Exact solution of bond percolation on small arbitrary graphs

We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution of the node partitions (i.e., the constrained distribution of the size of each component) in undirected graphs. Besides opening the way to the theoretical prediction of percolation on arbitrary graphs of large but finite size, we show how our results find application in graph theory, epidemiology, percolation and fragmentation theory.Comment: 5 pages and 3 figure

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.Comment: 11 pages, 8 figures, 1 appendix. To be published in Physical Review

Strategic tradeoffs in competitor dynamics on adaptive networks

Recent empirical work highlights the heterogeneity of social competitions such as political campaigns: proponents of some ideologies seek debate and conversation, others create echo chambers. While symmetric and static network structure is typically used as a substrate to study such competitor dynamics, network structure can instead be interpreted as a signature of the competitor strategies, yielding competition dynamics on adaptive networks. Here we demonstrate that tradeoffs between aggressiveness and defensiveness (i.e., targeting adversaries vs. targeting like-minded individuals) creates paradoxical behaviour such as non-transitive dynamics. And while there is an optimal strategy in a two competitor system, three competitor systems have no such solution; the introduction of extreme strategies can easily affect the outcome of a competition, even if the extreme strategies have no chance of winning. Not only are these results reminiscent of classic paradoxical results from evolutionary game theory, but the structure of social networks created by our model can be mapped to particular forms of payoff matrices. Consequently, social structure can act as a measurable metric for social games which in turn allows us to provide a game theoretical perspective on online political debates.Comment: 20 pages (11 pages for the main text and 9 pages of supplementary material

Ressources territoriales et destinations touristiques : des couples en devenir ?: Les expériences de production du safran à Taliouine (Maroc) et de l'oignon dans l'Aïr (Niger)

L'article est en cours d'édition dans la Revue de Géographie Alpinecultural tourism rests on the construction of destinations carrying recognized and sought outside qualities. It is a set of specific resources whose singularity is justified by an anchoring with the territories which produce them. This article proposes a grid of analysis of the resource, through three stages: the revelation, the development and the articulation with other resources. This grid of analysis is then applied to various situations observed in Morocco and Niger. This approach makes it possible to look further into the concept of quality associated with a resource and to question the conditions of formation of the basket of goods, associating commercial objects and non-commercial objects. This Co-construction leads to the association of objects of which certain qualities could be transposed to other objects, because of their anchoring with the territory.Le tourisme culturel repose sur la construction de destinations porteuses de qualités reconnues et recherchées à l'extérieur. C'est un ensemble de ressources spécifiques dont la singularité est justifiée par un ancrage aux territoires qui les produisent. Le présent article propose une grille d'analyse de la ressource, en approfondissant la phase de révélation. Cette grille est ensuite appliquée à différentes situations observées au Maroc et au Niger. Cette approche permet d'approfondir la notion de qualité associée à une ressource et d'interroger les conditions de formation du panier de biens, associant des objets marchands et des objets non marchands. Cette co-construction aboutit à l'association d'objets dont certaines qualités vont pouvoir être transposées à d'autres objets, du fait de leur ancrage au territoire

Ressources territoriales et destinations touristiques : des couples en devenir ?: Les expériences de production du safran à Taliouine (Maroc) et de l'oignon dans l'Aïr (Niger)

L'article est en cours d'édition dans la Revue de Géographie Alpinecultural tourism rests on the construction of destinations carrying recognized and sought outside qualities. It is a set of specific resources whose singularity is justified by an anchoring with the territories which produce them. This article proposes a grid of analysis of the resource, through three stages: the revelation, the development and the articulation with other resources. This grid of analysis is then applied to various situations observed in Morocco and Niger. This approach makes it possible to look further into the concept of quality associated with a resource and to question the conditions of formation of the basket of goods, associating commercial objects and non-commercial objects. This Co-construction leads to the association of objects of which certain qualities could be transposed to other objects, because of their anchoring with the territory.Le tourisme culturel repose sur la construction de destinations porteuses de qualités reconnues et recherchées à l'extérieur. C'est un ensemble de ressources spécifiques dont la singularité est justifiée par un ancrage aux territoires qui les produisent. Le présent article propose une grille d'analyse de la ressource, en approfondissant la phase de révélation. Cette grille est ensuite appliquée à différentes situations observées au Maroc et au Niger. Cette approche permet d'approfondir la notion de qualité associée à une ressource et d'interroger les conditions de formation du panier de biens, associant des objets marchands et des objets non marchands. Cette co-construction aboutit à l'association d'objets dont certaines qualités vont pouvoir être transposées à d'autres objets, du fait de leur ancrage au territoire

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).Comment: Accepted for publication in Phys. Rev. E. 15 pages, 7 figure

Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal gas

Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal gas is studied in the framework of an exact analytic approach. For an initial symmetric three-velocity distribution, the problem can be solved exactly and it is shown that different regimes exist depending on the initial fraction of particles at rest. Extension to the case of a n-velocity distribution is discussed.Comment: 19 pages, latex, uses Revtex macro

Influence of support on intra-abdominal pressure, hepatic kinetics of indocyanine green and extravascular lung water during prone positioning in patients with ARDS: a randomized crossover study

INTRODUCTION: Prone positioning (PP) on an air-cushioned mattress is associated with a limited increase in intra-abdominal pressure (IAP) and an absence of organ dysfunction. The respective influence of posture by itself and the type of mattress on these limited modifications during the PP procedure remains unclear. The aim of this study was to evaluate whether the type of support modifies IAP, extravascular lung water (EVLW) and the plasma disappearance rate of indocyanine green (PDR(ICG)) during PP. METHODS: A prospective, randomized, crossover study of 20 patients with acute respiratory distress syndrome (ARDS) was conducted in a medical intensive care unit in a teaching hospital. Measurements were made at baseline and repeated after 1 and 6 hours of two randomized periods of 6 hours of PP with one of two support types: conventional foam mattress or air-cushioned mattress. RESULTS: After logarithmic transformation of the data, an analysis of variance (ANOVA) showed that IAP and PDR(ICG )were significantly influenced by the type of support during PP with an increase in IAP (P < 0.05 by ANOVA) and a decrease in PDR(ICG )on the foam mattress (P < 0.05 by ANOVA). Conversely, the measurements of EVLW did not show significant modification between the two supports whatever the posture. The ratio of the arterial oxygen tension to the fraction of inspired oxygen significantly increased in PP (P < 0.0001 by ANOVA) without any influence of the support. CONCLUSION: In comparison with a conventional foam mattress, the use of an air-cushioned mattress limited the increase in IAP and prevented the decrease in PDR(ICG )related to PP in patients with ARDS. Conversely, the type of support did not influence EVLW or oxygenation

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.Comment: 10 pages, 5 figures, 1 Appendix. Published in Phys. Rev. E (mistakes in the PRE version are corrected here