Invariant barriers to reactive front propagation in fluid flows

We present theory and experiments on the dynamics of reaction fronts in two-dimensional, vortex-dominated flows, for both time-independent and periodically driven cases. We find that the front propagation process is controlled by one-sided barriers that are either fixed in the laboratory frame (time-independent flows) or oscillate periodically (periodically driven flows). We call these barriers burning invariant manifolds (BIMs), since their role in front propagation is analogous to that of invariant manifolds in the transport and mixing of passive impurities under advection. Theoretically, the BIMs emerge from a dynamical systems approach when the advection-reaction-diffusion dynamics is recast as an ODE for front element dynamics. Experimentally, we measure the location of BIMs for several laboratory flows and confirm their role as barriers to front propagation.

ANALYSIS AND VISUALIZATION OF FLOW FIELDS USING INFORMATION-THEORETIC TECHNIQUES AND GRAPH-BASED REPRESENTATIONS

Three-dimensional flow visualization plays an essential role in many areas of science and engineering, such as aero- and hydro-dynamical systems which dominate various physical and natural phenomena. For popular methods such as the streamline visualization to be effective, they should capture the underlying flow features while facilitating user observation and understanding of the flow field in a clear manner. My research mainly focuses on the analysis and visualization of flow fields using various techniques, e.g. information-theoretic techniques and graph-based representations. Since the streamline visualization is a popular technique in flow field visualization, how to select good streamlines to capture flow patterns and how to pick good viewpoints to observe flow fields become critical. We treat streamline selection and viewpoint selection as symmetric problems and solve them simultaneously using the dual information channel [81]. To the best of my knowledge, this is the first attempt in flow visualization to combine these two selection problems in a unified approach. This work selects streamline in a view-independent manner and the selected streamlines will not change for all viewpoints. My another work [56] uses an information-theoretic approach to evaluate the importance of each streamline under various sample viewpoints and presents a solution for view-dependent streamline selection that guarantees coherent streamline update when the view changes gradually. When projecting 3D streamlines to 2D images for viewing, occlusion and clutter become inevitable. To address this challenge, we design FlowGraph [57, 58], a novel compound graph representation that organizes field line clusters and spatiotemporal regions hierarchically for occlusion-free and controllable visual exploration. We enable observation and exploration of the relationships among field line clusters, spatiotemporal regions and their interconnection in the transformed space. Most viewpoint selection methods only consider the external viewpoints outside of the flow field. This will not convey a clear observation when the flow field is clutter on the boundary side. Therefore, we propose a new way to explore flow fields by selecting several internal viewpoints around the flow features inside of the flow field and then generating a B-Spline curve path traversing these viewpoints to provide users with closeup views of the flow field for detailed observation of hidden or occluded internal flow features [54]. This work is also extended to deal with unsteady flow fields. Besides flow field visualization, some other topics relevant to visualization also attract my attention. In iGraph [31], we leverage a distributed system along with a tiled display wall to provide users with high-resolution visual analytics of big image and text collections in real time. Developing pedagogical visualization tools forms my other research focus. Since most cryptography algorithms use sophisticated mathematics, it is difficult for beginners to understand both what the algorithm does and how the algorithm does that. Therefore, we develop a set of visualization tools to provide users with an intuitive way to learn and understand these algorithms.

Barry Saltzman and the Theory of Climate

Barry Saltzman was a giant in the fields of meteorology and climate science. A leading figure in the study of weather and climate for over 40 yr, he has frequently been referred to as the "father of modern climate theory." Ahead of his time in many ways, Saltzman made significant contributions to our understanding of the general circulation and spectral energetics budget of the atmosphere, as well as climate change across a wide spectrum of time scales. In his endeavor to develop a unified theory of how the climate system works, lie played a role in the development of energy balance models, statistical dynamical models, and paleoclimate dynamical models. He was a pioneer in developing meteorologically motivated dynamical systems, including the progenitor of Lorenz's famous chaos model. In applying his own dynamical-systems approach to long-term climate change, he recognized the potential for using atmospheric general circulation models in a complimentary way. In 1998, he was awarded the Carl-Gustaf Rossby medal, the highest honor of the American Meteorological Society "for his life-long contributions to the study of the global circulation and the evolution of the earth's climate." In this paper, the authors summarize and place into perspective some of the most significant contributions that Barry Saltzman made during his long and distinguished career. This short review also serves as an introduction to the papers in this special issue of the Journal of Climate dedicated to Barry's memory.

Early dysfunction of functional connectivity in healthy elderly with subjective memory complaints

It is still an open question whether subjective memory complaints (SMC) can actually be considered to be clinically relevant predictors for the development of an objective memory impairment and even dementia. There is growing evidence that suggests that SMC are associated with an increased risk of dementia and with the presence of biological correlates of early Alzheimer's disease. In this paper, in order to shed some light on this issue, we try to discern whether subjects with SMC showed a different profile of functional connectivity compared with subjects with mild cognitive impairment (MCI) and healthy elderly subjects. In the present study, we compare the degree of synchronization of brain signals recorded with magnetoencephalography between three groups of subjects (56 in total): 19 with MCI, 12 with SMC and 25 healthy controls during a memory task. Synchronization likelihood, an index based on the theory of nonlinear dynamical systems, was used to measure functional connectivity. Briefly, results show that subjects with SMC have a very similar pattern of connectivity to control group, but on average, they present a lower synchronization value. These results could indicate that SMC are representing an initial stage with a hypo-synchronization (in comparison with the control group) where the brain system is still not compensating for the failing memory networks, but behaving as controls when compared with the MCI subjects.

Analytical properties of horizontal visibility graphs in the Feigenbaum scenario

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here, we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree distributions, mean distances, clustering coefficients, etc., associated to the bifurcation cascades and their accumulation points. We describe how the resultant families of graphs can be framed into a renormalization group scheme in which fixed-point graphs reveal their scaling properties. These fixed points are then re-derived from an entropy optimization process defined for the graph sets, confirming a suggested connection between renormalization group and entropy optimization. Finally, we provide analytical and numerical results for the graph entropy and show that it emulates the Lyapunov exponent of the map independently of its sign.

Approximate entropy of network parameters

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.

A Lagrangian descriptor applied to the Kuroshio current

The understanding of the circulation of ocean currents, the exchange of CO2 between atmosphere and oceans, and the in uence of the oceans on the distribution of heat on a global scale is key to our ability to predict and assess the future evolution of climate.

Computational Methods for Identification of Vibrating Structures

System identification deals with the problem of building mathematical models of dynamical systems based on observed data from the system" [1]. In the context of civil engineering, the system refers to a large scale structure such as a building, bridge, or an offshore structure, and identification mostly involves the determination of modal parameters (the natural frequencies, damping ratios, and mode shapes). This paper presents some modal identification results obtained using a state-of-the-art time domain system identification method (data-driven stochastic subspace algorithms [2]) applied to the output-only data measured in a steel arch bridge. First, a three dimensional finite element model was developed for the numerical analysis of the structure using ANSYS. Modal analysis was carried out and modal parameters were extracted in the frequency range of interest, 0-10 Hz. The results obtained from the finite element modal analysis were used to determine the location of the sensors. After that, ambient vibration tests were conducted during April 23-24, 2009. The response of the structure was measured using eight accelerometers. Two stations of three sensors were formed (triaxial stations). These sensors were held stationary for reference during the test. The two remaining sensors were placed at the different measurement points along the bridge deck, in which only vertical and transversal measurements were conducted (biaxial stations). Point estimate and interval estimate have been carried out in the state space model using these ambient vibration measurements. In the case of parametric models (like state space), the dynamic behaviour of a system is described using mathematical models. Then, mathematical relationships can be established between modal parameters and estimated point parameters (thus, it is common to use experimental modal analysis as a synonym for system identification). Stable modal parameters are found using a stabilization diagram. Furthermore, this paper proposes a method for assessing the precision of estimates of the parameters of state-space models (confidence interval). This approach employs the nonparametric bootstrap procedure [3] and is applied to subspace parameter estimation algorithm. Using bootstrap results, a plot similar to a stabilization diagram is developed. These graphics differentiate system modes from spurious noise modes for a given order system. Additionally, using the modal assurance criterion, the experimental modes obtained have been compared with those evaluated from a finite element analysis. A quite good agreement between numerical and experimental results is observed.

HERMES: A user-friendly connectivity analysis software

The analysis of the interdependence between time series has become an important field of research, mainly as a result of advances in the characterization of dynamical systems from the signals they produce, and the introduction of concepts such as Generalized (GS) and Phase synchronization (PS). This increase in the number of approaches to tackle the existence of the so-called functional (FC) and effective connectivity (EC) (Friston 1994) between two, (or among many) neural networks, along with their mathematical complexity, makes it desirable to arrange them into a unified toolbox, thereby allowing neuroscientists, neurophysiologists and researchers from related fields to easily access and make use of them.

HERMES: Towards an Integrated Toolbox to Characterize Functional and Effective Brain Connectivity

The analysis of the interdependence between time series has become an important field of research in the last years, mainly as a result of advances in the characterization of dynamical systems from the signals they produce, the introduction of concepts such as generalized and phase synchronization and the application of information theory to time series analysis. In neurophysiology, different analytical tools stemming from these concepts have added to the ‘traditional’ set of linear methods, which includes the cross-correlation and the coherency function in the time and frequency domain, respectively, or more elaborated tools such as Granger Causality. This increase in the number of approaches to tackle the existence of functional (FC) or effective connectivity (EC) between two (or among many) neural networks, along with the mathematical complexity of the corresponding time series analysis tools, makes it desirable to arrange them into a unified-easy-to-use software package. The goal is to allow neuroscientists, neurophysiologists and researchers from related fields to easily access and make use of these analysis methods from a single integrated toolbox. Here we present HERMES (http://hermes.ctb.upm.es), a toolbox for the Matlab® environment (The Mathworks, Inc), which is designed to study functional and effective brain connectivity from neurophysiological data such as multivariate EEG and/or MEG records. It includes also visualization tools and statistical methods to address the problem of multiple comparisons. We believe that this toolbox will be very helpful to all the researchers working in the emerging field of brain connectivity analysis.

Modelización de series temporales complejas: de las redes de telecomunicación a los mercados financieros

Este trabajo aborda el problema de modelizar sistemas din´amicos reales a partir del estudio de sus series temporales, usando una formulaci´on est´andar que pretende ser una abstracci´on universal de los sistemas din´amicos, independientemente de su naturaleza determinista, estoc´astica o h´ıbrida. Se parte de modelizaciones separadas de sistemas deterministas por un lado y estoc´asticos por otro, para converger finalmente en un modelo h´ıbrido que permite estudiar sistemas gen´ericos mixtos, esto es, que presentan una combinaci´on de comportamiento determinista y aleatorio. Este modelo consta de dos componentes, uno determinista consistente en una ecuaci´on en diferencias, obtenida a partir de un estudio de autocorrelaci´on, y otro estoc´astico que modeliza el error cometido por el primero. El componente estoc´astico es un generador universal de distribuciones de probabilidad, basado en un proceso compuesto de variables aleatorias, uniformemente distribuidas en un intervalo variable en el tiempo. Este generador universal es deducido en la tesis a partir de una nueva teor´ıa sobre la oferta y la demanda de un recurso gen´erico. El modelo resultante puede formularse conceptualmente como una entidad con tres elementos fundamentales: un motor generador de din´amica determinista, una fuente interna de ruido generadora de incertidumbre y una exposici´on al entorno que representa las interacciones del sistema real con el mundo exterior. En las aplicaciones estos tres elementos se ajustan en base al hist´orico de las series temporales del sistema din´amico. Una vez ajustados sus componentes, el modelo se comporta de una forma adaptativa tomando como inputs los nuevos valores de las series temporales del sistema y calculando predicciones sobre su comportamiento futuro. Cada predicci´on se presenta como un intervalo dentro del cual cualquier valor es equipro- bable, teniendo probabilidad nula cualquier valor externo al intervalo. De esta forma el modelo computa el comportamiento futuro y su nivel de incertidumbre en base al estado actual del sistema. Se ha aplicado el modelo en esta tesis a sistemas muy diferentes mostrando ser muy flexible para afrontar el estudio de campos de naturaleza dispar. El intercambio de tr´afico telef´onico entre operadores de telefon´ıa, la evoluci´on de mercados financieros y el flujo de informaci´on entre servidores de Internet son estudiados en profundidad en la tesis. Todos estos sistemas son modelizados de forma exitosa con un mismo lenguaje, a pesar de tratarse de sistemas f´ısicos totalmente distintos. El estudio de las redes de telefon´ıa muestra que los patrones de tr´afico telef´onico presentan una fuerte pseudo-periodicidad semanal contaminada con una gran cantidad de ruido, sobre todo en el caso de llamadas internacionales. El estudio de los mercados financieros muestra por su parte que la naturaleza fundamental de ´estos es aleatoria con un rango de comportamiento relativamente acotado. Una parte de la tesis se dedica a explicar algunas de las manifestaciones emp´ıricas m´as importantes en los mercados financieros como son los “fat tails”, “power laws” y “volatility clustering”. Por ´ultimo se demuestra que la comunicaci´on entre servidores de Internet tiene, al igual que los mercados financieros, una componente subyacente totalmente estoc´astica pero de comportamiento bastante “d´ocil”, siendo esta docilidad m´as acusada a medida que aumenta la distancia entre servidores. Dos aspectos son destacables en el modelo, su adaptabilidad y su universalidad. El primero es debido a que, una vez ajustados los par´ametros generales, el modelo se “alimenta” de los valores observables del sistema y es capaz de calcular con ellos comportamientos futuros. A pesar de tener unos par´ametros fijos, la variabilidad en los observables que sirven de input al modelo llevan a una gran riqueza de ouputs posibles. El segundo aspecto se debe a la formulaci´on gen´erica del modelo h´ıbrido y a que sus par´ametros se ajustan en base a manifestaciones externas del sistema en estudio, y no en base a sus caracter´ısticas f´ısicas. Estos factores hacen que el modelo pueda utilizarse en gran variedad de campos. Por ´ultimo, la tesis propone en su parte final otros campos donde se han obtenido ´exitos preliminares muy prometedores como son la modelizaci´on del riesgo financiero, los algoritmos de routing en redes de telecomunicaci´on y el cambio clim´atico. Abstract This work faces the problem of modeling dynamical systems based on the study of its time series, by using a standard language that aims to be an universal abstraction of dynamical systems, irrespective of their deterministic, stochastic or hybrid nature. Deterministic and stochastic models are developed separately to be merged subsequently into a hybrid model, which allows the study of generic systems, that is to say, those having both deterministic and random behavior. This model is a combination of two different components. One of them is deterministic and consisting in an equation in differences derived from an auto-correlation study and the other is stochastic and models the errors made by the deterministic one. The stochastic component is an universal generator of probability distributions based on a process consisting in random variables distributed uniformly within an interval varying in time. This universal generator is derived in the thesis from a new theory of offer and demand for a generic resource. The resulting model can be visualized as an entity with three fundamental elements: an engine generating deterministic dynamics, an internal source of noise generating uncertainty and an exposure to the environment which depicts the interactions between the real system and the external world. In the applications these three elements are adjusted to the history of the time series from the dynamical system. Once its components have been adjusted, the model behaves in an adaptive way by using the new time series values from the system as inputs and calculating predictions about its future behavior. Every prediction is provided as an interval, where any inner value is equally probable while all outer ones have null probability. So, the model computes the future behavior and its level of uncertainty based on the current state of the system. The model is applied to quite different systems in this thesis, showing to be very flexible when facing the study of fields with diverse nature. The exchange of traffic between telephony operators, the evolution of financial markets and the flow of information between servers on the Internet are deeply studied in this thesis. All these systems are successfully modeled by using the same “language”, in spite the fact that they are systems physically radically different. The study of telephony networks shows that the traffic patterns are strongly weekly pseudo-periodic but mixed with a great amount of noise, specially in the case of international calls. It is proved that the underlying nature of financial markets is random with a moderate range of variability. A part of this thesis is devoted to explain some of the most important empirical observations in financial markets, such as “fat tails”, “power laws” and “volatility clustering”. Finally it is proved that the communication between two servers on the Internet has, as in the case of financial markets, an underlaying random dynamics but with a narrow range of variability, being this lack of variability more marked as the distance between servers is increased. Two aspects of the model stand out as being the most important: its adaptability and its universality. The first one is due to the fact that once the general parameters have been adjusted , the model is “fed” on the observable manifestations of the system in order to calculate its future behavior. Despite the fact that the model has fixed parameters the variability in the observable manifestations of the system, which are used as inputs of the model, lead to a great variability in the possible outputs. The second aspect is due to the general “language” used in the formulation of the hybrid model and to the fact that its parameters are adjusted based on external manifestations of the system under study instead of its physical characteristics. These factors made the model suitable to be used in great variety of fields. Lastly, this thesis proposes other fields in which preliminary and promising results have been obtained, such as the modeling of financial risk, the development of routing algorithms for telecommunication networks and the assessment of climate change.

Optimisation of algorithms to compute information theoretic indexes

Analysis of big amount of data is a field with many years of research. It is centred in getting significant values, to make it easier to understand and interpret data. Being the analysis of interdependence between time series an important field of research, mainly as a result of advances in the characterization of dynamical systems from the signals they produce. In the medicine sphere, it is easy to find many researches that try to understand the brain behaviour, its operation mode and its internal connections. The human brain comprises approximately 1011 neurons, each of which makes about 103 synaptic connections. This huge number of connections between individual processing elements provides the fundamental substrate for neuronal ensembles to become transiently synchronized or functionally connected. A similar complex network configuration and dynamics can also be found at the macroscopic scales of systems neuroscience and brain imaging. The emergence of dynamically coupled cell assemblies represents the neurophysiological substrate for cognitive function such as perception, learning, thinking. Understanding the complex network organization of the brain on the basis of neuroimaging data represents one of the most impervious challenges for systems neuroscience. Brain connectivity is an elusive concept that refers to diferent interrelated aspects of brain organization: structural, functional connectivity (FC) and efective connectivity (EC). Structural connectivity refers to a network of physical connections linking sets of neurons, it is the anatomical structur of brain networks. However, FC refers to the statistical dependence between the signals stemming from two distinct units within a nervous system, while EC refers to the causal interactions between them. This research opens the door to try to resolve diseases related with the brain, like Parkinson’s disease, senile dementia, mild cognitive impairment, etc. One of the most important project associated with Alzheimer’s research and other diseases are enclosed in the European project called Blue Brain. The center for Biomedical Technology (CTB) of Universidad Politecnica de Madrid (UPM) forms part of the project. The CTB researches have developed a magnetoencephalography (MEG) data processing tool that allow to visualise and analyse data in an intuitive way. This tool receives the name of HERMES, and it is presented in this document. Analysis of big amount of data is a field with many years of research. It is centred in getting significant values, to make it easier to understand and interpret data. Being the analysis of interdependence between time series an important field of research, mainly as a result of advances in the characterization of dynamical systems from the signals they produce. In the medicine sphere, it is easy to find many researches that try to understand the brain behaviour, its operation mode and its internal connections. The human brain comprises approximately 1011 neurons, each of which makes about 103 synaptic connections. This huge number of connections between individual processing elements provides the fundamental substrate for neuronal ensembles to become transiently synchronized or functionally connected. A similar complex network configuration and dynamics can also be found at the macroscopic scales of systems neuroscience and brain imaging. The emergence of dynamically coupled cell assemblies represents the neurophysiological substrate for cognitive function such as perception, learning, thinking. Understanding the complex network organization of the brain on the basis of neuroimaging data represents one of the most impervious challenges for systems neuroscience. Brain connectivity is an elusive concept that refers to diferent interrelated aspects of brain organization: structural, functional connectivity (FC) and efective connectivity (EC). Structural connectivity refers to a network of physical connections linking sets of neurons, it is the anatomical structur of brain networks. However, FC refers to the statistical dependence between the signals stemming from two distinct units within a nervous system, while EC refers to the causal interactions between them. This research opens the door to try to resolve diseases related with the brain, like Parkinson’s disease, senile dementia, mild cognitive impairment, etc. One of the most important project associated with Alzheimer’s research and other diseases are enclosed in the European project called Blue Brain. The center for Biomedical Technology (CTB) of Universidad Politecnica de Madrid (UPM) forms part of the project. The CTB researches have developed a magnetoencephalography (MEG) data processing tool that allow to visualise and analyse data in an intuitive way. This tool receives the name of HERMES, and it is presented in this document.

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.