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We consider the directed evolution of a population after an intervention that has significantly altered the underlying fitness landscape. We model the space of genotypes as a distributive lattice; the fitness landscape is a real-valued…
Many central problems in geometry, topology, and mathematical physics lead to questions concerning the long-time dynamics of solutions to ordinary and partial differential equations. Examples range from the Einstein field equations of…
This paper is concerned with the well-posedness analysis of the Hartree-Fock system modeling the time evolution of a quantum system comprised of fermions. We consider quantum states with finite mass and finite kinetic energy, and the…
We consider a numerical scheme for the approximation of a system that couples the evolution of a two--dimensional hypersurface to a reaction--diffusion equation on the surface. The surfaces are assumed to be graphs and evolve according to…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
Motivated by present activities in (statistical) physics directed towards biological evolution, we review the interplay of three evolutionary forces: mutation, selection, and genetic drift. The review addresses itself to physicists and…
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic…
We propose a new dark energy model for solving the cosmological fine-tuning and coincidence problems. A default assumption is that the fine-tuning problem disappears if we do not interpret dark energy as vacuum energy. The key idea to…
This paper is the first in a series which develops the theory of emittance dynamics based on simple statistical reasoning. Emittance is a central quantity used to characterize the quality of electron microscopes, photon sources and particle…
Obstacles to integrability in perturbed evolution equations are overcome by allowing higher-order terms in the expansion of the solution to depend explicitly on time and position. With a special expansion algorithm, obstacles vanish…
Growing efforts to measure fitness landscapes in molecular and microbial systems are premised on a tight relationship between landscape topography and evolutionary trajectories. This relationship, however, is far from being straightforward:…
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…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
One of the central challenges in kinetic theory is the derivation of macroscopic evolution equations--describing, for example, the dynamics of an electron gas--from the underlying fundamental microscopic laws of classical or quantum…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
A lattice model is used to estimate the self-diffusivity of entangled cyclic and linear polymers in blends of varying compositions. To interpret simulation results, we suggest a minimal model based on the physical idea that constraints…
Biodiversity and extinction are central issues in evolution. Dynamical balance among different species in ecosystems is often described by deterministic replicator equations with moderate success. However, fluctuations are inevitable,…
We present a perturbative treatment of the evolution under their mutual self-gravity of particles displaced off an infinite perfect lattice, both for a static space and for a homogeneously expanding space as in cosmological N-body…
We reconsider the Eigen's quasi-species model for competing self-reproductive macromolecules in populations characterized by a single-peaked fitness landscape. The use of ideas and tools borrowed from polymers theory and statistical…