Related papers: Bounds on the state vector growth rate in stochast…
Stochastic dynamic control systems relate in a prob- abilistic fashion the space of control signals to the space of corresponding future states. Consequently, stochastic dynamic systems can be interpreted as an information channel between…
We consider a nearly-elastic model system with one degree of freedom. In each collision with the "wall", the system can either lose or gain a small amount of energy due to stochastic perturbation. The weak limit of the corresponding slow…
We propose a simple model that describes the dynamics of efficiencies of competing agents. Agents communicate leading to increase of efficiencies of underachievers, and an efficiency of each agent can increase or decrease irrespectively of…
Some deterministic cellular automata have been observed to follow the pattern of the second law of thermodynamics: starting from a partially disordered state, the system evolves towards a state of equilibrium characterized by maximal…
The propagation of a state vector is governed by a set of time-invariant state transition matrices that switch arbitrarily between two values. The evolution of the state is also perturbed by white Gaussian noise with a variance that…
We consider the problem of estimating a random state vector when there is information about the maximum distances between its subvectors. The estimation problem is posed in a Bayesian framework in which the minimum mean square error (MMSE)…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
A dynamical systems scenario for developmental cell biology is proposed, based on numerical studies of a system with interacting units with internal dynamics and reproduction. Diversification, formation of discrete and recursive types, and…
The material structure of bodies undergoing growth is considered. In the geometric framework of a general differential manifold modeling the physical space and a fiber bundle modeling spacetime, body points may be defined for any extensive…
A dynamic mean field theory is developed for finite state and action Bayesian reinforcement learning in the large state space limit. In an analogy with statistical physics, the Bellman equation is studied as a disordered dynamical system;…
We analyze the phenomenon of system size stochastic resonance in a simple spatially extended system by exploiting the knowledge of the nonequilibrium potential. We show that through the analysis of that potential, and particularly its…
The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation are proved, under a general set of assumptions. Under further assumptions on the evolution…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…
A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or…
The complexity of gene regulatory networks in multicellular organisms makes interpretable low-dimensional models highly desirable. An attractive geometric picture, attributed to Waddington, visualizes the differentiation of a cell into…
We propose a new deterministic growth model which captures certain features of both the Gompertz and Korf laws. We investigate its main properties, with special attention to the correction factor, the relative growth rate, the inflection…
We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. This defines a stochastic linear program for which, under general conditions, we characterize the fluctuations…
We study the singular limit of a system of partial differential equations which is a model for an aggregation of amoebae subjected to three effects: diffusion, growth and chemotaxis. The limit problem involves motion by mean curvature…