Alpha Entanglement Codes: Practical Erasure Codes to Archive Data in Unreliable Environments

Data centres that use consumer-grade disks drives and distributed peer-to-peer systems are unreliable environments to archive data without enough redundancy. Most redundancy schemes are not completely effective for providing high availability, durability and integrity in the long-term. We propose alpha entanglement codes, a mechanism that creates a virtual layer of highly interconnected storage devices to propagate redundant information across a large scale storage system. Our motivation is to design flexible and practical erasure codes with high fault-tolerance to improve data durability and availability even in catastrophic scenarios. By flexible and practical, we mean code settings that can be adapted to future requirements and practical implementations with reasonable trade-offs between security, resource usage and performance. The codes have three parameters. Alpha increases storage overhead linearly but increases the possible paths to recover data exponentially. Two other parameters increase fault-tolerance even further without the need of additional storage. As a result, an entangled storage system can provide high availability, durability and offer additional integrity: it is more difficult to modify data undetectably. We evaluate how several redundancy schemes perform in unreliable environments and show that alpha entanglement codes are flexible and practical codes. Remarkably, they excel at code locality, hence, they reduce repair costs and become less dependent on storage locations with poor availability. Our solution outperforms Reed-Solomon codes in many disaster recovery scenarios.Comment: The publication has 12 pages and 13 figures. This work was partially supported by Swiss National Science Foundation SNSF Doc.Mobility 162014, 2018 48th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN

Molecular biogeography of prickly lettuce (lactuca serriola l.) shows traces of recent range expansion

Prickly lettuce (Lactuca serriola L., Asteraceae), a wild relative of cultivated lettuce, is an autogamous species which greatly expanded throughout Western and Northern Europe during the last 2 centuries. Here, we present a large-scale biogeographic genetic analysis performed on a dataset represented by 2622 individuals from 110 wild European populations. Thirty-two maternally inherited chloroplast RFLP-markers and 10 nuclear microsatellite loci were used. Microsatellites revealed low genetic variation and high inbreeding coefficients within populations, as well as strong genetic differentiation between populations, which was in accordance with the autogamous breeding system. Analysis of molecular variance based clustering indicated the presence of 3 population clusters, which showed strong geographical patterns. One cluster occupied United Kingdom and part of Northern Europe, and characterized populations with a single predominant genotype. The second mostly combined populations from Northern Europe, while the third cluster grouped populations particularly from Southern Europe. Kriging of gene diversity for L. serriola corroborated northwards and westwards spread from Central (Eastern) Europe. Significant lower genetic diversity characterized the newly colonized parts of the range compared to the historical ones, confirming the importance of founder effects. Stronger pattern of isolation by distance was assessed in the newly colonized areas than in the historical areas (Mantel’s r = 0.20). In the newly colonized areas, populations at short geographic distances were genetically more similar than those in the historical areas. Our results corroborate the species’ recent and rapid northward and westward colonization from Eastern Europe, as well as a decrease of genetic diversity in recently established populations