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Correlation functions measured as a function of $\Delta \eta, \Delta \phi$ have emerged as a powerful tool to study the dynamics of particle production in nuclear collisions at high energy. They are however subject, like any other…
Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more…
In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic…
This paper is a survey of recent contributions on estimation in stochastic differential equations with mixed-effects. These models involve N stochastic differential equations with common drift and diffusion functions but random parameters…
We have developed a numerical approach to compute real-time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral (ISPI) for the…
We consider the problem of combining data from observational and experimental sources to make causal conclusions. This problem is increasingly relevant, as the modern era has yielded passive collection of massive observational datasets in…
We investigate exact solutions for isothermal shock problems in different one-dimensional geometries. These solutions are given as analytical expressions if possible, or are computed using standard numerical methods for solving ordinary…
Higher order numerical schemes for stochastic partial differential equations that do not possess commutative noise require the simulation of iterated stochastic integrals. In this work, we extend the algorithms derived by Kloeden, Platen,…
In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative operators in the sense that the tempered fractional derivative…
By returning to the underlying discrete time formalism, we relate spurious results in coherent state path integral calculations to the high frequency structure of their propagators. We show how to modify the standard expressions for…
This paper aims to provide practitioners of causal mediation analysis with a better understanding of estimation options. We take as inputs two familiar strategies (weighting and model-based prediction) and a simple way of combining them…
Determining the adsorption isotherms is an issue of significant importance in preparative chromatography. A modern technique for estimating adsorption isotherms is to solve an inverse problem so that the simulated batch separation coincides…
Stochastic parameterizations are used in numerical weather prediction and climate modeling to help capture the uncertainty in the simulations and improve their statistical properties. Convergence issues can arise when time integration…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
We introduce a tempering approach with stochastic density functional theory (sDFT), labeled t-sDFT, which reduces the statistical errors in the estimates of observable expectation values. This is achieved by rewriting the electronic density…
Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher-order corrections by integration over linear statistics…
We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces with passive and active immersed particles. Our approaches…
A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite…
Stochastic optimization methods have been hugely successful in making large-scale optimization problems feasible when computing the full gradient is computationally prohibitive. Using the theory of modified equations for numerical…
Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…