Related papers: $\mathtt{bimEX}$: A Mathematica package for exact …
This paper introduces the first release of Pytearcat, a Python package developed to compute tensor algebra operations in the context of theoretical physics, for instance, in general relativity. Given that working with tensors can become a…
The Neyman-Scott point process is a widely used point process model which is easily interpretable and easily extendable to include various types of inhomogeneity. The inference for such complex models is then complicated and fast methods,…
A new method of analysing positive bistochastic maps on the algebra of complex matrices $M_{3}$ has been proposed. By identifying the set of such maps with a convex set of linear operators on $\mathbb{R}^{8}$, one can employ techniques from…
(This is a report for the Proceedings of ``Journees Relativistes 1993'' written in September 1993. Containes a short description of the results published elsewhere in the joint paper with A. Ashtekar) Integral calculus on the space of gauge…
We describe the package "IncidenceCorrespondenceCohomology" for the computer algebra system Macaulay2. The main feature concerns the computation of characters and dimensions for the cohomology groups of line bundles on the incidence…
Exact analytic expression is derived for the matrix elements of the Coulomb interaction in two dimensions in the form of a closed finite sum expression. The orthonormal complete set of eigenfunctions of the harmonic oscillator is used as…
GroupMath is a Mathematica package which performs several calculations related to semi-simple Lie algebras and the permutation groups, both of which are important in particle physics as well as in other areas of research.
SecDec is a program which can be used for the evaluation of parametric integrals, in particular multi-loop integrals. For a given set of propagators defining the graph, the program constructs the graph polynomials, factorizes the endpoint…
We continue our study on Hermitian manifolds that are {\em Bismut torsion parallel,} or {\em BTP} for brevity, which means that the Bismut connection has parallel torsion tensor. For $n\geq 3$, BTP metrics can be balanced (and…
This paper examines the relationship between the symplectic quotient X//G of a Hamiltonian G-manifold X, and the associated symplectic quotient X//T, where T is a maximal torus, in the case in which X//G is a compact manifold or orbifold.…
We present a prototype of a software tool for exploration of multiple combinatorial optimisation problems in large real-world and synthetic complex networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial Explorer),…
The calculation of (co)irreducible representations of energy bands at high-symmetry points (HSPs) is essential for high-throughput research on topological materials based on symmetry-indicators or topological quantum chemistry. However,…
We introduce a formal operational semantics that describes the fused execution of variable contraction problems, which compute indexed arithmetic over a semiring and generalize sparse and dense tensor algebra, relational algebra, and graph…
We construct a sequence of geodesics on the modular surface such that the complement of the canonical lifts to the unit tangent bundle are arithmetic 3-manifolds.
In this paper, we introduce discrete approximate circle bundles, a class of objects designed to serve as the data science analog of circle bundles from algebraic topology. We show that, under appropriate conditions, one can meaningfully and…
Data collected by the Interstellar Boundary Explorer (IBEX) satellite, recording heliospheric energetic neutral atoms (ENAs), exhibit a phenomenon that has caused space scientists to revise hypotheses about the physical processes, and…
The usual dictionary between geometry and commutative algebra is not appropriate for Arithmetic geometry because addition is a singular operation at the "Real prime". We replace Rings, with addition and multiplication, by Props (=strict…
We present an explicit formula for the expected value of a product of several independent symplectically invariant matrices in which the trace and real part function may be applied, possibly to different subexpressions. This takes the form…
A program to calculate the three-particle hyperspherical brackets is presented. Test results are listed and it is seen that the program is well applicable up to very high values of the hypermomentum and orbital momenta. The listed runs show…
These lecture notes present a method for symbolic tensor calculus that (i) runs on fully specified smooth manifolds (described by an atlas), (ii) is not limited to a single coordinate chart or vector frame, (iii) runs even on…