Related papers: Generating nested quadrature rules with positive w…
We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian…
Solving the population balance equation (PBE) for the dynamics of a dispersed phase coupled to a continuous fluid is expensive. Still, one can reduce the cost by representing the evolving particle density function in terms of its moments.…
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…
We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting…
Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…
In this paper, we study gravitational waves generated by binary systems within an extension of General Relativity which is described by the addition of quadratic in curvature tensor terms to the Einstein-Hilbert action. Treating quadratic…
Many flexible families of positive random variables exhibit non-closed forms of the density and distribution functions and this feature is considered unappealing for modelling purposes. However, such families are often characterized by a…
We develop a novel computationally efficient and general framework for robust hypothesis testing. The new framework features a new way to construct uncertainty sets under the null and the alternative distributions, which are sets centered…
The Born rule provides a probability vector (distribution) with a quantum state for a measurement setting. For two settings, we have a pair of vectors from the same quantum state. Each pair forms a combined-probability vector that obeys…
A network of independently trained Gaussian processes (StackedGP) is introduced to obtain predictions of quantities of interest with quantified uncertainties. The main applications of the StackedGP framework are to integrate different…
Many applications require multi-dimensional numerical integration, often in the form of a cubature formula. These cubature formulas are desired to be positive and exact for certain finite-dimensional function spaces (and weight functions).…
This work presents a weighted quadrature (WQ) method to fast assemble Galerkin matrices based on unstructured spline surfaces. The method is developed upon a particular variant of unstructured splines, namely the bicubic analysis-suitable…
Density tracking by quadrature (DTQ) is a numerical procedure for computing solutions to Fokker-Planck equations that describe probability densities for stochastic differential equations (SDEs). In this paper, we extend upon existing…
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…
Kernel quadratures and other kernel-based approximation methods typically suffer from prohibitive cubic time and quadratic space complexity in the number of function evaluations. The problem arises because a system of linear equations needs…
Turning pass-through network architectures into iterative ones, which use their own output as input, is a well-known approach for boosting performance. In this paper, we argue that such architectures offer an additional benefit: The…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…
The problem of nearest neighbor condensing has enjoyed a long history of study, both in its theoretical and practical aspects. In this paper, we introduce the problem of weighted distance nearest neighbor condensing, where one assigns…