Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set

A RELATION BETWEEN THE CATEGORIES Set * , SetT, Set AND SetT

In this article, we have shown, for the add-point monad T, thepartial morphism category Set*is isomorphic to the Kleisli category SetT. Alsowe have proved that the category, SetT, of T-algebras is isomorphic to thecategory Set of pointed sets. Finally we have established commutative squaresinvolving these categories.

Stability results for set solution of fuzzy integro-differential systems

Singleton free set partitions avoiding a 3-element set

The definition and study of pattern avoidance for set partitions, which is an analogue of pattern avoidance for permutations, begun with Klazar. Sagan continued his work by considering set partitions which avoids a single partition of three elements, and Goyt generalized these results by considering partitions which avoids any family of partitions of a 3-element set. In this paper we enumerate ...

Inference and Learning of Boolean Networks using Answer Set Programming

A Boolean Network is a compact mathematical representation of biological systems widely used in bioinformatics. However, in practice, experiments are usually not sufficient to infer a Boolean network which represents the whole biological system. Previous works relied on inferring and learning techniques to complete those models, or to learn new networks satisfying experimental properties repres...

Pattern-Avoiding Set Partitions and Catalan Numbers

We identify several subsets of the partitions of [n], each characterized by the avoidance of a pair of patterns, respectively of lengths four and five. Each of the classes we consider is enumerated by the Catalan numbers. Furthermore, the members of each class having a prescribed number of blocks are enumerated by the Narayana numbers. We use both algebraic and combinatorial methods to establis...