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We give a quantum algorithm for evaluating formulas over an extended gate set, including all two- and three-bit binary gates (e.g., NAND, 3-majority). The algorithm is optimal on read-once formulas for which each gate's inputs are balanced…
Numerical solutions of partial differential equations enable a broad range of scientific research. The Dedalus Project is a flexible, open-source, parallelized computational framework for solving general partial differential equations using…
We propose a new application of quantum computing to the field of natural language processing. Ongoing work in this field attempts to incorporate grammatical structure into algorithms that compute meaning. In (Coecke, Sadrzadeh and Clark,…
Equivariant atomistic machine learning models have largely been built on spherical-tensor representations, where explicit angular-momentum coupling introduces substantial complexity and systematic extensions beyond energies and forces…
Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of…
In multi-objective optimization, multiple loss terms are weighted and added together to form a single objective. These weights are chosen to properly balance the competing losses according to some meta-goal. For example, in physics-informed…
In the modelling of blazars and other radiating plasma flows, correctly evolving in time a series of kinetic equation coupled for different particle species is a computationally challenging problem. In this paper we introduce the code Katu,…
In CAGD/CAD research and education, users are involved with development of mathematical algorithms and followed by the analysis of the resultant algorithm. This process involves geometric display which can only be carried out with high end…
Package-X, a Mathematica package for the analytic computation of one-loop integrals dimensionally regulated near 4 spacetime dimensions is described. Package-X computes arbitrarily high rank tensor integrals with up to three propagators,…
We consider a linear inhomogeneous fractional evolution equation which is obtained from a Cauchy problem by replacing its first-order time derivative with Caputo's fractional derivative. The operator in the fractional evolution equation is…
Numerous applications necessitate the computation of numerical solutions to differential equations across a wide range of initial conditions and system parameters, which feeds the demand for efficient yet accurate numerical integration…
The modeling of physical processes is an integral part of scientific and technical research. In this area, the Extendible C++ Application in Quantum Technologies (ECAQT) package provides the numerical simulations and modeling of complex…
Canonical Correlation Analysis (CCA) is a widely used spectral technique for finding correlation structures in multi-view datasets. In this paper, we tackle the problem of large scale CCA, where classical algorithms, usually requiring…
We describe the special relativistic extension of the CRONOS code, which has been used for studies of gamma-ray binaries in recent years. The code was designed to be easily adaptable, allowing the user to easily change existing…
We present a simulation code which can solve broad ranges of partial differential equations in a full sphere. The code expands tensorial variables in a spectral series of spin-weighted spherical harmonics in the angular directions and a…
We present the tensor computer algebra package xTras, which provides functions and methods frequently needed when doing (classical) field theory. Amongst others, it can compute contractions, make Ans\"atze, and solve tensorial equations. It…
Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…
We describe an algorithm and a C++ implementation that we have written and made available for calculating the fully nonlinear evolution of 5D braneworld models with scalar fields. Bulk fields allow for the stabilization of the extra space.…
We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large and complex spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as…
To solve Math Word Problems, human students leverage diverse reasoning logic that reaches different possible equation solutions. However, the mainstream sequence-to-sequence approach of automatic solvers aims to decode a fixed solution…