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Motivated by the problem of nonparametric inference in high level digital image analysis, we introduce a general extrinsic approach for data analysis on Hilbert manifolds with a focus on means of probability distributions on such sample…
The predictions of parameteric property models and their uncertainties are sensitive to systematic errors such as inconsistent reference data, parametric model assumptions, or inadequate computational methods. Here, we discuss the…
Nonequilibrium self-assembly is the root of all emergent complexity, including life. In quantum materials emergent metastable states have become a very fashionable topic of research, but the study of resulting mesoscopic state dynamics is…
Early stopping of iterative algorithms is an algorithmic regularization method to avoid over-fitting in estimation and classification. In this paper, we show that early stopping can also be applied to obtain the minimax optimal testing in a…
Research in diabetes, especially when it comes to building data-driven models to forecast future glucose values, is hindered by the sensitive nature of the data. Because researchers do not share the same data between studies, progress is…
This paper studies adaptive first-order least-squares finite element methods for second-order elliptic partial differential equations in non-divergence form. Unlike the classical finite element method which uses weak formulations of PDEs…
Efficient simulation of SDEs is essential in many applications, particularly for ergodic systems that demand efficient simulation of both short-time dynamics and large-time statistics. However, locally Lipschitz SDEs often require special…
State estimators often provide self-assessed uncertainty metrics, such as covariance matrices, whose credibility is critical for downstream tasks. However, these self-assessments can be misleading due to underlying modeling violations like…
Objective: Bland and Altman plot method is a widely cited and applied graphical approach for assessing the equivalence of quantitative measurement techniques, usually aiming to replace a traditional technique with a new, less invasive, or…
Quantum metrology studies the use of entanglement and other quantum resources to improve precision measurement. An interferometer using N independent particles to measure a parameter X can achieve at best the "standard quantum limit" (SQL)…
We present the results of numerical studies for selected materials with strongly correlated electrons using a combination of the local-density approximation and dynamical mean-field theory (DMFT). For the solution of the DMFT equations a…
An overarching question in strongly correlated electron systems is how the landscape of quantum phases emerges from electron correlations. The method of extended dynamical mean field theory (EDMFT) has been developed for clean lattice…
Simulating complex spin systems, known for high frustration and entanglement, presents significant challenges due to their intricate energy landscapes. This study focuses on the $J_{1}-J_{2}$ Heisenberg model, renowned for its rich phase…
Two different Perfectly Matched Layer (PML) formulations with efficient pseudo-spectral numerical schemes are derived for the standard and non-relativistic nonlinear Klein-Gordon equations (NKGE). A pseudo-spectral explicit exponential…
A technique allowing for a perturbative treatment of nonlocal corrections to the single-site dynamical mean-field theory (DMFT) in finite dimensions is developed. It is based on the observation that in the case of strong electron…
Employing the neural network framework, we obtain empirical fits to the electron-scattering cross sections for carbon over a broad kinematic region, extending from the quasielastic peak through resonance excitation to the onset of…
Collisional and radiative dynamics of a plasma is exposed by so-called Collisional Radiative Models [1] that simplify the chemical kinetics by quasi-steady state assignment on certain types of particles. The assignment is conventionally…
The electron density is a key parameter to characterize any plasma. Most of the plasma applications and research in the area of low-temperature plasmas (LTPs) are based on the accurate estimations of plasma density and plasma temperature.…
Measurement error arises commonly in clinical research settings that rely on data from electronic health records or large observational cohorts. In particular, self-reported outcomes are typical in cohort studies for chronic diseases such…
This paper aims to investigate the numerical approximation of semilinear non-autonomous stochastic partial differential equations (SPDEs) driven by multiplicative or additive noise. Such equations are more realistic than autonomous SPDEs…