Related papers: Self-Switching Markov Chains: emerging dominance p…
This paper introduces a novel methodology for the identification of switching dynamics for switched autoregressive linear models. Switching behavior is assumed to follow a Markov model. The system's outputs are contaminated by possibly…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
We propose a new definition of metastability of Markov processes on countable state spaces. We obtain sufficient conditions for a sequence of processes to be metastable. In the reversible case these conditions are expressed in terms of the…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
Time-varying connections are crucial in understanding the structures and dynamics of complex networks. In this paper, we propose a continuous-time switching topology model for temporal networks that is driven by bursty behavior and study…
We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…
This paper introduces a decentralized state-dependent Markov chain synthesis (DSMC) algorithm for finite-state Markov chains. We present a state-dependent consensus protocol that achieves exponential convergence under mild technical…
We investigate theoretically the dynamics of the system that consists of a cascade three-level emitter interacting with a single-mode resonator in the deep-strong-coupling regime. We show that the dynamical evolution of the system can only…
We propose a new model based on the Ising model with the aim to study synaptic plasticity phenomena in neural networks. It is today well established in biology that the synapses or connections between certain types of neurons are…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
We investigate recurrence and transience of Branching Markov Chains (BMC) in discrete time. Branching Markov Chains are clouds of particles which move (according to an irreducible underlying Markov Chain) and produce offspring…
This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. A corresponding random dynamical system is formulated in a two-step procedure, at…
Identifiability is central to the interpretability of deep latent variable models, ensuring parameterisations are uniquely determined by the data-generating distribution. However, it remains underexplored for deep regime-switching time…
A block Markov chain is a Markov chain whose state space can be partitioned into a finite number of clusters such that the transition probabilities only depend on the clusters. Block Markov chains thus serve as a model for Markov chains…
Classical metastability manifests as noise-driven switching between disjoint basins of attraction and slowing down of relaxation, quantum systems like qubits and Rydberg atoms exhibit analogous behavior through collective quantum jumps and…
Recent single molecule experiments probing the passage process of a short single-stranded DNA (ssDNA) through a membrane channel (translocation) allow to measure the passage time distribution. Building on a recent modelling approach (D. K.…
Markov Chains with variable length are useful stochastic models for data compression that avoid the curse of dimensionality faced by that full Markov Chains. In this paper we introduce a Variable Length Markov Chain whose transition…
We study finite state random dynamical systems (RDS) and their induced Markov chains (MC) as stochastic models for complex dynamics. The linear representation of deterministic maps in RDS are matrix-valued random variables whose…
In this article we propose a novel MCMC method based on deterministic transformations T: X x D --> X where X is the state-space and D is some set which may or may not be a subset of X. We refer to our new methodology as Transformation-based…