In order to benefit from the presence of modularity, hierarchy, or repetition in a problem, a necessary first step is to identify precise notions of these problem features. Modularity, hierarchy, and repetition have often been used as terms to characterize the operation of a search method. However, if these features are to improve the efficiency of a search method, then there must exist corresp...

A modular semilattice is a semilattice S in which w > a A ft implies that there exist i,jeS such that x > a. y > b and x A y = x A w. This is equivalent to modularity in a lattice and in the semilattice of ideals of the semilattice, and the condition implies the Kurosh-Ore replacement property for irreducible elements in a semilattice. The main results provide extensions of the classical charac...

G. Aglieri Rinellaa,V. Carassitic,A. Ceccuccia,E. Cortinad ,J. Daguina,G. Dellacasab,M. Fiorinia,P. Jarrona,J. Kaplona,A. Klugea,F. Marchettoa,E. Martind ,A. Mapellia, f ,G. Mazzab,M. Morela,M. Noya,G. Nüssled ,P. Petagnaa,L. Perktolda,F. Petruccic,e,A. Cotta Ramusinoc,P. Riedlera,A. Rivettib,R. Wheadonb aCERN, Geneva Switzerland,bINFN Torino, Italy,cINFN Ferrare, Italy,dUCL Louvain la Neuve, B...

Open Source Software (OSS) Projects are gaining popularity these days, and they become alternatives in building software system. Despite many failures in these projects, there are some success stories with one of the identified success factors is modularity. This paper presents the first quantitative software metrics to measure modularity level of Java-based OSS Projects called Modularity Index...

Network modularity is an important structural feature in metabolic networks. A previous study suggested that the variability in natural habitat promotes metabolic network modularity in bacteria. However, since many factors influence the structure of the metabolic network, this phenomenon might be limited and there may be other explanations for the change in metabolic network modularity. Therefo...

Based on optimization modularity, many algorithms were proposed to detect community structure in complex networks. As a optimization measure, modularity has resolution limits problems. A new measure named by modularity density was introduced, which can overcome the resolution limits drawbacks of modularity function. In this paper, we propose a immune clone selection algorithm for detecting comm...

Measuring modularity is important to understand the structure of networks, and has an important number of real-world implications. However, several measures exists to assess the modularity, and give both different modularity values and different modules composition. In this article, I propose an a posteriori measure of modularity, which represents the ratio of interactions between members of th...

The mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection. We show that finding the modularity of a network is analogous to finding the ground-state energy of a spin system. Moreover, we demonstrate that, due to fluctuations, stochastic network models give rise to modular network...

Modularity is an important topological attribute for functional brain networks. Recent human fMRI studies have reported that modularity of functional networks varies not only across individuals being related to demographics and cognitive performance, but also within individuals co-occurring with fluctuations in network properties of functional connectivity, estimated over short time intervals. ...

Modularity, often observed in biological systems, does not easily arise in computational evolution. We explore the effect of adding a small fitness cost for each connection between neurons on the modularity of neural networks produced by the NEAT neuroevolution algorithm. We find that this connection cost does not increase the modularity of the best network produced by each run of the algorithm...