Optimal Locally Repairable Linear Codes

Linear erasure codes with local repairability are desirable for distributed data storage systems. An [n, k, d] code having all-symbol (r, \delta})-locality, denoted as (r, {\delta})a, is considered optimal if it also meets the minimum Hamming distance bound. The existing results on the existence and the construction of optimal (r, {\delta})a codes are limited to only the special case of {\delta} = 2, and to only two small regions within this special case, namely, m = 0 or m >= (v+{\delta}-1) > ({\delta}-1), where m = n mod (r+{\delta}-1) and v = k mod r. This paper investigates the existence conditions and presents deterministic constructive algorithms for optimal (r, {\delta})a codes with general r and {\delta}. First, a structure theorem is derived for general optimal (r, {\delta})a codes which helps illuminate some of their structure properties. Next, the entire problem space with arbitrary n, k, r and {\delta} is divided into eight different cases (regions) with regard to the specific relations of these parameters. For two cases, it is rigorously proved that no optimal (r, {\delta})a could exist. For four other cases the optimal (r, {\delta})a codes are shown to exist, deterministic constructions are proposed and the lower bound on the required field size for these algorithms to work is provided. Our new constructive algorithms not only cover more cases, but for the same cases where previous algorithms exist, the new constructions require a considerably smaller field, which translates to potentially lower computational complexity. Our findings substantially enriches the knowledge on (r, {\delta})a codes, leaving only two cases in which the existence of optimal codes are yet to be determined.Comment: Under Revie

Error Correction for Cooperative Data Exchange

This paper considers the problem of error correction for a cooperative data exchange (CDE) system, where some clients are compromised or failed and send false messages. Assuming each client possesses a subset of the total messages, we analyze the error correction capability when every client is allowed to broadcast only one linearly-coded message. Our error correction capability bound determines the maximum number of clients that can be compromised or failed without jeopardizing the final decoding solution at each client. We show that deterministic, feasible linear codes exist that can achieve the derived bound. We also evaluate random linear codes, where the coding coefficients are drawn randomly, and then develop the probability for a client to withstand a certain number of compromised or failed peers and successfully deduce the complete message for any network size and any initial message distributions

A Geometry-Inclusive Analysis for Single-Relay Systems

Successful message relay, or the quality of the interuser channel, is critical to fully realize the cooperative benefits promised by the theory. This in turn points out the importance of the geometry of cooperative system. This paper investigates the impact of the relay's location on the system capacity and outage probability for both amplify-forward (AF) and decode-forward (DF) schemes. Signal attenuation is modeled using power laws, and capacity is evaluated using the max-flow min-cut theory. A capacity contour for DF, the more popular mode of the two, is provided to facilitate the derivation of engineering rules. Finally, a selective singlerelay system, which selects the best relay node among a host of candidates according to their locations, is analyzed. The average system capacity and outage, averaged over all possible candidates' locations, are evaluated. The result shows that the availability of a small candidate pool of 3 to 5 nodes suffices to reap most of the cooperative gains promised by a selective single-relay system

A Geometry-Inclusive Analysis for Single-Relay Systems

Successful message relay, or the quality of the interuser channel, is critical to fully realize the cooperative benefits promised by the theory. This in turn points out the importance of the geometry of cooperative system. This paper investigates the impact of the relay's location on the system capacity and outage probability for both amplify-forward (AF) and decode-forward (DF) schemes. Signal attenuation is modeled using power laws, and capacity is evaluated using the max-flow min-cut theory. A capacity contour for DF, the more popular mode of the two, is provided to facilitate the derivation of engineering rules. Finally, a selective single-relay system, which selects the best relay node among a host of candidates according to their locations, is analyzed. The average system capacity and outage, averaged over all possible candidates' locations, are evaluated. The result shows that the availability of a small candidate pool of 3 to 5 nodes suffices to reap most of the cooperative gains promised by a selective single-relay system

Land Use and Pollinator Dependency Drives Global Patterns of Pollen Limitation in the Anthropocene

Land use change, by disrupting the co-evolved interactions between plants and their pollinators, could be causing plant reproduction to be limited by pollen supply. Using a phylogenetically controlled meta-analysis on over 2200 experimental studies and more than 1200 wild plants, we ask if land use intensification is causing plant reproduction to be pollen limited at global scales. Here we report that plants reliant on pollinators in urban settings are more pollen limited than similarly pollinator-reliant plants in other landscapes. Plants functionally specialized on bee pollinators are more pollen limited in natural than managed vegetation, but the reverse is true for plants pollinated exclusively by a non-bee functional group or those pollinated by multiple functional groups. Plants ecologically specialized on a single pollinator taxon were extremely pollen limited across land use types. These results suggest that while urbanization intensifies pollen limitation, ecologically and functionally specialized plants are at risk of pollen limitation across land use categories

Glopl, a global data base on pollen limitation of plant reproduction

Plant reproduction relies on transfer of pollen from anthers to stigmas, and the majority of flowering plants depend on biotic or abiotic agents for this transfer. A key metric for characterizing if pollen receipt is insufficient for reproduction is pollen limitation, which is assessed by pollen supplementation experiments. In a pollen supplementation experiment, fruit or seed production by flowers exposed to natural pollination is compared to that following hand pollination either by pollen supplementation (i.e. manual outcross pollen addition without bagging) or manual outcrossing of bagged flowers, which excludes natural pollination. The GloPL database brings together data from 2969 unique pollen supplementation experiments reported in 927 publications published from 1981 to 2015, allowing assessment of the strength and variability of pollen limitation in 1265 wild plant species across all biomes and geographic regions globally. The GloPL database will be updated and curated with the aim of enabling the continued study of pollen limitation in natural ecosystems and highlighting significant gaps in our understanding of pollen limitation.<p>Correction in: Scientific Data, vol. 6, article number: 2. DOI: 10.1038/s41597-018-0006-1</p

Multi -ancestry genome-wide association analyses identify novel genetic mechanisms in rheumatoid arthritis.

Rheumatoid arthritis (RA) is a highly heritable complex disease with unknown etiology. Multi-ancestry genetic research of RA promises to improve power to detect genetic signals, fine-mapping resolution and performances of polygenic risk scores (PRS). Here, we present a large-scale genome-wide association study (GWAS) of RA, which includes 276,020 samples from five ancestral groups. We conducted a multi-ancestry meta-analysis and identified 124 loci (P < 5 × 10−8), of which 34 are novel. Candidate genes at the novel loci suggest essential roles of the immune system (for example, TNIP2 and TNFRSF11A) and joint tissues (for example, WISP1) in RA etiology. Multi-ancestry fine-mapping identified putatively causal variants with biological insights (for example, LEF1). Moreover, PRS based on multi-ancestry GWAS outperformed PRS based on single-ancestry GWAS and had comparable performance between populations of European and East Asian ancestries. Our study provides several insights into the etiology of RA and improves the genetic predictability of RA.We thank the Director of Health Malaysia for supporting the work described in the South Asian (SAS) population: the Malaysian Epidemiological Investigation of Rheumatoid Arthritis (MyEIRA) study. The MyEIRA study was funded by grants from Ministry of Health Malaysia (NMRR-08-820-1975) and the Swedish National Research Council (DNR-348-2009-6468). The GENRA study and the CARDERA genetics cohort genotyping were funded by Versus Arthritis (grant reference 19739 to I.C.S.). The Nurses’ Health Study (NHS cohort) is funded by the National Institutes of Health (NIH) (R01 AR049880, UM1 CA186107, R01 CA49449, U01 CA176726 and R01 CA67262). The Swedish EIRA study was supported by the Swedish Research Council (to L.K., L.P. and L.A.). S.S. was in part supported by the Mochida Memorial Foundation for Medical and Pharmaceutical Research, Kanae Foundation for the Promotion of Medical Science, Astellas Foundation for Research on Metabolic Disorders, JCR Grant for Promoting Basic Rheumatology, and Manabe Scholarship Grant for Allergic and Rheumatic Diseases. I.C.S. is funded by the National Institute for Health and Care Research (NIHR) Advanced Research Fellowship (grant reference NIHR300826). The views expressed are those of the authors and not necessarily those of the NIHR or the Department of Health and Social Care. K.A.S. is supported by the Sherman Family Chair in Genomic Medicine and by a Canadian Institutes for Health Research Foundation Grant (FDN 148457) and grants from the Ontario Research Fund (RE-09-090) and Canadian Foundation for Innovation (33374). S.-C.B. is supported by the Basic Science Research Program through the NRF funded by the Ministry of Education (NRF-2021R1A6A1A03038899). R.P.K. and J.C.E. are funded by NIH (UL1 TR003096). C.M.L. is partly funded by the NIHR Maudsley Biomedical Research Centre at South London and Maudsley NHS Foundation Trust and King’s College London. T. Arayssi was partially supported by the National Priorities Research Program (grant 4-344-3-105 from the Qatar National Research Fund, a member of Qatar Foundation). M. Kerick and J.M. are funded by Rheumatology Cooperative Research Thematic Network program RD16/0012/0013 from the Instituto de Salud Carlos III (Spanish Ministry of Science and Innovation). Y.O. is funded by JSPS KAKENHI (19H01021 and 20K21834), AMED (JP21km0405211, JP21ek0109413, JP21ek0410075, JP21gm4010006 and JP21km0405217), JST Moonshot R&D (JPMJMS2021 and JPMJMS2024), Takeda Science Foundation, and the Bioinformatics Initiative of Osaka University Graduate School of Medicine. Y. Kochi is funded by grants from Nanken-Kyoten, TMDU and Medical Research Center Initiative for High Depth Omics. S.R. is supported by UH2AR067677, U01HG009379, R01AR063759 and U01HG012009

The Diabetes Technology Society Error Grid and Trend Accuracy Matrix for Glucose Monitors.

INTRODUCTION: An error grid compares measured versus reference glucose concentrations to assign clinical risk values to observed errors. Widely used error grids for blood glucose monitors (BGMs) have limited value because they do not also reflect clinical accuracy of continuous glucose monitors (CGMs). METHODS: Diabetes Technology Society (DTS) convened 89 international experts in glucose monitoring to (1) smooth the borders of the Surveillance Error Grid (SEG) zones and create a user-friendly tool-the DTS Error Grid; (2) define five risk zones of clinical point accuracy (A-E) to be identical for BGMs and CGMs; (3) determine a relationship between DTS Error Grid percent in Zone A and mean absolute relative difference (MARD) from analyzing 22 BGM and nine CGM accuracy studies; and (4) create trend risk categories (1-5) for CGM trend accuracy. RESULTS: The DTS Error Grid for point accuracy contains five risk zones (A-E) with straight-line borders that can be applied to both BGM and CGM accuracy data. In a data set combining point accuracy data from 18 BGMs, 2.6% of total data pairs equally moved from Zones A to B and vice versa (SEG compared with DTS Error Grid). For every 1% increase in percent data in Zone A, the MARD decreased by approximately 0.33%. We also created a DTS Trend Accuracy Matrix with five trend risk categories (1-5) for CGM-reported trend indicators compared with reference trends calculated from reference glucose. CONCLUSION: The DTS Error Grid combines contemporary clinician input regarding clinical point accuracy for BGMs and CGMs. The DTS Trend Accuracy Matrix assesses accuracy of CGM trend indicators

Mapping genomic loci implicates genes and synaptic biology in schizophrenia

Schizophrenia has a heritability of 60-80%1, much of which is attributable to common risk alleles. Here, in a two-stage genome-wide association study of up to 76,755 individuals with schizophrenia and 243,649 control individuals, we report common variant associations at 287 distinct genomic loci. Associations were concentrated in genes that are expressed in excitatory and inhibitory neurons of the central nervous system, but not in other tissues or cell types. Using fine-mapping and functional genomic data, we identify 120 genes (106 protein-coding) that are likely to underpin associations at some of these loci, including 16 genes with credible causal non-synonymous or untranslated region variation. We also implicate fundamental processes related to neuronal function, including synaptic organization, differentiation and transmission. Fine-mapped candidates were enriched for genes associated with rare disruptive coding variants in people with schizophrenia, including the glutamate receptor subunit GRIN2A and transcription factor SP4, and were also enriched for genes implicated by such variants in neurodevelopmental disorders. We identify biological processes relevant to schizophrenia pathophysiology; show convergence of common and rare variant associations in schizophrenia and neurodevelopmental disorders; and provide a resource of prioritized genes and variants to advance mechanistic studies