Social games in a social network

We study an evolutionary version of the Prisoner's Dilemma game, played by agents placed in a small-world network. Agents are able to change their strategy, imitating that of the most successful neighbor. We observe that different topologies, ranging from regular lattices to random graphs, produce a variety of emergent behaviors. This is a contribution towards the study of social phenomena and transitions governed by the topology of the community

Exact results and scaling properties of small-world networks

We study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance, $\bar{\ell}$, and its variance, $\sigma^2$. We also discuss the scaling properties of the distribution function. Finally, we study the limit of large system sizes and obtain some analytic results.Comment: RevTeX, 4 pages, 5 figures included. Minor corrections and addition

Relaxation Properties of Small-World Networks

Recently, Watts and Strogatz introduced the so-called small-world networks in order to describe systems which combine simultaneously properties of regular and of random lattices. In this work we study diffusion processes defined on such structures by considering explicitly the probability for a random walker to be present at the origin. The results are intermediate between the corresponding ones for fractals and for Cayley trees.Comment: 16 pages, 6 figure

Modulated Scale-free Network in the Euclidean Space

A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its $i$-th predecessor of degree $k_i$ with a directed link of length $\ell$ using a probability proportional to $k_i \ell^{\alpha}$. Our numerical study indicates that the network is Scale-free for all values of $\alpha > \alpha_c$ and the degree distribution decays stretched exponentially for the other values of $\alpha$. The link length distribution follows a power law: $D(\ell) \sim \ell^{\delta}$ where $\delta$ is calculated exactly for the whole range of values of $\alpha$.Comment: 4 pages, 4 figures. To be published in Physical Review

Elasticity of Semiflexible Biopolymer Networks

We develop a model for gels and entangled solutions of semiflexible biopolymers such as F-actin. Such networks play a crucial structural role in the cytoskeleton of cells. We show that the rheologic properties of these networks can result from nonclassical rubber elasticity. This model can explain a number of elastic properties of such networks {\em in vitro}, including the concentration dependence of the storage modulus and yield strain.Comment: Uses RevTeX, full postscript with figures available at http://www.umich.edu/~fcm/preprints/agel/agel.htm

Effective dimensions and percolation in hierarchically structured scale-free networks

We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial character of this network that displays scale-free connectivity among other features, it turns out to be approximately one-dimensional. The dimensional characterization is in agreement with the results on statistics of site percolation and other dynamical processes implemented on such a network.Comment: 5 pages, 5 figure

Two-dimensional SIR epidemics with long range infection

We extend a recent study of susceptible-infected-removed epidemic processes with long range infection (referred to as I in the following) from 1-dimensional lattices to lattices in two dimensions. As in I we use hashing to simulate very large lattices for which finite size effects can be neglected, in spite of the assumed power law $p({\bf x})\sim |{\bf x}|^{-\sigma-2}$ for the probability that a site can infect another site a distance vector ${\bf x}$ apart. As in I we present detailed results for the critical case, for the supercritical case with $\sigma = 2$, and for the supercritical case with $0< \sigma < 2$. For the latter we verify the stretched exponential growth of the infected cluster with time predicted by M. Biskup. For $\sigma=2$ we find generic power laws with $\sigma-$dependent exponents in the supercritical phase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Instead of diverging exponentially with the distance from the critical point, the correlation length increases with an inverse power, as in an ordinary critical point. Finally we study the dependence of the critical exponents on $\sigma$ in the regime $0<\sigma <2$, and compare with field theoretic predictions. In particular we discuss in detail whether the critical behavior for $\sigma$ slightly less than 2 is in the short range universality class, as conjectured recently by F. Linder {\it et al.}. As in I we also consider a modified version of the model where only some of the contacts are long range, the others being between nearest neighbors. If the number of the latter reaches the percolation threshold, the critical behavior is changed but the supercritical behavior stays qualitatively the same.Comment: 14 pages, including 29 figure

Shortest paths on systems with power-law distributed long-range connections

We discuss shortest-path lengths $\ell(r)$ on periodic rings of size L supplemented with an average of pL randomly located long-range links whose lengths are distributed according to P_l \sim l^{-\xpn}. Using rescaling arguments and numerical simulation on systems of up to $10^7$ sites, we show that a characteristic length $\xi$ exists such that $\ell(r) \sim r$ for $r>\xi$. For small p we find that the shortest-path length satisfies the scaling relation \ell(r,\xpn,p)/\xi = f(\xpn,r/\xi). Three regions with different asymptotic behaviors are found, respectively: a) \xpn>2 where $\theta_s=1$, b) 1<\xpn<2 where 0<\theta_s(\xpn)<1/2 and, c) \xpn<1 where $\ell(r)$ behaves logarithmically, i.e. $\theta_s=0$. The characteristic length $\xi$ is of the form $\xi \sim p^{-\nu}$ with \nu=1/(2-\xpn) in region b), but depends on L as well in region c). A directed model of shortest-paths is solved and compared with numerical results.Comment: 10 pages, 10 figures, revtex4. Submitted to PR

Toward understanding covid-19 recovery: national institutes of health workshop on postacute covid-19

Over the past year, the SARS-CoV-2 pandemic has swept the globe, resulting in an enormous worldwide burden of infection and mortality. However, the additional toll resulting from long-term consequences of the pandemic has yet to be tallied. Heterogeneous disease manifestations and syndromes are now recognized among some persons after their initial recovery from SARS-CoV-2 infection, representing in the broadest sense a failure to return to a baseline state of health after acute SARS-CoV-2 infection. On 3 to 4 December 2020, the National Institute of Allergy and Infectious Diseases, in collaboration with other Institutes and Centers of the National Institutes of Health, convened a virtual workshop to summarize existing knowledge on postacute COVID-19 and to identify key knowledge gaps regarding this condition

Explosive volcanic activity on Venus: The roles of volatile contribution, degassing, and external environment

We investigate the conditions that will promote explosive volcanic activity on Venus. Conduit processes were simulated using a steady-state, isothermal, homogeneous flow model in tandem with a degassing model. The response of exit pressure, exit velocity, and degree of volatile exsolution was explored over a range of volatile concentrations (H2O and CO2), magma temperatures, vent altitudes, and conduit geometries relevant to the Venusian environment. We find that the addition of CO2 to an H2O-driven eruption increases the final pressure, velocity, and volume fraction gas. Increasing vent elevation leads to a greater degree of magma fragmentation, due to the decrease in the final pressure at the vent, resulting in a greater likelihood of explosive activity. Increasing the magmatic temperature generates higher final pressures, greater velocities, and lower final volume fraction gas values with a correspondingly lower chance of explosive volcanism. Cross-sectionally smaller, and/or deeper, conduits were more conducive to explosive activity. Model runs show that for an explosive eruption to occur at Scathach Fluctus, at Venus’ mean planetary radius (MPR), 4.5% H2O or 3% H2O with 3% CO2 (from a 25 m radius conduit) would be required to initiate fragmentation; at Ma’at Mons (~9 km above MPR) only ~2% H2O is required. A buoyant plume model was used to investigate plume behaviour. It was found that it was not possible to achieve a buoyant column from a 25 m radius conduit at Scathach Fluctus, but a buoyant column reaching up to ~20 km above the vent could be generated at Ma’at Mons with an H2O concentration of 4.7% (at 1300 K) or a mixed volatile concentration of 3% H2O with 3% CO2 (at 1200 K). We also estimate the flux of volcanic gases to the lower atmosphere of Venus, should explosive volcanism occur. Model results suggest explosive activity at Scathach Fluctus would result in an H2O flux of ~107 kg s-1. Were Scathach Fluctus emplaced in a single event, our model suggests that it may have been emplaced in a period of ~15 days, supplying 1-2 x 104 Mt H2O to the atmosphere locally. An eruption of this scale might increase local atmospheric H2O abundance by several ppm over an area large enough to be detectable by near-infrared nightside sounding using the 1.18 µm spectral window such as that carried out by the Venus Express/VIRTIS spectrometer. Further interrogation of the VIRTIS dataset is recommended to search for ongoing volcanism on Venus