Related papers: Spectral rate theory for projected two-state kinet…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…
In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate…
A general semiclassical theory for the calculation of reaction rate constants is developed. The theory can be understood as a formal framework that encompasses existing semiclassical methods: instanton theory and semiclassical transition…
We consider a two-state model of non-Markovian stochastic resonance (SR) within the framework of the theory of renewal processes. Residence time intervals are assumed to be mutually independent and characterized by some arbitrary…
Sequential rate-distortion (SRD) theory provides a framework for studying the fundamental trade-off between data-rate and data-quality in real-time communication systems. In this paper, we consider the SRD problem for multi-dimensional…
We give a development of the ODE method for the analysis of recursive algorithms described by a stochastic recursion. With variability modelled via an underlying Markov process, and under general assumptions, the following results are…
Rate processes are often modeled using Markov-State Models (MSM). Suppose you know a prior MSM, and then learn that your prediction of some particular observable rate is wrong. What is the best way to correct the whole MSM? For example,…
Markov state models (MSMs) are widely employed to analyze the kinetics of complex systems. But despite their effectiveness in many applications, MSMs are prone to systematic or statistical errors, often exacerbated by suboptimal…
The problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered. Assuming a Markov evolution of the system (in particular, the pair…
We present a systematic mathematical analysis of the qualitative steady-state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions,…
It is known that under fixed-rate information constraints, adaptive quantizers can be used to stabilize an open-loop-unstable linear system on $\mathbb{R}^n$ driven by unbounded noise. These adaptive schemes can be designed so that they…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the…
We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical…
For smooth random dynamical systems we consider the quenched linear and higher-order response of equivariant physical measures to perturbations of the random dynamics. We show that the spectral perturbation theory of Gou\"ezel, Keller, and…
Gene expression levels, hormone secretion, and internal body temperature each oscillate over an approximately 24-hour cycle, or display circadian rhythms. Many circadian biology studies have investigated how these rhythms vary across…
In this thesis we consider stochastic resonance for a diffusion with drift given by a potential, which has two metastable states and two pathways between them. Depending on the direction of the forcing the height of the two barriers, one…
We obtain pointwise ergodic theorems with rate under conditions expressed in terms of the convergence of series involving $\|\sum_{k=1} ^nf\circ \theta^k\|_2$, improving previous results. Then, using known results on martingale…
Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to…
This work investigates two physics-based models that simulate the non-linear partial differential algebraic equations describing an electric double layer supercapacitor. In one model the linear dependence between electrolyte concentration…