3,351 research outputs found
Stability of Localized Wave Fronts in Bistable Systems
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation, and spatially inhomogeneous activating agents. We determine the conditions under which wave-front localization is possible and analyze the stability thereof with respect to extrinsic perturbations and internal noise. It is found that stability is enhanced upon regulating a positional signal and, surprisingly, also for a low degree of binding cooperativity. We further show a contrasting impact of self-activation to the stability of these two sources of destabilization. DOI: 10.1103/PhysRevLett.110.03810
Особенности попередельного способа калькуляции себестоимости продукции в перерабатывающем производстве
We are interested in the asymptotic stability of equilibria of structured populations modelled in terms of systems of Volterra functional equations coupled with delay differential equations. The standard approach based on studying the characteristic equation of the linearized system is often involved or even unattainable. Therefore, we propose and investigate a numerical method to compute the eigenvalues of the associated infinitesimal generator. The latter is discretized by using a pseudospectral approach, and the eigenvalues of the resulting matrix are the sought approximations. An algorithm is presented to explicitly construct the matrix from the model coefficients and parameters. The method is tested first on academic examples, showing its suitability also for a class of mathematical models much larger than that mentioned above, including neutral- and mixed-type equations. Applications to cannibalism and consumer\u2013resource models are then provided in order to illustrate the efficacy of the proposed technique, especially for studying bifurcations
Multilevel mesh partitioning for optimising domain shape
Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem for mapping meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut-edge weight in the graph with the aim of minimising the parallel communication overhead. However it has been shown that for certain classes of problem, the convergence of the underlying solution algorithm is strongly influenced by the shape or aspect ratio of the subdomains. In this paper therefore, we modify the multilevel algorithms in order to optimise a cost function based on aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results
Epidemic threshold in structured scale-free networks
We analyze the spreading of viruses in scale-free networks with high
clustering and degree correlations, as found in the Internet graph. For the
Suscetible-Infected-Susceptible model of epidemics the prevalence undergoes a
phase transition at a finite threshold of the transmission probability.
Comparing with the absence of a finite threshold in networks with purely random
wiring, our result suggests that high clustering and degree correlations
protect scale-free networks against the spreading of viruses. We introduce and
verify a quantitative description of the epidemic threshold based on the
connectivity of the neighborhoods of the hubs.Comment: 4 pages, 4 figure
Epidemic variability in complex networks
We study numerically the variability of the outbreak of diseases on complex
networks. We use a SI model to simulate the disease spreading at short times,
in homogeneous and in scale-free networks. In both cases, we study the effect
of initial conditions on the epidemic's dynamics and its variability. The
results display a time regime during which the prevalence exhibits a large
sensitivity to noise. We also investigate the dependence of the infection time
on nodes' degree and distance to the seed. In particular, we show that the
infection time of hubs have large fluctuations which limit their reliability as
early-detection stations. Finally, we discuss the effect of the multiplicity of
shortest paths between two nodes on the infection time. Furthermore, we
demonstrate that the existence of even longer paths reduces the average
infection time. These different results could be of use for the design of
time-dependent containment strategies
Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation
We investigate saturation effects in susceptible-infected-susceptible (SIS)
models of the spread of epidemics in heterogeneous populations. The structure
of interactions in the population is represented by networks with connectivity
distribution ,including scale-free(SF) networks with power law
distributions . Considering cases where the transmission
of infection between nodes depends on their connectivity, we introduce a
saturation function which reduces the infection transmission rate
across an edge going from a node with high connectivity . A mean
field approximation with the neglect of degree-degree correlation then leads to
a finite threshold for SF networks with . We
also find, in this approximation, the fraction of infected individuals among
those with degree for close to . We investigate via
computer simulation the contact process on a heterogeneous regular lattice and
compare the results with those obtained from mean field theory with and without
neglect of degree-degree correlations.Comment: 6 figure
Partitioning Complex Networks via Size-constrained Clustering
The most commonly used method to tackle the graph partitioning problem in
practice is the multilevel approach. During a coarsening phase, a multilevel
graph partitioning algorithm reduces the graph size by iteratively contracting
nodes and edges until the graph is small enough to be partitioned by some other
algorithm. A partition of the input graph is then constructed by successively
transferring the solution to the next finer graph and applying a local search
algorithm to improve the current solution.
In this paper, we describe a novel approach to partition graphs effectively
especially if the networks have a highly irregular structure. More precisely,
our algorithm provides graph coarsening by iteratively contracting
size-constrained clusterings that are computed using a label propagation
algorithm. The same algorithm that provides the size-constrained clusterings
can also be used during uncoarsening as a fast and simple local search
algorithm.
Depending on the algorithm's configuration, we are able to compute partitions
of very high quality outperforming all competitors, or partitions that are
comparable to the best competitor in terms of quality, hMetis, while being
nearly an order of magnitude faster on average. The fastest configuration
partitions the largest graph available to us with 3.3 billion edges using a
single machine in about ten minutes while cutting less than half of the edges
than the fastest competitor, kMetis
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