Related papers: Exact Evolution Law for Canonical Path Ensembles w…
Sample-based trajectory optimisers are a promising tool for the control of robotics with non-differentiable dynamics and cost functions. Contemporary approaches derive from a restricted subclass of stochastic optimal control where the…
For a class of path-dependent stochastic evolution equations driven by cylindrical $Q$-Wiener process, we study the Pontryagin's maximum principle for the stochastic recursive optimal control problem. In this infinite-dimensional control…
We prove that deterministic motion in dissipative systems emerges as a strict geometric attractor of contact flow, not a statistical approximation. Building on the contact geometry of stochastic vector bundles, we develop time-dependent…
We study the spread of a novel state in a network, in the presence of an exogenous control. The considered controlled evolutionary dynamics is a non-homogeneous Markov process that describes the evolution of the states of all nodes in the…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
Exact law of mortality dynamics in changing populations and environment is derived. The law is universal for all species, from single cell yeast to humans. It includes no characteristics of animal- environment interactions (metabolism etc)…
Despite significant empirical and theoretically supported evidence that non-static parameter choices can be strongly beneficial in evolutionary computation, the question how to best adjust parameter values plays only a marginal role in…
The exact evolution of a system coupled to a complex environment can be described by a stochastic mean-field evolution of the reduced system density. The formalism developed in Ref. [D.Lacroix, Phys. Rev. E77, 041126 (2008)] is illustrated…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…
The compact Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. It is further developed to be more flexible in solving the…
Decision-making societies may vary in their level of cooperation and degree of conservatism, both of which influence their overall performance. Moreover, these factors are not fixed -- they can change based on the decisions agents in the…
The evolution of entropy is derived with respect to dynamical systems. For a stochastic system, its relative entropy $D$ evolves in accordance with the second law of thermodynamics; its absolute entropy $H$ may also be so, provided that the…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
The long-term behaviour of dynamic systems can be classified in two different regimes, regular or chaotic, depending on the values of the control parameters, which are kept constant during the time evolution. Starting from slightly…
Local interactions drive emergent collective behavior, which pervades biological and social complex systems. But uncovering the interactions that produce a desired behavior remains a core challenge. In this paper, we present EvoSOPS, an…
The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work, we develop such a theory for a new…
A natural process is defined as an act, by which a system organizes itself with time. Any natural process drives a system to a state of greater organization. Organization is a progressive change, while evolution is expressed in the effects…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…
A key challenge to make effective use of evolutionary algorithms is to choose appropriate settings for their parameters. However, the appropriate parameter setting generally depends on the structure of the optimisation problem, which is…