Related papers: SimpleTensor -- a user-friendly Mathematica packag…
In this paper we express some simple random tensor models in a Givental-like fashion i.e. as differential operators acting on a product of generic 1-Hermitian matrix models. Finally we derive Hirota's equations for these tensor models. Our…
This paper presents a brief but comprehensive introduction to certain mathematical techniques in General Relativity. Familiar mathematical procedures are investigated taking into account the complications of introducing a non trivial…
This article introduces TinyDEM, a lightweight implementation of a full-fledged discrete element method (DEM) solver in 3D. Newton's damped equations of motion are solved explicitly for translations and rotations of a polydisperse ensemble…
Many scientific computing problems can be reduced to Matrix-Matrix Multiplications (MMM), making the General Matrix Multiply (GEMM) kernels in the Basic Linear Algebra Subroutine (BLAS) of interest to the high-performance computing…
Ordinary Differential Equations (ODE) are used throughout science where the capture of rates of change in states is sought. While both pieces of commercial and open software exist to study such systems, their efficient and accurate usage…
Graphical calculus is an intuitive visual notation for manipulating tensors and index contractions. Using graphical calculus leads to simple and memorable derivations, and with a bit of practice one can learn to prove complex identities…
Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and…
The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main…
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point…
We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is…
Task arithmetic, representing downstream tasks through linear operations on task vectors, has emerged as a simple yet powerful paradigm for transferring knowledge across diverse settings. However, maintaining a large collection of task…
We introduce new features in the MathPartner service that have recently become available to users. We highlight the functions for calculating both arithmetic-geometric mean and geometric-harmonic mean. They allow calculating complete…
General classical theories of material fields in an arbitrary Riemann-Cartan space are considered. For these theories, with the help of equations of balance, new non-trivially generalized, manifestly generally covariant expressions for…
In scientific computing and machine learning applications, matrices and more general multidimensional arrays (tensors) can often be approximated with the help of low-rank decompositions. Since matrices and tensors of fixed rank form smooth…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
This paper shows how to generate efficient tensor algebra code that compute on dynamic sparse tensors, which have sparsity structures that evolve over time. We propose a language for precisely specifying recursive, pointer-based data…
Nonlinear mixed effects modeling is a powerful tool when analyzing data from several entities in an experiment. In this paper, we present NLMEModeling, a package for mixed effects modeling in Wolfram Mathematica. NLMEModeling supports mixed…
In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a…