Related papers: Contraction and decomposition matrices for vacuum …
The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex analysis and optimization over spaces of tensors is now gaining…
This paper studies 3-polygraphs as a framework for rewriting on two-dimensional words. A translation of term rewriting systems into 3-polygraphs with explicit resource management is given, and the respective computational properties of each…
We study tridimensional tensors on the complex field from the point of view of hypermatrices, taking into consideration the problem of determining whether they are degenerate or not, concise or not, what is their essential format if they…
This paper explores a new version of the Levenberg-Marquardt algorithm used for Tensor Canonical Polyadic (CP) decomposition with an emphasis on image compression and reconstruction. Tensor computation, especially CP decomposition, holds…
We show how all possible one-particle reducible tadpole diagrams in constant electromagnetic fields can be constructed from one-particle irreducible constant-field diagrams. The construction procedure is essentially algebraic and involves…
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex…
The decay of the electrical energy in a resistor-vacuum capacitor circuit is shown to involve multiple relaxation processes, with dramatically different time constants. This is measured using a vacuum capacitor to eliminate the effect of a…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
This correspondence proposes a new rotated codebook for three-dimensional (3D) multi-input-multi-output (MIMO) system under spatially correlated channel. To avoid the problem of high dimensionality led by large antenna array, the rotation…
A complete analytical reduction of general one-loop Feynman integrals with five legs for tensors up to rank R=3 and six legs for tensors up to rank 4 is reviewed. An elegant formalism with extensive use of signed minors was developed for…
We give reconstruction algorithms for subclasses of depth-3 arithmetic circuits. In particular, we obtain the first efficient algorithm for finding tensor rank, and an optimal tensor decomposition as a sum of rank-one tensors, when given…
The contributions of one-loop diagrams with dynamical vector mesons to masses and decay constants of pseudoscalar mesons are determined. Hereby, a relativistic Lagrangian for both the pseudoscalar-meson octet and the vector-meson nonet is…
While dealing with the nontrivial task of classifying Mueller matrices, of special interest is the study of the degenerate Mueller matrices (matrices with vanishing determinant, for which the law of multiplication holds, but there exists no…
We discuss new ideas for consideration of loop diagrams and angular integrals in $D$-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of…
In this note we summarize four important matrix decompositions commonly used in quantum optics, namely the Takagi/Autonne, Bloch-Messiah/Euler, Iwasawa, and Williamson decompositions. The first two of these decompositions are specialized…
Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the $20^{\text{th}}$ century, they have since then spread to…
We study the combinatorial description of the LDU decomposition of totally positive matrices. We give a description of the lower triangular L, the diagonal D, and the upper triangular U matrices of the LDU decomposition of totally positive…
In this text we review a few structural properties of matrix models that should at least partly generalize to random tensor models. We review some aspects of the loop equations for matrix models and their algebraic counterpart for tensor…
Dimensional Reduction is applied to \qcd{} in order to compute various renormalization constants in the \drbar{} scheme at higher orders in perturbation theory. In particular, the $\beta$ function and the anomalous dimension of the quark…
The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…