Closure operators associated with networks

Submajorization inequalities associated with $tau$-measurable operators

The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..

Encoding Closure Operators into Neural Networks

Motivated by basic ideas from formal concept analysis, we propose two ways to directly encode closure operators on finite sets in a 3-layered feed forward neural network.

Closure Operators Associated to Partially Ordered Sets

From torsion theories to closure operators and factorization systems

Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].

Using FCA for Encoding Closure Operators into Neural Networks

After decades of concurrent development of symbolic and connectionist methods, recent years have shown intensifying efforts of integrating those two paradigms. This paper contributes to the development of methods for transferring present symbolic knowledge into connectionist representations. Motivated by basic ideas from formal concept analysis, we propose two ways of directly encoding closure ...