The sky didn\u27t fall

We show how different explicit statistical moment closures, including the mean field and the Kirkwood approximations as well as an Ursell-type expansion for the moments, compare with the equation-free approach in the case of a stochastic epidemic model evolving on Erdős–Rényi networks. For illustration purposes we use a simple, discrete susceptible–infected–recovered stochastic model with a nonlinear recovering probability. For every closure scheme, we derive the corresponding macroscopic evolution equations and we construct the bifurcation diagrams with respect to the probability of infection. Finally, we construct the coarse-grained bifurcation diagram obtained with the equation-free method acting directly on the microscopic simulations, bypassing the derivation of explicit closures. We show that the equation-free approach captures the actual emergent nonlinear behavior and outperforms all the other explicit schemes.info:eu-repo/semantics/publishe

Optimal Link Deployment for Minimizing Average Path Length in Chain Networks

Part 8: Resource Management and OptimizationInternational audienceThis study considers chain-topology networks, which has certain inherent limitations, and presents an optimization model that augments the network by the addition of a new link, with the objective of minimizing Average Path Length (APL).We built up a mathematical model for APL, and formulated our problem as Integer Programming. Then, we solved the problem experimentally by brute-force, trying all possible topologies, and found the optimal solutions that minimize APL for certain network sizes up to 1000 nodes. Later on, we derived analytical solution of the problem by applying Linear Regression method on the experimental results obtained.We showed that APL on a chain-topology network is decreased by the proposed optimization model, at a gradually increasing rate from 24.81 % to asymptotic value of 41.4 % as network grows. Additionally, we found that normalized length of the optimal solutions decreases logarithmically from 100 % to 58.6048 % as network size gets larger

Multi-scale network analysis shows scale-dependency of significance of individual protected areas for connectivity

Context: The problem of how ecological mechanisms create and interact with patterns across different scales is fundamental not only for understanding ecological processes, but also for interpretations of ecological dynamics and the strategies that organisms adopt to cope with variability and cross-scale influences.\ud \ud Objectives: Our objective was to determine the consistency of the role of individual habitat patches in pattern-process relationships (focusing on the potential for dispersal within a network of patches in a fragmented landscape) across a range of scales.\ud \ud Methods: Network analysis was used to assess and compare the potential connectivity and spatial distribution of highland fynbos habitat in and between protected areas of the Western Cape of South Africa. Connectivity of fynbos patches was measured using ten maximum threshold distances, ranging from five to 50 km, based on the known average dispersal distances of fynbos endemic bird species.\ud \ud Results: Network connectivity increased predictably with scale. More interestingly, however, the relative contributions of individual protected areas to network connectivity showed strong scale dependence.\ud \ud Conclusions: Conservation approaches that rely on single-scale analyses of connectivity and context (e.g., based on data for a single species with a given dispersal distance) are inadequate to identify key land parcels. Landscape planning, and specifically the assessment of the value of individual areas for dispersal, must therefore be undertaken with a multi-scale approach. Developing a better understanding of scaling dependencies in fragmenting landscapes is of high importance for both ecological theory and conservation planning