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The central notion of this work is that of a functor between categories of finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically solve inhomogeneous linear equations with coefficients in R.…
Based on the OPP technique and the HELAC framework, HELAC-1LOOP is a program that is capable of numerically evaluating QCD virtual corrections to scattering amplitudes. A detailed presentation of the algorithm is given, along with…
We construct the universal enveloping algebra of a Hom-Lie algebra and endow it with a Hom-Hopf algebra structure. We discuss group-like elements that we see as a Hom-group integrating the initial Hom-Lie algebra.
The twisted group ring isomorphism problem (TGRIP) is a variation of the classical group ring isomorphism problem. It asks whether the ring structure of the twisted group ring determines the group up to isomorphism. In this article, we…
We proved a new Siegel-Weil formula for orthogonal and symplectic groups, which will be used later to prove a generalization of Siegel-Weil formula for loop groups.
Spin-orbit coupling of planetary systems plays an important role in the dynamics and habitability of planets. However, symplectic integrators that can accurately simulate not only how orbit affects spin but also how spin affects orbit have…
This is an expository article on recent developments in the theory of group relaxations in integer programming from an algebraic perspective.
Current state-of-the-art solvers for mixed-integer programming (MIP) problems are designed to perform well on a wide range of problems. However, for many real-world use cases, problem instances come from a narrow distribution. This has…
We present IntU package for Mathematica computer algebra system. The presented package performs a symbolic integration of polynomial functions over the unitary group with respect to unique normalized Haar measure. We describe a number of…
We present the notion of injective hom-complexity, leading to a connection between the covering number of a group and the sectional number of a group homomorphism, and provide estimates for computing this invariant.
OGRePy is a modern, open-source Python package designed to perform symbolic tensor calculations, with a particular focus on applications in general relativity. Built on an object-oriented architecture, OGRePy encapsulates tensors, metrics,…
We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations by convexifying finite sets of strategically chosen points,…
We present an elliptic version of Selberg's integral formula.
This is a report from the Libraries and Tools Working Group of the High Energy Physics Forum for Computational Excellence. It presents the vision of the working group for how the HEP software community may organize and be supported in order…
Recognizing Textual Entailment (RTE) was proposed as a unified evaluation framework to compare semantic understanding of different NLP systems. In this survey paper, we provide an overview of different approaches for evaluating and…
In this paper, we develop a new and efficient approach to the computation of envelope surfaces. We interpret one-parameter systems of surfaces as curves in the homogeneous spaces of suitable Lie groups. Using the formalism of Lie groups and…
This paper presents a procedure to perform fully autonomous on-orbit alignment of the interferometer on board the LISA Technology Package (LTP). LTP comprises two free-floating test masses as inertial sensors that additionally serve as end…
This paper develops the foundations of Hom-heaps, Hom-trusses, and Hom-braces as natural Hom-type analogues of their classical counterparts. We establish the correspondence between Hom-heaps and Hom-groups, showing that the retract of a…
In calculations of heavy-atom molecules with the shape-consistent Relativistic Effective Core Potential (RECP), only valence and some outer-core shells are treated explicitly, the shapes of spinors are smoothed in the atomic core regions…
We study Lp-improving properties as well as the type set of certain singular measures on the Heisenberg group.