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Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, there is a little tool support for transferring this expert knowledge to a wider…
An algorithm, based on the OPP reduction method, to automatically compute any one-loop amplitude, for all momentum, color and helicity configurations of the external particles, is presented. It has been implemented using the tree-order…
This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…
A Reduction -- an accumulation over a set of values, using an associative and commutative operator -- is a common computation in many numerical computations, including scientific computations, machine learning, computer vision, and…
Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In this context, the iterates are vectors generated from a…
We survey recent work on machine learning (ML) techniques for selecting cutting planes (or cuts) in mixed-integer linear programming (MILP). Despite the availability of various classes of cuts, the task of choosing a set of cuts to add to…
MatchingTools is a Python library for doing symbolic calculations in effective field theory. It provides the tools to construct general models by defining their field content and their interaction Lagrangian. Once a model is given, the…
Among many existing algorithms, convergence methods are the most popular means of computing square root and the reciprocal of square root of numbers. An initial approximation is required in these methods. Look up tables (LUT) are employed…
Integer linear programming (ILP) models a wide range of practical combinatorial optimization problems and significantly impacts industry and management sectors. This work proposes new characterizations of ILP with the concept of boundary…
I'll outline the latest version of my limits of math course. The purpose of this course is to illustrate the proofs of the key information-theoretic incompleteness theorems of algorithmic information theory by means of algorithms written in…
Iterative refinement is particularly popular for numerical solution of linear systems of equations. We extend it to Low Rank Approximation of a matrix (LRA) and observe close link of the resulting algorithm to oversampling techniques,…
A bitmap is a data structure designed to compactly represent sets of integers; it provides very fast operations for querying and manipulating such sets, exploiting bit-level parallelism. In this paper, we describe a technique for the…
Maritime Inventory Routing Problem (MIRP) plays a crucial role in the integration of global maritime commerce levels. However, there are still no well-established methodologies capable of efficiently solving large MIRP instances or their…
We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general…
Reductions combine collections of inputs with an associative (and here, also commutative) operator to produce collections of outputs. When the same value contributes to multiple outputs, there is an opportunity to reuse partial results,…
This tutorial (https://tum-nlp.github.io/low-resource-tutorial) is designed for NLP practitioners, researchers, and developers working with multilingual and low-resource languages who seek to create more equitable and socially impactful…
The increased interest in deep learning applications, and their hard-to-detect biases result in the need to validate and explain complex models. However, current explanation methods are limited as far as both the explanation of the…
Mathematical Information Retrieval (MIR) is the task of retrieving information from mathematical documents and plays a key role in various applications, including theorem search in mathematical libraries, answer retrieval on math forums,…
Structured matrices with symbolic sizes appear frequently in the literature, especially in the description of algorithms for linear algebra. Recent work has treated these symbolic structured matrices themselves as computational objects,…
FIRE7 is a major update to the FIRE program for integration-by-parts (IBP) reduction of Feynman integrals. A large part of improvements is related to the automatic reduction and reconstruction with the modular arithmetic approach, while the…