Related papers: Statistically Unbiased Free Energy Estimates from …
The simulation of electronic properties is a pivotal issue in modern electronic structure theory, driving significant efforts over the past decades to develop protocols for computing energy derivatives. In this work, we address this problem…
Best linear unbiased prediction is well known for its wide range of applications including small area estimation. While the theory is well established for mixed linear models and under normality of the error and mixing distributions, the…
Free energy calculation is critical in predictive tasks such as protein folding, docking and design. However, rigorous calculation of free energy change is prohibitively expensive in these practical applications. The minimum potential…
The Vlasov equation embodies the smooth field approximation of the self-consistent equation of motion for charged particle beams. This framework is fundamentally altered if we include the fluctuating forces that originate from the actual…
Simulations with an adaptive time-dependent bias, such as metadynamics, enable an efficient exploration of the conformational space of a system. However, the dynamic information of the system is altered by the bias. With infrequent…
The goal of these lecture notes is to review the problem of free energy minimization as a unified framework underlying the definition of maximum entropy modelling, generalized Bayesian inference, learning with latent variables, statistical…
State estimation allows to monitor power networks, exploiting field measurements to derive the most likely grid state. In the literature, measurement errors are usually assumed to follow zero-mean Gaussian distributions; however, it has…
Energy estimation is critical to impact identification on aerospace composites, where low-velocity impacts can induce internal damage that is undetectable at the surface. Current methodologies for energy prediction are often constrained by…
The Gibbs free energy is the fundamental thermodynamic potential underlying the relative stability of different states of matter under constant-pressure conditions. However, computing this quantity from atomic-scale simulations is far from…
In this paper we discuss how the information contained in atomistic simulations of homogeneous nucleation should be used when fitting the parameters in macroscopic nucleation models. We show how the number of solid and liquid atoms in such…
The absolute free energy -- or partition function, equivalently -- of a molecule can be estimated computationally using a suitable reference system. Here, we demonstrate a practical method for staging such calculations by growing a molecule…
Bayesian inference is a widely used statistical method. The free energy and generalization loss, which are used to estimate the accuracy of Bayesian inference, are known to be small in singular models that do not have a unique optimal…
Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given the difficulty in modeling spatial dependence, especially in non-stationary cases, model-based prediction intervals are at risk of…
We consider the common problem setting of an elastic sphere impacting on a flexible beam. In contrast to previous studies, we analyze the modal energy distribution induced by the impact, having in mind the particular application of impact…
We use analytical calculations and event-driven molecular dynamics simulations to study a small number of hard sphere particles in a spherical cavity. The cavity is taken also as the thermal bath so that the system thermalizes by collisions…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…
We describe a method that focuses sampling effort on a user-defined selection of a large system, which can lead to substantial decreases in computational effort by speeding up the calculation of nonbonded interactions. A naive approach can…
A review of computations of free energy for Gibbs states on stationary but not static gravitational and gauge backgrounds is given. On these backgrounds wave equations for free fields are reduced to eigen-value problems which depend…
We develop a systematic procedure to approximate generalized free energy in out of equilibrium stochastic systems. The procedure only requires knowledge of the averages of macroscopic observables and uses quasi-equilibrium distribution to…