Related papers: Some thoughts about matrix coordinate transformati…
Finite (or Discrete) Fourier Transforms (FFT) are essential tools in engineering disciplines based on signal transmission, which is the case in most of them. FFT are related with circulant matrices, which can be viewed as group matrices of…
Duality transformations reveal unexpected equivalences between seemingly distinct models. We introduce an out-of-equilibrium generalisation of matrix product operators to implement duality transformations in one-dimensional boundary-driven…
We introduce a convex optimization modeling framework that transforms a convex optimization problem expressed in a form natural and convenient for the user into an equivalent cone program in a way that preserves fast linear transforms in…
The most general coordinates transformations that allow for the exact separation of the kinetic energy operator of a quantum many-body system into total center of mass kinetic energy and internal kinetic energy are found and discussed. We…
Probabilistic programs with dynamic computation graphs can define measures over sample spaces with unbounded dimensionality, which constitute programmatic analogues to Bayesian nonparametrics. Owing to the generality of this model class,…
Large language models exhibit sophisticated capabilities, yet understanding how they work internally remains a central challenge. A fundamental obstacle is that training selects for behavior, not circuitry, so many weight configurations can…
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…
The quaternion spaces can be used to describe the property of electromagnetic field and gravitational field. In the quaternion space, some coordinate transformations can be deduced from the feature of quaternions, including Lorentz…
A definition for functions of multidimensional arrays is presented. The definition is valid for third-order tensors in the tensor t-product formalism, which regards third-order tensors as block circulant matrices. The tensor function…
In this paper we present a method for matrix inversion based on Cholesky decomposition with reduced number of operations by avoiding computation of intermediate results; further, we use fixed point simulations to compare the numerical…
Commutative analogues of Clifford algebras are algebras defined in the same way as Clifford algebras except that their generators commute with each other, in contrast to Clifford algebras in which the generators anticommute. In this paper,…
We introduce a new concept of the so-called {\it composite wavelet transforms}. These transforms are generated by two components, namely, a kernel function and a wavelet function (or a measure). The composite wavelet transforms and the…
We study generalized disformal transformations, including derivatives of the metric, in the context of the Effective Field Theory of Inflation. All these transformations do not change the late-time cosmological observables but change the…
Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…
It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…
We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models. In continuation and completion of our earlier work, we present two…
The division between two vectors belonging to the same vector space is obtained by elementary procedures of vector algebra and is defined by a matrix. This representation is obtained for two and three dimensional vector spaces. A new vector…
Coordinate systems are defined on general metric spaces with the purpose of generalizing vector fields on a manifold. Conversion formulae are available between metric and Cartesian coordinates on a Hilbert space. Nagumo's Invariance Theorem…
The aim of the current paper is to study the multiscalar-tensor theories of gravity without derivative couplings. We construct a few basic objects that are invariant under a Weyl rescaling of the metric and transform covariantly when the…
Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We…