How to design graphs with low forwarding index and limited number of edges

International audienceThe (edge) forwarding index of a graph is the minimum, over all possible rout-ings of all the demands, of the maximum load of an edge. This metric is of a great interest since it captures the notion of global congestion in a precise way: the lesser the forwarding-index, the lesser the congestion. In this paper, we study the following design question: Given a number e of edges and a number n of vertices, what is the least congested graph that we can construct? and what forwarding-index can we achieve? Our problem has some distant similarities with the well-known (∆, D) problem, and we sometimes build upon results obtained on it. The goal of this paper is to study how to build graphs with low forwarding indices and to understand how the number of edges impacts the forwarding index. We answer here these questions for different families of graphs: general graphs, graphs with bounded degree, sparse graphs with a small number of edges by providing constructions, most of them asymptotically optimal. For instance, we provide an asymptotically optimal construction for (n, n + k) cubic graphs-its forwarding index is ∼ n 2 3k log 2 (k). Our results allow to understand how the forwarding-index drops when edges are added to a graph and also to determine what is the best (i.e least congested) structure with e edges. Doing so, we partially answer the practical problem that initially motivated our work: If an operator wants to power only e links of its network, in order to reduce the energy consumption (or wiring cost) of its networks, what should be those links and what performance can be expected

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

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Pan-cancer analysis of whole genomes

Cancer is driven by genetic change, and the advent of massively parallel sequencing has enabled systematic documentation of this variation at the whole-genome scale(1-3). Here we report the integrative analysis of 2,658 whole-cancer genomes and their matching normal tissues across 38 tumour types from the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA). We describe the generation of the PCAWG resource, facilitated by international data sharing using compute clouds. On average, cancer genomes contained 4-5 driver mutations when combining coding and non-coding genomic elements; however, in around 5% of cases no drivers were identified, suggesting that cancer driver discovery is not yet complete. Chromothripsis, in which many clustered structural variants arise in a single catastrophic event, is frequently an early event in tumour evolution; in acral melanoma, for example, these events precede most somatic point mutations and affect several cancer-associated genes simultaneously. Cancers with abnormal telomere maintenance often originate from tissues with low replicative activity and show several mechanisms of preventing telomere attrition to critical levels. Common and rare germline variants affect patterns of somatic mutation, including point mutations, structural variants and somatic retrotransposition. A collection of papers from the PCAWG Consortium describes non-coding mutations that drive cancer beyond those in the TERT promoter(4); identifies new signatures of mutational processes that cause base substitutions, small insertions and deletions and structural variation(5,6); analyses timings and patterns of tumour evolution(7); describes the diverse transcriptional consequences of somatic mutation on splicing, expression levels, fusion genes and promoter activity(8,9); and evaluates a range of more-specialized features of cancer genomes(8,10-18).Peer reviewe

A global reference for human genetic variation

The 1000 Genomes Project set out to provide a comprehensive description of common human genetic variation by applying whole-genome sequencing to a diverse set of individuals from multiple populations. Here we report completion of the project, having reconstructed the genomes of 2,504 individuals from 26 populations using a combination of low-coverage whole-genome sequencing, deep exome sequencing, and dense microarray genotyping. We characterized a broad spectrum of genetic variation, in total over 88 million variants (84.7 million single nucleotide polymorphisms (SNPs), 3.6 million short insertions/deletions (indels), and 60,000 structural variants), all phased onto high-quality haplotypes. This resource includes >99% of SNP variants with a frequency of >1% for a variety of ancestries. We describe the distribution of genetic variation across the global sample, and discuss the implications for common disease studies.We thank the many people who were generous with contributing their samples to the project: the African Caribbean in Barbados; Bengali in Bangladesh; British in England and Scotland; Chinese Dai in Xishuangbanna, China; Colombians in Medellin, Colombia; Esan in Nigeria; Finnish in Finland; Gambian in Western Division – Mandinka; Gujarati Indians in Houston, Texas, USA; Han Chinese in Beijing, China; Iberian populations in Spain; Indian Telugu in the UK; Japanese in Tokyo, Japan; Kinh in Ho Chi Minh City, Vietnam; Luhya in Webuye, Kenya; Mende in Sierra Leone; people with African ancestry in the southwest USA; people with Mexican ancestry in Los Angeles, California, USA; Peruvians in Lima, Peru; Puerto Ricans in Puerto Rico; Punjabi in Lahore, Pakistan; southern Han Chinese; Sri Lankan Tamil in the UK; Toscani in Italia; Utah residents (CEPH) with northern and western European ancestry; and Yoruba in Ibadan, Nigeria. Many thanks to the people who contributed to this project: P. Maul, T. Maul, and C. Foster; Z. Chong, X. Fan, W. Zhou, and T. Chen; N. Sengamalay, S. Ott, L. Sadzewicz, J. Liu, and L. Tallon; L. Merson; O. Folarin, D. Asogun, O. Ikpwonmosa, E. Philomena, G. Akpede, S. Okhobgenin, and O. Omoniwa; the staff of the Institute of Lassa Fever Research and Control (ILFRC), Irrua Specialist Teaching Hospital, Irrua, Edo State, Nigeria; A. Schlattl and T. Zichner; S. Lewis, E. Appelbaum, and L. Fulton; A. Yurovsky and I. Padioleau; N. Kaelin and F. Laplace; E. Drury and H. Arbery; A. Naranjo, M. Victoria Parra, and C. Duque; S. Däkel, B. Lenz, and S. Schrinner; S. Bumpstead; and C. Fletcher-Hoppe. Funding for this work was from the Wellcome Trust Core Award 090532/Z/09/Z and Senior Investigator Award 095552/Z/11/Z (P.D.), and grants WT098051 (R.D.), WT095908 and WT109497 (P.F.), WT086084/Z/08/Z and WT100956/Z/13/Z (G.M.), WT097307 (W.K.), WT0855322/Z/08/Z (R.L.), WT090770/Z/09/Z (D.K.), the Wellcome Trust Major Overseas program in Vietnam grant 089276/Z.09/Z (S.D.), the Medical Research Council UK grant G0801823 (J.L.M.), the UK Biotechnology and Biological Sciences Research Council grants BB/I02593X/1 (G.M.) and BB/I021213/1 (A.R.L.), the British Heart Foundation (C.A.A.), the Monument Trust (J.H.), the European Molecular Biology Laboratory (P.F.), the European Research Council grant 617306 (J.L.M.), the Chinese 863 Program 2012AA02A201, the National Basic Research program of China 973 program no. 2011CB809201, 2011CB809202 and 2011CB809203, Natural Science Foundation of China 31161130357, the Shenzhen Municipal Government of China grant ZYC201105170397A (J.W.), the Canadian Institutes of Health Research Operating grant 136855 and Canada Research Chair (S.G.), Banting Postdoctoral Fellowship from the Canadian Institutes of Health Research (M.K.D.), a Le Fonds de Recherche duQuébec-Santé (FRQS) research fellowship (A.H.), Genome Quebec (P.A.), the Ontario Ministry of Research and Innovation – Ontario Institute for Cancer Research Investigator Award (P.A., J.S.), the Quebec Ministry of Economic Development, Innovation, and Exports grant PSR-SIIRI-195 (P.A.), the German Federal Ministry of Education and Research (BMBF) grants 0315428A and 01GS08201 (R.H.), the Max Planck Society (H.L., G.M., R.S.), BMBF-EPITREAT grant 0316190A (R.H., M.L.), the German Research Foundation (Deutsche Forschungsgemeinschaft) Emmy Noether Grant KO4037/1-1 (J.O.K.), the Beatriu de Pinos Program grants 2006 BP-A 10144 and 2009 BP-B 00274 (M.V.), the Spanish National Institute for Health Research grant PRB2 IPT13/0001-ISCIII-SGEFI/FEDER (A.O.), Ewha Womans University (C.L.), the Japan Society for the Promotion of Science Fellowship number PE13075 (N.P.), the Louis Jeantet Foundation (E.T.D.), the Marie Curie Actions Career Integration grant 303772 (C.A.), the Swiss National Science Foundation 31003A_130342 and NCCR “Frontiers in Genetics” (E.T.D.), the University of Geneva (E.T.D., T.L., G.M.), the US National Institutes of Health National Center for Biotechnology Information (S.S.) and grants U54HG3067 (E.S.L.), U54HG3273 and U01HG5211 (R.A.G.), U54HG3079 (R.K.W., E.R.M.), R01HG2898 (S.E.D.), R01HG2385 (E.E.E.), RC2HG5552 and U01HG6513 (G.T.M., G.R.A.), U01HG5214 (A.C.), U01HG5715 (C.D.B.), U01HG5718 (M.G.), U01HG5728 (Y.X.F.), U41HG7635 (R.K.W., E.E.E., P.H.S.), U41HG7497 (C.L., M.A.B., K.C., L.D., E.E.E., M.G., J.O.K., G.T.M., S.A.M., R.E.M., J.L.S., K.Y.), R01HG4960 and R01HG5701 (B.L.B.), R01HG5214 (G.A.), R01HG6855 (S.M.), R01HG7068 (R.E.M.), R01HG7644 (R.D.H.), DP2OD6514 (P.S.), DP5OD9154 (J.K.), R01CA166661 (S.E.D.), R01CA172652 (K.C.), P01GM99568 (S.R.B.), R01GM59290 (L.B.J., M.A.B.), R01GM104390 (L.B.J., M.Y.Y.), T32GM7790 (C.D.B., A.R.M.), P01GM99568 (S.R.B.), R01HL87699 and R01HL104608 (K.C.B.), T32HL94284 (J.L.R.F.), and contracts HHSN268201100040C (A.M.R.) and HHSN272201000025C (P.S.), Harvard Medical School Eleanor and Miles Shore Fellowship (K.L.), Lundbeck Foundation Grant R170-2014-1039 (K.L.), NIJ Grant 2014-DN-BX-K089 (Y.E.), the Mary Beryl Patch Turnbull Scholar Program (K.C.B.), NSF Graduate Research Fellowship DGE-1147470 (G.D.P.), the Simons Foundation SFARI award SF51 (M.W.), and a Sloan Foundation Fellowship (R.D.H.). E.E.E. is an investigator of the Howard Hughes Medical Institute

Average-case complexity for the execution of recursive definitions on relational databases

The execution costs of various types of database queries, expressed in terms of linear recusive definitions, are evaluated for two common query evaluation algorithms in the case where the database relations are represented by forests of labelled oriented trees. In a first stage, the execution costs are computed for a given forest. A key issue in this computation is the partition of the set of nodes in the forest into equivalence classes, the properties of which are explored. Moreover, the representation adopted is conceptually simple and provides additional results which are of interest by themselves. In a second stage, the averages of these costs, computed over all databases representable by forests with a given number of nodes, are also evaluated. Finally, the execution cost of the considered database queries is computed for the case where the underlined database relations are modelled as Hamiltonian digraphs.ou