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We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
Particle swarm optimisation is a metaheuristic algorithm which finds reasonable solutions in a wide range of applied problems if suitable parameters are used. We study the properties of the algorithm in the framework of random dynamical…
Modeling is a challenging topic and using parametric models is an important stage to reach flexible function for modeling. Weibull distribution has two parameters which are shape $\alpha$ and scale $\beta$. In this study, bimodality…
Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential…
Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the…
Statistical properties of a local fluctuational fluxes measured at the plasma edge are investigated in the work. It's shown that the amplitudes increments of the local fluctuational fluxes decrease by power law. For approximation of…
Nature-inspired algorithms are among the most powerful algorithms for optimization. This paper intends to provide a detailed description of a new Firefly Algorithm (FA) for multimodal optimization applications. We will compare the proposed…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
First-principles Markov Chain Monte Carlo sampling is used to investigate uncertainty quantification and uncertainty propagation in parameters describing hydrogen kinetics. Specifically, we sample the posterior distribution of thirty-one…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
A recently introduced theoretical framework for modeling the dynamics of X-ray amplified spontaneous emission is based on stochastic sampling of the density matrix of quantum emitters and the radiation field, similarly to other phase-space…
We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential…
Thanks to recent advances in generative AI, computers can now simulate realistic and complex natural processes. We apply this capability to predict how wildfires spread, a task made difficult by the unpredictable nature of fire and the…