Related papers: A Bayesian Approach for the Determination of the C…
Droplets of electrolyte solutions in an insulating medium are ubiquitous in nature. The net charges of these droplets are normally nonzero, and they fluctuate. However, a theory on the probability distribution function for the net charge of…
We describe a new method for imaging ultrafast dynamics in condensed matter using inelastic x-ray scattering (IXS). We use the concepts of causality and irreversibility to construct a general solution to the inverse scattering problem (or…
This paper focuses on an inverse problem associated with the plate equation which is derived from models in fluid mechanics and elasticity. We establish the unique identifying results in simultaneously determining both the unknown density…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
Elastic electron scattering is one of the primary means of investigating materials on the atomic scale. It is usually described by modeling the sample as a fixed, static, perturbative potential, thereby completely neglecting the quantum…
We present a practical scheme for performing error estimates for Density Functional Theory calculations. The approach which is based on ideas from Bayesian statistics involves creating an ensemble of exchange-correlation functionals by…
Accurate charge densities are essential for reliable electronic structure calculations because they significantly impact predictions of various chemical properties and in particular, according to the Hellmann-Feynman theorem, atomic forces.…
The increasing richness of data related to cold dense matter, from laboratory experiments to neutron-star observations, requires a framework for constraining the properties of such matter that makes use of all relevant information. Here, we…
A Bayesian model to infer edge electron density profiles is developed for the JET lithium beam emission spectroscopy system, measuring Li I line radiation using 26 channels with ~1 cm spatial resolution and 10~20 ms temporal resolution. The…
High intensity focused ultrasound is a non-invasive method for treatment of diseased tissue that uses a beam of ultrasound to generate heat within a small volume. A common challenge in application of this technique is that heterogeneity of…
In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration and reconstruction problems which has the property to be scale invariant. In general, Bayesian estimators are {\em…
In this paper, we consider Bayesian point estimation and predictive density estimation in the binomial case. After presenting preliminary results on these problems, we compare the risk functions of the Bayes estimators based on the…
This paper proposes a probabilistic model for uncontrolled charging of electric vehicles (EVs). EV charging will add significant load to power systems in the coming years and, due to the convenience of charging at home, this is likely to…
Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…
According to density functional theory, any chemical property can be inferred from the electron density, making it the most informative attribute of an atomic structure. In this work, we demonstrate the use of established physical methods…
This work addresses the electrostatic problem of a thin, curved, cylindrical conductor, or a conducting filament, and shows that the corresponding linear charge density slowly tends to uniformity as the inverse of the logarithm of a…
Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…
This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…
Statistically studied are the equilibrium characteristics of a subsystem of mobile charges of one sort, taking into account the subsystem of fixed charges of the opposite sign creating a compensating electric background. The distribution of…
A stochastic approach for charge transport in diodes is developed in consistency with the laws of electricity, thermodynamics, and microreversibility. In this approach, the electron and hole densities are ruled by diffusion-reaction…