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Gaussian elimination (GE) is the archetypal direct algorithm for solving linear systems of equations and this has been its primary application for thousands of years. In the last decade, GE has found another major use as an iterative…

In this paper, we propose an efficient ordered-statistics decoding (OSD) algorithm with an adaptive Gaussian elimination (GE) reduction technique. The proposed decoder utilizes two decoding conditions to adaptively remove GE in OSD. The…

Gaussian elimination with no pivoting and block Gaussian elimination are attractive alternatives to the customary but communication intensive Gaussian elimination with partial pivoting (hereafter we use the acronyms GENP, BGE, and GEPP}…

Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…

Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this…

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…

While 3D Gaussian Splatting (3DGS) has demonstrated remarkable performance in novel view synthesis and real-time rendering, the high memory consumption due to the use of millions of Gaussians limits its practicality. To mitigate this issue,…

We present a new numerical code, ECHO, based on an Eulerian Conservative High Order scheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at providing a…

Optimizing smooth convex functions in stochastic settings, where only noisy estimates of gradients and Hessians are available, is a fundamental problem in optimization. While first-order methods possess a low per-iteration cost, their…

Gaussian Mixture Models (GMMs) are one of the most potent parametric density models used extensively in many applications. Flexibly-tied factorization of the covariance matrices in GMMs is a powerful approach for coping with the challenges…

With the ever increasing complexity of specifications, manual sizing for analog circuits recently became very challenging. Especially for innovative, large-scale circuits designs, with tens of design variables, operating conditions and…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…

In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…

This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual…

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…

This study proposes an extension of the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulation in an arbitrary Lagrangian-Eulerian (ALE) formulation in unstructured mesh. The ALE method is achieved by subdividing…

Measurement error mitigation (MEM) techniques are postprocessing strategies to counteract systematic read-out errors on quantum computers (QC). Currently used MEM strategies face a tradeoff: methods that scale well with the number of qubits…