The theory of chi processes with the mismatch operator is studied. Two open congruence relations are investigated. These are weak early open congruence and weak late open congruence. Complete systems are given for both congruence relations. These systems use some new tau laws. The results of this paper correct some popular mistakes in literature.

A lattice identity is given such that it holds but its dual fails in the normal subgroup lattices of metaabelian groups. Thus the congruence variety of metaabelian groups is not self-dual; this is the first example for a modular congruence variety which is not self-dual. For a ring R with unit element let L(R) denote the class of lattices embeddable in submodule lattices of R-modules. Then HL(R...

This paper deenes a congruence relation on Gamma programs. Based on this congruence relation, laws for transforming programs are derived. We deene an axiomatic semantics for Gamma based on Brookes' transition assertions. The deenition of the congruence is in terms of provable satissability of such assertions. We consider the relationship between our congruence and other orderings that have been...

Abstract Modularity introduced by Newman and Girvan [Phys. Rev. E 69, 026113 (2004)] is a quality function for community detection. Numerous methods for modularity maximization have been developed so far. In 2007, Barber [Phys. Rev. E 76, 066102 (2007)] introduced a variant of modularity called bipartite modularity which is appropriate for bipartite networks. Although maximizing the standard mo...

This paper introduces a new representation for assemblies of small Lego-like elements: structures are indirectly encoded as construction plans. This representation shows some interesting properties such as hierarchy, modularity and easy constructibility checking by definition. Together with this representation, efficient GP operators are introduced that allow efficient and fast evolution, as wi...

We study congruences on the partial automorphism monoid of a finite rank free group action. determine decomposition congruence this into Rees congruence, Brandt semigroup and an idempotent separating congruence. The constituent parts are further described in terms subgroups direct semidirect products groups. utilize description to demonstrate how number depends

Objectives of classical projects are usually to apply and synthesize knowledge acquired during courses. Such projects are therefore result oriented. However, within the framework of project-based learning as developed in the new engineering curriculum at Université catholique de Louvain, the project should be oriented towards the acquisition of new knowledge and competencies. In this context, t...

The Independence Theorem for the congruence lattice and the auto-morphism group of a nite lattice was proved by V. A. Baranski and A. Urquhart. Both proofs utilize the characterization theorem of congruence lattices of nite lattices (as nite distributive lattices) and the characterization theorem of auto-morphism groups of nite lattices (as nite groups). In this paper, we introduce a new, stron...

While much has changed in product modularity research in the 18 years since the independence axiom, some basic questions remain unanswered. Perhaps the most fundamental of those questions is whether increasing modularity actually saves money. The goal of the research behind this paper was to clearly define the fundamental relationship between product modularity and product cost. Our previous wo...

We consider a model of daily newspapers’ competition to test the validity of the so called “theory of the circulation spiral”. According to it, the interaction between the newspapers and the advertising markets drives the newspaper with the smaller readership into a vicious circle, finally leading it to death. In a model with two newspapers, we show that, contrary to this conjecture, the dynami...