We consider (n-dimensional) array grammars in the accepting mode with various control mechanisms and compare these families of array grammars with the corresponding families obtained by array grammars in the generating mode.

We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of t...

Generating functions have long been used to analyze properties of sequences of numbers. In this note, we use generating functions to analyze a class of combinatorial objects, called interconnection networks. In particular, we prove that two families of interconnection networks are isomorphic by showing that the corresponding generating functions are isomorphic.

In this work, we introduce a novel network synthesis model that can generate families of evolutionarily related synthetic protein-protein interaction (PPI) networks. Given an ancestral network, the proposed model generates the network family according to a hypothetical phylogenetic tree, where the descendant networks are obtained through duplication and divergence of their ancestors, followed b...

We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomialpositivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include, for example, genera...

Finding suitable non-supersingular elliptic curves becomes an important issue for the growing area of pairing-based cryptosystems. For this purpose, many methods have been proposed when embedding degree k and cofactor h are taken different values. In this paper we propose a new method to find pairing-friendly elliptic curves without restrictions on embedding degree k and cofactor h. We propose ...

Generating families of linear models from nonlinear parameter-dependent equations requires explicit analytical characterization of the equilibrium surface. Doing so in terms of the original system parameters is generally not possible. Introducing an alternative parameterization, we propose an efficient method for computing local linear parameter-dependent families. Although local, these familie...

In this work we introduce and study various generalizations of the notion of increasingly labelled trees, where the label of a child node is always larger than the label of its parent node, to multilabelled tree families, where the nodes in the tree can get multiple labels. For all tree classes we show characterizations of suitable generating functions for the tree enumeration sequence via diff...