HFR Code: A Flexible Replication Scheme for Cloud Storage Systems

Fractional repetition (FR) codes are a family of repair-efficient storage codes that provide exact and uncoded node repair at the minimum bandwidth regenerating point. The advantageous repair properties are achieved by a tailor-made two-layer encoding scheme which concatenates an outer maximum-distance-separable (MDS) code and an inner repetition code. In this paper, we generalize the application of FR codes and propose heterogeneous fractional repetition (HFR) code, which is adaptable to the scenario where the repetition degrees of coded packets are different. We provide explicit code constructions by utilizing group divisible designs, which allow the design of HFR codes over a large range of parameters. The constructed codes achieve the system storage capacity under random access repair and have multiple repair alternatives for node failures. Further, we take advantage of the systematic feature of MDS codes and present a novel design framework of HFR codes, in which storage nodes can be wisely partitioned into clusters such that data reconstruction time can be reduced when contacting nodes in the same cluster.Comment: Accepted for publication in IET Communications, Jul. 201

The occurrence of sequence patterns in repeated experiments and hitting times in a Markov chain

A martingale argument is used to derive the generating function of the number of i.i.d. experiments it takes to observe a given string of outcomes for the first time. Then, a more general problem can be studied: How many trials does it take to observe a member of a finite set of strings for the first time? It is shown how the answer can be obtained within the framework of hitting times in a Markov chain. For these, a result of independent interest is derived.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24435/1/0000708.pd

Binary error correcting network codes

We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting schemes can be arbitrarily far from achieving the optimal network throughput. We propose a new metric for errors under this model. Using this metric, we prove a new Hamming-type upper bound on the network capacity. We also show a commensurate lower bound based on GV-type codes that can be used for error-correction. The codes used to attain the lower bound are non-coherent (do not require prior knowledge of network topology). The end-to-end nature of our design enables our codes to be overlaid on classical distributed random linear network codes. Further, we free internal nodes from having to implement potentially computationally intensive link-by-link error-correction

Digital search trees and chaos game representation

Version préliminaire (2006) d'un travail publié sous forme définitive (2009).International audienceIn this paper, we consider a possible representation of a DNA sequence in a quaternary tree, in which on can visualize repetitions of subwords. The CGR-tree turns a sequence of letters into a digital search tree (DST), obtained from the suffixes of the reversed sequence. Several results are known concerning the height and the insertion depth for DST built from i.i.d. successive sequences. Here, the successive inserted wors are strongly dependent. We give the asymptotic behaviour of the insertion depth and of the length of branches for the CGR-tree obtained from the suffixes of reversed i.i.d. or Markovian sequence. This behaviour turns out to be at first order the same one as in the case of independent words. As a by-product, asymptotic results on the length of longest runs in a Markovian sequence are obtained

Novel Common Genetic Susceptibility Loci for Colorectal Cancer

BACKGROUND: Previous genome-wide association studies (GWAS) have identified 42 loci (P < 5 × 10-8) associated with risk of colorectal cancer (CRC). Expanded consortium efforts facilitating the discovery of additional susceptibility loci may capture unexplained familial risk. METHODS: We conducted a GWAS in European descent CRC cases and control subjects using a discovery-replication design, followed by examination of novel findings in a multiethnic sample (cumulative n = 163 315). In the discovery stage (36 948 case subjects/30 864 control subjects), we identified genetic variants with a minor allele frequency of 1% or greater associated with risk of CRC using logistic regression followed by a fixed-effects inverse variance weighted meta-analysis. All novel independent variants reaching genome-wide statistical significance (two-sided P < 5 × 10-8) were tested for replication in separate European ancestry samples (12 952 case subjects/48 383 control subjects). Next, we examined the generalizability of discovered variants in East Asians, African Americans, and Hispanics (12 085 case subjects/22 083 control subjects). Finally, we examined the contributions of novel risk variants to familial relative risk and examined the prediction capabilities of a polygenic risk score. All statistical tests were two-sided. RESULTS: The discovery GWAS identified 11 variants associated with CRC at P < 5 × 10-8, of which nine (at 4q22.2/5p15.33/5p13.1/6p21.31/6p12.1/10q11.23/12q24.21/16q24.1/20q13.13) independently replicated at a P value of less than .05. Multiethnic follow-up supported the generalizability of discovery findings. These results demonstrated a 14.7% increase in familial relative risk explained by common risk alleles from 10.3% (95% confidence interval [CI] = 7.9% to 13.7%; known variants) to 11.9% (95% CI = 9.2% to 15.5%; known and novel variants). A polygenic risk score identified 4.3% of the population at an odds ratio for developing CRC of at least 2.0. CONCLUSIONS: This study provides insight into the architecture of common genetic variation contributing to CRC etiology and improves risk prediction for individualized screenin