Related papers: Characterization of matrices $B$ such that $(I,B,B…

The topology of digital images has been studied much in recent years, but no attempt has been made to exhaustively catalog the structure of binary images of small numbers of points. We produce enumerations of several classes of digital…

This work initiates a systematic investigation of testing high-dimensional structured distributions by focusing on testing Bayesian networks -- the prototypical family of directed graphical models. A Bayesian network is defined by a…

Let $(A,B)$ be a pair of skew-symmetric matrices over a field of characteristic not 2. Its regularization decomposition is a direct sum \[ (\underline{\underline A},\underline{\underline B})\oplus (A_1,B_1)\oplus\dots\oplus(A_t,B_t) \] that…

Many real networks such as the World Wide Web, financial, biological, citation and social networks have a power-law degree distribution. Networks with this feature are also called scale-free. Several models for producing scale-free networks…

In this paper we introduce digital nets over finite abelian groups which contain digital nets over finite fields and certain rings as a special case. We prove a MacWilliams type identity for such digital nets. This identity can be used to…

Let $F$ be a finite field with the characteristic $p > 2$ and let $G$ be the unitary Grassmann algebra generated by an infinite dimensional vector space $V$ over $F$. In this paper, we determine a basis for $\mathbb{Z}_{2}$-graded…

This paper examines the properties of real symmetric square matrices with a constant value for the main diagonal elements and another constant value for all off-diagonal elements. This matrix form is a simple subclass of circulant matrices,…

We study isogenies between K3 surfaces in positive characteristic. Our main result is a characterization of K3 surfaces isogenous to a given K3 surface $X$ in terms of certain integral sublattices of the second rational $\ell$-adic and…

Let F be a perfect field. Then the diagonal quadratic form $a_iX_i^2$ over $F$ is universal over $M_2(F)$ if and only if atleast two of the $a_i$ are non-zero.

For fields with more than $2$ elements, the classification of the vector spaces of matrices with rank at most $2$ is already known. In this work, we complete that classification for the field $\mathbb{F}_2$. We apply the results to obtain…

A square matrix $A$ is completely positive if $A=BB^T$, where $B$ is a (not necessarily square) nonnegative matrix. In general, a completely positive matrix may have many, even infinitely many, such CP factorizations. But in some cases a…

Conjugation covariants of matrices are applied to study the real algebraic variety consisting of complex Hermitian matrices with a bounded number of distinct eigenvalues. A minimal generating system of the vanishing ideal of degenerate…

In this paper we show that any Bohr-zero non-periodic set $B$ of traceless integer valued matrices, denoted by $\Lambda$, intersects non-trivially the conjugacy class of any matrix from $\Lambda$. As a corollary, we obtain that the family…

We use sequences of t-induced T-nets and p-induced P-nets to convert free-choice nets into T-nets and P-nets while preserving properties such as well-formedness, liveness, lucency, pc-safety, and perpetuality. The approach is general and…

Let $K$ be a field, $R=K[x, y]$ the polynomial ring and $\mathcal{M}(K)$ the set of all pairs of square matrices of the same size over $K.$ Pairs $P_1=(A_1,B_1)$ and $P_2=(A_2,B_2)$ from $\mathcal{M}(K)$ are called similar if…

We establish a factorisation theorem for invertible, cross-symmetric, totally nonnegative matrices, and illustrate the theory by verifying that certain cases of Holte's Amazing Matrix are totally nonnegative.

This article consists of three chapters.In Chapter 1, it is determined by the consecutive odd numbers, and study to the intrinsic properties of a class of matrix sequence. Through the establishment of matrix online number concept,…

We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial…

Let $\Delta$ be a bicolored quadriculated disk with black-to-white matrix $B_\Delta$. We show how to factor $B_\Delta = L\tilde DU$, where $L$ and $U$ are lower and upper triangular matrices, $\tilde D$ is obtained from a larger identity…

We introduce a concept of similarity between vertices of directed graphs. Let G_A and G_B be two directed graphs. We define a similarity matrix whose (i, j)-th real entry expresses how similar vertex j (in G_A) is to vertex i (in G_B. The…