Related papers: Quasi-potential landscape in complex multi-stable …
The epigenetic pathway of a cell as it differentiates from a stem cell state to a mature lineage-committed one has been historically understood in terms of Waddington's landscape, consisting of hills and valleys. The smooth top and…
The paper proposes two dynamical systems based on the generalized Lotka-Volterra model of three excitable elements interacting through excitatory couplings. It is shown that for some values of the coupling parameters in the phase space of…
Many processes in nature seem to be entirely controlled by transition rates and the corresponding statistical dynamics. Some of them are in essence quantum, like the decay of excited states, the tunneling through barriers or the decay of…
We investigate in detail a recent model of colliding mobile agents [Phys. Rev. Lett.~96, 088702], used as an alternative approach to construct evolving networks of interactions formed by the collisions governed by suitable dynamical rules.…
It is a fundamental problem to characterize the nonequilibrium processes. For a slowly moving one-dimensional potential, we explore the quasi adiabatic dynamics of the initial energy eigenstates for a confined quantum system interacting…
The concept of fitness is introduced, and a simple derivation of the Fundamental Theorem of Natural Selection (which states that the average fitness of a population increases if its variance is nonzero) is given. After a short discussion of…
In Mean Field Games of Controls, the dynamics of the single agent is influenced not only by the distribution of the agents, as in the classical theory, but also by the distribution of their optimal strategies. In this paper, we study…
The empirical-phenomenological quasi-deuteron photofission description is theoretically justified within the semiclassical, intermediate statistics model. The transmutational fermion (nucleon) - boson (quasi-deuteron) potential plays an…
Quantifying stochastic processes is essential to understand many natural phenomena, particularly in biology, including cell-fate decision in developmental processes as well as genesis and progression of cancers. While various attempts have…
We construct a stochastic dynamical systems theory in which sustainability is a structural boundary property of a fully coupled Earth--Human--Production system. Each subsystem is modelled as a vector-valued process governed by stochastic…
The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its thermodynamic functions is studied. For finite systems, each saddle point is found to cause a nonanalyticity in…
Quasistatic evolutions of critical points of time-dependent energies exhibit piecewise smooth behavior, making them useful for modeling continuum mechanics phenomena like elastic-plasticity and fracture. Traditionally, such evolutions have…
A two-dimensional lattice system of non-interacting electrons in a homogeneous magnetic field with half a flux quantum per plaquette and a random potential is considered. For the large scale behavior a supersymmetric theory with collective…
A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival…
We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation…
Cells can often choose among several stably heritable phenotypes. Examples are the expression of genes in eukaryotic cells where long chromosomal regions can adopt persistent and heritable silenced or active states, that may be associated…
In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…
Many-body long-range interacting systems can remain approximately in a quasi-stationary state far-from-thermodynamic equilibrium. These states are typically characterized by a pair of counter-propagating density clusters, or by a single…
We examine how systems in non-equilibrium steady states close to a continuous phase transition can still be described by a Landau potential if one forgoes the assumption of analyticity. In a system simultaneously coupled to several baths at…
In systems characterized by a rough potential energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and…