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Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…
The Tutte equations are ported (or set-pointed) when the equations F(N) = g_e F(N/e) + r_e F(N\e) are omitted for elements e in a distinguished set called ports. Solutions F can distinguish different orientations of the same matroid. A…
We consider the problem of finding a basis of a matroid with weight exactly equal to a given target. Here weights can be discrete values from $\{-\Delta,\ldots,\Delta\}$ or more generally $m$-dimensional vectors of such discrete values. We…
In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `matrix properties'. In this paper we extend this algorithm to…
This paper presents an analysis of the orientation selectivity properties of idealized models of complex cells in terms of affine quasi quadrature measures, which combine the responses of idealized models of simple cells in terms of affine…
Matrix quasi exactly solvable operators are considered and new conditions are determined to test whether a matrix differential operator possesses one or several finite dimensional invariant vector spaces. New examples of $2\times 2$-matrix…
We present new alternative complete asymptotic expansions for the time harmonic low--frequency magnetic field perturbation caused by the presence of a conducting permeable object as its size tends to zero for the eddy current approximation…
Partial-transpose (PT) moments are among the most practically relevant nonlinear quantities accessible from local Pauli classical shadows, because they directly underpin mixed-state entanglement certification and recent PT-moment-based…
We present attributed hierarchical port graphs (AHP) as an extension of port graphs that aims at facilitating the design of modular port graph models for complex systems. AHP consist of a number of interconnected layers, where each layer…
Symmetry Protected Topological (SPT) phases describe trivially-acting symmetries. We argue that a symmetry-based description of SPT phases ought to include the topological twist fields associated to the symmetry. Doing so allows us to…
The computation of a matrix function $f(A)$ is an important task in scientific computing appearing in machine learning, network analysis and the solution of partial differential equations. In this work, we use only matrix-vector products…
Cyclotomic fast Fourier transforms (CFFTs) are efficient implementations of discrete Fourier transforms over finite fields, which have widespread applications in cryptography and error control codes. They are of great interest because of…
We consider integer programs whose constraint matrix has a special block structure: $\min\{f(x):H_{com}x=b, l\le x\le u,x\in\mathbb{Z}^{t_B+nt_A}\}$, where the objective function $f$ is separable convex and the constraint matrix $H_ {com}$…
The transfer matrix and matrix multiplication ansatz, when applied to nonequilibrium steady states in asymmetric exclusion processed and traffic models, has given many exact results for phase diagrams, bulk densities and fluxes, as well as…
In this paper, we study the convergence of Alternating Projection (AP) algorithm for the matrix completion and compressed sensing problems. We also present computational evidence for the excellent performance of the algorithm. Also, in the…
How can we effectively find the best structures in tree models? Tree models have been favored over complex black box models in domains where interpretability is crucial for making irreversible decisions. However, searching for a tree…
In this article, we employ a standard convex argument to obtain new and refined inequalities related to the matrix mean of two accretive matrices, the numerical radius and the Tsallis relative operator entropy.
In this paper, we consider a system of homogeneous algebraic equations in complex variables and their conjugates, which arise naturally from the range criterion for separability of PPT states. We examine systematically these equations to…
We prove that the principal pivot transform (also known as the partial inverse, sweep operator, or exchange operator in various contexts) maps matrices with positive imaginary part to matrices with positive imaginary part. We show that the…
We generalize the background gauge in the Matrix model to propose a new gauge which is useful for discussing the conformal symmetry. In this gauge, the special conformal transformation (SCT) as the isometry of the near-horizon geometry of…