Related papers: Ultrametric Diffusion, Rugged Energy Landscapes an…
In this article we study certain ultradiffusion equations connected with energy landscapes of exponential type. These equations are connected with the p-adic models of complex systems introduced by Avetisov et al. We show that the…
We demonstrate that p-adic analysis is a natural basis for the construction of a wide variety of the ultrametric diffusion models constrained by hierarchical energy landscapes. A general analytical description in terms of p-adic analysis is…
In this work, we study the dynamics of complex systems with time-dependent transition rates, focusing on $p$-adic analysis in modeling such systems. Starting from the master equation that governs the stochastic dynamics of a system with a…
Nakao and Mikhailov proposed using continuous models (mean-field models) to study reaction-diffusion systems on networks and the corresponding Turing patterns. This work aims to show that p-adic analysis is the natural tool to carry out…
We construct and study a fundamental solution of Cauchy's problem for p-adic parabolic equations of a certain the type. The fundamental solution is the transition density of a p-adic Markov process.
Under certain conditions, the dynamics of coarse-grained models of solvated proteins can be described using a Markov state model, which tracks the evolution of populations of configurations. The transition rates among states that appear in…
Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose…
We discuss the interbasin kinetics approximation for random walk on a complex landscape. We show that for a generic landscape the corresponding model of interbasin kinetics is equivalent to an ultrametric diffusion, generated by an…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
Multiple dynamic pathways always exist in biological networks, but their robustness against internal fluctuations and relative stability have not been well recognized and carefully analyzed yet. Here we try to address these issues through…
River networks are hierarchical transport systems in which the timing and position of headwater confluences govern hydrologic response, solute transport, and ecological connectivity. Despite the recognized importance of headwater sources in…
We investigate absorption, i.e., almost sure convergence to an absorbing state, in time-varying (non-homogeneous) discrete-time Markov chains with finite state space. We consider systems that can switch among a finite set of transition…
This paper explores a discrete energy state transition model for energy harvesting (EH) in cell-free massive multiple-input multiple-output (CF-mMIMO) networks. Multiple-antenna access points (APs) provide wireless power and information to…
In this paper, we equip the conventional discrete-time queueing network with a Markovian input process, that, in addition to the usual short-term stochastics, governs the mid- to long-term behavior of the links between the network nodes.…
Associative memory models such as the Hopfield network and its dense generalizations with higher-order interactions exhibit a "blackout catastrophe" -- a discontinuous transition where stable memory states abruptly vanish when the number of…
We initiate the study of non-Archimedean reaction-ultradiffusion equations and their connections with models of complex hierarchic systems. From a mathematical perspective, the equations studied here are the p-adic counterpart of the…
Key features of biological activity can often be captured by transitions between a finite number of semi-stable states that correspond to behaviors or decisions. We present here a broad class of dynamical systems that are ideal for modeling…
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit…
We consider the $p$-adic random walk model in a potential, which can be viewed as a generalization of $p$-adic random walk models used for description of protein conformational dynamics. This model is based on the Kolmogorov--Feller…
We address the problem of inferring the topology of a wireless network using limited observational data. Specifically, we assume that we can detect when a node is transmitting, but no further information regarding the transmission is…