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We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…
This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and…
A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…
In the past few decades, the development of fluorescent technologies and microscopic techniques has greatly improved scientists' ability to observe real-time single-cell activities. In this paper, we consider the filtering problem associate…
Self-organized network dynamics prevails for systems across physics, biology and engineering. How external signals generate distributed responses in networked systems fundamentally underlies their function, yet is far from fully understood.…
The effects of intrinsic noise on stochastic delay systems is studied within an expansion in the inverse system size. We show that the stochastic nature of the underlying dynamics may induce oscillatory behaviour in parameter ranges where…
We perform network analysis of a system described by the master equation to estimate the lower bound of the steady-state current noise, starting from the level 2.5 large deviation function and using the graph theory approach. When the…
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space…
We investigate Turing pattern formation in a stochastic and spatially discretized version of a reaction diffusion advection (RDA) equation, which was previously introduced to model synaptogenesis in \textit{C. elegans}. The model describes…
It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' on a wide class of biologically relevant,…
Fluctuations in the abundance of molecules in the living cell may affect its growth and well being. For regulatory molecules (e.g., signaling proteins or transcription factors), fluctuations in their expression can affect the levels of…
This paper investigates the problem of distributed stochastic approximation in multi-agent systems. The algorithm under study consists of two steps: a local stochastic approximation step and a diffusion step which drives the network to a…
The focus of this paper is to quantify measures of aggregate fluctuations for a class of consensus-seeking multiagent networks subject to exogenous noise with alpha-stable distributions. This type of noise is generated by a class of random…
In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly…
We propose a method for approximating the large deviation rate function of time-integrated observables of diffusion processes, used in statistical physics to characterize the fluctuations of nonequilibrium systems. The method is based on…
The stochastic reaction-diffusion model driven by a multiplicative noise is examined. We construct the gradient discretisation method (GDM), an abstract framework combining several numerical method families. The paper provides the…
Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…
We model chaotic diffusion, in a symplectic 4D map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a…
Machine Learning and Deep Learning are computational tools that fall within the domain of artificial intelligence. In recent years, numerous research works have advanced the application of machine and deep learning in various fields,…
Although stochastic approximation learning methods have been widely used in the machine learning literature for over 50 years, formal theoretical analyses of specific machine learning algorithms are less common because stochastic…