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...
We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition there are one or several possibilities to opt out from the game by adopting lo...
The symmetric nonnegative inverse eigenvalue problem (SNIEP) asks which sets of numbers (counting multiplicities) can be the eigenvalues of a symmetric matrix with nonnegative entries. While examples of such matrices are abundant in linear algebra an...
Both reference and MATRIX original sol files (⭐ 199)
We consider a mobile edge computing scenario where a number of devices want to perform a linear inference $\boldsymbol{W}\boldsymbol{x}$ on some local data $\boldsymbol{x}$ given a network-side matrix $\boldsymbol{W}$. The computation is performed at...
We consider a mobile edge computing scenario where users want to perform a linear inference operation $\boldsymbol{W} \boldsymbol{x}$ on local data $\boldsymbol{x}$ for some network-side matrix $\boldsymbol{W}$. The inference is performed in a distri...
We present a model selection framework for the extraction of the CKM matrix element $|V_{cb}|$ from exclusive $B \to D^* l ν$ decays. By framing the truncation of the Boyd-Grinstein-Lebed (BGL) parameterization as a model selection task, we apply th...
The confusion matrix is a standard tool for evaluating classifiers by providing insights into class-level errors. In heterogeneous settings, its values are shaped by two main factors: class similarity -- how easily the model confuses two classes -- a...
Reservoir rocks are usually composed of a coherent heterogeneous porous matrix saturated by multiple fluids. At long wavelength limit, the composite material of solid skeleton is usually regarded as homogeneous media. However, at grain scale or high...
In this paper, we investigate the butterfly factorization problem, i.e., the problem of approximating a matrix by a product of sparse and structured factors. We propose a new formal mathematical description of such factors, that encompasses many diff...
This paper introduces the interpolative butterfly factorization for nearly optimal implementation of several transforms in harmonic analysis, when their explicit formulas satisfy certain analytic properties and the matrix representations of these tra...
Butterfly matrix multiplication in PyTorch (⭐ 178)
We present a calculation of jet activity associated with pair production of top quarks at hadron colliders and supercolliders. Our approach is based upon a merger of $2\rightarrow 3$ matrix elements with initial and final state parton showers. We t...
Low-rank structure have been profoundly studied in data mining and machine learning. In this paper, we show a dense matrix $X$'s low-rank approximation can be rapidly built from its left and right random projections $Y_1=XA_1$ and $Y_2=X^TA_2$, or bi...
Time evolution of macroscopic systems is re-examined primarily through further analysis and extension of the equation of motion for the density matrix $ρ(t)$. Because $ρ$ contains both classical and quantum-mechanical probabilities it is necessar...
The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be defined un...
We investigate the sparsity of null vectors of real symmetric matrices whose off-diagonal pattern of zero and nonzero entries is described by the adjacencies of a graph. We use the definition of the spark of a matrix, the smallest number of nonzero c...
In this paper, we prove the Gallai-Edmonds structure theorem for the most general matching polynomial. Our result implies the Parter-Wiener theorem and its recent generalization about the existence of principal submatrices of a Hermitian matrix whose...
The path-following scheme in [Loisel and Maxwell, SIAM J. Matrix Anal. Appl., 39-4 (2018), pp. 1726-1749] is adapted to efficiently calculate the dispersion relation curve for linear surface waves on an arbitrary vertical shear current. This is equiv...
I give my view of the early history of the discovery of hyperbolic structures on knot complements from my early work on representations of knot groups into matrix groups to my meeting with William Thurston in 1976. (This article was written by Robert...
The file contains PhD Dissertation by Oskar Jakub Szymański. This work ends his study at Doctoral School of Exact and Natural Sciences at Jagiellonian University where the Author has attended in years 2019-2024. The subject of the Thesis is the stab...