Louis J. Dubé

Adaptive networks: Coevolution of disease and topology

Adaptive networks have been recently introduced in the context of disease propagation on complex networks. They account for the mutual interaction between the network topology and the states of the nodes. Until now, existing models have been analyzed using low complexity analytical formalisms, revealing nevertheless some novel dynamical features. However, current methods have failed to reproduce with accuracy the simultaneous time evolution of the disease and the underlying network topology. In the framework of the adaptive susceptible-infectious-susceptible (SIS) model of Gross [Phys. Rev. Lett. 96, 208701 (2006)]10.1103/PhysRevLett.96.208701, we introduce an improved compartmental formalism able to handle this coevolutionary task successfully. With this approach, we analyze the interplay and outcomes of both dynamical elements, process and structure, on adaptive networks featuring different degree distributions at the initial stage.

Modeling the dynamical interaction between epidemics on overlay networks.

Epidemics seldom occur as isolated phenomena. Typically, two or more viral agents spread within the same host population and may interact dynamically with each other. We present a general model where two viral agents interact via an immunity mechanism as they propagate simultaneously on two networks connecting the same set of nodes. By exploiting a correspondence between the propagation dynamics and a dynamical process performing progressive network generation, we develop an analytical approach that accurately captures the dynamical interaction between epidemics on overlay networks. The formalism allows for overlay networks with arbitrary joint degree distribution and overlap. To illustrate the versatility of our approach, we consider a hypothetical delayed intervention scenario in which an immunizing agent is disseminated in a host population to hinder the propagation of an undesirable agent (e.g., the spread of preventive information in the context of an emerging infectious disease).

Heterogeneous bond percolation on multitype networks with an application to epidemic dynamics

Considerable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes-in which the final state can be obtained by studying the underlying network percolation properties-have raised formidable interest. In this paper, we present a bond percolation model of multitype networks with an arbitrary joint degree distribution that allows heterogeneity in the edge occupation probability. As previously demonstrated, the multitype approach allows many nontrivial mixing patterns such as assortativity and clustering between nodes. We derive a number of useful statistical properties of multitype networks as well as a general phase transition criterion. We also demonstrate that a number of previous models based on probability generating functions are special cases of the proposed formalism. We further show that the multitype approach, by naturally allowing heterogeneity in the bond occupation probability, overcomes some of the correlation issues encountered by previous models. We illustrate this point in the context of contact network epidemiology.

Global efficiency of local immunization on complex networks

Epidemics occur in all shapes and forms: infections propagating in our sparse sexual networks, rumours and diseases spreading through our much denser social interactions, or viruses circulating on the Internet. With the advent of large databases and efficient analysis algorithms, these processes can be better predicted and controlled. In this study, we use different characteristics of network organization to identify the influential spreaders in 17 empirical networks of diverse nature using 2 epidemic models. We find that a judicious choice of local measures, based either on the networks connectivity at a microscopic scale or on its community structure at a mesoscopic scale, compares favorably to global measures, such as betweenness centrality, in terms of efficiency, practicality and robustness. We also develop an analytical framework that highlights a transition in the characteristic scale of different epidemic regimes. This allows to decide which local measure should govern immunization in a given scenario.

Continuum Distorted Wave Methods in Ion—Atom Collisions

Publisher Summary This chapter discusses the continuum distorted wave method in both time-dependent and time-independent form and presents the clarification of its physical interpretation. An extension of the continuum distorted wave (CDW) Ansatz has been developed to a multistate variational close coupling theory that removes the normalization difficulties encountered in the standard CDW approximation. In addition, it shows the new formalism to possess the desirable properties of Galilean invariance, gauge invariance, flux conservation and, above all, the absence of divergences. This last point has been seen to emerge in a natural and essential way from the use of wave functions that satisfy the correct Coulomb asymptotic boundary conditions. The CDW theory is understood most easily within the impact parameter treatment, which indeed was the format originally used by Cheshire (1964) in its inaugural presentation. By contrast, both Oppenheimer–Brinkman–Kramers (OBK) and strong-potential Born (SPB) wave theories are obliged to resort to off shell effects in a futile attempt to compensate for failure to satisfy the correct asymptotic boundary conditions.

Propagation dynamics on networks featuring complex topologies

Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently couple the dynamics of the network elements (such as nodes, vertices, individuals, etc.) on the one hand and their recurrent topological patterns (such as subgraphs, groups, etc.) on the other hand. In a susceptible-infectious-susceptible (SIS) model of epidemic spread on social networks with community structure, this approach yields a set of ordinary differential equations for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria. The results obtained are in good agreement with numerical simulations and reproduce the behavior of random networks in the appropriate limits which highlights the influence of topology on the processes. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.

Beam shaping using genetically optimized two-dimensional photonic crystals.

We propose the use of two-dimensional (2D) photonic crystals (PhCs) with engineered defects for the generation of an arbitrary-profile beam from a focused input beam. The cylindrical harmonics expansion of complex-source beams is derived and used to compute the scattered wave function of a 2D PhC via the multiple scattering method. The beam shaping problem is then solved using a genetic algorithm. We illustrate our procedure by generating different orders of Hermite-Gauss profiles, while maintaining reasonable losses and tolerance to variations in the input beam and the slab refractive index.

Ab initio investigation of lasing thresholds in photonic molecules

We investigate lasing thresholds in a representative photonic molecule composed of two coupled active cylinders of slightly different radii. Specifically, we use the recently formulated steady-state ab initio laser theory (SALT) to assess the effect of the underlying gain transition on lasing frequencies and thresholds. We find that the order in which modes lase can be modified by choosing suitable combinations of the gain center frequency and linewidth, a result that cannot be obtained using the conventional approach of quasi-bound modes. The impact of the gain transition center on the lasing frequencies, the frequency pulling effect, is also quantified.

Bond percolation on a class of correlated and clustered random graphs

We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the configuration model where nodes of different types are connected via different types of hyperedges, edges that can link more than two nodes. We argue that the multitype approach coupled with the use of clustered hyperedges can reproduce a wide spectrum of complex patterns, and thus enhances our capability to model real complex networks. As an illustration of this claim, we use our formalism to highlight unusual behaviours of the size and composition of the components (small and giant) in a synthetic, albeit realistic, social network.

Structural preferential attachment: network organization beyond the link.

We introduce a mechanism which models the emergence of the universal properties of complex networks, such as scale independence, modularity and self-similarity, and unifies them under a scale-free organization beyond the link. This brings a new perspective on network organization where communities, instead of links, are the fundamental building blocks of complex systems. We show how our simple model can reproduce social and information networks by predicting their community structure and more importantly, how their nodes or communities are interconnected, often in a self-similar manner.