arXiv subjects

Louis J. Dubé

Publications and source records attributed to Louis J. Dubé.

44 records · Page 3Linked to original sources

arXiv2011

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.

physics.soc-ph↗

arXiv2011

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. Exploiting a correspondence between the propagation dynamics and a dynamical process performing progressive network generation, we develop an analytic 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).

physics.soc-ph↗

arXiv2010

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 (nodes, vertices, individuals...) on the one hand and their recurrent topological patterns (subgraphs, groups...) on the other hand. In a SIS model of epidemic spread on social networks with community structure, this approach yields a set of ODEs 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 random networks behavior 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.

cond-mat.stat-mech↗

arXiv2010

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 analytic 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 SIS model of Gross et al. [Phys. Rev. Lett. 96, 208701 (2006)], 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.

cond-mat.stat-mech↗

arXiv2010

Phase Space Engineering in Optical Microcavities II: Controlling the far-field

Optical microcavities support Whispering Gallery Modes (WGMs) with a very high quality factor Q. However, WGMs typically display a far-field isotropic emission profile and modifying this far-field profile without spoiling the associated high Q remains a challenge. Using a 2D annular cavity, we present a procedure capable to achieve these two apparently conflicting goals. With the correspondence between the classical and the wave picture, properties of the classical phase space shed some light on the characteristics of the wave dynamics. Specifically, the annular cavity has a well separated mixed phase space, a characteristic that proves to be of crucial importance in the emission properties of WGMs. While the onset of directionality in the far-field may be achieved through parametric deformation of the distance cavity-hole centers, this contribution presents a method to control the emission profile via a second parameter, the hole radius. The influence of the classical dynamics to control and predict the field emission will be demonstrated.

physics.optics↗

arXiv2010

Phase Space Engineering in Optical Microcavities I: Preserving near-field uniformity while inducing far-field directionality

Optical microcavities have received much attention over the last decade from different research fields ranging from fundamental issues of cavity QED to specific applications such as microlasers and bio-sensors. A major issue in the latter applications is the difficulty to obtain directional emission of light in the far-field while keeping high energy densities inside the cavity (i.e. high quality factor). To improve our understanding of these systems, we have studied the annular cavity (a dielectric disk with a circular hole), where the distance cavity-hole centers, d, is used as a parameter to alter the properties of cavity resonances. We present results showing how one can affect the directionality of the far-field while preserving the uniformity (hence the quality factor) of the near-field simply by increasing the value of d. Interestingly, the transition between a uniform near- and far-field to a uniform near- and directional far-field is rather abrupt. We can explain this behavior quite nicely with a simple model, supported by full numerical calculations, and we predict that the effect will also be found in a large class of eigenmodes of the cavity.

physics.optics↗

arXiv2009

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 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 non-trivial 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.

q-bio.PE↗

arXiv2007

Time Evolution of Disease Spread on Networks with Degree Heterogeneity

Two crucial elements facilitate the understanding and control of communicable disease spread within a social setting. These components are, the underlying contact structure among individuals that determines the pattern of disease transmission; and the evolution of this pattern over time. Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches to incorporate these elements. The first approach, generally known as compartmental modeling, addresses the time evolution of disease spread at the expense of simplifying the pattern of transmission. On the other hand, the second approach uses network theory to incorporate detailed information pertaining to the underlying contact structure among individuals. However, while providing accurate estimates on the final size of outbreaks/epidemics, this approach, in its current formalism, disregards the progression of time during outbreaks. So far, the only alternative that enables the integration of both aspects of disease spread simultaneously has been to abandon the analytical approach and rely on computer simulations. We offer a new analytical framework based on percolation theory, which incorporates both the complexity of contact network structure and the time progression of disease spread. Furthermore, we demonstrate that this framework is equally effective on finite- and "infinite"-size networks. Application of this formalism is not limited to disease spread; it can be equally applied to similar percolation phenomena on networks in other areas in science and technology.

q-bio.PE↗