem is solved via a new wiring algorithm. Both algorithms can be combined to efficiently determine the number of required controllers and observers as well as the new required connections in order to guarantee controllability and observability in real complex networks. An application to a Twitter social network with over 100,000 nodes illustrates the proposed algorithms.

On the localization of the personalized PageRank of complex networks

In this paper new results on personalized PageRank are shown. We consider directed graphs that may contain dangling nodes. The main result presented gives an analytical characterization of all the possible values of the personalized PageRank for any node.We use this result to give a theoretical justification of a recent model that uses the personalized PageRank to classify users of Social Networks Sites. We introduce new concepts concerning competitivity and leadership in complex networks. We also present some theoretical techniques to locate leaders and competitors which are valid for any personalization vector and by using only information related to the adjacency matrix of the graph and the distribution of its dangling nodes.

Mathematical foundations for efficient structural controllability and observability analysis of complex systems

The relationship between structural controllability and observability of complex systems is studied. Algebraic and graph theoretic tools are combined to prove the extent of some controller/observer duality results. Two types of control design problems are addressed and some fundamental theoretical results are provided. In addition new algorithms are presented to compute optimal solutions for monitoring large scale real networks.

Feasibility assessment of the interactive use of a Monte Carlo algorithm in treatment planning for intraoperative electron radiation therapy

This work analysed the feasibility of using a fast, customized Monte Carlo (MC) method to perform accurate computation of dose distributions during pre- and intraplanning of intraoperative electron radiation therapy (IOERT) procedures. The MC method that was implemented, which has been integrated into a specific innovative simulation and planning tool, is able to simulate the fate of thousands of particles per second, and it was the aim of this work to determine the level of interactivity that could be achieved. The planning workflow enabled calibration of the imaging and treatment equipment, as well as manipulation of the surgical frame and insertion of the protection shields around the organs at risk and other beam modifiers. In this way, the multidisciplinary team involved in IOERT has all the tools necessary to perform complex MC dosage simulations adapted to their equipment in an efficient and transparent way. To assess the accuracy and reliability of this MC technique, dose distributions for a monoenergetic source were compared with those obtained using a general-purpose software package used widely in medical physics applications. Once accuracy of the underlying simulator was confirmed, a clinical accelerator was modelled and experimental measurements in water were conducted. A comparison was made with the output from the simulator to identify the conditions under which accurate dose estimations could be obtained in less than 3 min, which is the threshold imposed to allow for interactive use of the tool in treatment planning. Finally, a clinically relevant scenario, namely early-stage breast cancer treatment, was simulated with pre- and intraoperative volumes to verify that it was feasible to use the MC tool intraoperatively and to adjust dose delivery based on the simulation output, without compromising accuracy. The workflow provided a satisfactory model of the treatment head and the imaging system, enabling proper configuration of the treatment planning system and providing good accuracy in the dosage simulation.