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We assess numerical stabilization methods employed in fermion many-body quantum Monte Carlo simulations. In particular, we empirically compare various matrix decomposition and inversion schemes to gain control over numerical instabilities…
This paper describes an approach to computer aided calculations in the cohomology of arithmetic groups. It complements existing literature on the topic by emphasizing homotopies and perturbation techniques, rather than cellular subdivision,…
Julia is a new language for writing data analysis programs that are easy to implement and run at high performance. Similarly, the Dynamic Distributed Dimensional Data Model (D4M) aims to clarify data analysis operations while retaining…
Implementing and executing numerical algorithms to solve fractional differential equations has been less straightforward than using their integer-order counterparts, posing challenges for practitioners who wish to incorporate fractional…
Numerical simulations are ubiquitous in mathematics and computational science. Several industrial and clinical applications entail modeling complex multiphysics systems that evolve over a variety of spatial and temporal scales. This study…
We present Groebner.jl, a Julia package for computing Groebner bases with the F4 algorithm. Groebner.jl is an efficient, portable, and open-source software. Groebner.jl works over integers modulo a prime and over the rationals, supports…
We apply various seq2seq models on programming language correction tasks on Juliet Test Suite for C/C++ and Java of Software Assurance Reference Datasets(SARD), and achieve 75\%(for C/C++) and 56\%(for Java) repair rates on these tasks. We…
Classical methods to simulate quantum systems are not only a key element of the physicist's toolkit for studying many-body models but are also increasingly important for verifying and challenging upcoming quantum computers. Pauli…
Several quantum and classical Monte Carlo algorithms for Betti Number Estimation (BNE) on clique complexes have recently been proposed, though it is unclear how their performances compare. We review these algorithms, emphasising their…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
Although metaheuristics have been widely recognized as efficient techniques to solve real-world optimization problems, implementing them from scratch remains difficult for domain-specific experts without programming skills. In this…
Scorio.jl is a Julia package for evaluating and ranking systems from repeated responses to shared tasks. It provides a common tensor-based interface for direct score-based, pairwise, psychometric, voting, graph, and listwise methods, so the…
We present the library Moore, which implements Interval Arithmetic in modern C++. This library is based on a new feature in the C++ language called concepts, which reduces the problems caused by template meta programming, and leads to a new…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
Motivation: Estimating model parameters from experimental observations is one of the key challenges in systems biology and can be computationally very expensive. While the Julia programming language was recently developed as a high-level…
TopologicalNumbers.jl is an open-source Julia package designed to calculate topological invariants, mathematical quantities that characterize the properties of materials in condensed matter physics. These invariants, such as the Chern…
We introduce JuliQAOA, a simulation package specifically built for the Quantum Alternating Operator Ansatz (QAOA). JuliQAOA does not require a circuit-level description of QAOA problems, or another package to simulate such circuits, instead…
A recent GPU implementation of the Restarted Primal-Dual Hybrid Gradient Method for Linear Programming was proposed in Lu and Yang (2023). Its computational results demonstrate the significant computational advantages of the GPU-based…
Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring…
Quantum computers promise exponential speed ups over classical computers for various tasks. This emerging technology is expected to have its first huge impact in High Performance Computing (HPC), as it can solve problems beyond the reach of…