Related papers: Efficient Generation of Binary Magic Squares
In this paper, we count the number of matrices whose rows generate different $\mathbb{Z}_2\mathbb{Z}_8$ additive codes. This is a natural generalization of the well known Gaussian numbers that count the number of matrices whose rows…
The probability that a tuple of matrices together with all scalars generates a finite incidence ring is calculated. It is proved that all real and complex finite-dimensional incidence algebras are generated by two randomly chosen matrices.
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…
Matrix-matrix multiplication is a fundamental operation of great importance to scientific computing and, increasingly, machine learning. It is a simple enough concept to be introduced in a typical high school algebra course yet in practice…
We consider the problem of sparse matrix multiplication by the column row method in a distributed setting where the matrix product is not necessarily sparse. We present a surprisingly simple method for "consistent" parallel processing of…
In this paper we propose an algorithm to generate binary words with no more 0's than 1's having a fixed number of 1's and avoiding the pattern $(10)^j1$ for any fixed $j \geq 1$. We will prove that this generation is exhaustive, that is,…
We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the…
In this paper, new schemes for a squarer, multiplier and divider of complex numbers are proposed. Traditional structural solutions for each of these operations require the presence some number of general-purpose binary multipliers. The…
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…
A novel Mathematical Random Number Generator (MRNG) is presented here. In this case, "mathematical" refers to the fact that to construct that generator it is not necessary to resort to a physical phenomenon, such as the thermal noise of an…
Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
We address here the problem of generating random graphs uniformly from the set of simple connected graphs having a prescribed degree sequence. Our goal is to provide an algorithm designed for practical use both because of its ability to…
This paper investigates the column generation (CG) for solving cutting stock problems (CSP). Traditional CG method, which repeatedly solves a restricted master problem (RMP), often suffers from two critical issues in practice -- the loss of…
We present a fast algorithm for linear least squares problems governed by hierarchically block separable (HBS) matrices. Such matrices are generally dense but data-sparse and can describe many important operators including those derived…
We find the numbers of $3 \times 3$ magic, semimagic, and magilatin squares, as functions either of the magic sum or of an upper bound on the entries in the square. Our results on magic and semimagic squares differ from previous ones in…
Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…
A magic square of order $n$ with all subsquares of possible orders (ASMS$(n)$) is a magic square which contains a general magic square of each order $k\in\{3, 4, \cdots, n-2\}$. Since the conjecture on the existence of an ASMS was proposed…
An algorithm implemented in an open-source python library was developed for building periodic coincidence site lattice (CSL) grain boundary models in a universal fashion. The software framework aims to generate tilt and twist grain…
Quantum optimal control plays a crucial role in the development of quantum technologies, particularly in the design and implementation of fast and accurate gates for quantum computing. Here, we present a method to synthesize gates using the…