ResearchPad - polymer-soft-matter-biological-climate-and-interdisciplinary-physics https://www.researchpad.co Default RSS Feed en-us © 2020 Newgen KnowledgeWorks <![CDATA[Critical Stretching of Mean-Field Regimes in Spatial Networks]]> https://www.researchpad.co/article/elastic_article_7364 We study a spatial network model with exponentially distributed link lengths on an underlying grid of points, undergoing a structural crossover from a random, Erdős-Rényi graph, to a d-dimensional lattice at the characteristic interaction range ζ. We find that, whilst far from the percolation threshold the random part of the giant component scales linearly with ζ, close to criticality it extends in space until the universal length scale ζ6/(6-d), for d<6, before crossing over to the spatial one. We demonstrate the universal behavior of the spatiotemporal scales characterizing this critical stretching phenomenon of mean-field regimes in percolation and in dynamical processes on d=2 networks, and we discuss its general implications to real-world phenomena, such as neural activation, traffic flows or epidemic spreading.

]]>
<![CDATA[Degree Dispersion Increases the Rate of Rare Events in Population Networks]]> https://www.researchpad.co/article/elastic_article_7363 There is great interest in predicting rare and extreme events in complex systems, and in particular, understanding the role of network topology in facilitating such events. In this Letter, we show that degree dispersion—the fact that the number of local connections in networks varies broadly—increases the probability of large, rare fluctuations in population networks generically. We perform explicit calculations for two canonical and distinct classes of rare events: network extinction and switching. When the distance to threshold is held constant, and hence stochastic effects are fairly compared among networks, we show that there is a universal, exponential increase in the rate of rare events proportional to the variance of a network’s degree distribution over its mean squared.

]]>
<![CDATA[Finite Temperature Phase Behavior of Viral Capsids as Oriented Particle Shells]]> https://www.researchpad.co/article/elastic_article_7354 A general phase plot is proposed for discrete particle shells that allows for thermal fluctuations of the shell geometry and of the inter-particle connectivities. The phase plot contains a first-order melting transition, a buckling transition, and a collapse transition and is used to interpret the thermodynamics of microbiological shells.

]]>
<![CDATA[Epidemic Threshold in Continuous-Time Evolving Networks]]> https://www.researchpad.co/article/elastic_article_7351 Current understanding of the critical outbreak condition on temporal networks relies on approximations (time scale separation, discretization) that may bias the results. We propose a theoretical framework to compute the epidemic threshold in continuous time through the infection propagator approach. We introduce the weak commutation condition allowing the interpretation of annealed networks, activity-driven networks, and time scale separation into one formalism. Our work provides a coherent connection between discrete and continuous time representations applicable to realistic scenarios.

]]>
<![CDATA[Critical Behaviors in Contagion Dynamics]]> https://www.researchpad.co/article/elastic_article_7350 We study the critical behavior of a general contagion model where nodes are either active (e.g., with opinion A, or functioning) or inactive (e.g., with opinion B, or damaged). The transitions between these two states are determined by (i) spontaneous transitions independent of the neighborhood, (ii) transitions induced by neighboring nodes, and (iii) spontaneous reverse transitions. The resulting dynamics is extremely rich including limit cycles and random phase switching. We derive a unifying mean-field theory. Specifically, we analytically show that the critical behavior of systems whose dynamics is governed by processes (i)–(iii) can only exhibit three distinct regimes: (a) uncorrelated spontaneous transition dynamics, (b) contact process dynamics, and (c) cusp catastrophes. This ends a long-standing debate on the universality classes of complex contagion dynamics in mean field and substantially deepens its mathematical understanding.

]]>
<![CDATA[Epidemic Extinction and Control in Heterogeneous Networks]]> https://www.researchpad.co/article/elastic_article_7349 We consider epidemic extinction in finite networks with a broad variation in local connectivity. Generalizing the theory of large fluctuations to random networks with a given degree distribution, we are able to predict the most probable, or optimal, paths to extinction in various configurations, including truncated power laws. We find that paths for heterogeneous networks follow a limiting form in which infection first decreases in low-degree nodes, which triggers a rapid extinction in high-degree nodes, and finishes with a residual low-degree extinction. The usefulness of our approach is further demonstrated through optimal control strategies that leverage the dependence of finite-size fluctuations on network topology. Interestingly, we find that the optimal control is a mix of treating both high- and low-degree nodes based on theoretical predictions, in contrast to methods that ignore dynamical fluctuations.

]]>
<![CDATA[Predicting the Speed of Epidemics Spreading in Networks]]> https://www.researchpad.co/article/N71f7f60d-64f4-4c76-afb1-44ee0ca8116c

Global transport and communication networks enable information, ideas, and infectious diseases to now spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like processes, there is a need to predict the speed of a particular contagion in a particular network, and to distinguish between nodes that are more likely to become infected sooner or later during an outbreak. Here, we study these quantities using a message-passing approach to derive simple and effective predictions that are validated against epidemic simulations on a variety of real-world networks with good agreement. In addition to individualized predictions for different nodes, we find an overall sudden transition from low density to almost full network saturation as the contagion progresses in time. Our theory is developed and explained in the setting of simple contagions on treelike networks, but we are also able to show how the method extends remarkably well to complex contagions and highly clustered networks.

]]>