Summary. The lasso penalizes a least squares regression by the sum of the absolute values (L 1 -norm) of the coefficients. The form of this penalty encourages sparse solutions (with many coefficients equal to 0). We propose the 'fused lasso', a generalization that is designed for problems with features that can be ordered in some meaningful way. The fused lasso penalizes the L 1 -norm of both the coefficients and their successive differences. Thus it encourages sparsity of the coefficients and also sparsity of their differences-i.e. local constancy of the coefficient profile. The fused lasso is especially useful when the number of features p is much greater than N, the sample size. The technique is also extended to the 'hinge' loss function that underlies the support vector classifier.We illustrate the methods on examples from protein mass spectroscopy and gene expression data.

MYH9 has been proposed as a major genetic risk locus for a spectrum of nondiabetic end stage kidney disease (ESKD). We use recently released sequences from the 1000 Genomes Project to identify two western African-specific missense mutations (S342G and I384M) in the neighboring APOL1 gene, and demonstrate that these are more strongly associated with ESKD than previously reported MYH9 variants. The APOL1 gene product, apolipoprotein L-1, has been studied for its roles in trypanosomal lysis, autophagic cell death, lipid metabolism, as well as vascular and other biological activities. We also show that the distribution of these newly identified APOL1 risk variants in African populations is consistent with the pattern of African ancestry ESKD risk previously attributed to MYH9.Mapping by admixture linkage disequilibrium (MALD) localized an interval on chromosome 22, in a region that includes the MYH9 gene, which was shown to contain African ancestry risk variants associated with certain forms of ESKD (Kao et al. 2008; Kopp et al. 2008). MYH9 encodes nonmuscle myosin heavy chain IIa, a major cytoskeletal nanomotor protein expressed in many cell types, including podocyte cells of the renal glomerulus. Moreover, 39 different coding region mutations in MYH9 have been identified in patients with a group of rare syndromes, collectively termed the Giant Platelet Syndromes, with clear autosomal dominant inheritance, and various clinical manifestations, sometimes also including glomerular pathology and chronic kidney disease (Kopp 2010; Sekine et al. 2010). Accordingly, MYH9 was further explored in these studies as the leading candidate gene responsible for the MALD signal. Dense mapping of MYH9 identified individual single nucleotide polymorphisms (SNPs) and sets of such SNPs grouped as haplotypes that were found to be highly associated with a large and important group of ESKD risk phenotypes, which as a consequence were designated as MYH9-associated nephropathies (Bostrom and Freedman 2010). These included HIV-associated nephropathy (HIVAN), primary nonmonogenic forms of focal segmental glomerulosclerosis, and hypertension affiliated chronic kidney disease not attributed to other etiologies (Bostrom and Freedman 2010). The MYH9 SNP and haplotype associations observed with these forms of ESKD yielded the largest odds ratios (OR) reported to date for the association of common variants with common disease risk (Winkler et al. 2010). Two specific MYH9 variants (rs5750250 of S-haplotype and rs11912763 of F-haplotype) were designated as most strongly predictive on the basis of Receiver Operating Characteristic analysis (Nelson et al. 2010). These MYH9 association studies were then also extended to earlier stage and related kidney disease phenotypes and to population groups with varying degrees of recent African ancestry admixture (Behar et al. 2010; Freedman et al. 2009a, b; Nelson et al. 2010), and led to the expectation of finding a functional African ancestry causative variant within MYH9. However, despite intensive efforts inc...

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Contemporary Jews comprise an aggregate of ethno-religious communities whose worldwide members identify with each other through various shared religious, historical and cultural traditions. Historical evidence suggests common origins in the Middle East, followed by migrations leading to the establishment of communities of Jews in Europe, Africa and Asia, in what is termed the Jewish Diaspora. This complex demographic history imposes special challenges in attempting to address the genetic structure of the Jewish people. Although many genetic studies have shed light on Jewish origins and on diseases prevalent among Jewish communities, including studies focusing on uniparentally and biparentally inherited markers, genome-wide patterns of variation across the vast geographic span of Jewish Diaspora communities and their respective neighbours have yet to be addressed. Here we use high-density bead arrays to genotype individuals from 14 Jewish Diaspora communities and compare these patterns of genome-wide diversity with those from 69 Old World non-Jewish populations, of which 25 have not previously been reported. These samples were carefully chosen to provide comprehensive comparisons between Jewish and non-Jewish populations in the Diaspora, as well as with non-Jewish populations from the Middle East and north Africa. Principal component and structure-like analyses identify previously unrecognized genetic substructure within the Middle East. Most Jewish samples form a remarkably tight subcluster that overlies Druze and Cypriot samples but not samples from other Levantine populations or paired Diaspora host populations. In contrast, Ethiopian Jews (Beta Israel) and Indian Jews (Bene Israel and Cochini) cluster with neighbouring autochthonous populations in Ethiopia and western India, respectively, despite a clear paternal link between the Bene Israel and the Levant. These results cast light on the variegated genetic architecture of the Middle East, and trace the origins of most Jewish Diaspora communities to the Levant.

The quest to explain demographic history during the early part of human evolution has been limited because of the scarce paleoanthropological record from the Middle Stone Age. To shed light on the structure of the mitochondrial DNA (mtDNA) phylogeny at the dawn of Homo sapiens, we constructed a matrilineal tree composed of 624 complete mtDNA genomes from sub-Saharan Hg L lineages. We paid particular attention to the Khoi and San (Khoisan) people of South Africa because they are considered to be a unique relic of hunter-gatherer lifestyle and to carry paternal and maternal lineages belonging to the deepest clades known among modern humans. Both the tree phylogeny and coalescence calculations suggest that Khoisan matrilineal ancestry diverged from the rest of the human mtDNA pool 90,000-150,000 years before present (ybp) and that at least five additional, currently extant maternal lineages existed during this period in parallel. Furthermore, we estimate that a minimum of 40 other evolutionarily successful lineages flourished in sub-Saharan Africa during the period of modern human dispersal out of Africa approximately 60,000-70,000 ybp. Only much later, at the beginning of the Late Stone Age, about 40,000 ybp, did introgression of additional lineages occur into the Khoisan mtDNA pool. This process was further accelerated during the recent Bantu expansions. Our results suggest that the early settlement of humans in Africa was already matrilineally structured and involved small, separately evolving isolated populations.

Mutational events along the human mtDNA phylogeny are traditionally identified relative to the revised Cambridge Reference Sequence, a contemporary European sequence published in 1981. This historical choice is a continuous source of inconsistencies, misinterpretations, and errors in medical, forensic, and population genetic studies. Here, after having refined the human mtDNA phylogeny to an unprecedented level by adding information from 8,216 modern mitogenomes, we propose switching the reference to a Reconstructed Sapiens Reference Sequence, which was identified by considering all available mitogenomes from Homo neanderthalensis. This "Copernican" reassessment of the human mtDNA tree from its deepest root should resolve previous problems and will have a substantial practical and educational influence on the scientific and public perception of human evolution by clarifying the core principles of common ancestry for extant descendants.

1-regularized linear inverse problems are frequently used in signal processing, image analysis, and statistics. The correct choice of the regularization parameter t ∈ R ≥0 is a delicate issue. Instead of solving the variational problem for a fixed parameter, the idea of the homotopy method is to compute a complete solution path u(t) as a function of t. In a celebrated paper by Osborne, Presnell, and Turlach, it has been shown that the computational cost of this approach is often comparable to the cost of solving the corresponding least squares problem. Their analysis relies on the one-at-a-time condition, which requires that different indices enter or leave the support of the solution at distinct regularization parameters. In this paper, we introduce a generalized homotopy algorithm based on a nonnegative least squares problem, which does not require such a condition, and prove its termination after finitely many steps. At every point of the path, we give a full characterization of all possible directions. To illustrate our results, we discuss examples in which the standard homotopy method either fails or becomes infeasible. To the best of our knowledge, our algorithm is the first to provably compute a full solution path for an arbitrary combination of an input matrix and a data vector.

Short tandem repeats (STRs) have a wide range of applications, including medical genetics, forensics, and genetic genealogy. High-throughput sequencing (HTS) has the potential to profile hundreds of thousands of STR loci. However, mainstream bioinformatics pipelines are inadequate for the task. These pipelines treat STR mapping as gapped alignment, which results in cumbersome processing times and a biased sampling of STR alleles. Here, we present lobSTR, a novel method for profiling STRs in personal genomes. lobSTR harnesses concepts from signal processing and statistical learning to avoid gapped alignment and to address the specific noise patterns in STR calling. The speed and reliability of lobSTR exceed the performance of current mainstream algorithms for STR profiling. We validated lobSTR's accuracy by measuring its consistency in calling STRs from whole-genome sequencing of two biological replicates from the same individual, by tracing Mendelian inheritance patterns in STR alleles in whole-genome sequencing of a HapMap trio, and by comparing lobSTR results to traditional molecular techniques. Encouraged by the speed and accuracy of lobSTR, we used the algorithm to conduct a comprehensive survey of STR variations in a deeply sequenced personal genome. We traced the mutation dynamics of close to 100,000 STR loci and observed more than 50,000 STR variations in a single genome. lobSTR's implementation is an end-to-end solution. The package accepts raw sequencing reads and provides the user with the genotyping results. It is written in C/C++, includes multi-threading capabilities, and is compatible with the BAM format.