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Wavelet theory has been well studied in recent decades. Due to their appealing features such as sparse multiscale representation and fast algorithms, wavelets have enjoyed many tremendous successes in the areas of signal/image processing…
GMP-Featurizer is a lightweight, accurate, efficient, and scalable software package for calculating the Gaussian Multipole (GMP) features \cite{GMP} for a variety of atomic systems with elements across the periodic table. Starting from the…
Pattern matching is a powerful tool for symbolic computations, based on the well-defined theory of term rewriting systems. Application domains include algebraic expressions, abstract syntax trees, and XML and JSON data. Unfortunately, no…
State-of-the-art algorithms generate scattering amplitudes for high-energy physics at leading order for high-multiplicity processes as compiled code (in Fortran, C or C++). For complicated processes the size of these libraries can become…
Quantum computing with qudits, an extension of qubits to multiple levels, is a research field less mature than qubit-based quantum computing. However, qudits can offer some advantages over qubits, by representing information with fewer…
High performance computing has been used in various fields of astrophysical research. But most of it is implemented on massively parallel systems (supercomputers) or graphical processing unit clusters. With the advent of multicore…
We present a new Monte Carlo tool that computes full tree-level matrix elements in high-energy physics. The program accepts user-defined models and has no restrictions on the process multiplicity. To achieve acceptable performance, CAMORRA…
Low-discrepancy (LD) sequences have been extensively used as efficient experimental designs across many scientific disciplines. QMCPy (https://qmcsoftware.github.io/QMCSoftware/) is an accessible Python library which provides a unified…
HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincar\'e disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of…
Seismology has witnessed significant advancements in recent years with the application of deep learning methods to address a broad range of problems. These techniques have demonstrated their remarkable ability to effectively extract…
Generalizing wavelets by adding desired redundancy and flexibility,framelets are of interest and importance in many applications such as image processing and numerical algorithms. Several key properties of framelets are high vanishing…
We introduce a new general purpose multiresolution preconditioner for symmetric linear systems. Most existing multiresolution preconditioners use some standard wavelet basis that relies on knowledge of the geometry of the underlying domain.…
Fourier transforms are an often necessary component in many computational tasks, and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a…
I present libcommute, a C++11/14/17 template library that implements a domain-specific language for easy manipulating of polynomial operators used in the quantum many-body theory, as well as a software development toolkit for exact…
The solution of a partial differential equation can be obtained by computing the inverse operator map between the input and the solution space. Towards this end, we introduce a \textit{multiwavelet-based neural operator learning scheme}…
Despite advancements in the areas of parallel and distributed computing, the complexity of programming on High Performance Computing (HPC) resources has deterred many domain experts, especially in the areas of machine learning and…
Some connections between operator theory and wavelet analysis: Since the mid eighties, it has become clear that key tools in wavelet analysis rely crucially on operator theory. While isolated variations of wavelets, and wavelet…
WavePacket is an open-source program package for the numerical simulation of quantum-mechanical dynamics. It can be used to solve time-independent or time-dependent linear Schr\"odinger and Liouville-von Neumann-equations in one or more…
The linear canonical wavelet transform has been shown to be a valuable and powerful time-frequency analyzing tool for optics and signal processing. In this article, we propose a novel transform called quaternion linear canonical wavelet…
Quantum computers have the potential to solve some important industrial and scientific problems with greater efficiency than classical computers. While most current realizations focus on two-level qubits, the underlying physics used in most…