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Optimal power flow (OPF) is a key problem in power system operations. OPF problems that use the nonlinear AC power flow equations to accurately model the network physics have inherent challenges associated with non-convexity. To address…
The paper proposes an implicit (i.e., machine-independent) complexity approach to studying computation by polynomial-size, constant-depth circuits with gates counting modulo a constant through the lens of discrete ordinary differential…
Radiative corrections to processes that involve the production and subsequent decay of unstable particles are complex due to various theoretical and practical problems. The so-called double-pole approximation offers a way out of these…
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…
In representations using frames, oblique duality appears in situations where the analysis and the synthesis has to be done in different subspaces. In some cases, we cannot obtain an explicit expression for the oblique duals and in others…
In this paper we have derived explicitly computable bounds on the error in energy norms for the fully nonlinear Poisson-Boltzmann equation. Together with the computable bounds, we have also obtained efficient error indicators which can…
A software tool, computing observed and expected upper limits on Poissonian process rates using a hybrid frequentist-Bayesian CLs method, is presented. This tool can be used for simple counting experiments where only signal, background and…
The precision measurement of the mass of the $W$ boson is an important goal of the Fermilab Tevatron and the CERN Large Hadron Collider (LHC). It requires accurate theoretical calculations which incorporate both higher-order QCD and…
We reevaluate the vacuum polarization functions for electroweak gauge bosons at three loops in QCD, employing state-of-the-art perturbative techniques. We apply these results to determine the ${\mathcal{O}}(\alpha \alpha_s^2)$ corrections…
With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…
This paper contains a review of recent precision measurements of electroweak observables and resulting tests of the electroweak Standard Model.
Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs), also known as ODE filters, have been established as efficient methods for quantifying numerical uncertainty in the solution of ODEs. In practical…
Ordinary Differential Equations (ODEs) are widely used in physics, chemistry, and biology to model dynamic systems, including reaction kinetics, population dynamics, and biological processes. In this work, we integrate GPU-accelerated ODE…
Calibration refers to the statistical estimation of unknown model parameters in computer experiments, such that computer experiments can match underlying physical systems. This work develops a new calibration method for imperfect computer…
The status of precision electroweak data, tests of the standard model, determination of its parameters, and constraints on new physics, are surveyed.
Fluid models are a popular formalism in the quantitative modeling of biochemical systems and analytical performance models. The main idea is to approximate a large-scale Markov chain by a compact set of ordinary differential equations…
Bayesian model selection is a tool to decide whether the introduction of a new parameter is warranted by data. I argue that the usual sampling statistic significance tests for a null hypothesis can be misleading, since they do not take into…
Confidence calibration is of great importance to the reliability of decisions made by machine learning systems. However, discriminative classifiers based on deep neural networks are often criticized for producing overconfident predictions…
Accurate temperature measurements are essential for the proper monitoring and control of industrial furnaces. However, measurement uncertainty is a risk for such a critical parameter. Certain instrumental and environmental errors must be…
We present new software to cross-match low-frequency radio catalogues: the Positional Update and Matching Algorithm (PUMA). PUMA combines a positional Bayesian probabilistic approach with spectral matching criteria, allowing for confusing…