Related papers: CARTAN: A Mathematica package for tensor computati…
We study properties of Newton-Cartan gravity under transformations into all noninertial, nonrelativistic reference frames. The set of these transformations has the structure of an infinite dimensional Lie group, called the Galilean line…
Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…
Tensor contraction (TC) is an important computational kernel widely used in numerous applications. It is a multi-dimensional generalization of matrix multiplication (GEMM). While Strassen's algorithm for GEMM is well studied in theory and…
The computational power increases over the past decades havegreatly enhanced the ability to simulate chemical reactions andunderstand ever more complex transformations. Tensor contractions are the fundamental computational building block of…
Irreducible Cartesian tensors (ICTs) play a crucial role in the design of equivariant graph neural networks, as well as in theoretical chemistry and chemical physics. Meanwhile, the design space of available linear operations on tensors…
We are upgrading the Python-version of RTNI, which symbolically integrates tensor networks over the Haar-distributed unitary matrices. Now, PyRTNI2 can treat the Haar-distributed orthogonal matrices and the real and complex normal Gaussian…
This work presents TorchRadon -- an open source CUDA library which contains a set of differentiable routines for solving computed tomography (CT) reconstruction problems. The library is designed to help researchers working on CT problems to…
We explain what Cartan geometries are, aiming at an audience of graduate students familiar with manifolds, Lie groups and differential forms.
The tetrad partial differential equations formulated by Buchman and Bardeen for vacuum gravity are shown to be well posed by calculation of the Cartan characters of an associated exterior differential system. Gauge specializations are…
Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…
A Riemann-Cartan manifold is a Riemannian manifold endowed with an affine connection which is compatible with the metric tensor. This affine connection is not necessarily torsion free. Under the assumption that the manifold is a homogeneous…
This paper develops a theory of thin shells within the context of the Einstein-Cartan theory by extending the known formalism of general relativity. In order to perform such an extension, we require the general non symmetric stress-energy…
We present TopoTB, a software package written in the Mathematica language, designed to compute electronic structures, topological properties, and phase diagrams based on tight-binding models. TopoTB is user-friendly, with an interactive…
We perform a covariant 1+3 split of the Newton-Cartan equations. The resulting 3-dimensional system of equations, called \textit{the 1+3-Newton-Cartan equations}, is structurally equivalent to the 1+3-Einstein equations. In particular it…
The absorption and emission of light by exoplanet atmospheres encode details of atmospheric composition, temperature, and dynamics. Fundamentally, simulating these processes requires detailed knowledge of the opacity of gases within an…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
Cartan's spacetime reformulation of the Newtonian theory of gravity is a generally-covariant Galilean-relativistic limit-form of Einstein's theory of gravity known as the Newton-Cartan theory. According to this theory, space is flat, time…
We present ktrain, a low-code Python library that makes machine learning more accessible and easier to apply. As a wrapper to TensorFlow and many other libraries (e.g., transformers, scikit-learn, stellargraph), it is designed to make…
In this report, we introduce DocXChain, a powerful open-source toolchain for document parsing, which is designed and developed to automatically convert the rich information embodied in unstructured documents, such as text, tables and…
Deep neural networks (DNNs) are of critical use in different domains. To accelerate DNN computation, tensor compilers are proposed to generate efficient code on different domain-specific accelerators. Existing tensor compilers mainly focus…