Worst-Case Scenarios for Greedy, Centrality-Based Network Protection Strategies

The task of allocating preventative resources to a computer network in order to protect against the spread of viruses is addressed. Virus spreading dynamics are described by a linearized SIS model and protection is framed by an optimization problem which maximizes the rate at which a virus in the network is contained given finite resources. One approach to problems of this type involve greedy heuristics which allocate all resources to the nodes with large centrality measures. We address the worst case performance of such greedy algorithms be constructing networks for which these greedy allocations are arbitrarily inefficient. An example application is presented in which such a worst case network might arise naturally and our results are verified numerically by leveraging recent results which allow the exact optimal solution to be computed via geometric programming

Optimal curing policy for epidemic spreading over a community network with heterogeneous population

The design of an efficient curing policy, able to stem an epidemic process at an affordable cost, has to account for the structure of the population contact network supporting the contagious process. Thus, we tackle the problem of allocating recovery resources among the population, at the lowest cost possible to prevent the epidemic from persisting indefinitely in the network. Specifically, we analyze a susceptible-infected-susceptible epidemic process spreading over a weighted graph, by means of a first-order mean-field approximation. First, we describe the influence of the contact network on the dynamics of the epidemics among a heterogeneous population, that is possibly divided into communities. For the case of a community network, our investigation relies on the graph-theoretical notion of equitable partition; we show that the epidemic threshold, a key measure of the network robustness against epidemic spreading, can be determined using a lower-dimensional dynamical system. Exploiting the computation of the epidemic threshold, we determine a cost-optimal curing policy by solving a convex minimization problem, which possesses a reduced dimension in the case of a community network. Lastly, we consider a two-level optimal curing problem, for which an algorithm is designed with a polynomial time complexity in the network size.Comment: to be published on Journal of Complex Network

Message Passing Techniques For Statistical Physics And Optimization In Complex Systems

Optimization problem has always been considered as a central topic in various areas of science and engineering. It aims at finding the configuration of a large number of variables with which the objective function is optimal. The close relation between optimization problems and statistical physics through the probability measure of the Boltzmann type has brought new theoretical tools from statistical physics of disordered systems to optimization problems. In this thesis, we use message passing techniques, in particular cavity method, developed in the last decades within spin glass theory to study optimization problems in complex systems. In the study of force transmission in jammed disordered systems, we develop a mean-field theory based on the consideration of the contact network as a random graph where the force transmission becomes a constraint satisfaction problem, with which the constraints enforce force and torque balances on each particle. We thus use cavity method to compute the force distribution for random packings of hard particles of any shape, with or without friction and find a new signature of jamming in the small force behavior whose exponent has attracted recent active interest. Furthermore, we relate the force distribution to a lower bound of the average coordination number of jammed packings of frictional spheres. The theoretical framework describes different types of systems, such as non-spherical objects in arbitrary dimensions, providing a common mean-field scenario to investigate force transmission, contact networks and coordination numbers of jammed disordered packings. Another application of the cavity method is immunization strategies. We study the problem of finding the most influential set of nodes in interaction networks to immunize against epidemics. By means of cavity method approach, we propose a new immunization strategy to identify immunization targets efficiently with respect to the susceptable-infected-recovered epidemic model. We implement our method on computer-generated random graphs and real networks and find that our new immunization strategy can significantly reduce the size of epidemic

Computational framework for modeling infrastructure network performance and vulnerability

Networked infrastructures serve as essential backbones of our society. Examples of such critical infrastructures whose destruction severely impacts the defense or economic security of our society include transportation, telecommunications, power grids, and water supply networks. Among them, road transportation networks have a principal role in people's everyday lives since they facilitate physical connectivity. The performance of a road transportation network is governed by the three principal components: (a) structure, (b) dynamics, and (c) external causes. The structure defines the topology of a network including links and nodes. The dynamics (i.e., traffic flow) defines what processes are happening on the network. The external causes (e.g., disasters and driver distraction) are the phenomena that impact either structure or dynamics. These principal components do tend to influence each other. For example, the collapse of a bridge (i.e., external cause) could render certain nodes and links (i.e., structure) ineffective thereby affecting traffic flow (i.e., dynamics). A distracted driver (i.e., external cause) on a road can also cause accidents that can negatively impact traffic flow. Thus, to model the performance and vulnerability of a network, it is necessary to consider such interactions among these principal components. The main objective of this research is to formalize and develop a computational framework that can: (a) predict the macroscopic performance of a transportation network based on its multiple structural and dynamical attributes (Chapter 2), (b) analyze its vulnerability as a result of man-made/natural disruption that minimizes network connectivity (Chapter 3), and (c) evaluate network vulnerability due to driver distraction (Chapter 4). An integrated framework to address these challenges--which have largely been investigated as separate research topics, such as distracted driving, infrastructure vulnerability assessment and traffic demand modeling--needs to simultaneously consider all three principal components (i.e., structure, dynamics, and external causes) of a network. In this research, the integrated framework is built upon recent developments (theories and methods) in interdisciplinary domains, such as network science, cognitive science and transportation engineering. This is the novelty of the proposed framework compared to existing approaches. Finally, the framework were validated using real-world data, existing studies and traffic simulated results.Ph.D., Civil Engineering -- Drexel University, 201

Higher-order dynamics on complex networks

L’estudi de les xarxes complexes ha esdevingut un nou paradigma a l’hora d’entendre i modelar sistemes físics. Uns dels principals punts d’interès són les dinàmiques que hi podem modelar. Però com en tot model, la quantitat de informació que podem representar-hi està limitada per la seva complexitat. La motivació principal d’aquesta tesi és l’estudi de l’efecte que un increment de la complexitat estructural, relacional i temporal té sobre tres importants àrees d’estudi: l’evolució de la cooperació, la propagació de malalties, i l’estudi de la mobilitat humana. En aquest treball hem utilitzat dilemes socials per estudiar com evoluciona la cooperació dins d’una població. Incrementant l’ordre de complexitat estructural de les xarxes, permetent que els individus és puguin relacionar en diferents contextos socials, s’ha mostrat cabdal a l’hora d’explicar algunes característiques sobre l’aparició de comportaments altruistes. Utilitzant aquestes noves estructures, les xarxes multicapa, permetem als membres de la població cooperar en determinat contextos i de no fer-ho en d’altres i això, com analíticament demostrem, augmenta l’espectre d’escenaris allà on cooperació i defecció poden sobreviure. Seguidament, estudiem els models de propagació de malalties des de el punt de vista dels enllaços entre individus. Amb aquest augment de la complexitat relacional dels models epidèmics, aconseguim extreure informació que ens permet, entre altres coses, definir una mesura d’influència d’un enllaç a la propagació de l’epidèmia. Utilitzem aquest fet per a proposar una nova mesura de contenció, basada en l’eliminació dels enllaços més influents, que es mostra més eficient que altres mètodes previs. Finalment, proposem un mètode per a descriure la mobilitat que permet capturar patrons recurrents i heterogeneïtats en els temps que els individus estan en un lloc abans de desplaçar-se a un altre. Aquestes propietats són intrínseques a la mobilitat humana i el fet de poder-les capturar, tot i el cost d’augmentar l’ordre temporal, és crític, com demostrem, a l’hora de modelar com les epidèmies és difonen per mitja del moviment de les persones.El estudio de redes complejas se ha convertido en un nuevo paradigma para comprender y modelar sistemas físicos. Uno de los principales puntos de interés son las dinámicas que podemos modelar. Pero como en todo modelo, la cantidad de información que podemos representar está limitada por su complejidad. La motivación principal de esta tesis es estudiar el efecto que un incremento de la complejidad estructural, relacional y temporal tiene sobre tres importantes áreas de estudio: la evolución de la cooperación, la propagación de enfermedades, y el estudio de la movilidad humana. En este trabajo hemos utilizado dilemas sociales para estudiar cómo evoluciona la cooperación dentro de una población. Incrementando el orden de complejidad estructural de las redes, permitiendo que los individuos se puedan relacionar en diferentes contextos sociales, se ha demostrado capital para explicar algunas de las características sobre la aparición de comportamientos altruistas. Utilizando estas nuevas estructuras, las redes multicapa, permitimos a los miembros de la población cooperar en determinados contextos y no hacerlo en otros, con lo que, como demostramos analíticamente, aumenta el espectro de escenarios en los que la cooperación y la defección pueden sobrevivir. A continuación, estudiamos modelos de propagación de enfermedades desde el punto de vista de los enlaces entre individuos. Con este aumento de complejidad relacional de los modelos epidémicos, conseguimos extraer información que nos permite, entre otras cosas, definir una medida de contención, basada en la eliminación de los enlaces más influyentes, que se muestra más eficaz que otros métodos previos. Finalmente, proponemos un método para describir la movilidad que permite capturar patrones recurrentes y heterogeneidades en los tiempos que los individuos están en un lugar antes de desplazarse a otro. Estas propiedades son intrínsecas a la movilidad humana y el hecho de poder capturarlas, a pesar de incrementar el orden temporal, es crítico, como demostramos, para modelar cómo las epidemias se difunden por medio del movimiento de las personas.The study of complex networks has become a new paradigm to understand and model physical systems. One of the points of interest is the dynamics that we can model. However, as with any model, the amount of information that we can represent is limited by its complexity. The primary motivation of this thesis is the study of the effect that an increase in structural, relational and temporal complexity has on three critical areas of study: the evolution of cooperation, epidemic spreading and human mobility. In this work, we have used social dilemmas to study how cooperation within a population evolves. Increasing the order of structural complexity of the networks, allowing individuals to interact in different social contexts, has shown to be crucial to explain some features about the emergence of altruistic behaviors. Using these new structures, multilayer networks, we allow members of the population to cooperate in specific contexts and defect in others, and this, as we analytically demonstrate, increases the spectrum of scenarios where both strategies can survive. Next, we study the models of epidemic spreading from the point of view of the links between individuals. With this increase in the relational complexity of the epidemic models, we can extract information that allows us, among other things, to define a measure of the contribution of a link to the spreading. We use this metric to propose a new containment measure, based on the elimination of the most influential links, which is more effective than other previous methods. Finally, we propose a method to describe mobility that allows capturing recurrent and heterogeneous patterns in the times that individuals stay in a place before moving to another. These properties are intrinsic to human mobility, and the fact of being able to capture them, despite the cost of increasing the temporal order is critical, as we demonstrate, when it comes to modeling how epidemics spread through the movement of the people