arXiv subjects

Victor M. Preciado

Publications and source records attributed to Victor M. Preciado.

At least 91 records · Page 5Linked to original sources

arXiv2014

Optimal Resource Allocation for Network Protection Against Spreading Processes

We study the problem of containing spreading processes in arbitrary directed networks by distributing protection resources throughout the nodes of the network. We consider two types of protection resources are available: (i) Preventive resources able to defend nodes against the spreading (such as vaccines in a viral infection process), and (ii) corrective resources able to neutralize the spreading after it has reached a node (such as antidotes). We assume that both preventive and corrective resources have an associated cost and study the problem of finding the cost-optimal distribution of resources throughout the nodes of the network. We analyze these questions in the context of viral spreading processes in directed networks. We study the following two problems: (i) Given a fixed budget, find the optimal allocation of preventive and corrective resources in the network to achieve the highest level of containment, and (ii) when a budget is not specified, find the minimum budget required to control the spreading process. We show that both resource allocation problems can be solved in polynomial time using Geometric Programming (GP) for arbitrary directed graphs of nonidentical nodes and a wide class of cost functions. Furthermore, our approach allows to optimize simultaneously over both preventive and corrective resources, even in the case of cost functions being node-dependent. We illustrate our approach by designing optimal protection strategies to contain an epidemic outbreak that propagates through an air transportation network.

math.OC↗

arXiv2014

Joint Estimation and Localization in Sensor Networks

This paper addresses the problem of collaborative tracking of dynamic targets in wireless sensor networks. A novel distributed linear estimator, which is a version of a distributed Kalman filter, is derived. We prove that the filter is mean square consistent in the case of static target estimation. When large sensor networks are deployed, it is common that the sensors do not have good knowledge of their locations, which affects the target estimation procedure. Unlike most existing approaches for target tracking, we investigate the performance of our filter when the sensor poses need to be estimated by an auxiliary localization procedure. The sensors are localized via a distributed Jacobi algorithm from noisy relative measurements. We prove strong convergence guarantees for the localization method and in turn for the joint localization and target estimation approach. The performance of our algorithms is demonstrated in simulation on environmental monitoring and target tracking tasks.

cs.MA↗

arXiv2014

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.

cs.SI↗

arXiv2013

Traffic Control for Network Protection Against Spreading Processes

Epidemic outbreaks in human populations are facilitated by the underlying transportation network. We consider strategies for containing a viral spreading process by optimally allocating a limited budget to three types of protection resources: (i) Traffic control resources, (ii), preventative resources and (iii) corrective resources. Traffic control resources are employed to impose restrictions on the traffic flowing across directed edges in the transportation network. Preventative resources are allocated to nodes to reduce the probability of infection at that node (e.g. vaccines), and corrective resources are allocated to nodes to increase the recovery rate at that node (e.g. antidotes). We assume these resources have monetary costs associated with them, from which we formalize an optimal budget allocation problem which maximizes containment of the infection. We present a polynomial time solution to the optimal budget allocation problem using Geometric Programming (GP) for an arbitrary weighted and directed contact network and a large class of resource cost functions. We illustrate our approach by designing optimal traffic control strategies to contain an epidemic outbreak that propagates through a real-world air transportation network.

eess.SY↗

arXiv2013

Laplacian Spectral Properties of Graphs from Random Local Samples

The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and the structure of `local' subgraphs of the network. We call a subgraph \emph{local} when it is induced by the set of nodes obtained from a breath-first search (BFS) of radius $r$ around a node. In this paper, we propose techniques to estimate spectral properties of the normalized Laplacian matrix from a random collection of induced local subgraphs. In particular, we provide an algorithm to estimate the spectral moments of the normalized Laplacian matrix (the power-sums of its eigenvalues). Moreover, we propose a technique, based on convex optimization, to compute upper and lower bounds on the spectral radius of the normalized Laplacian matrix from local subgraphs. We illustrate our results studying the normalized Laplacian spectrum of a large-scale online social network.

cs.SI↗

arXiv2013

Traffic Optimization to Control Epidemic Outbreaks in Metapopulation Models

We propose a novel framework to study viral spreading processes in metapopulation models. Large subpopulations (i.e., cities) are connected via metalinks (i.e., roads) according to a metagraph structure (i.e., the traffic infrastructure). The problem of containing the propagation of an epidemic outbreak in a metapopulation model by controlling the traffic between subpopulations is considered. Controlling the spread of an epidemic outbreak can be written as a spectral condition involving the eigenvalues of a matrix that depends on the network structure and the parameters of the model. Based on this spectral condition, we propose a convex optimization framework to find cost-optimal approaches to traffic control in epidemic outbreaks.

physics.soc-ph↗

arXiv2013

A Convex Framework for Optimal Investment on Disease Awareness in Social Networks

We consider the problem of controlling the propagation of an epidemic outbreak in an arbitrary network of contacts by investing on disease awareness throughout the network. We model the effect of agent awareness on the dynamics of an epidemic using the SAIS epidemic model, an extension of the SIS epidemic model that includes a state of "awareness". This model allows to derive a condition to control the spread of an epidemic outbreak in terms of the eigenvalues of a matrix that depends on the network structure and the parameters of the model. We study the problem of finding the cost-optimal investment on disease awareness throughout the network when the cost function presents some realistic properties. We propose a convex framework to find cost-optimal allocation of resources. We validate our results with numerical simulations in a real online social network.

cs.SI↗

arXiv2013

Topology Identification of Directed Dynamical Networks via Power Spectral Analysis

We address the problem of identifying the topology of an unknown weighted, directed network of LTI systems stimulated by wide-sense stationary noises of unknown power spectral densities. We propose several reconstruction algorithms based on the cross-power spectral densities of the network's response to the input noises. Our first algorithm reconstructs the Boolean structure (i.e., existence and directions of links) of a directed network from a series of dynamical responses. Moreover, we propose a second algorithm to recover the exact structure of the network (including edge weights), as well as the power spectral density of the input noises, when an eigenvalue-eigenvector pair of the connectivity matrix is known (for example, Laplacian connectivity matrices). Finally, for the particular cases of nonreciprocal networks (i.e., networks with no directed edges pointing in opposite directions) and undirected networks, we propose specialized algorithms that result in a lower computational cost.

eess.SY↗

arXiv2013

Detection and Isolation of Link Failures under the Agreement Protocol

In this paper a property of the multi-agent consensus dynamics that relates the failure of links in the network to jump discontinuities in the derivatives of the output responses of the nodes is derived and verified analytically. At the next step, an algorithm for sensor placement is proposed, which would enable the designer to detect and isolate any link failures across the network based on the observed jump discontinuities in the derivatives of the responses of a subset of nodes. These results are explained through elaborative examples.

eess.SY↗

arXiv2013

Optimal Vaccine Allocation to Control Epidemic Outbreaks in Arbitrary Networks

We consider the problem of controlling the propagation of an epidemic outbreak in an arbitrary contact network by distributing vaccination resources throughout the network. We analyze a networked version of the Susceptible-Infected-Susceptible (SIS) epidemic model when individuals in the network present different levels of susceptibility to the epidemic. In this context, controlling the spread of an epidemic outbreak can be written as a spectral condition involving the eigenvalues of a matrix that depends on the network structure and the parameters of the model. We study the problem of finding the optimal distribution of vaccines throughout the network to control the spread of an epidemic outbreak. We propose a convex framework to find cost-optimal distribution of vaccination resources when different levels of vaccination are allowed. We also propose a greedy approach with quality guarantees for the case of all-or-nothing vaccination. We illustrate our approaches with numerical simulations in a real social network.

cs.SI↗

arXiv2013

Reconstruction of Directed Networks from Consensus Dynamics

This paper addresses the problem of identifying the topology of an unknown, weighted, directed network running a consensus dynamics. We propose a methodology to reconstruct the network topology from the dynamic response when the system is stimulated by a wide-sense stationary noise of unknown power spectral density. The method is based on a node-knockout, or grounding, procedure wherein the grounded node broadcasts zero without being eliminated from the network. In this direction, we measure the empirical cross-power spectral densities of the outputs between every pair of nodes for both grounded and ungrounded consensus to reconstruct the unknown topology of the network. We also establish that in the special cases of undirected or purely unidirectional networks, the reconstruction does not need grounding. Finally, we extend our results to the case of a directed network assuming a general dynamics, and prove that the developed method can detect edges and their direction.

cs.SI↗

arXiv2012

Moment-Based Spectral Analysis of Large-Scale Networks Using Local Structural Information

The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the importance of nodes in the network. A common approach to study the relationship between the structure of a network and its eigenvalues is to use synthetic random networks in which structural properties of interest, such as degree distributions, are prescribed. Although very common, synthetic models present two major flaws: (\emph{i}) These models are only suitable to study a very limited range of structural properties, and (\emph{ii}) they implicitly induce structural properties that are not directly controlled and can deceivingly influence the network eigenvalue spectrum. In this paper, we propose an alternative approach to overcome these limitations. Our approach is not based on synthetic models, instead, we use algebraic graph theory and convex optimization to study how structural properties influence the spectrum of eigenvalues of the network. Using our approach, we can compute with low computational overhead global spectral properties of a network from its local structural properties. We illustrate our approach by studying how structural properties of online social networks influence their eigenvalue spectra.

cs.SI↗

arXiv2012

Spectral Design of Dynamic Networks via Local Operations

Motivated by the relationship between the eigenvalue spectrum of the Laplacian matrix of a network and the behavior of dynamical processes evolving in it, we propose a distributed iterative algorithm in which a group of $n$ autonomous agents self-organize the structure of their communication network in order to control the network's eigenvalue spectrum. In our algorithm, we assume that each agent has access only to a local (myopic) view of the network around it. In each iteration, agents in the network peform a decentralized decision process to determine the edge addition/deletion that minimizes a distance function defined in the space of eigenvalue spectra. This spectral distance presents interesting theoretical properties that allow an efficient distributed implementation of the decision process. Our iterative algorithm is stable by construction, i.e., locally optimizes the network's eigenvalue spectrum, and is shown to perform extremely well in practice. We illustrate our results with nontrivial simulations in which we design networks matching the spectral properties of complex networks, such as small-world and power-law networks.

math.OC↗

arXiv2012

Structural Analysis of Laplacian Spectral Properties of Large-Scale Networks

Using methods from algebraic graph theory and convex optimization, we study the relationship between local structural features of a network and spectral properties of its Laplacian matrix. In particular, we derive expressions for the so-called spectral moments of the Laplacian matrix of a network in terms of a collection of local structural measurements. Furthermore, we propose a series of semidefinite programs to compute bounds on the spectral radius and the spectral gap of the Laplacian matrix from a truncated sequence of Laplacian spectral moments. Our analysis shows that the Laplacian spectral moments and spectral radius are strongly constrained by local structural features of the network. On the other hand, we illustrate how local structural features are usually not enough to estimate the Laplacian spectral gap.

math.OC↗

arXiv2012

Structural Analysis of Viral Spreading Processes in Social and Communication Networks Using Egonets

We study how the behavior of viral spreading processes is influenced by local structural properties of the network over which they propagate. For a wide variety of spreading processes, the largest eigenvalue of the adjacency matrix of the network plays a key role on their global dynamical behavior. For many real-world large-scale networks, it is unfeasible to exactly retrieve the complete network structure to compute its largest eigenvalue. Instead, one usually have access to myopic, egocentric views of the network structure, also called egonets. In this paper, we propose a mathematical framework, based on algebraic graph theory and convex optimization, to study how local structural properties of the network constrain the interval of possible values in which the largest eigenvalue must lie. Based on this framework, we present a computationally efficient approach to find this interval from a collection of egonets. Our numerical simulations show that, for several social and communication networks, local structural properties of the network strongly constrain the location of the largest eigenvalue and the resulting spreading dynamics. From a practical point of view, our results can be used to dictate immunization strategies to tame the spreading of a virus, or to design network topologies that facilitate the spreading of information virally.

math.OC↗

arXiv2011

Analysis of Equilibria and Strategic Interaction in Complex Networks

This paper studies $n$-person simultaneous-move games with linear best response function, where individuals interact within a given network structure. This class of games have been used to model various settings, such as, public goods, belief formation, peer effects, and oligopoly. The purpose of this paper is to study the effect of the network structure on Nash equilibrium outcomes of this class of games. Bramoullé et al. derived conditions for uniqueness and stability of a Nash equilibrium in terms of the smallest eigenvalue of the adjacency matrix representing the network of interactions. Motivated by this result, we study how local structural properties of the network of interactions affect this eigenvalue, influencing game equilibria. In particular, we use algebraic graph theory and convex optimization to derive new bounds on the smallest eigenvalue in terms of the distribution of degrees, cycles, and other relevant substructures. We illustrate our results with numerical simulations involving online social networks.

cs.GT↗

arXiv2011

From Local Measurements to Network Spectral Properties: Beyond Degree Distributions

It is well-known that the behavior of many dynamical processes running on networks is intimately related to the eigenvalue spectrum of the network. In this paper, we address the problem of inferring global information regarding the eigenvalue spectrum of a network from a set of local samples of its structure. In particular, we find explicit relationships between the so-called spectral moments of a graph and the presence of certain small subgraphs, also called motifs, in the network. Since the eigenvalues of the network have a direct influence on the network dynamical behavior, our result builds a bridge between local network measurements (i.e., the presence of small subgraphs) and global dynamical behavior (via the spectral moments). Furthermore, based on our result, we propose a novel decentralized scheme to compute the spectral moments of a network by aggregating local measurements of the network topology. Our final objective is to understand the relationships between the behavior of dynamical processes taking place in a large-scale complex network and its local topological properties.

math.OC↗

arXiv2010

Spectral Control of Mobile Robot Networks

The eigenvalue spectrum of the adjacency matrix of a network is closely related to the behavior of many dynamical processes run over the network. In the field of robotics, this spectrum has important implications in many problems that require some form of distributed coordination within a team of robots. In this paper, we propose a continuous-time control scheme that modifies the structure of a position-dependent network of mobile robots so that it achieves a desired set of adjacency eigenvalues. For this, we employ a novel abstraction of the eigenvalue spectrum by means of the adjacency matrix spectral moments. Since the eigenvalue spectrum is uniquely determined by its spectral moments, this abstraction provides a way to indirectly control the eigenvalues of the network. Our construction is based on artificial potentials that capture the distance of the network's spectral moments to their desired values. Minimization of these potentials is via a gradient descent closed-loop system that, under certain convexity assumptions, ensures convergence of the network topology to one with the desired set of moments and, therefore, eigenvalues. We illustrate our approach in nontrivial computer simulations.

cs.MA↗