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Atomic force microscopy (AFM) is a mechanical profiling technique that allows to image surfaces with atomic resolution. Recent progress in reducing the noise of this technique has led to a resolution level where previously undetectable…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
Atomic-level modeling performed at large scales enables the investigation of mesoscale materials properties with atom-by-atom resolution. The spatial complexity of such cross-scale simulations renders them unsuitable for simple human visual…
In radio interferometric observations, the main source of information is the complex visibility function, which includes amplitude and phase. In this paper, the dependence of the phase of the visibility function on the base projection is…
Ab initio calculations face the challenge of describing a complex multiscale quantum many-body system. The nuclear wave function has both strong short-range correlations and long-range contributions. Natural orbitals provide a means of…
Most accurate predictions are typically obtained by learning machines with complex feature spaces (as e.g. induced by kernels). Unfortunately, such decision rules are hardly accessible to humans and cannot easily be used to gain insights…
Practitioners use feature importance to rank and eliminate weak predictors during model development in an effort to simplify models and improve generality. Unfortunately, they also routinely conflate such feature importance measures with…
One of the key elements of explanatory analysis of a predictive model is to assess the importance of individual variables. Rapid development of the area of predictive model exploration (also called explainable artificial intelligence or…
Importance weighting is a fundamental procedure in statistics and machine learning that weights the objective function or probability distribution based on the importance of the instance in some sense. The simplicity and usefulness of the…
Large atomic-orbital (AO) basis sets of at least triple and preferably quadruple-zeta (QZ) size are required to adequately converge Kohn-Sham density functional theory (DFT) calculations towards the complete basis set limit. However,…
In this paper, we propose {\it \underline{R}ecursive} {\it \underline{I}mportance} {\it \underline{S}ketching} algorithm for {\it \underline{R}ank} constrained least squares {\it \underline{O}ptimization} (RISRO). The key step of RISRO is…
To solve the Kohn-Sham equation within the framework of density functional theory, we develop a scheme to construct numerical atomic orbital (NAO) basis sets by contracting truncated spherical waves (TSWs). The contraction minimizes the…
Given a classification model and a prediction for some input, there are heuristic strategies for ranking features according to their importance in regard to the prediction. One common approach to this task is rooted in propositional logic…
The standard algorithm for the numerical evaluation of the prolate spheroidal wave function $\mathsf{Ps}\hskip.05em{}_{n}(x;\gamma^2)$ of order $0$, bandlimit $\gamma > 0$ and characteristic exponent $n$ has running time which grows with…
The Quantum Approximate Optimization Algorithm, QAOA, uses a shallow depth quantum circuit to produce a parameter dependent state. For a given combinatorial optimization problem instance, the quantum expectation of the associated cost…
Atomistic simulations have become a powerful tool in materials research due to the extremely fine spatial and temporal resolution provided by such techniques. In order to understand the fundamental principles which govern material behavior…
In density functional theory, charge density is the core attribute of atomic systems from which all chemical properties can be derived. Machine learning methods are promising in significantly accelerating charge density prediction, yet…
Randomized protocols are procedures that incorporate probabilistic choices during their execution and they play a central role in quantum algorithms, spanning Hamiltonian simulation, noise mitigation, and measurement tasks. In practical…
Complex problems may require sophisticated, non-linear learning methods such as kernel machines or deep neural networks to achieve state of the art prediction accuracies. However, high prediction accuracies are not the only objective to…
Precision spectroscopy has long played a central role in testing the foundations of physics, from the early insights that led to the development of quantum mechanics to the validation of quantum electrodynamics and the determination of…