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.

Species richness and similarity of vascular plants in the Spanish dehesas at two spatial scales

Aims of study: The goals of this paper are to summarize and to compare plant species richness and floristic similarity at two spatial scales; mesohabitat (normal, eutrophic, and oligotrophic dehesas) and dehesa habitat; and to establish guidelines for conserving species diversity in dehesas. Area of study: We considered four dehesa sites in the western Peninsular Spain, located along a climatic and biogeographic gradient from north to south. Main results: Average alpha richness for mesohabitats was 75.6 species, and average alpha richness for dehesa sites was 146.3. Gamma richness assessed for the overall dehesa habitat was 340.0 species. The species richness figures of normal dehesa mesohabitat were significantly lesser than of the eutrophic mesohabitat and lesser than the oligotrophic mesohabitat too. No significant differences were found for species richness among dehesa sites. We have found more dissimilarity at local scale (mesohabitat) than at regional scale (habitat). Finally, the results of the similarity assessment between dehesa sites reflected both climatic and biogeographic gradients. Research highlights: An effective conservation of dehesas must take into account local and regional conditions all along their distribution range for ensuring the conservation of the main vascular plant species assemblages as well as the associated fauna

Residential self-selection and geographical scales in trip frequency.

Neighbourhood representation and scale used to measure the built environment have been treated in many ways. However, it is anything but clear what representation of neighbourhood is the most feasible in the existing literature. This paper presents an exhaustive analysis of built environment attributes through three spatial scales. For this purpose multiple data sources are integrated, and a set of 943 observations is analysed. This paper simultaneously analyses the influence of two methodological issues in the study of the relationship between built environment and travel behaviour: (1) detailed representation of neighbourhood by testing different spatial scales; (2) the influence of unobserved individual sensitivity to built environment attributes. The results show that different spatial scales of built environment attributes produce different results. Hence, it is important to produce local and regional transport measures, according to geographical scale. Additionally, the results show significant sensitivity to built environment attributes depending on place of residence. This effect, called residential sorting, acquires different magnitudes depending on the geographical scale used to measure the built environment attributes. Spatial scales risk to the stability of model results. Hence, transportation modellers and planners must take into account both effects of self-selection and spatial scales.

Sustainable development in North Bohuslän (Sweden): an analysis in three scales

Partiendo del estudio de la zona que discurre por la carretera E6 en su recorrido desde el municipio de Uddevala, al suroeste de Suecia hasta la frontera con Noruega se analizan las afecciones producidas en los asentamientos y el paisaje. El proyecto se estructura en tres escalas diferentes: regional, intermedia y local para entender la fuerte conexión entre las mismas. A nivel regional se analizan los tipos de paisaje por medio de un inventario utilizando el método PEBOSCA, dentro del programa Hábitat de las Naciones Unidas estudiando todos los recursos (físicos, biológicos, sociales, económicos, organizacionales... ) de una zona determianda ; y el método DAFO (en inglés SWOT)que se ocupa de las fuerzas y debilidades de la región. Se identifican los problemas más importantes, a saber, ampliar los servicios durante todo el año, mejorar la conectividad extendiendo el transporte público y carriles para bicicletas y mejorar la calidad del agua mitigando su efecto barrera. En un nivel intermedio, el proyecto se centra en la localidad de Hogdalsnäset por estar afectado por una falta de estructura urbana y por su proximidad a la frontera con Noruega. En el plano local se analiza la zona de Nordby presentando un plan alternativo de desarrollo a corto, medio y largo plazo. Por último, la autora concluye con la propuesta de construcción del "Parque del Humedal".

Time scales in cognitive neuroscience

Cognitive neuroscience boils down to describing the ways in which cognitive function results from brain activity. In turn, brain activity shows complex fluctuations, with structure at many spatio-temporal scales. Exactly how cognitive function inherits the physical dimensions of neural activity, though, is highly non-trivial, and so are generally the corresponding dimensions of cognitive phenomena. As for any physical phenomenon, when studying cognitive function, the first conceptual step should be that of establishing its dimensions. Here, we provide a systematic presentation of the temporal aspects of task-related brain activity, from the smallest scale of the brain imaging technique's resolution, to the observation time of a given experiment, through the characteristic time scales of the process under study. We first review some standard assumptions on the temporal scales of cognitive function. In spite of their general use, these assumptions hold true to a high degree of approximation for many cognitive (viz. fast perceptual) processes, but have their limitations for other ones (e.g., thinking or reasoning). We define in a rigorous way the temporal quantifiers of cognition at all scales, and illustrate how they qualitatively vary as a function of the properties of the cognitive process under study. We propose that each phenomenon should be approached with its own set of theoretical, methodological and analytical tools. In particular, we show that when treating cognitive processes such as thinking or reasoning, complex properties of ongoing brain activity, which can be drastically simplified when considering fast (e.g., perceptual) processes, start playing a major role, and not only characterize the temporal properties of task-related brain activity, but also determine the conditions for proper observation of the phenomena. Finally, some implications on the design of experiments, data analyses, and the choice of recording parameters are discussed.

Pre-investigation of water electrolysis for flexible energy storage at large scales: the case of the Spanish power system

This report analyzes the basis of hydrogen and power integration strategies, by using water electrolysis processes as a means of flexible energy storage at large scales.

Mapping variability of soil water content and flux across 1¿1000 m scales using the actively heated fiber optic method

The Actively Heated Fiber Optic (AHFO) method is shown to be capable of measuring soil water content several times per hour at 0.25 m spacing along cables of multiple kilometers in length. AHFO is based on distributed temperature sensing (DTS) observation of the heating and cooling of a buried fiber-optic cable resulting from an electrical impulse of energy delivered from the steel cable jacket. The results presented were collected from 750 m of cable buried in three 240 m colocated transects at 30, 60, and 90 cm depths in an agricultural field under center pivot irrigation. The calibration curve relating soil water content to the thermal response of the soil to a heat pulse of 10 W m−1 for 1 min duration was developed in the lab. This calibration was found applicable to the 30 and 60 cm depth cables, while the 90 cm depth cable illustrated the challenges presented by soil heterogeneity for this technique. This method was used to map with high resolution the variability of soil water content and fluxes induced by the nonuniformity of water application at the surface.

Pre-investigation of water electrolysis for flexible energy storage at large scales: the case of the Spanish power system

This report analyzes the basis of hydrogen and power integration strategies, by using water electrolysis processes as a means of flexible energy storage at large scales. It is a prospective study, where the scope is to describe the characteristics of current power systems (like the generation technologies, load curves and grid constraints), and define future scenarios of hydrogen for balancing the electrical grids, considering the efficiency, economy and easiness of operations. We focus in the "Spanish case", which is a good example for planning the transition from a power system holding large reserve capacities, high penetration of renewable energies and limited interconnections, to a more sustainable energy system being capable to optimize the volumes, the regulation modes, the utilization ratios and the impacts of the installations. Thus, we explore a novel aspect of the "hydrogen economy" which is based in the potentials of existing power systems and the properties of hydrogen as energy carrier, by considering the electricity generation and demand globally and determining the optimal size and operation of the hydrogen production processes along the country; e.g. the cost production of hydrogen becomes viable for a base-load scenario with 58 TWh/year of power surplus at 0.025 V/kWh, and large number electrolyzer plants (50 MW) running in variable mode (1-12 kA/m2)

Spatial scales of desert locust gregarization

Central to swarm formation in migratory locusts is a crowding-induced change from a “solitarious” to a “gregarious” phenotype. This change can occur within the lifetime of a single locust and accrues across generations. It represents an extreme example of phenotypic plasticity. We present computer simulations and a laboratory experiment that show how differences in resource distributions, conspicuous only at small spatial scales, can have significant effects on phase change at the population level; local spatial concentration of resource induces gregarization. Simulations also show that populations inhabiting a locally concentrated resource tend to change phase rapidly and synchronously in response to altered population densities. Our results show why information about the structure of resource at small spatial scales should become key components in monitoring and control strategies.

Nature of the spin-glass phase at experimental length scales

We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L = 32 lattices down to T ≈ 0.64Tc. We demonstrate the relevance of equilibrium finite-size simulations to understand experimental non-equilibrium spin glasses in the thermodynamical limit by establishing a time-length dictionary. We conclude that non-equilibrium experiments performed on a time scale of one hour can be matched with equilibrium results on L ≈ 110 lattices. A detailed investigation of the probability distribution functions of the spin and link overlap, as well as of their correlation functions, shows that Replica Symmetry Breaking is the appropriate theoretical framework for the physically relevant length scales. Besides, we improve over existing methodologies to ensure equilibration in parallel tempering simulations.

LR property of non-well-formed scales

This article studies generated scales having exactly three different step sizes within the language of algebraic combinatorics on words. These scales and their corresponding step-patterns are called non well formed. We prove that they can be naturally inserted in the Christoffel tree of well-formed words. Our primary focus in this study is on the left- and right-Lyndon factorization of these words. We will characterize the non-well-formed words for which both factorizations coincide. We say that these words satisfy the LR property and show that the LR property is satisfied exactly for half of the non-well-formed words. These are symmetrically distributed in the extended Christoffel tree. Moreover, we find a surprising connection between the LR property and the Christoffel duality. Finally, we prove that there are infinitely many Christoffel–Lyndon words among the set of non-well-formed words and thus there are infinitely many generated scales having as step-pattern a Christoffel–Lyndon word.

Checking the concurrence among macrobenthic organism distribution patterns at different taxonomic scales in relation to environmental factors

The interaction of both natural conditions and anthropogenic environmental impacts can lead to different soft-bottom macrobenthic distribution patterns. Soft-bottom macrobenthic community was analysed at different taxonomic scales in order to evaluate whether diverse subset of organisms respond to the variability of the environmental pressures (natural and human induced) showing or not similar distribution patterns. Therefore, this long-term survey had been focused on a heterogeneous area, where both anthropogenic and natural stress may affect the community. Three perpendicular transects to the coast were established and stations at 4, 10 and 15 m depths were sampled at each transect twice a year (summer- winter) from 2004 to 2009. Non-parametric multivariate techniques were used to analyse soft-bottom macrobenthic community distribution and its relation to the environmental factors. Similar distribution patterns between investigated taxonomic levels were detected and they were mainly related to depth.

Synthesis of Robust Hierarchical Silica Monoliths by Surface-Mediated Solution/Precipitation Reactions over Different Scales: Designing Capillary Microreactors for Environmental Applications

A synthetic procedure to prepare novel materials (surface-mediated fillings) based on robust hierarchical monoliths is reported. The methodology includes the deposition of a (micro- or mesoporous) silica thin film on the support followed by growth of a porous monolithic SiO2 structure. It has been demonstrated that this synthesis is viable for supports of different chemical nature with different inner diameters without shrinkage of the silica filling. The formation mechanism of the surface-mediated fillings is based on a solution/precipitation process and the anchoring of the silica filling to the deposited thin film. The interaction between the two SiO2 structures (monolith and thin film) depends on the porosity of the thin film and yields composite materials with different mechanical stability. By this procedure, capillary microreactors have been prepared and have been proved to be highly active and selective in the total and preferential oxidation of carbon monoxide (TOxCO and PrOxCO).