Related papers: xPPN: An implementation of the parametrized post-N…
$\delta N$ formalism is a useful method to calculate the curvature perturbation. Contrary to what it is typically done in the literature, we re-formulate the $\delta N$ formalism by using the $e$-folding number $n$ counted forward in time.…
Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous studies have…
An arithmetic progression is a sequence of integers in which the difference between any two consecutive elements is the same. We investigate the parameterized complexity of two problems related to arithmetic progressions, called Cover by…
A scalar theory of gravitation with a preferred reference frame (PRF) is considered, that accounts for special relativity and reduces to it if the gravitational field cancels. The gravitating system consists of a finite number of…
We derive Keplerian-type parametrization for the solution of post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The PN accurate dynamics that we consider consists of the third…
We introduce MixFunn, a novel neural network architecture designed to solve differential equations with enhanced precision, interpretability, and generalization capability. The architecture comprises two key components: the mixed-function…
Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…
The main objective of this thesis is to discuss scalar-tensor theories in the Palatini approach. Both scalar-tensor theories and Palatini formalism are means of alternating classical theory of gravity, general relativity, in order to…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
A new, field-theory-based framework for discussing and interpreting tests of gravity, notably at the second post-Newtonian (2PN) level, is introduced. Contrary to previous frameworks which attempted at parametrizing any conceivable…
A new formulation of the Maxwell equations based on two vector and two scalar potentials is proposed. The use of these potentials allows the electromagnetic field equations to be written in the form of a hyperbolic system. In contrast to…
In this paper, we aim to accelerate a preconditioned alternating direction method of multipliers (pADMM), whose proximal terms are convex quadratic functions, for solving linearly constrained convex optimization problems. To achieve this,…
This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…
This paper describes a new approach to solving some stochastic optimization problems for linear dynamic system with various parametric uncertainties. Proposed approach is based on application of tensor formalism for creation the…
Undirected graphical models have been especially popular for learning the conditional independence structure among a large number of variables where the observations are drawn independently and identically from the same distribution.…
This paper presents eXtended Physics-Informed Neural Network (X-PINN), a novel and robust framework for addressing fracture mechanics problems involving multiple cracks in fractured media. To address this, an energy-based loss function,…
The present thesis aims at an extension of the canonical formalism of Arnowitt, Deser, and Misner from self-gravitating point-masses to objects with spin. This would allow interesting applications, e.g., within the post-Newtonian (PN)…
This paper investigates the low-rank tensor completion problem, which is about recovering a tensor from partially observed entries. We consider this problem in the tensor train format and extend the preconditioned metric from the matrix…
The most general operator product expansion in conformal field theory is obtained using the embedding space formalism and a new uplift for general quasi-primary operators. The uplift introduced here, based on quasi-primary operators with…
I present the tensor computer algebra package FieldsX, which extends the xAct suite of tensor algebra packages to perform computations in field theory with fermions and gauge fields. This includes the standard tools of curved-space $\gamma$…