Contagion à effet de seuil dans les réseaux complexes

Networks arise frequently in the study of complex systems, since interactions among the components of such systems are critical. Networks can act as a substrate for dynamical process, such as the diffusion of information or disease throughout populations. Network structure can determine the temporal evolution of a dynamical process, including the characteristics of the steady state.The simplest representation of a complex system is an undirected, unweighted, single layer graph. In contrast, real systems exhibit heterogeneity of interaction strength and type. Such systems are frequently represented as weighted multiplex networks, and in this work we incorporate these heterogeneities into a master equation formalism in order to study their effects on spreading processes. We also carry out simulations on synthetic and empirical networks, and show that spreading dynamics, in particular the speed at which contagion spreads via threshold mechanisms, depend non-trivially on these heterogeneities. Further, we show that an important family of networks undergo reentrant phase transitions in the size and frequency of global cascades as a result of these interactions.A challenging feature of real systems is their tendency to evolve over time, since the changing structure of the underlying network is critical to the behaviour of overlying dynamical processes. We show that one aspect of temporality, the observed “burstiness” in interaction patterns, leads to non-monotic changes in the spreading time of threshold driven contagion processes.The above results shed light on the effects of various network heterogeneities, with respect to dynamical processes that evolve on these networks.Les interactions entre les composants des systèmes complexes font émerger différents types de réseaux. Ces réseaux peuvent jouer le rôle d’un substrat pour des processus dynamiques tels que la diffusion d’informations ou de maladies dans des populations. Les structures de ces réseaux déterminent l’évolution d’un processus dynamique, en particulier son régime transitoire, mais aussi les caractéristiques du régime permanent.Les systèmes complexes réels manifestent des intéractions hétérogènes en type et en intensité. Ces systèmes sont représetés comme des réseaux pondérés à plusieurs couches. Dans cette thèse, nous développons une équation maîtresse afin d’intégrer ces hétérogénéités et d’étudier leurs effets sur les processus de diffusion. À l’aide de simulations mettant en jeu des réseaux réels et générés, nous montrons que les dynamiques de diffusion sont liées de manière non triviale à l’hétérogénéité de ces réseaux, en particulier la vitesse de propagation d’une contagion basée sur un effet de seuil. De plus, nous montrons que certaines classes de réseaux sont soumises à des transitions de phase réentrantes fonctions de la taille des “global cascades”.La tendance des réseaux réels à évoluer dans le temps rend difficile la modélisation des processus de diffusion. Nous montrons enfin que la durée de diffusion d’un processus de contagion basé sur un effet de seuil change de manière non-monotone du fait de la présence de“rafales” dans les motifs d’intéractions. L’ensemble de ces résultats mettent en lumière les effets de l’hétérogénéité des réseaux vis-à-vis des processus dynamiques y évoluant

Diffusion and Supercritical Spreading Processes on Complex Networks

Die große Menge an Datensätzen, die in den letzten Jahren verfügbar wurden, hat es ermöglicht, sowohl menschlich-getriebene als auch biologische komplexe Systeme in einem beispiellosen Ausmaß empirisch zu untersuchen. Parallel dazu ist die Vorhersage und Kontrolle epidemischer Ausbrüche für Fragen der öffentlichen Gesundheit sehr wichtig geworden. In dieser Arbeit untersuchen wir einige wichtige Aspekte von Diffusionsphänomenen und Ausbreitungsprozeßen auf Netzwerken. Wir untersuchen drei verschiedene Probleme im Zusammenhang mit Ausbreitungsprozeßen im überkritischen Regime. Zunächst untersuchen wir die Reaktionsdiffusion auf Ensembles zufälliger Netzwerke, die durch die beobachteten Levy-Flugeigenschaften der menschlichen Mobilität charakterisiert sind. Das zweite Problem ist die Schätzung der Ankunftszeiten globaler Pandemien. Zu diesem Zweck leiten wir geeignete verborgene Geometrien netzgetriebener Streuprozeße, unter Nutzung der Random-Walk-Theorie, her und identifizieren diese. Durch die Definition von effective distances wird das Problem komplexer raumzeitlicher Muster auf einfache, homogene Wellenausbreitungsmuster reduziert. Drittens führen wir durch die Einbettung von Knoten in den verborgenen Raum, der durch effective distances im Netzwerk definiert ist, eine neuartige Netzwerkzentralität ein, die ViralRank genannt wird und quantifiziert, wie nahe ein Knoten, im Durchschnitt, den anderen Knoten im Netzwerk ist. Diese drei Studien bilden einen einheitlichen Rahmen zur Charakterisierung von Diffusions- und Ausbreitungsprozeßen, die sich auf komplexen Netzwerken allgemein abzeichnen, und bieten neue Ansätze für herausfordernde theoretische Probleme, die für die Bewertung künftiger Modelle verwendet werden können.The large amount of datasets that became available in recent years has made it possible to empirically study humanly-driven, as well as biological complex systems to an unprecedented extent. In parallel, the prediction and control of epidemic outbreaks have become very important for public health issues. In this thesis, we investigate some important aspects of diffusion phenomena and spreading processes unfolding on networks. We study three different problems related to spreading processes in the supercritical regime. First, we study reaction-diffusion on ensembles of random networks characterized by the observed Levy-flight properties of human mobility. The second problem is the estimation of the arrival times of global pandemics. To this end, we derive and identify suitable hidden geometries of network-driven spreading processes, leveraging on random-walk theory. Through the definition of network effective distances, the problem of complex spatiotemporal patterns is reduced to simple, homogeneous wave propagation patterns. Third, by embedding nodes in the hidden space defined by network effective distances, we introduce a novel network centrality, called ViralRank, which quantifies how close a node is, on average, to the other nodes. These three studies constitute a unified framework to characterize diffusion and spreading processes unfolding on complex networks in very general settings, and provide new approaches to challenging theoretical problems that can be used to benchmark future models

Multiscale Modeling of Calcium-Induced Arrhythmias

Sudden cardiac death occurs when an unexpected ventricular arrhythmia degenerates into fibrillation, which prevents the heart from pumping blood through the body. Heart diseases such as heart failure are significant risk factors for arrhythmias and are characterized by severely altered calcium (Ca2+) handling in cardiac myocytes. However, the Ca2+-dependent mechanisms underlying cardiac arrhythmia initiation are not well understood. In this work, mathematical models were developed to investigate the molecular mechanisms of pathological Ca2+ dynamics in ventricular cardiac myocytes. A biophysically-detailed three-dimensional model of a subcellular Ca2+ release site was used to study mechanisms of spontaneous spatially-confined Ca2+ release events, known as Ca2+ “sparks,” which underlie cell-wide Ca2+ release and arrhythmogenic Ca2+ waves. It revealed a correlation between Ca2+ spark frequency and the maximum eigenvalue of the adjacency matrix describing the Ca2+ release channel lattice. This relationship was further investigated using a mathematical contact network model describing the Ca2+ spark initiation process. A multiscale model of a 1D fiber of myocytes was also developed to investigate the mechanisms of ectopic excitation of cardiac tissue. The model was used to study the stochastic variability of delayed afterdepolarizations caused by spontaneous propagating waves of Ca2+ sparks. Large delayed afterdepolarizations triggered ectopic beats probabilistically due to the stochasticity of Ca2+ release channel gating. A novel method was developed to estimate the probability of rare arrhythmic events

Stories from different worlds in the universe of complex systems: A journey through microstructural dynamics and emergent behaviours in the human heart and financial markets

A physical system is said to be complex if it exhibits unpredictable structures, patterns or regularities emerging from microstructural dynamics involving a large number of components. The study of complex systems, known as complexity science, is maturing into an independent and multidisciplinary area of research seeking to understand microscopic interactions and macroscopic emergence across a broad spectrum systems, such as the human brain and the economy, by combining specific modelling techniques, data analytics, statistics and computer simulations. In this dissertation we examine two different complex systems, the human heart and financial markets, and present various research projects addressing specific problems in these areas. Cardiac fibrillation is a diffuse pathology in which the periodic planar electrical conduction across the cardiac tissue is disrupted and replaced by fast and disorganised electrical waves. In spite of a century-long history of research, numerous debates and disputes on the mechanisms of cardiac fibrillation are still unresolved while the outcomes of clinical treatments remain far from satisfactory. In this dissertation we use cellular automata and mean-field models to qualitatively replicate the onset and maintenance of cardiac fibrillation from the interactions among neighboring cells and the underlying topology of the cardiac tissue. We use these models to study the transition from paroxysmal to persistent atrial fibrillation, the mechanisms through which the gap-junction enhancer drug Rotigaptide terminates cardiac fibrillation and how focal and circuital drivers of fibrillation may co-exist as projections of transmural electrical activities. Financial markets are hubs in which heterogeneous participants, such as humans and algorithms, adopt different strategic behaviors to exchange financial assets. In recent decades the widespread adoption of algorithmic trading, the electronification of financial transactions, the increased competition among trading venues and the use of sophisticated financial instruments drove the transformation of financial markets into a global and interconnected complex system. In this thesis we introduce agent-based and state-space models to describe specific microstructural dynamics in the stock and foreign exchange markets. We use these models to replicate the emergence of cross-currency correlations from the interactions between heterogeneous participants in the currency market and to disentangle the relationships between price fluctuations, market liquidity and demand/supply imbalances in the stock market.Open Acces

Bodily sensation in contemporary extreme horror film

Bodily Sensation in Contemporary Extreme Horror Film provides a theory of horror film spectatorship rooted in the physiology of the viewer. In a novel contribution to the field of film studies research, it seeks to integrate contemporary scientific theories of mind with psychological paradigms of film interpretation. Proceeding from a connectionist model of brain function that proposes psychological processes are underpinned by neurology, this thesis contends that whilst conscious engagement with film often appears to be driven by psychosocial conditions – including cultural influence, gender dynamics and social situation – it is physiology and bodily sensation that provide the infrastructure upon which this superstructure rests. Drawing upon the philosophical works of George Lakoff, Mark Johnson and Alain Berthoz, the argument concentrates upon explicating the specific bodily sensations and experiences that contribute to the creation of implicit structures of understanding, or embodied schemata, that we apply to the world round us. Integrating philosophy with contemporary neurological research in the spheres of cognition and neurocinematics, a number of correspondences are drawn between physiological states and the concomitant psychological states often perceived to arise simultaneously alongside them. The thesis offers detailed analysis of a selection of extreme horror films that, it is contended, conscientiously incorporate the body of the viewer in the process of spectatorship through manipulation of visual, auditory, vestibular, gustatory and nociceptive sensory stimulations, simulations and the embodied schemata that arise from everyday physiological experience. The phenomenological film criticism of Vivian Sobchack and Laura U. Marks is adopted and expanded upon in order to suggest that the organicity of the human body guides and structures the psychosocial engagement with, and interpretation of, contemporary extreme horror film. This project thus exposes the body as the architectural foundation upon which conscious interaction with film texts occurs

Reentrant phase transitions in threshold driven contagion on multiplex networks

Models of threshold driven contagion explain the cascading spread of information, behavior, systemic risk, and epidemics on social, financial, and biological networks. At odds with empirical observations, these models predict that single-layer unweighted networks become resistant to global cascades after reaching sufficient connectivity. We investigate threshold driven contagion on weight heterogeneous multiplex networks and show that they can remain susceptible to global cascades at any level of connectivity, and with increasing edge density pass through alternating phases of stability and instability in the form of reentrant phase transitions of contagion. Our results provide a theoretical explanation for the observation of large-scale contagion in highly connected but heterogeneous networks.Peer reviewe

Threshold driven contagion on complex networks

Networks arise frequently in the study of complex systems, since interactions among the components of such systems are critical. Net- works can act as a substrate for dynamical process, such as the diffusion of information or disease throughout populations. Network structure can determine the temporal evolution of a dynamical process, including the characteristics of the steady state. The simplest representation of a complex system is an undirected, unweighted, single layer graph. In contrast, real systems exhibit heterogeneity of interaction strength and type. Such systems are frequently represented as weighted multiplex networks, and in this work we in- corporate these heterogeneities into a master equation formalism in order to study their effects on spreading processes. We also carry out simulations on synthetic and empirical networks, and show that spread- ing dynamics, in particular the speed at which contagion spreads via threshold mechanisms, depend non-trivially on these heterogeneities. Further, we show that an important family of networks undergo reentrant phase transitions in the size and frequency of global cascades as a result of these interactions. A challenging feature of real systems is their tendency to evolve over time, since the changing structure of the underlying network is critical to the behaviour of overlying dynamical processes. We show that one aspect of temporality, the observed “burstiness” in interaction patterns, leads to non-monotic changes in the spreading time of threshold driven contagion processes. The above results shed light on the effects of various network heterogeneities, with respect to dynamical processes that evolve on these networks.Les interactions entre les composants des systèmes complexes font émerger différents types de réseaux. Ces réseaux peuvent jouer le rôle d’un substrat pour des processus dynamiques tels que la diffusion d’informations ou de maladies dans des populations. Les structures de ces réseaux déterminent l’évolution d’un processus dynamique, en particulier son régime transitoire, mais aussi les caractéristiques du régime permanent. Les systèmes complexes réels manifestent des interactions hétérogènes en type et en intensité. Ces systèmes sont représentés comme des réseaux pondérés à plusieurs couches. Dans cette thèse, nous développons une équation maîtresse afin d’intégrer ces hétérogénéités et d’étudier leurs effets sur les processus de diffusion. À l’aide de simulations mettant en jeu des réseaux réels et générés, nous montrons que les dynamiques de diffusion sont liées de manière non triviale à l’hétérogénéité de ces réseaux, en particulier la vitesse de propagation d’une contagion basée sur un effet de seuil. De plus, nous montrons que certaines classes de réseaux sont soumises à des transitions de phase réentrantes fonctions de la taille des “global cascades”. La tendance des réseaux réels à évoluer dans le temps rend difficile la modélisation des processus de diffusion. Nous montrons enfin que la durée de diffusion d’un processus de contagion basé sur un effet de seuil change de manière non-monotone du fait de la présence de “rafales” dans les motifs d’interactions. L’ensemble de ces résultats mettent en lumière les effets de l’hétérogénéité des réseaux vis-à-vis des processus dynamiques y évoluant

Threshold driven contagion on complex networks

Networks arise frequently in the study of complex systems, since interactions among the components of such systems are critical. Net- works can act as a substrate for dynamical process, such as the diffusion of information or disease throughout populations. Network structure can determine the temporal evolution of a dynamical process, including the characteristics of the steady state. The simplest representation of a complex system is an undirected, unweighted, single layer graph. In contrast, real systems exhibit heterogeneity of interaction strength and type. Such systems are frequently represented as weighted multiplex networks, and in this work we in- corporate these heterogeneities into a master equation formalism in order to study their effects on spreading processes. We also carry out simulations on synthetic and empirical networks, and show that spread- ing dynamics, in particular the speed at which contagion spreads via threshold mechanisms, depend non-trivially on these heterogeneities. Further, we show that an important family of networks undergo reentrant phase transitions in the size and frequency of global cascades as a result of these interactions. A challenging feature of real systems is their tendency to evolve over time, since the changing structure of the underlying network is critical to the behaviour of overlying dynamical processes. We show that one aspect of temporality, the observed “burstiness” in interaction patterns, leads to non-monotic changes in the spreading time of threshold driven contagion processes. The above results shed light on the effects of various network heterogeneities, with respect to dynamical processes that evolve on these networks.Les interactions entre les composants des systèmes complexes font émerger différents types de réseaux. Ces réseaux peuvent jouer le rôle d’un substrat pour des processus dynamiques tels que la diffusion d’informations ou de maladies dans des populations. Les structures de ces réseaux déterminent l’évolution d’un processus dynamique, en particulier son régime transitoire, mais aussi les caractéristiques du régime permanent. Les systèmes complexes réels manifestent des interactions hétérogènes en type et en intensité. Ces systèmes sont représentés comme des réseaux pondérés à plusieurs couches. Dans cette thèse, nous développons une équation maîtresse afin d’intégrer ces hétérogénéités et d’étudier leurs effets sur les processus de diffusion. À l’aide de simulations mettant en jeu des réseaux réels et générés, nous montrons que les dynamiques de diffusion sont liées de manière non triviale à l’hétérogénéité de ces réseaux, en particulier la vitesse de propagation d’une contagion basée sur un effet de seuil. De plus, nous montrons que certaines classes de réseaux sont soumises à des transitions de phase réentrantes fonctions de la taille des “global cascades”. La tendance des réseaux réels à évoluer dans le temps rend difficile la modélisation des processus de diffusion. Nous montrons enfin que la durée de diffusion d’un processus de contagion basé sur un effet de seuil change de manière non-monotone du fait de la présence de “rafales” dans les motifs d’interactions. L’ensemble de ces résultats mettent en lumière les effets de l’hétérogénéité des réseaux vis-à-vis des processus dynamiques y évoluant