Estructura versus función en redes complejas cerebrales

Este trabajo trata de relacionar el comportamiento global de un sistema con el individual de cada uno de sus elementos. Con este fin, estudiamos las redes cerebrales; en concreto, nos centramos en el estudio de redes neuronales formadas en cultivos y en el fenómeno de emergencia de sincronización. Para ello hemos empleado redes complejas y desarrollado un modelo de formación de enlaces entre neuronas que imita el observado experimentalmente. Asimismo, hemos caracterizado mediante el modelo de Izhikevich las dinámicas individuales de cada neurona y cómo éstas interactúan para dar lugar el fenómeno de sincronización, el cual detectamos mediante la utilización de medidas expresamente diseñadas para este objetivo

Estructura y dinámica de redes complejas con signo

Este trabajo trata de relacionar el comportamiento global de un sistema con el individual de cada uno de sus elementos. Con este fin, estudiamos las redes cerebrales; en concreto, nos centramos en el estudio de redes neuronales formadas en cultivos, en el fenómeno de emergencia de sincronización y en el estudio de la influencia que tiene la topología de la red en la dinámica del cultivo. Para ello hemos empleado redes complejas y desarrollado un modelo de formación de enlaces entre neuronas que imita el observado experimentalmente. Asimismo, hemos caracterizado mediante el modelo de Izhikevich las dinámicas individuales de cada neurona y cómo éstas interactúan para dar lugar el fenómeno de sincronización, el cual detectamos mediante la utilización de medidas expresamente diseñadas para este objetivo. Finalmente hemos alterado la red mediante ataques dirigidos para observar la respuesta del cultivo

Mean-field nature of synchronization stability in networks with multiple interaction layers

The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of synchronization in dynamical systems. However, the resulting equations are computationally expensive, and therefore difficult, if not impossible, to solve for large systems. To bridge this gap, we develop a mean-field theory of synchronization for networks with multiple interaction layers. By assuming quasi-identical layers, we obtain accurate assessments of synchronization stability that are comparable with the exact results. In fact, the accuracy of our theory remains high even for networks with very dissimilar layers, thus posing a general question about the mean-field nature of synchronization stability in multilayer networks. Moreover, the computational complexity of our approach is only quadratic in the number of nodes, thereby allowing the study of systems whose investigation was thus far precluded. Multilayer networks can achieve synchronization, both for homogeneous and heterogeneous layers, whose dynamics is described by a system of equations often computationally complex and expensive. Here, the authors propose a mean-field approach for estimating the stability of the synchronized state of multilayer networks and show this applies to both homogeneous and heterogeneous layers, lowering computational complexity

Dynamical and topological conditions triggering the spontaneous activation of Izhikevich neuronal networks

Understanding the dynamic behavior of neuronal networks in silico is crucial for tackling the analysis of their biological counterparts and making accurate predictions. Of particular importance is determining the structural and dynamical conditions necessary for a neuronal network to activate spontaneously, transitioning from a quiescent ensemble of neurons to a network-wide coherent burst. Drawing from the versatility of the Master Stability Function, we have applied this formalism to a system of coupled neurons described by the Izhikevich model to derive the required conditions for activation. These conditions are expressed as a critical effective coupling , grounded in both topology and dynamics, above which the neuronal network will activate. For regular spiking neurons, average connectivity and noise play a significant role in their ability to activate. We have tested these conditions against numerical simulations of in silico networks, including both synthetic topologies and a biologically-realistic spatial network, showing that the theoretical conditions are well satisfied. Our findings indicate that neuronal networks readily meet the criteria for spontaneous activation, and that this capacity is weakly dependent on the microscopic details of the network as long as average connectivity and noise are sufficiently strong

Aplicación de Teoría de Control en el diseño de estrategias epidemiológicas

En este trabajo se ha tratado de simular un modelo epidemiológico en el que se establecían distintas estrategias de control dirigidas a los contactos entre personas, con el fin de conocer la repercusión de las distintas medidas y de evitar el colapso sanitario en una situación de esas características. Para el desarrollo del estudio se han analizado las diversas estrategias de control a estudiar así como el periodo de implementación de estas, para así obtener una estrategia a optimizar en función de los parámetros establecidos de manera externa como son el umbral de intervención o la libertad de los agentes a lo largo de las medidas de restricción. Tras ello, se focaliza el control en distintos grupos de población y en ámbitos de contacto, para comprobar si son más favorables que dirigirlas a toda la población. <br /

Sincronización en redes de neuronas

Este trabajo pretende estudiar la dinámica de redes de neuronas y ver cómo afecta la estructura de la red al fenómeno de sincronización. Para ello, hemos creado cultivos bicapa con redes complejas, tanto libres de escala como aleatorias, y hemos caracterizado su dinámica con el modelo de Izhikevich. Finalmente, hemos alterado los cultivos realizando ataques dirigidos y fallos aleatorios sobre ellos, estudiando así la diferencia en la dinámica de redes libres de escala y aleatorias y su respuesta funcional ante los ataques.<br /

Impact of targeted attack on the spontaneous activity in spatial and biologically-inspired neuronal networks

We study the structural and dynamical consequences of damage in spatial neuronal networks. Inspired by real in vitro networks, we construct directed networks embedded in a two-dimensional space and follow biological rules for designing the wiring of the system. As a result, synthetic cultures display strong metric correlations similar to those observed in real experiments. In its turn, neuronal dynamics is incorporated through the Izhikevich model adopting the parameters derived from observation in real cultures. We consider two scenarios for damage, targeted attacks on those neurons with the highest out-degree and random failures. By analyzing the evolution of both the giant connected component and the dynamical patterns of the neurons as nodes are removed, we observe that network activity halts for a removal of 50% of the nodes in targeted attacks, much lower than the 70% node removal required in the case of random failures. Notably, the decrease of neuronal activity is not gradual. Both damage scenarios portray "boosts" of activity just before full silencing that are not present in equivalent random (Erdös-Rényi) graphs. These boosts correspond to small, spatially compact subnetworks that are able to maintain high levels of activity. Since these subnetworks are absent in the equivalent random graphs, we hypothesize that metric correlations facilitate the existence of local circuits sufficiently integrated to maintain activity, shaping an intrinsic mechanism for resilience

Self-organized explosive synchronization in complex networks: Emergence of synchronization bombs

We introduce the concept of synchronization bombs as large networks of coupled heterogeneous oscillators that operate in a bistable regime and abruptly transit from incoherence to phase-locking (or vice-versa) by adding (or removing) one or a few links. Here we build a self-organized and stochastic version of these bombs, by optimizing global synchrony with decentralized information in a competitive link-percolation process driven by a local rule. We find explosive fingerprints on the emerging network structure, including frequency-degree correlations, disassortative patterns and a delayed percolation threshold. We show that these bomb-like transitions can be designed both in systems of Kuramoto -- periodic -- and R\"ossler -- chaotic -- oscillators and in a model of cardiac pacemaker cells. We analytically characterize the transitions in the Kuramoto case by combining a precise collective coordinates approach and the Ott-Antonsen ansatz. Furthermore, we study the robustness of the phenomena under changes in the main parameters and the unexpected effect of optimal noise in our model. Our results propose a minimal self-organized mechanism of network growth to understand and control explosive synchronization in adaptive biological systems like the brain and engineered ones like power-grids or electronic circuits. From a theoretical standpoint, the emergence of synchronization explosions and bistability induced by localized structural perturbations -- without any fine-tuning of global parameters -- joins explosive synchronization and percolation under the same mechanistic framework.Comment: 17 pages, 9 figure

Emergencia de estados polarizados en redes complejas

In this Final Degree Project, we not only address the classical question of dynamics reaching consensus but also opinion plurality in social systems. We will propose different mathematical approaches to provide insight into the transition between global consensus and the emergence ofpolarized states and echo chambers. Empirical evidence points to both social influence and controversy of the subject matter as the main elements that promote this transition, both off and online arguments. Therefore, it is critical to use these two elements to describe the rise of polarization and echo chambers. With this purpose in mind, we will start by characterizing social systems as complex networks where social phenomena emerge from the pattern of interactions between humans. Our focus is on creating simple models that can reproduce complex macroscopic social outcomes from reasonably easy rules of behaviour on the fine scale.<br /

Dynamical robustness of collective neuronal activity upon targeted damage in interdependent networks

In the last decades, the availability of data about the structure of social, technological and biological systems has provided important insights on the mechanisms governing their correct functioning and robustness. These mechanisms are grounded on the complex backbone of interactions among the constituents of the system, which include both topological and dynamical aspects. Here, we analyze interdependent networks composed of two layers of interacting neuronal units and explore their robustness when these synthetic cultures are subjected to damage in the form of either targeted attack or failure. Our results show that the functionality of these networks does not decrease monotonically with damage but, on the contrary, they are able to increase their level of activity when the experienced damage is sufficiently strong