Related papers: Selection mechanisms in front invasion

We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…

A classification of dynamical systems in terms of their variational properties is reviewed. Within this classification, front propagation is discussed in a non-gradient relaxational potential flow. The model is motivated by transient…

We discuss the problem of fronts propagating into metastable and unstable states. We examine the time development of the leading edge, discovering a precursor which in the metastable case propagates out ahead of the front at a velocity more…

We consider the problem of state selection for a stochastic system, initially in an unstable stationary state, when multiple metastable states compete for occupation. Using path-integral techniques we derive remarkably simple and accurate…

We establish selection of critical pulled fronts in invasion processes. Our result shows convergence to a pulled front with a logarithmic shift for open sets of steep initial data, including one-sided compactly supported initial conditions.…

The question addressed here is the long time evolution of the solutions to a class of one-dimensional reaction-diffusion equations, in which the diffusion is given by an integral operator. The underlying motivation, discussed in the first…

Different evolutionary models are known to make disparate predictions for the success of an invading mutant in some situations. For example, some evolutionary mechanics lead to amplification of selection in structured populations, while…

Machine learning is vulnerable to adversarial examples: inputs carefully modified to force misclassification. Designing defenses against such inputs remains largely an open problem. In this work, we revisit defensive distillation---which is…

Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena…

Stochastic chemical reaction or population dynamics in finite systems often terminates in an absorbing state. Yet in large spatially extended systems, the time to reach species extinction (or fixation) becomes exceedingly long. Tuning…

We study the invasion of an unstable state by a propagating front in a peculiar but generic situation where the invasion process exhibits a remnant instability. Here, remnant instability refers to the fact that the spatially constant…

This is a brief tutorial review of the dynamics of the voter model and the invasion process on complex networks.

Future energy systems are subject to various uncertain influences. As resilient systems they should maintain a constantly high operational performance whatever happens. We explore different levels and time scales of decision making in…

The dynamics of protection processes has been a fundamental challenge in systemic risk analysis. The conceptual principle and methodological techniques behind the mechanisms involved [in such dynamics] have been harder to grasp than…

A critical issue in the evolution of software models is change propagation: given a primary change that is made to a model in order to meet a new or changed requirement, what additional secondary changes are needed to maintain consistency…

We explore the commonalities between methods for assuring the security of computer systems (cybersecurity) and the mechanisms that have evolved through natural selection to protect vertebrates against pathogens, and how insights derived…

Front propagation into unstable states is often determined by the linearization, that is, propagation speeds agree with predictions from the linearized equation at the unstable state. The leading edge behavior is then a Gaussian tail…

The study of complex systems has attracted widespread attention from researchers in the fields of natural sciences, social sciences, and engineering. Prediction is one of the central issues in this field. Although most related studies have…

The advent of large-scale, complex computing systems has dramatically increased the difficulties of securing accesses to systems' resources. To ensure confidentiality and integrity, the exploitation of access control mechanisms has thus…

We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such resonant invasion speeds can be determined solely based on…