Colouring random graphs and maximising local diversity

We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any vertex. Two efficient algorithms, belief propagation and Walksat are adapted to carry out this task. We present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution. The problem and the suggested algorithms have practical relevance since various applications, such as distributed storage, can be mapped onto this problem.Comment: 10 pages, 10 figure

Survey propagation for the cascading Sourlas code

We investigate how insights from statistical physics, namely survey propagation, can improve decoding of a particular class of sparse error correcting codes. We show that a recently proposed algorithm, time averaged belief propagation, is in fact intimately linked to a specific survey propagation for which Parisi's replica symmetry breaking parameter is set to zero, and that the latter is always superior to belief propagation in the high connectivity limit. We briefly look at further improvements available by going to the second level of replica symmetry breaking.Comment: 14 pages, 5 figure

Survey propagation at finite temperature: application to a Sourlas code as a toy model

In this paper we investigate a finite temperature generalization of survey propagation, by applying it to the problem of finite temperature decoding of a biased finite connectivity Sourlas code for temperatures lower than the Nishimori temperature. We observe that the result is a shift of the location of the dynamical critical channel noise to larger values than the corresponding dynamical transition for belief propagation, as suggested recently by Migliorini and Saad for LDPC codes. We show how the finite temperature 1-RSB SP gives accurate results in the regime where competing approaches fail to converge or fail to recover the retrieval state

Genetic History of Hepatitis C Virus in East Asia ▿

The hepatitis C virus (HCV), which currently infects an estimated 3% of people worldwide, has been present in some human populations for several centuries, notably HCV genotypes 1 and 2 in West Africa and genotype 6 in Southeast Asia. Here we use newly developed methods of sequence analysis to conduct the first comprehensive investigation of the epidemic and evolutionary history of HCV in Asia. Our analysis includes new HCV core (n = 16) and NS5B (n = 14) gene sequences, obtained from serum samples of jaundiced patients from Laos. These exceptionally diverse isolates were analyzed in conjunction with all available reference strains using phylogenetic and Bayesian coalescent methods. We performed statistical tests of phylogeographic structure and applied a recently developed “relaxed molecular clock” approach to HCV for the first time, which indicated an unexpectedly high degree of rate variation. Our results reveal a >1,000-year-long development of genotype 6 in Asia, characterized by substantial phylogeographic structure and two distinct phases of epidemic history, before and during the 20th century. We conclude that HCV lineages representing preexisting and spatially restricted strains were involved in multiple, independent local epidemics during the 20th century. Our analysis explains the generation and maintenance of HCV diversity in Asia and could provide a template for further investigations of HCV spread in other regions