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The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
Understanding and quantifying node importance is a fundamental problem in network science and engineering, underpinning a wide range of applications such as influence maximization, social recommendation, and network dismantling. Prior…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
The crucial step in designing a particle filter for a particular application is the choice of importance density. The optimal scheme is to use the conditional posterior density of the state, but this cannot be sampled or calculated…
Machine learning, and representation learning in particular, has the potential to facilitate drug discovery by screening a large chemical space in silico. A successful approach for representing molecules is to treat them as a graph and…
Adaptive sparse coding methods learn a possibly overcomplete set of basis functions, such that natural image patches can be reconstructed by linearly combining a small subset of these bases. The applicability of these methods to visual…
A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis…
Modern quantum chemistry can make quantitative predictions on an immense array of chemical systems. However, the interpretation of those predictions is often complicated by the complex wave function expansions used. Here we show that an…
Light-pulse atom interferometers rely on the wave nature of matter and its manipulation with coherent laser pulses. They are used for precise gravimetry and inertial sensing as well as for accurate measurements of fundamental constants.…
Pulsar timing array (PTA) is expected to detect gravitational wave background (GWB) in the nanohertz band within the next decade. This provides an opportunity to test the gravity theory and cosmology. A typical data analysis method to…
Closed-form expressions for the ringdown complex amplitudes of nonspinning unequal-mass binaries in arbitrarily eccentric orbits are presented. They are built upon 237 numerical simulations contained within the RIT catalog, through the…
Hypergraph visualization has many applications in network data analysis. Recently, a polygon-based representation for hypergraphs has been proposed with demonstrated benefits. However, the polygon-based layout often suffers from excessive…
With the ubiquity of sensors in the IoT era, statistical observations are becoming increasingly available in the form of massive (multivariate) time-series. Formulated as unsupervised anomaly detection tasks, an abundance of applications…
We introduce analysis of orbital parities as a concept and a tool for understanding radicals. Based on fundamental reduced one- and two-electron density matrices, our approach allows us to evaluate a total measure of radical character and…
Despite the success of deep learning methods in quantum chemistry, their representational capacity is most often confined to neutral, closed-shell molecules. However, real-world chemical systems often exhibit complex characteristics,…
Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding…
We give explicit real-analytic functions whose zero sets characterize the images of the standard maps of wave-front singularities. Such functions are realizations of the main-analytic sets in the sense of Ishikawa-Koike-Shiota (1984). More…
We train a model atom to recognize hand-written digits between 0 and 9, employing intense light--matter interaction as a computational resource. For training, individual images of hand-written digits in the range 0-9 are converted into…
Reduced basis methods provide a powerful framework for building efficient and accurate emulators. Although widely applied in many fields to simplify complex models, reduced basis methods have only been recently introduced into nuclear…
Shape matching is a fundamental task in computer graphics and vision, with deep functional maps becoming a prominent paradigm. However, existing methods primarily focus on learning informative feature representations by constraining…