An algorithm for information organization based on rectangular decomposition of a binary relation is introduced, Rectangular decomposition allows a classification of databases presented as a binary relation. This problem, being NP-Complete problem, has been the subject of several previous works. However, we found out necessary the proposition of an approximate polynomial algorithm and to give a...

A stronger form of the theorem constructing a rigid binary relation on any set Apoloniusz Tyszka Summary. On every set A there is a rigid binary relation i.e. such a relation R ⊆ A × A that there is no homomorphism A, R → A, R except the identity (Vopěnka et al. [1965]). We prove that for each infinite cardinal number κ if card A ≤ 2 κ , then there exists a relation R ⊆ A × A with the following...

In this paper x, r are real numbers. Let A be a set. We say that A is symmetrical if and only if: (Def. 1) For every complex number x such that x ∈ A holds −x ∈ A. Let us note that there exists a subset of C which is symmetrical. Let us observe that there exists a subset of R which is symmetrical. In the sequel A denotes a symmetrical subset of C. Let R be a binary relation. We say that R has s...

Biomedical relation extraction aims to uncover high-quality relations from life science literature with high accuracy and efficiency. Early biomedical relation extraction tasks focused on capturing binary relations, such as protein-protein interactions, which are crucial for virtually every process in a living cell. Information about these interactions provides the foundations for new therapeut...