Related papers: Generalized Tensor Analysis Method Applied to Non-…
Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…
In this paper, we establish and employ a local framework to the first order of Riemann's curvature tensor in order to develop the corresponding coordinate non commutativity into general manifolds. We also exploit a new translation of…
The global time is defined in covariant form under the condition of a constant mean curvature slicing of spacetime. The background static metric is taken in the tangent space. The global intrinsic time is identified with the logarithmic…
Gaussian mixture models (GMMs) are fundamental tools in statistical and data sciences. We study the moments of multivariate Gaussians and GMMs. The $d$-th moment of an $n$-dimensional random variable is a symmetric $d$-way tensor of size…
General relativity uses curved space-time to describe accelerating frames. The movement of particles in different curved space-times can be regarded as equivalent physical processes based on the covariant transformation between different…
The basic and fundamental aspects of General Relativity are in general analysed in mathematical level of coordinate basis or holonomic frame by several authors in the literature. However, for many purposes it is more convenient to use a…
A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame…
General relativity under the assumption of noncommuting components of the tetrad field is considered in this paper. Since the algebraic properties of the tetrad field representing the gravitational field are assumed to correspond to the…
Several applications of spectral methods to problems related to the relativistic astrophysics of compact objects are presented. Based on a proper definition of the analytical properties of regular tensorial functions we have developed a…
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…
Higher order data is modeled using matrices whose entries are numerical arrays of a fixed size. These arrays, called t-scalars, form a commutative ring under the convolution product. Matrices with elements in the ring of t-scalars are…
Recent proposals suggested quantum clock interferometry for tests of the Einstein equivalence principle. However, atom interferometric models often include relativistic effects only in an ad hoc fashion. Here, instead, we start from the…
The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…
Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
In this paper we give a review of the most general approach to description of reference frames, the monad formalism. This approach is explicitly general covariant at each step, permitting to use abstract representation of tensor quantities;…
Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are…
In the quantum theory, it has been shown that one can see if a process has the time reversal symmetry by applying the matrix transposition and examining if it remains physical. However, recent discoveries regarding the indefinite causal…
In the context of the teleparallel equivalent of general relativity, we show that the energy-momentum density for the gravitational field can be described by a true spacetime tensor. It is also invariant under local (gauge) translations of…
A general formula is calculated for the connection of a central metric w.r.t.\ a noncommutative spacetime of Lie-algebraic type. This is done by using the framework of linear connections on central bi-modules. The general formula is further…