Related papers: The TAP equation: evaluating combinatorial innovat…
We study the asymptotic behavior of complex discrete evolution equations of Ginzburg- Landau type. Depending on the nonlinearity and the data of the problem, we find different dynamical behavior ranging from global existence of solutions…
Modern ecology has re-emphasized the need for a quantitative understanding of the original 'survival of the fittest theme' based on analyzis of the intricate trade-offs between competing evolutionary strategies that characterize the…
We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both types diffuse as simple random walks with possibly…
This study investigates the cosmological dynamics of an accelerating universe within the framework of teleparallel gravity using an exponential f(T) functional form. To obtain exact cosmological solutions, a hybrid scale factor is employed…
The Bouchaud-Anderson model (BAM) is a generalisation of the parabolic Anderson model (PAM) in which the driving simple random walk is replaced by a random walk in an inhomogeneous trapping landscape; the BAM reduces to the PAM in the case…
We introduce the logistic model of consumption growth, which captures a negative feedback loop preventing an unlimited growth of consumption due to finite biophysical resources of our planet. This simple dynamic model allows for derivation…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension $d\geq 3$ and find two critical curves intersecting at one same point which separate the global existence and blow up of weak solutions to the problem.…
The challenge in combined task and motion planning (TAMP) is the effective integration of a search over a combinatorial space, usually carried out by a task planner, and a search over a continuous configuration space, carried out by a…
In this paper we consider the issue of paradigm evaluation by applying Bayes' theorem along the following nested hierarchy of progressively more complex structures: i) parameter estimation (within a model), ii) model selection and…
We study linear pseudoparabolic equations with unbounded and time-dependent coefficients. We solve the case which has remained open in several recent studies of pseudoparabolic equations with unbounded and time-dependent coefficients. In…
We formulate a model that describes the escape dynamics in a leaky chaotic system in which the size of the leak depends on the number of the in-falling particles. The basic motivation of this work is the astrophysical process which…
The dynamics of the expansion of a Lennard-Jones system, initially confined at high density and subsequently expanding freely in the vacuum, is confronted to an expanding statistical ensemble, derived in the diluted quasi-ideal Boltzmann…
We develop a thermodynamic framework for modeling innovation adoption and abandonment dynamics using statistical mechanics. Starting from a mathematical model for an adoption distribution that fits empirically obtained date, we construct a…
Growth (and resorption) of biological tissue is formulated in the continuum setting. The treatment is macroscopic, rather than cellular or sub-cellular. Certain assumptions that are central to classical continuum mechanics are revisited,…
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe…
In this paper we present a sufficient condition for the existence of a solution for an equilibrium problem on an Hadamard manifold and under suitable assumptions on the sectional curvature, we propose a framework for the convergence…
We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet.…