Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, Wu et al. characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A subspace based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.Comment: 7 pages, 2 figures, in the Proceedings of Allerton Conference on Communication, Control and Computing, September 200

Interference Alignment in Regenerating Codes for Distributed Storage: Necessity and Code Constructions

Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any arbitrary k of n nodes. However regenerating codes possess in addition, the ability to repair a failed node by connecting to any arbitrary d nodes and downloading an amount of data that is typically far less than the size of the data file. This amount of download is termed the repair bandwidth. Minimum storage regenerating (MSR) codes are a subclass of regenerating codes that require the least amount of network storage; every such code is a maximum distance separable (MDS) code. Further, when a replacement node stores data identical to that in the failed node, the repair is termed as exact. The four principal results of the paper are (a) the explicit construction of a class of MDS codes for d = n-1 >= 2k-1 termed the MISER code, that achieves the cut-set bound on the repair bandwidth for the exact-repair of systematic nodes, (b) proof of the necessity of interference alignment in exact-repair MSR codes, (c) a proof showing the impossibility of constructing linear, exact-repair MSR codes for d < 2k-3 in the absence of symbol extension, and (d) the construction, also explicit, of MSR codes for d = k+1. Interference alignment (IA) is a theme that runs throughout the paper: the MISER code is built on the principles of IA and IA is also a crucial component to the non-existence proof for d < 2k-3. To the best of our knowledge, the constructions presented in this paper are the first, explicit constructions of regenerating codes that achieve the cut-set bound.Comment: 38 pages, 12 figures, submitted to the IEEE Transactions on Information Theory;v3 - The title has been modified to better reflect the contributions of the submission. The paper is extensively revised with several carefully constructed figures and example

Silencing of directional migration in roundabout4 knockdown endothelial cells

<p>Abstract</p> <p>Background</p> <p>Roundabouts are axon guidance molecules that have recently been identified to play a role in vascular guidance as well. In this study, we have investigated gene knockdown analysis of endothelial Robos, in particular <it>roundabout 4 </it>(<it>robo4</it>), the predominant Robo in endothelial cells using small interfering RNA technology <it>in vitro</it>.</p> <p>Results</p> <p><it>Robo1 and Robo4 </it>knockdown cells display distinct activity in endothelial cell migration assay. The knockdown of <it>robo4 </it>abrogated the chemotactic response of endothelial cells to serum but enhanced a chemokinetic response to Slit2, while <it>robo1 </it>knockdown cells do not display chemotactic response to serum or VEGF. <it>Robo4 </it>knockdown endothelial cells unexpectedly show up regulation of Rho GTPases. Zebrafish Robo4 rescues both Rho GTPase homeostasis and serum reduced chemotaxis in <it>robo4 </it>knockdown cells. Robo1 and Robo4 interact and share molecules such as Slit2, Mena and Vilse, a Cdc42-GAP. In addition, this study mechanistically implicates IRSp53 in the signaling nexus between activated Cdc42 and Mena, both of which have previously been shown to be involved with Robo4 signaling in endothelial cells.</p> <p>Conclusion</p> <p>This study identifies specific components of the Robo signaling apparatus that work together to guide directional migration of endothelial cells.</p

Identification of candidate tumour suppressor genes frequently methylated in renal cell carcinoma

Promoter region hyermethylation and transcriptional silencing is a frequent cause of tumour suppressor gene (TSG) inactivation in many types of human cancers. Functional epigenetic studies, in which gene expression is induced by treatment with demethylating agents, may identify novel genes with tumour-specific methylation. We used high-density gene expression microarrays in a functional epigenetic study of 11 renal cell carcinoma (RCC) cell lines. Twenty-eight genes were then selected for analysis of promoter methylation status in cell lines and primary RCC. Eight genes (BNC1, PDLIM4, RPRM, CST6, SFRP1, GREM1, COL14A1 and COL15A1) showed frequent (30% of RCC tested) tumour-specific promoter region methylation. Hypermethylation was associated with transcriptional silencing. Re-expression of BNC1, CST6, RPRM and SFRP1 suppressed the growth of RCC cell lines and RNA interference knock-down of BNC1, SFRP1 and COL14A1 increased the growth of RCC cell lines. Methylation of BNC1 or COL14A1 was associated with a poorer prognosis independent of tumour size, stage or grade. The identification of these epigenetically inactivated candidate RCC TSGs can provide insights into renal tumourigenesis and a basis for developing novel therapies and biomarkers for prognosis and detection. © 2010 Macmillan Publishers Limited.Published versio

Twist1 Directly Regulates Genes That Promote Cell Proliferation and Migration in Developing Heart Valves

Twist1, a basic helix-loop-helix transcription factor, is expressed in mesenchymal precursor populations during embryogenesis and in metastatic cancer cells. In the developing heart, Twist1 is highly expressed in endocardial cushion (ECC) valve mesenchymal cells and is down regulated during valve differentiation and remodeling. Previous studies demonstrated that Twist1 promotes cell proliferation, migration, and expression of primitive extracellular matrix (ECM) molecules in ECC mesenchymal cells. Furthermore, Twist1 expression is induced in human pediatric and adult diseased heart valves. However, the Twist1 downstream target genes that mediate increased cell proliferation and migration during early heart valve development remain largely unknown. Candidate gene and global gene profiling approaches were used to identify transcriptional targets of Twist1 during heart valve development. Candidate target genes were analyzed for evolutionarily conserved regions (ECRs) containing E-box consensus sequences that are potential Twist1 binding sites. ECRs containing conserved E-box sequences were identified for Twist1 responsive genes Tbx20, Cdh11, Sema3C, Rab39b, and Gadd45a. Twist1 binding to these sequences in vivo was determined by chromatin immunoprecipitation (ChIP) assays, and binding was detected in ECCs but not late stage remodeling valves. In addition identified Twist1 target genes are highly expressed in ECCs and have reduced expression during heart valve remodeling in vivo, which is consistent with the expression pattern of Twist1. Together these analyses identify multiple new genes involved in cell proliferation and migration that are differentially expressed in the developing heart valves, are responsive to Twist1 transcriptional function, and contain Twist1-responsive regulatory sequences