These are lecture notes from the 44th IFF Spring School "Quantum Information Processing" in Juelich, discussing applications of entanglement theory in condensed matter. The focus of the notes is on tensor network states, in particular Matrix Product...
The aim of this work is to extend to finite potent endomorphisms the notion of G-Drazin inverse of a finite square matrix. Accordingly, we determine the structure and the properties of a G-Drazin inverse of a finite potent endomorphism and, as an app...
When solving systems of banded Toeplitz equations or calculating their inverses, it is necessary to determine the invertibility of the matrices beforehand. In this paper, we equate the invertibility of an $n$-order banded Toeplitz matrix with bandwid...
In the first part of this paper we give an elementary proof of the fact that if an infinite matrix $A$, which is invertible as a bounded operator on $\ell^2$, can be uniformly approximated by banded matrices then so can the inverse of $A$. We give...
Holas and March (Phys. Rev. A51, 2040 (1995)) wrote the gradient of the one-body potential V(r) in terms of low-order derivatives of the idempotent Dirac density matrix built from a single Slater determinant of Kohn-Sham orbitals. Here, this is first...
Greedy BST (or simply Greedy) is an online self-adjusting binary search tree defined in the geometric view ([Lucas, 1988; Munro, 2000; Demaine, Harmon, Iacono, Kane, Patrascu, SODA 2009). Along with Splay trees (Sleator, Tarjan 1985), Greedy is consi...
We present the manual for the program BRIDGE: Branching Ratio Inquiry/Decay Generated Events. The program is designed to operate with arbitrary models defined within matrix element generators, so that one can simulate events with small final-state...
Aug 29, 2024 · Attached to this Electronic Announcement is the 2024-25 FAFSA Verification-IRS Tax Return Transcript Matrix that institutions can use for 2024-25 verification of tax return information …
The Tracy-Widom beta distribution is the large dimensional limit of the top eigenvalue of beta random matrix ensembles. We use the stochastic Airy operator representation to show that as a tends to infinity the tail of the Tracy Widom distribution sa...
We establish the relation between two objects: an integrable system related to Painlevé II equation, and the symplectic invariants of a certain plane curve S(TW). This curve describes the average eigenvalue density of a random hermitian matrix spect...
We propose two provably accurate methods for low CP-rank tensor completion - one using adaptive sampling and one using nonadaptive sampling. Both of our algorithms combine matrix completion techniques for a small number of slices along with Jennrich'...
We study Hodge loci as leaf schemes of foliations. The main ingredient is the Gauss-Manin connection matrix of families of projective varieties. We also aim to investigate a conjecture on the ring of definition of leaf schemes and its consequences su...
We present a general framework of localized operators, i.e., operators whose matrix coefficients with respect to the Gabor frame are concentrated on the diagonal. We show that localized operators are bounded between modulation spaces, and we deduce t...
John Holte [16] introduced a family of "amazing matrices" which give the transition probabilities of "carries" when adding a list of numbers. It was subsequently shown that these same matrices arise in the combinatorics of the Veronese embedding of c...
A full fp calculation is performed for states which were degenerate in a single-j-shell calculation in which isospin-zero two-body matrix elements were set to zero energy. Most of the splitting in a complete shell calculation (but not all) comes fr...
In this paper, we investigate the degrees of freedom ($\dof$) of penalized $\ell_1$ minimization (also known as the Lasso) for linear regression models. We give a closed-form expression of the $\dof$ of the Lasso response. Namely, we show that for an...
In this work, we study the coupling matrix of $\mathcal{N}=2$ Superconformal QCD in vicinity of the special vacuum. We find that although there are $\lfloor\frac{N}{2}\rfloor$ independent coupling constants of the theory, only one of them plays a spe...
In this text I present a couple of new principles and thereon based iterative methods for numerical solution of sequences of systems of linear equations with fixed system matrix and changing right-hand-sides. The use of the new methods is to recycle...
Given a data-set of consumer behaviour, the Revealed Preference Graph succinctly encodes inferred relative preferences between observed outcomes as a directed graph. Not all graphs can be constructed as revealed preference graphs when the market dime...
Forecasting project expenses is a crucial step for businesses to avoid budget overruns and project failures. Traditionally, this has been done by financial analysts or data science techniques such as time-series analysis. However, these approaches ca...