Abstract The theory of topological modular forms (TMF) predicts that elliptic genera physical theories satisfy a certain divisibility property, determined by the theory’s gravitational anomaly. In this note we verify prediction in Duncan’s supermoonshine module, as well tensor products and orbifolds thereof. Along way develop machinery for computing general alternating discuss relation construc...

Open Source Software (OSS) Projects are gaining popularity worldwide. Studies by many researchers show that the important key success factor is modularity of the source code. This paper presents the revised Modularity Index which is a software metrics to measure the modularity level of a javabased OSS Projects. To show its effectiveness in analyzing OSS Project, the Modularity Index and its sup...

In a recent preprint of F. Gouvea and N. Yui (see arxiv.org/abs/0902.1466) a detailed account is given of a patching argument due to Serre that proves that the modularity of all rigid Calabi-Yau threefolds defined over Q follows from Serre’s modularity conjecture. In this note (a letter to N. Yui) we give an alternative proof of this implication. The main difference with Serre’s argument is tha...

Lipson et al. (2002) presented an elegant linear algebraic formalism to define and study the evolution of modularity in an artificial evolving system. They employed simulation data to support their suggestion that modularity arises spontaneously in temporally fluctuating systems in response to selection for enhanced evolvability. We show analytically and by simulation that their correlate of mo...

Deciphering the modular organization of metabolic networks and understanding how modularity evolves have attracted tremendous interest in recent years. Here, we present a comprehensive large scale characterization of modularity across the bacterial tree of life, systematically quantifying the modularity of the metabolic networks of >300 bacterial species. Three main determinants of metabolic ne...

When Fodor titled his (1983) book the Modularity of Mind, he overstated his position. His actual view is that the mind divides into systems some of which are modular and others of which are not. The book would have been more aptly, if less provocatively, called The Modularity of Low-Level Peripheral Systems. High-level perception and cognitive systems are non-modular on Fodor’s theory. In recen...