Related papers: A tool for teaching General Relativity
The task of natural language table retrieval (NLTR) seeks to retrieve semantically relevant tables based on natural language queries. Existing learning systems for this task often treat tables as plain text based on the assumption that…
This is a short note to announce the availability of some movies that may be useful in classroom discussions on the photographic appearance of objects moving at relativistic speeds. The images are based on special relativity with no account…
These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications:…
Tensors or {\em multi-way arrays} are functions of three or more indices $(i,j,k,\cdots)$ -- similar to matrices (two-way arrays), which are functions of two indices $(r,c)$ for (row,column). Tensors have a rich history, stretching over…
We present a fit-for-purpose introduction to tensors and their operations. It is envisaged to help the reader become acquainted with its underpinning concepts for the study of path signatures. The text includes exercises, solutions and many…
GeoGebra is an open source mathematics education software tool being used in thousands of schools worldwide. Since version 4.2 (December 2012) it supports symbolic computation of locus equations as a result of joint effort of mathematicians…
This book is a manual for the course of electrodynamics and theory of relativity. It is recommended primarily for students of mathematical departments. This defines its style: I use elements of vectorial and tensorial analysis, differential…
TensorKit.jl is a Julia-based software package for tensor computations, especially focusing on tensors with internal symmetries. This paper introduces the design philosophy, core functionalities, and distinctive features, including how to…
In this paper we present the development of an open-source simulation toolbox, PowerSimulationsDynamics.jl, to study the dynamic response of power systems, focusing on the requirements to model systems with high penetrations of…
These lecture notes, suitable for a two-semester introductory course or self-study, offer an elementary and self-contained exposition of the basic tools and concepts that are encountered in practical computations in perturbative thermal…
Performing diagnosis or exploratory analysis during the training of deep learning models is challenging but often necessary for making a sequence of decisions guided by the incremental observations. Currently available systems for this…
Mathematical educational soft explore, investigating in a dynamical way, some algebraically, geometrically problems, the expected results being used to involve a lot of mathematical results. One such software soft is GeoGebra. The software…
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final…
A major challenge in the field of education is providing review schedules that present learned items at appropriate intervals to each student so that memory is retained over time. In recent years, attempts have been made to formulate item…
Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…
Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection…
GRTresna is a multigrid solver designed to solve the constraint equations for the initial data required in numerical relativity simulations. In particular, it is focussed on scenarios with fundamental fields around black holes and…
A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…
We have developed a Java-based teaching tool, "Appreciating Hubble at Hyper-speed" ($\textit{AHaH}$), intended for use by students and instructors in beginning astronomy and cosmology courses, which we have made available online. This tool…