Related papers: Reduze - Feynman Integral Reduction in C++
Optimizing deep learning models is generally performed in two steps: (i) high-level graph optimizations such as kernel fusion and (ii) low level kernel optimizations such as those found in vendor libraries. This approach often leaves…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from…
Robust optimization is a very popular means to address decision-making problems affected by uncertainty. Its success has been fueled by its attractive robustness and scalability properties, by ease of modeling, and by the limited…
We describe a modular rewriting system for translating optimization problems written in a domain-specific language to forms compatible with low-level solver interfaces. Translation is facilitated by reductions, which accept a category of…
LaTeX is a free document preparation system that handles the typesetting of mathematical expressions smoothly and elegantly. It has become the standard format for creating and publishing research articles in mathematics and many scientific…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
Uncomputation is a feature in quantum programming that allows the programmer to discard a value without losing quantum information, and that allows the compiler to reuse resources. Whereas quantum information has to be treated linearly by…
The multi-resolution approximation (MRA) of Gaussian processes was recently proposed to conduct likelihood-based inference for massive spatial data sets. An advantage of the methodology is that it can be parallelized. We implemented the MRA…
The C-Algorithm introduced in [Chouikha2007] is designed to determine isochronous centers for Lienard-type differential systems, in the general real analytic case. However, it has a large complexity that prevents computations, even in the…
The concurrent refinement algebra has been developed to support rely/guarantee reasoning about concurrent programs. The algebra supports atomic commands and defines parallel composition as a synchronous operation, as in Milner's SCCS. In…
The success of language models in code assistance has spurred the proposal of repository-level code completion as a means to enhance prediction accuracy, utilizing the context from the entire codebase. However, this amplified context can…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
Robust Principal Component Analysis (PCA) has received massive attention in recent years. It aims to recover a low-rank matrix and a sparse matrix from their sum. This paper proposes a novel nonconvex Robust PCA algorithm, coined Riemannian…
Difference constraints have been used for termination analysis in the literature, where they denote relational inequalities of the form x' <= y + c, and describe that the value of x in the current state is at most the value of y in the…
We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The…
From a theoretical point of view, finding the solution set of a system of inequalities in only two variables is easy. However, if we want to get rigorous bounds on this set with floating point arithmetic, in all possible cases, then things…
The use of Physics-informed neural networks (PINNs) has shown promise in solving forward and inverse problems of fractional diffusion equations. However, due to the fact that automatic differentiation is not applicable for fractional…
Sequences of linear systems arise in the predictor-corrector method when computing the Pareto front for multi-objective optimization. Rather than discarding information generated when solving one system, it may be advantageous to recycle…
Kleene algebra (KA) is an important tool for reasoning about general program equivalences, with a decidable and complete equational theory. However, KA cannot always prove equivalences between specific programs. For this purpose, one adds…