Complex sochastic boolean systems : new properties of the intrinsic order graph

[EN]A complex stochastic Boolean system (CSBS) is a system depending on an arbitrary number n of stochastic Boolean variables. The analysis of CSBSs is mainly based on the intrinsic order: a partial order relation defined on the set f0; 1gn of binary n-tuples. The usual graphical representation for a CSBS is the intrinsic order graph: the Hasse diagram of the intrinsic order. In this paper, some new properties of the intrinsic order graph are studied. Particularly, the set and the number of its edges, the degree and neighbors of each vertex, as well as typical properties, such as the symmetry and fractal structure of this graph, are analyzed…

Energy-efficient Communication and Estimation in Wireless Sensor Networks

This thesis focuses on the energy efficiency in wireless networks under the transmission and information diffusion points of view. In particular, on one hand, the communication efficiency is investigated, attempting to reduce the consumption during transmissions, while on the other hand the energy efficiency of the procedures required to distribute the information among wireless nodes in complex networks is taken into account. For what concerns energy efficient communications, an innovative transmission scheme reusing source of opportunity signals is introduced. This kind of signals has never been previously studied in literature for communication purposes. The scope is to provide a way for transmitting information with energy consumption close to zero. On the theoretical side, starting from a general communication channel model subject to a limited input amplitude, the theme of low power transmission signals is tackled under the perspective of stating sufficient conditions for the capacity achieving input distribution to be discrete. Finally, the focus is shifted towards the design of energy efficient algorithms for the diffusion of information. In particular, the endeavours are aimed at solving an estimation problem distributed over a wireless sensor network. The proposed solutions are deeply analyzed both to ensure their energy efficiency and to guarantee their robustness against losses during the diffusion of information (against information diffusion truncation more in general).

Extracting FSA descriptions of robot behaviours from the dynamics of automatically designed controller networks

Automatic design has become a common approach to evolve complex networks, such as artificial neural networks (ANNs) and random boolean networks (RBNs), and many evolutionary setups have been discussed to increase the efficiency of this process. However networks evolved in this way have few limitations that should not be overlooked. One of these limitations is the black-box problem that refers to the impossibility to analyze internal behaviour of complex networks in an efficient and meaningful way. The aim of this study is to develop a methodology that make it possible to extract finite-state automata (FSAs) descriptions of robot behaviours from the dynamics of automatically designed complex controller networks. These FSAs unlike complex networks from which they're extracted are both readable and editable thus making the resulting designs much more valuable.

A Multi-agent System for Emergency Decision Support

This paper describes the multi-agent organization of a computer system that was designed to assist operators in decision making in the presence of emergencies. The application was developed for the case of emergencies caused by river floods. It operates on real-time receiving data recorded by sensors (rainfall, water levels, flows, etc.) and applies multi-agent techniques to interpret the data, predict the future behavior and recommend control actions. The system includes an advanced knowledge based architecture with multiple symbolic representation with uncertainty models (bayesian networks). This system has been applied and validated at two particular sites in Spain (the Jucar basin and the South basin).

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

Functional Brain Networks: beyond the small-world paradigm

This contribution reviews the current state of art comprising the application of Complex Networks Theory to the analysis of functional brain networks. We briefly overview the main advances in this field during the last decade and we explain how graph analysis has increased our knowledge about how the brain behaves when performing a specific task or how it fails when a certain pathology arises. We also show the limitations of this kind of analysis, which have been a source of confusion and misunderstanding when interpreting the results obtained. Finally, we discuss about a possible direction to follow in the next years.

Análisis y modelización de la dinámica emergente durante el proceso de difusión de información en las redes sociales de internet

Durante la actividad diaria, la sociedad actual interactúa constantemente por medio de dispositivos electrónicos y servicios de telecomunicaciones, tales como el teléfono, correo electrónico, transacciones bancarias o redes sociales de Internet. Sin saberlo, masivamente dejamos rastros de nuestra actividad en las bases de datos de empresas proveedoras de servicios. Estas nuevas fuentes de datos tienen las dimensiones necesarias para que se puedan observar patrones de comportamiento humano a grandes escalas. Como resultado, ha surgido una reciente explosión sin precedentes de estudios de sistemas sociales, dirigidos por el análisis de datos y procesos computacionales. En esta tesis desarrollamos métodos computacionales y matemáticos para analizar sistemas sociales por medio del estudio combinado de datos derivados de la actividad humana y la teoría de redes complejas. Nuestro objetivo es caracterizar y entender los sistemas emergentes de interacciones sociales en los nuevos espacios tecnológicos, tales como la red social Twitter y la telefonía móvil. Analizamos los sistemas por medio de la construcción de redes complejas y series temporales, estudiando su estructura, funcionamiento y evolución en el tiempo. También, investigamos la naturaleza de los patrones observados por medio de los mecanismos que rigen las interacciones entre individuos, así como medimos el impacto de eventos críticos en el comportamiento del sistema. Para ello, hemos propuesto modelos que explican las estructuras globales y la dinámica emergente con que fluye la información en el sistema. Para los estudios de la red social Twitter, hemos basado nuestros análisis en conversaciones puntuales, tales como protestas políticas, grandes acontecimientos o procesos electorales. A partir de los mensajes de las conversaciones, identificamos a los usuarios que participan y construimos redes de interacciones entre los mismos. Específicamente, construimos una red para representar quién recibe los mensajes de quién y otra red para representar quién propaga los mensajes de quién. En general, hemos encontrado que estas estructuras tienen propiedades complejas, tales como crecimiento explosivo y distribuciones de grado libres de escala. En base a la topología de estas redes, hemos indentificado tres tipos de usuarios que determinan el flujo de información según su actividad e influencia. Para medir la influencia de los usuarios en las conversaciones, hemos introducido una nueva medida llamada eficiencia de usuario. La eficiencia se define como el número de retransmisiones obtenidas por mensaje enviado, y mide los efectos que tienen los esfuerzos individuales sobre la reacción colectiva. Hemos observado que la distribución de esta propiedad es ubicua en varias conversaciones de Twitter, sin importar sus dimensiones ni contextos. Con lo cual, sugerimos que existe universalidad en la relación entre esfuerzos individuales y reacciones colectivas en Twitter. Para explicar los factores que determinan la emergencia de la distribución de eficiencia, hemos desarrollado un modelo computacional que simula la propagación de mensajes en la red social de Twitter, basado en el mecanismo de cascadas independientes. Este modelo nos permite medir el efecto que tienen sobre la distribución de eficiencia, tanto la topología de la red social subyacente, como la forma en que los usuarios envían mensajes. Los resultados indican que la emergencia de un grupo selecto de usuarios altamente eficientes depende de la heterogeneidad de la red subyacente y no del comportamiento individual. Por otro lado, hemos desarrollado técnicas para inferir el grado de polarización política en redes sociales. Proponemos una metodología para estimar opiniones en redes sociales y medir el grado de polarización en las opiniones obtenidas. Hemos diseñado un modelo donde estudiamos el efecto que tiene la opinión de un pequeño grupo de usuarios influyentes, llamado élite, sobre las opiniones de la mayoría de usuarios. El modelo da como resultado una distribución de opiniones sobre la cual medimos el grado de polarización. Aplicamos nuestra metodología para medir la polarización en redes de difusión de mensajes, durante una conversación en Twitter de una sociedad políticamente polarizada. Los resultados obtenidos presentan una alta correspondencia con los datos offline. Con este estudio, hemos demostrado que la metodología propuesta es capaz de determinar diferentes grados de polarización dependiendo de la estructura de la red. Finalmente, hemos estudiado el comportamiento humano a partir de datos de telefonía móvil. Por una parte, hemos caracterizado el impacto que tienen desastres naturales, como innundaciones, sobre el comportamiento colectivo. Encontramos que los patrones de comunicación se alteran de forma abrupta en las áreas afectadas por la catástofre. Con lo cual, demostramos que se podría medir el impacto en la región casi en tiempo real y sin necesidad de desplegar esfuerzos en el terreno. Por otra parte, hemos estudiado los patrones de actividad y movilidad humana para caracterizar las interacciones entre regiones de un país en desarrollo. Encontramos que las redes de llamadas y trayectorias humanas tienen estructuras de comunidades asociadas a regiones y centros urbanos. En resumen, hemos mostrado que es posible entender procesos sociales complejos por medio del análisis de datos de actividad humana y la teoría de redes complejas. A lo largo de la tesis, hemos comprobado que fenómenos sociales como la influencia, polarización política o reacción a eventos críticos quedan reflejados en los patrones estructurales y dinámicos que presentan la redes construidas a partir de datos de conversaciones en redes sociales de Internet o telefonía móvil. ABSTRACT During daily routines, we are constantly interacting with electronic devices and telecommunication services. Unconsciously, we are massively leaving traces of our activity in the service providers’ databases. These new data sources have the dimensions required to enable the observation of human behavioral patterns at large scales. As a result, there has been an unprecedented explosion of data-driven social research. In this thesis, we develop computational and mathematical methods to analyze social systems by means of the combined study of human activity data and the theory of complex networks. Our goal is to characterize and understand the emergent systems from human interactions on the new technological spaces, such as the online social network Twitter and mobile phones. We analyze systems by means of the construction of complex networks and temporal series, studying their structure, functioning and temporal evolution. We also investigate on the nature of the observed patterns, by means of the mechanisms that rule the interactions among individuals, as well as on the impact of critical events on the system���s behavior. For this purpose, we have proposed models that explain the global structures and the emergent dynamics of information flow in the system. In the studies of the online social network Twitter, we have based our analysis on specific conversations, such as political protests, important announcements and electoral processes. From the messages related to the conversations, we identify the participant users and build networks of interactions with them. We specifically build one network to represent whoreceives- whose-messages and another to represent who-propagates-whose-messages. In general, we have found that these structures have complex properties, such as explosive growth and scale-free degree distributions. Based on the topological properties of these networks, we have identified three types of user behavior that determine the information flow dynamics due to their influence. In order to measure the users’ influence on the conversations, we have introduced a new measure called user efficiency. It is defined as the number of retransmissions obtained by message posted, and it measures the effects of the individual activity on the collective reacixtions. We have observed that the probability distribution of this property is ubiquitous across several Twitter conversation, regardlessly of their dimension or social context. Therefore, we suggest that there is a universal behavior in the relationship between individual efforts and collective reactions on Twitter. In order to explain the different factors that determine the user efficiency distribution, we have developed a computational model to simulate the diffusion of messages on Twitter, based on the mechanism of independent cascades. This model, allows us to measure the impact on the emergent efficiency distribution of the underlying network topology, as well as the way that users post messages. The results indicate that the emergence of an exclusive group of highly efficient users depends upon the heterogeneity of the underlying network instead of the individual behavior. Moreover, we have also developed techniques to infer the degree of polarization in social networks. We propose a methodology to estimate opinions in social networks and to measure the degree of polarization in the obtained opinions. We have designed a model to study the effects of the opinions of a small group of influential users, called elite, on the opinions of the majority of users. The model results in an opinions distribution to which we measure the degree of polarization. We apply our methodology to measure the polarization on graphs from the messages diffusion process, during a conversation on Twitter from a polarized society. The results are in very good agreement with offline and contextual data. With this study, we have shown that our methodology is capable of detecting several degrees of polarization depending on the structure of the networks. Finally, we have also inferred the human behavior from mobile phones’ data. On the one hand, we have characterized the impact of natural disasters, like flooding, on the collective behavior. We found that the communication patterns are abruptly altered in the areas affected by the catastrophe. Therefore, we demonstrate that we could measure the impact of the disaster on the region, almost in real-time and without needing to deploy further efforts. On the other hand, we have studied human activity and mobility patterns in order to characterize regional interactions on a developing country. We found that the calls and trajectories networks present community structure associated to regional and urban areas. In summary, we have shown that it is possible to understand complex social processes by means of analyzing human activity data and the theory of complex networks. Along the thesis, we have demonstrated that social phenomena, like influence, polarization and reaction to critical events, are reflected in the structural and dynamical patterns of the networks constructed from data regarding conversations on online social networks and mobile phones.

Transiciones irreversibles en redes complejas

En esta tesis se aborda la emergencia de sincronización en sistemas de osciladores acoplados. En particular, nos centraremos en la emergencia de un tipo de transición discontinua entre el estado incoherente y el estado síncrono, llamada transición explosiva. Este fenómeno es análogo al de las transiciones de fase de primer orden asociadas a los cambios de agregación de la materia, cuya importancia abarca diversos campos, desde la sincronización espontánea de redes neuronales al riesgo de desincronización súbita entre los osciladores que componen la red de suministro de potencia eléctrica. Para analizar el problema, se introducen varios métodos de creciente generalidad cuyo efecto es inducir una transición explosiva al imponer una serie condiciones sobre la topología y las frecuencias naturales de cada oscilador. Así mismo, se aborda el estudio de un modelo algo más complejo con características similares para entender en mayor profundidad las características asociadas a este tipo de transiciones, siendo la histéresis una de las más destacadas. Finalmente, se propone un método cuantitativo para describir la importancia de cada nodo en el proceso de sincronización con el objetivo de estudiar y caracterizar el efecto sobre los nodos del sistema de los diversos métodos que inducen una transición explosiva. Este nuevo enfoque permite descubrir un proceso de frustración de la sincronización local en redes de osciladores acoplados, siendo el responsable de la emergencia de la sincronización explosiva. ABSTRACT In this thesis we address the emergence of synchronization in systems of coupled oscillators in complex networks. We focus our attention on a particular kind of discontinuous transitions, named explosive synchronization, where the system changes abruptly from an incoherent state to a synchronous state. This emergent phenomena is analogous to those first order transitions typically associated with changes among the aggregate states of matter, and it is important in many different fields, such as spontaneous synchronization of neurons or spontaneous desynchronization in power grids. To analyze it, we introduce some methods of increasing generality in order to induce such a discontinuous transition by acting over the topology and the natural frequencies in several different ways. Likewise, we address the study of a more complex model in order to acquire deeper knowledge on the properties of this kind of transitions, where a hysteretic behavior is specially relevant. Finally, we propose a new quantitative approach in order to find the importance of each node in the route to synchronization, aiming to provide a characterization of the effects over the network’s units of the different methods able to induce an explosive transition. This approach allows us to show the inner mechanisms behind such explosive behavior in networks of coupled oscillators, being rooted by a frustration of the local synchronization process previous to the emergence of global coherence.

VHDL-based system design of a cognitive sensorimotor loop (CSL) for haptic Human-Machine Interaction (HMI)

This document is a summary of the Bachelor thesis titled “VHDL-Based System Design of a Cognitive Sensorimotor Loop (CSL) for Haptic Human-Machine Interaction (HMI)” written by Pablo de Miguel Morales, Electronics Engineering student at the Universidad Politécnica de Madrid (UPM Madrid, Spain) during an Erasmus+ Exchange Program at the Beuth Hochschule für Technik (BHT Berlin, Germany). The tutor of this project is Dr. Prof. Hild. This project has been developed inside the Neurobotics Research Laboratory (NRL) in close collaboration with Benjamin Panreck, a member of the NRL, and another exchange student from the UPM Pablo Gabriel Lezcano. For a deeper comprehension of the content of the thesis, a deeper look in the document is needed as well as the viewing of the videos and the VHDL design. In the growing field of automation, a large amount of workforce is dedicated to improve, adapt and design motor controllers for a wide variety of applications. In the specific field of robotics or other machinery designed to interact with humans or their environment, new needs and technological solutions are often being discovered due to the existing, relatively unexplored new scenario it is. The project consisted of three main parts: Two VHDL-based systems and one short experiment on the haptic perception. Both VHDL systems are based on a Cognitive Sensorimotor Loop (CSL) which is a control loop designed by the NRL and mainly developed by Dr. Prof. Hild. The CSL is a control loop whose main characteristic is the fact that it does not use any external sensor to measure the speed or position of the motor but the motor itself. The motor always generates a voltage that is proportional to its angular speed so it does not need calibration. This method is energy efficient and simplifies control loops in complex systems. The first system, named CSL Stay In Touch (SIT), consists in a one DC motor system controller by a FPGA Board (Zynq ZYBO 7000) whose aim is to keep contact with any external object that touches its Sensing Platform in both directions. Apart from the main behavior, three features (Search Mode, Inertia Mode and Return Mode) have been designed to enhance the haptic interaction experience. Additionally, a VGA-Screen is also controlled by the FPGA Board for the monitoring of the whole system. This system has been completely developed, tested and improved; analyzing its timing and consumption properties. The second system, named CSL Fingerlike Mechanism (FM), consists in a fingerlike mechanical system controlled by two DC motors (Each controlling one part of the finger). The behavior is similar to the first system but in a more complex structure. This system was optional and not part of the original objectives of the thesis and it could not be properly finished and tested due to the lack of time. The haptic perception experiment was an experiment conducted to have an insight into the complexity of human haptic perception in order to implement this knowledge into technological applications. The experiment consisted in testing the capability of the subjects to recognize different objects and shapes while being blindfolded and with their ears covered. Two groups were done, one had full haptic perception while the other had to explore the environment with a plastic piece attached to their finger to create a haptic handicap. The conclusion of the thesis was that a haptic system based only on a CSL-based system is not enough to retrieve valuable information from the environment and that other sensors are needed (temperature, pressure, etc.) but that a CSL-based system is very useful to control the force applied by the system to interact with haptic sensible surfaces such as skin or tactile screens. RESUMEN. Este documento es un resumen del proyecto fin de grado titulado “VHDL-Based System Design of a Cognitive Sensorimotor Loop (CSL) for Haptic Human-Machine Interaction (HMI)” escrito por Pablo de Miguel, estudiante de Ingeniería Electrónica de Comunicaciones en la Universidad Politécnica de Madrid (UPM Madrid, España) durante un programa de intercambio Erasmus+ en la Beuth Hochschule für Technik (BHT Berlin, Alemania). El tutor de este proyecto ha sido Dr. Prof. Hild. Este proyecto se ha desarrollado dentro del Neurorobotics Research Laboratory (NRL) en estrecha colaboración con Benjamin Panreck (un miembro del NRL) y con Pablo Lezcano (Otro estudiante de intercambio de la UPM). Para una comprensión completa del trabajo es necesaria una lectura detenida de todo el documento y el visionado de los videos y análisis del diseño VHDL incluidos en el CD adjunto. En el creciente sector de la automatización, una gran cantidad de esfuerzo está dedicada a mejorar, adaptar y diseñar controladores de motor para un gran rango de aplicaciones. En el campo específico de la robótica u otra maquinaria diseñada para interactuar con los humanos o con su entorno, nuevas necesidades y soluciones tecnológicas se siguen desarrollado debido al relativamente inexplorado y nuevo escenario que supone. El proyecto consta de tres partes principales: Dos sistemas basados en VHDL y un pequeño experimento sobre la percepción háptica. Ambos sistemas VHDL están basados en el Cognitive Sesnorimotor Loop (CSL) que es un lazo de control creado por el NRL y cuyo desarrollador principal ha sido Dr. Prof. Hild. El CSL es un lazo de control cuya principal característica es la ausencia de sensores externos para medir la velocidad o la posición del motor, usando el propio motor como sensor. El motor siempre genera un voltaje proporcional a su velocidad angular de modo que no es necesaria calibración. Este método es eficiente en términos energéticos y simplifica los lazos de control en sistemas complejos. El primer sistema, llamado CSL Stay In Touch (SIT), consiste en un sistema formado por un motor DC controlado por una FPGA Board (Zynq ZYBO 7000) cuyo objetivo es mantener contacto con cualquier objeto externo que toque su plataforma sensible en ambas direcciones. Aparte del funcionamiento básico, tres modos (Search Mode, Inertia Mode y Return Mode) han sido diseñados para mejorar la interacción. Adicionalmente, se ha diseñado el control a través de la FPGA Board de una pantalla VGA para la monitorización de todo el sistema. El sistema ha sido totalmente desarrollado, testeado y mejorado; analizando su propiedades de timing y consumo energético. El segundo sistema, llamado CSL Fingerlike Mechanism (FM), consiste en un mecanismo similar a un dedo controlado por dos motores DC (Cada uno controlando una falange). Su comportamiento es similar al del primer sistema pero con una estructura más compleja. Este sistema no formaba parte de los objetivos iniciales del proyecto y por lo tanto era opcional. No pudo ser plenamente desarrollado debido a la falta de tiempo. El experimento de percepción háptica fue diseñado para profundizar en la percepción háptica humana con el objetivo de aplicar este conocimiento en aplicaciones tecnológicas. El experimento consistía en testear la capacidad de los sujetos para reconocer diferentes objetos, formas y texturas en condiciones de privación del sentido del oído y la vista. Se crearon dos grupos, en uno los sujetos tenían plena percepción háptica mientras que en el otro debían interactuar con los objetos a través de una pieza de plástico para generar un hándicap háptico. La conclusión del proyecto fue que un sistema háptico basado solo en sistemas CSL no es suficiente para recopilar información valiosa del entorno y que debe hacer uso de otros sensores (temperatura, presión, etc.). En cambio, un sistema basado en CSL es idóneo para el control de la fuerza aplicada por el sistema durante la interacción con superficies hápticas sensibles tales como la piel o pantallas táctiles.

Association Patterns in Saproxylic Insect Networks in Three Iberian Mediterranean Woodlands and Their Resistance to Microhabitat Loss

The assessment of the relationship between species diversity, species interactions and environmental characteristics is indispensable for understanding network architecture and ecological distribution in complex networks. Saproxylic insect communities inhabiting tree hollow microhabitats within Mediterranean woodlands are highly dependent on woodland configuration and on microhabitat supply they harbor, so can be studied under the network analysis perspective. We assessed the differences in interacting patterns according to woodland site, and analysed the importance of functional species in modelling network architecture. We then evaluated their implications for saproxylic assemblages’ persistence, through simulations of three possible scenarios of loss of tree hollow microhabitat. Tree hollow-saproxylic insect networks per woodland site presented a significant nested pattern. Those woodlands with higher complexity of tree individuals and tree hollow microhabitats also housed higher species/interactions diversity and complexity of saproxylic networks, and exhibited a higher degree of nestedness, suggesting that a higher woodland complexity positively influences saproxylic diversity and interaction complexity, thus determining higher degree of nestedness. Moreover, the number of insects acting as key interconnectors (nodes falling into the core region, using core/periphery tests) was similar among woodland sites, but the species identity varied on each. Such differences in insect core composition among woodland sites suggest the functional role they depict at woodland scale. Tree hollows acting as core corresponded with large tree hollows near the ground and simultaneously housing various breeding microsites, whereas core insects were species mediating relevant ecological interactions within saproxylic communities, e.g. predation, competitive or facilitation interactions. Differences in network patterns and tree hollow characteristics among woodland sites clearly defined different sensitivity to microhabitat loss, and higher saproxylic diversity and woodland complexity showed positive relation with robustness. These results highlight that woodland complexity goes hand in hand with biotic and ecological complexity of saproxylic networks, and together exhibited positive effects on network robustness.

Optimization and Machine Learning Frameworks for Complex Network Analysis

Thesis (Ph.D.)--University of Washington, 2016-06

Inter-organisational networks, value creation and the process of technology integration in research and development

Traditional methods of R&D management are no longer sufficient for embracing innovations and leveraging complex new technologies to fully integrated positions in established systems. This paper presents the view that the technology integration process is a result of fundamental interactions embedded in inter-organisational activities. Emerging industries, high technology companies and knowledge intensive organisations owe a large part of their viability to complex networks of inter-organisational interactions and relationships. R&D organisations are the gatekeepers in the technology integration process with their initial sanction and motivation to develop technologies providing the first point of entry. Networks rely on the activities of stakeholders to provide the foundations of collaborative R&D activities, business-to-business marketing and strategic alliances. Such complex inter-organisational interactions and relationships influence value creation and organisational goals as stakeholders seek to gain investment opportunities. A theoretical model is developed here that contributes to our understanding of technology integration (adoption) as a dynamic process, which is simultaneously structured and enacted through the activities of stakeholders and organisations in complex inter-organisational networks of sanction and integration.

Accelerating, hyperaccelerating, and decelerating networks

Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular, biological networks can display a quadratic growth in regulator number with genome size even while remaining sparsely connected. These features are mutually incompatible in standard treatments of network theory which typically require that every new network node possesses at least one connection. To model sparsely connected networks, we generalize existing approaches and add each new node with a probabilistic number of links to generate either accelerating, hyperaccelerating, or even decelerating network statistics in different regimes. Under preferential attachment for example, slowly accelerating networks display stationary scale-free statistics relatively independent of network size while more rapidly accelerating networks display a transition from scale-free to exponential statistics with network growth. Such transitions explain, for instance, the evolutionary record of single-celled organisms which display strict size and complexity limits.

Asymptotic theory of time varying networks with memory and heterogeneous activation pattern

In this thesis work we develop a new generative model of social networks belonging to the family of Time Varying Networks. The importance of correctly modelling the mechanisms shaping the growth of a network and the dynamics of the edges activation and inactivation are of central importance in network science. Indeed, by means of generative models that mimic the real-world dynamics of contacts in social networks it is possible to forecast the outcome of an epidemic process, optimize the immunization campaign or optimally spread an information among individuals. This task can now be tackled taking advantage of the recent availability of large-scale, high-quality and time-resolved datasets. This wealth of digital data has allowed to deepen our understanding of the structure and properties of many real-world networks. Moreover, the empirical evidence of a temporal dimension in networks prompted the switch of paradigm from a static representation of graphs to a time varying one. In this work we exploit the Activity-Driven paradigm (a modeling tool belonging to the family of Time-Varying-Networks) to develop a general dynamical model that encodes fundamental mechanism shaping the social networks' topology and its temporal structure: social capital allocation and burstiness. The former accounts for the fact that individuals does not randomly invest their time and social interactions but they rather allocate it toward already known nodes of the network. The latter accounts for the heavy-tailed distributions of the inter-event time in social networks. We then empirically measure the properties of these two mechanisms from seven real-world datasets and develop a data-driven model, analytically solving it. We then check the results against numerical simulations and test our predictions with real-world datasets, finding a good agreement between the two. Moreover, we find and characterize a non-trivial interplay between burstiness and social capital allocation in the parameters phase space. Finally, we present a novel approach to the development of a complete generative model of Time-Varying-Networks. This model is inspired by the Kaufman's adjacent possible theory and is based on a generalized version of the Polya's urn. Remarkably, most of the complex and heterogeneous feature of real-world social networks are naturally reproduced by this dynamical model, together with many high-order topological properties (clustering coefficient, community structure etc.).