Related papers: An online version of Rota's basis conjecture

We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that…

This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…

Tabular foundation models with different architectures converge in accuracy across a range of classification and regression tasks. This raises questions a leaderboard cannot answer: (i) whether the models execute the same in-context…

We show that the theory of sorting by reversals fits into the well-established theory of circuit partitions of 4-regular multigraphs (which also involves the combinatorial structures of circle graphs and delta-matroids). In this way, we…

We investigate $(0,1)$-matrices that are {\em convex}, which means that the ones are consecutive in every row and column. These matrices occur in discrete tomography. The notion of ranked essential sets, known for permutation matrices, is…

Matrix reordering is a task to permute the rows and columns of a given observed matrix such that the resulting reordered matrix shows meaningful or interpretable structural patterns. Most existing matrix reordering techniques share the…

Necessary and sufficient conditions are given for the similarity between two perturbations of the (backward) shift by rank one operators, under certain assumptions on the perturbations. The proof of similarity is based on an explicit…

We show that in a vector space over Z_3, the union of any four linear bases is an additive basis, thus proving the Additive Basis Conjecture for p=3, and providing an alternative proof of the weak 3-flow conjecture.

Causality serves as an abstract notion of time for concurrent systems. A computation is causal, or simply valid, if each observation of a computation event is preceded by the observation of its causes. The present work establishes that this…

We propose the use of a conjecturing machine that suggests feature relationships in the form of bounds involving nonlinear terms for numerical features and boolean expressions for categorical features. The proposed Conjecturing framework…

We present the theorem which determines, by a permutation, the cardinal ordering of fixed points for any orbit of a period doubling cascade. The inverse permutation generates the orbit and the symbolic sequence of the orbit is obtained as a…

A Bayesian framework is attractive in the context of prediction, but a fast recursive update of the predictive distribution has apparently been out of reach, in part because Monte Carlo methods are generally used to compute the predictive.…

A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast inversion (or solution), and reduced…

A commutative Rota-Baxter algebra can be regarded as a commutative algebra that carries an abstraction of the integral operator. With the motivation of generalizing the study of algebraic geometry to Rota-Baxter algebra, we extend the…

In this article, we discuss a novel approach to solving number sequence problems, in which sequences of numbers following unstated rules are given, and missing terms are to be inferred. We develop a methodology of decomposing test sequences…

The "Modularity Conjecture" is the assertion that the join of two nonmodular varieties is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent varieties. We also establish analogous results concerning…

Data vectors generalise finite multisets: they are finitely supported functions into a commutative monoid. We study the question if a given data vector can be expressed as a finite sum of others, only assuming that 1) the domain is…

We show that the change of basis matrices of a set of $m$ bases of a finite vector space is a connected groupoid of order $m^2$. We define a general method to express the elements of change of basis matrices as algebraic expressions using…

Pasting and Reversing operations have been used successfully over the set of integer numbers, simple permutations, rings and recently over a generalized vector product. In this paper, these operations are defined from a natural way to be…

Radial-basis-function networks are traditionally defined for sets of vector-based observations. In this short paper, we reformulate such networks so that they can be applied to adjacency-matrix representations of weighted, directed graphs…