相关论文: Sur l'existence d'une cat\'egorie ayant une matric…

We consider three forms of composition of matroids, each of which extends the category of bimatroids to a rigid monoidal category. Many well-known constructions are functorial or defined by morphisms in these categories. Motivating examples…

The performance of a binary classifier is described by a confusion matrix with four entries: the number of true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN). The Matthews Correlation Coefficient (MCC),…

Let $n$ be a positive integer and let $f_1, \ldots, f_r$ be polynomials in $n^2$ indeterminates over an algebraically closed field $K$. We describe an algorithm to decide if the invertible matrices contained in the variety of $f_1, \ldots,…

Main result: If a C*-algebra is simple, $\sigma$-unital, has finitely many extremal traces, and has strict comparison of positive elements by traces, then its multiplier also has strict comparison of positive elements by traces. The same…

If $A$ is an integer valued, strictly expansive matrix, then there exists an orthonormal $A$-wavelet whose Fourier transform is compactly supported and smooth. We show that strongly connected diagonally dominant integer matrices are…

The girth of a matrix is the least number of linearly dependent columns, in contrast to the rank which is the largest number of linearly independent columns. This paper considers the construction of {\it high-girth} matrices, whose…

A real square matrix is algebraically positive if there exists a real polynomial $f$ such that $f(A)$ is a positive matrix. In this paper, we give a sufficient condition for a sign pattern matrix to allow algebraic positivity, and give some…

We prove that the problem of determining whether a finite logical matrix determines an algebraizable logic is complete for EXPTIME. The same result holds for the classes of order algebraizable, weakly algebraizable, equivalential and…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

We consider blind, deterministic, finite automata equipped with a register which stores an element of a given monoid, and which is modified by right multiplication by monoid elements. We show that, for monoids M drawn from a large class…

The finitistic dimension of a triangulated category is introduced. For the category of perfect complexes over a ring it is shown that this dimension is finite if and only if the small finitistic dimension of the ring is finite.

We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…

The paper studies the set of all square binary matrices containing an exact number of 1's in each rows and in each column. A connection is established between the cardinal number of this set and the cardinal number of its subset of matrices…

Written to be contributed as the "mathematical modeling" chapter of a book, edited by Elaine Landry, to be titled "Categories for the Working Philosopher". In this chapter, category theory is presented as a mathematical modeling framework…

The following theorem is proved: Suppose $M = (a_{i,j})$ be a $k \times k$ matrix with positive entries and $a_{i,j}a_{i+1,j+1} > 4\cos ^2 \frac{\pi}{k+1} a_{i,j+1}a_{i+1,j} \quad (1 \leq i \leq k-1, 1 \leq j \leq k-1).$ Then $\det M > 0 .$…

We prove that the only entrywise transforms of rectangular matrices which preserve total positivity or total non-negativity are either constant or linear. This follows from an extended classification of preservers of these two properties…

We aim to use the concept of sheaf to establish a link between certain aspects of the set of positive integers numbers, a topic corresponding to the elementary mathematics, and some fundamental ideas of contemporary mathematics. We hope…

We show that in any symmetric monoidal category, if a weight for colimits is absolute, then the resulting colimit of any diagram of dualizable objects is again dualizable. Moreover, in this case, if an endomorphism of the colimit is induced…

We define the affinization of an arbitrary monoidal category $\mathcal{C}$, corresponding to the category of $\mathcal{C}$-diagrams on the cylinder. We also give an alternative characterization in terms of adjoining dot generators to…

Higher-dimensional binary shifts of number-theoretic origin with positive topological entropy are considered. We are particularly interested in analysing their symmetries and extended symmetries. They form groups, known as the topological…