A Message Passing Strategy for Decentralized Connectivity Maintenance in Agent Removal

In a multi-agent system, agents coordinate to achieve global tasks through local communications. Coordination usually requires sufficient information flow, which is usually depicted by the connectivity of the communication network. In a networked system, removal of some agents may cause a disconnection. In order to maintain connectivity in agent removal, one can design a robust network topology that tolerates a finite number of agent losses, and/or develop a control strategy that recovers connectivity. This paper proposes a decentralized control scheme based on a sequence of replacements, each of which occurs between an agent and one of its immediate neighbors. The replacements always end with an agent, whose relocation does not cause a disconnection. We show that such an agent can be reached by a local rule utilizing only some local information available in agents' immediate neighborhoods. As such, the proposed message passing strategy guarantees the connectivity maintenance in arbitrary agent removal. Furthermore, we significantly improve the optimality of the proposed scheme by incorporating $\delta$-criticality (i.e. the criticality of an agent in its $\delta$-neighborhood).Comment: 9 pages, 9 figure

Automated design of bacterial genome sequences

Background: Organisms have evolved ways of regulating transcription to better adapt to varying environments. Could the current functional genomics data and models support the possibility of engineering a genome with completely rearranged gene organization while the cell maintains its behavior under environmental challenges? How would we proceed to design a full nucleotide sequence for such genomes? Results: As a first step towards answering such questions, recent work showed that it is possible to design alternative transcriptomic models showing the same behavior under environmental variations than the wild-type model. A second step would require providing evidence that it is possible to provide a nucleotide sequence for a genome encoding such transcriptional model. We used computational design techniques to design a rewired global transcriptional regulation of Escherichia coli, yet showing a similar transcriptomic response than the wild-type. Afterwards, we “compiled” the transcriptional networks into nucleotide sequences to obtain the final genome sequence. Our computational evolution procedure ensures that we can maintain the genotype-phenotype mapping during the rewiring of the regulatory network. We found that it is theoretically possible to reorganize E. coli genome into 86% fewer regulated operons. Such refactored genomes are constituted by operons that contain sets of genes sharing around the 60% of their biological functions and, if evolved under highly variable environmental conditions, have regulatory networks, which turn out to respond more than 20% faster to multiple external perturbations. Conclusions: This work provides the first algorithm for producing a genome sequence encoding a rewired transcriptional regulation with wild-type behavior under alternative environments

Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)

Although the ``scale-free'' literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and verifiably false claims. In this paper, we propose a new, mathematically precise, and structural definition of the extent to which a graph is scale-free, and prove a series of results that recover many of the claimed properties while suggesting the potential for a rich and interesting theory. With this definition, scale-free (or its opposite, scale-rich) is closely related to other structural graph properties such as various notions of self-similarity (or respectively, self-dissimilarity). Scale-free graphs are also shown to be the likely outcome of random construction processes, consistent with the heuristic definitions implicit in existing random graph approaches. Our approach clarifies much of the confusion surrounding the sensational qualitative claims in the scale-free literature, and offers rigorous and quantitative alternatives.Comment: 44 pages, 16 figures. The primary version is to appear in Internet Mathematics (2005