相关论文: A tool for teaching General Relativity

Online Learning Management Systems (LMSs), such as Blackboard and Canvas, have existed for decades. Yet, course readings, when provided at all, consistently exist as simple digital twins to their real-life counterparts. While online tools…

Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.

Due to the effectiveness of using machine learning in physics, it has been widely received increased attention in the literature. However, the notion of applying physics in machine learning has not been given much awareness to. This work is…

This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We…

A brief characteristic of the specialized computer algebra system GRG_EC intended for symbolic computations in the field of general relativity is given.

A natural two-metric formalism, generated by the world function of the space-time, is used. This circumstance admits one to localize the relative gravitational field, which is described by a tensor.

The paper is constructed in two parts.In the first part we introduce the concept of the algebra of Q-meromorphic functions on the quantum plane.The A (q)-algebra of Q-analytic functions considered in[6]is seen as a proper subalgebra. In the…

Gravitational lensing occurs as the path of light from distant celestial bodies is distorted due to gravitational attraction by other celestial bodies, whose mass is partly invisible, being so-called dark matter. When observed through a…

Latent class models are powerful statistical modeling tools widely used in psychological, behavioral, and social sciences. In the modern era of data science, researchers often have access to response data collected from large-scale surveys…

In this paper, we introduce MCTensor, a library based on PyTorch for providing general-purpose and high-precision arithmetic for DL training. MCTensor is used in the same way as PyTorch Tensor: we implement multiple basic, matrix-level…

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in…

Gravitational lenses are presently playing an important role in astrophysics. By means of these lenses the parameters of the deflector such as its mass, ellipticity, etc. and Hubble's constant can be determined. Using C, Xforms, Mesa and…

This book provides a compact, derivation-oriented introduction to the mathematical foundations of modern generative artificial intelligence. Rather than surveying every recent architecture or implementation detail, it develops a coherent…

Sector models are tools that make it possible to teach the basic principles of the general theory of relativity without going beyond elementary mathematics. This contribution shows how sector models can be used to determine geodesics. We…

Recently, tensor algebra have witnessed significant applications across various domains. Each operator in tensor algebra features different computational workload and precision. However, current general accelerators, such as VPU, GPGPU, and…

General Relativity (GR) represents the most recent theory of gravity, on which all modern astrophysics is based, including some of the most astonishing results of physics research. Nevertheless, its study is limited to university courses,…

This paper develops and evaluates a new tensor field representation to express the geometric affordance of one object over another. We expand the well known bisector surface representation to one that is weight-driven and that retains the…

We consider the question: what is the abstraction that should be implemented by the computational engine of a machine learning system? Current machine learning systems typically push whole tensors through a series of compute kernels such as…

Ray-tracing is a central tool for constructing mock observations of compact object emission and for comparing physical emission models with observations. We present Arcmancer, a publicly available general ray-tracing and tensor algebra…

Tensor time series (TTS) data, a generalization of one-dimensional time series on a high-dimensional space, is ubiquitous in real-world scenarios, especially in monitoring systems involving multi-source spatio-temporal data (e.g.,…