The Complexity of Finding Small Triangulations of Convex 3-Polytopes

The problem of finding a triangulation of a convex three-dimensional polytope with few tetrahedra is proved to be NP-hard. We discuss other related complexity results.Comment: 37 pages. An earlier version containing the sketch of the proof appeared at the proceedings of SODA 200

VirtSC: Combining Virtualization Obfuscation with Self-Checksumming

Self-checksumming (SC) is a tamper-proofing technique that ensures certain program segments (code) in memory hash to known values at runtime. SC has few restrictions on application and hence can protect a vast majority of programs. The code verification in SC requires computation of the expected hashes after compilation, as the machine-code is not known before. This means the expected hash values need to be adjusted in the binary executable, hence combining SC with other protections is limited due to this adjustment step. However, obfuscation protections are often necessary, as SC protections can be otherwise easily detected and disabled via pattern matching. In this paper, we present a layered protection using virtualization obfuscation, yielding an architecture-agnostic SC protection that requires no post-compilation adjustment. We evaluate the performance of our scheme using a dataset of 25 real-world programs (MiBench and 3 CLI games). Our results show that the SC scheme induces an average overhead of 43% for a complete protection (100% coverage). The overhead is tolerable for less CPU-intensive programs (e.g. games) and when only parts of programs (e.g. license checking) are protected. However, large overheads stemming from the virtualization obfuscation were encountered

Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures

We consider a class of self-adjoint extensions using the boundary triple technique. Assuming that the associated Weyl function has the special form M(z)=\big(m(z)\Id-T\big) n(z)^{-1} with a bounded self-adjoint operator $T$ and scalar functions $m,n$ we show that there exists a class of boundary conditions such that the spectral problem for the associated self-adjoint extensions in gaps of a certain reference operator admits a unitary reduction to the spectral problem for $T$. As a motivating example we consider differential operators on equilateral metric graphs, and we describe a class of boundary conditions that admit a unitary reduction to generalized discrete laplacians.Comment: 19 page

Heterocellular OSM-OSMR signalling reprograms fibroblasts to promote pancreatic cancer growth and metastasis

Pancreatic ductal adenocarcinoma (PDA) is a lethal malignancy with a complex microenvironment. Dichotomous tumour-promoting and -restrictive roles have been ascribed to the tumour microenvironment, however the effects of individual stromal subsets remain incompletely characterised. Here, we describe how heterocellular Oncostatin M (OSM) - Oncostatin M Receptor (OSMR) signalling reprograms fibroblasts, regulates tumour growth and metastasis. Macrophage-secreted OSM stimulates inflammatory gene expression in cancer-associated fibroblasts (CAFs), which in turn induce a pro-tumourigenic environment and engage tumour cell survival and migratory signalling pathways. Tumour cells implanted in Osm-deficient (Osm(−/−)) mice display an epithelial-dominated morphology, reduced tumour growth and do not metastasise. Moreover, the tumour microenvironment of Osm(−/−) animals exhibit increased abundance of α smooth muscle actin positive myofibroblasts and a shift in myeloid and T cell phenotypes, consistent with a more immunogenic environment. Taken together, these data demonstrate how OSM-OSMR signalling coordinates heterocellular interactions to drive a pro-tumourigenic environment in PDA

Genomic analyses of hair from Ludwig van Beethoven

Ludwig van Beethoven (1770–1827) remains among the most influential and popular classical music composers. Health problems significantly impacted his career as a composer and pianist, including progressive hearing loss, recurring gastrointestinal complaints, and liver disease. In 1802, Beethoven requested that following his death, his disease be described and made public. Medical biographers have since proposed numerous hypotheses, including many substantially heritable conditions. Here we attempt a genomic analysis of Beethoven in order to elucidate potential underlying genetic and infectious causes of his illnesses. We incorporated improvements in ancient DNA methods into existing protocols for ancient hair samples, enabling the sequencing of high-coverage genomes from small quantities of historical hair. We analyzed eight independently sourced locks of hair attributed to Beethoven, five of which originated from a single European male. We deemed these matching samples to be almost certainly authentic and sequenced Beethoven\u27s genome to 24-fold genomic coverage. Although we could not identify a genetic explanation for Beethoven\u27s hearing disorder or gastrointestinal problems, we found that Beethoven had a genetic predisposition for liver disease. Metagenomic analyses revealed furthermore that Beethoven had a hepatitis B infection during at least the months prior to his death. Together with the genetic predisposition and his broadly accepted alcohol consumption, these present plausible explanations for Beethoven\u27s severe liver disease, which culminated in his death. Unexpectedly, an analysis of Y chromosomes sequenced from five living members of the Van Beethoven patrilineage revealed the occurrence of an extra-pair paternity event in Ludwig van Beethoven\u27s patrilineal ancestry

Assessing variation in maize grain nitrogen concentration and its implications for estimating nitrogen balance in the US North Central region

Accurate estimation of nitrogen (N) balance (a measure of potential N losses) in producer fields requires information on grain N concentration (GNC) to estimate grain-N removal, which is rarely measured by producers. The objectives of this study were to (i) examine the degree to which variation in GNC can affect estimation of grain-N removal, (ii) identify major factors influencing GNC, and (iii) develop a predictive model to estimate GNC, analyzing the uncertainty in predicted grain-N removal at field and regional levels. We compiled GNC data from published literature and unpublished databases using explicit criteria to only include experiments that portray the environments and dominant management practices where maize is grown in the US North Central region, which accounts for one-third of global maize production. We assessed GNC variation using regression tree analysis and evaluated the ability of the resulting model to estimate grain-N removal relative to the current approach using a fixed GNC. Across all site-year-treatment cases, GNC averaged 1.15%, ranging from 0.76 to 1.66%. At any given grain yield, GNC varied substantially and resulted in large variation in estimated grain-N removal and N balance. However, compared with GNC, yield differences explained much more variability in grain-N removal. Our regression tree model accounted for 35% of the variation in GNC, and returned physiologically meaningful associations with mean air temperature and water balance in July (i.e., silking) and August (i.e., grain filling), and with N fertilizer rate. The predictive model has a slight advantage over the typical approach based on a fixed GNC for estimating grain-N removal for individual site-years (root mean square error: 17 versus 21 kg N ha−1, respectively). Estimates of grain-N removal with both approaches were more reliable when aggregated at climate-soil domain level relative to estimates for individual site-years

Runs of homozygosity in killer whale genomes provide a global record of demographic histories

Runs of homozygosity (ROH) occur when offspring inherit haplotypes that are identical by descent from each parent. Length distributions of ROH are informative about population history; specifically, the probability of inbreeding mediated by mating system and/or population demography. Here, we investigated whether variation in killer whale (Orcinus orca) demographic history is reflected in genome-wide heterozygosity and ROH length distributions, using a global data set of 26 genomes representative of geographic and ecotypic variation in this species, and two F1 admixed individuals with Pacific-Atlantic parentage. We first reconstructed demographic history for each population as changes in effective population size through time using the pairwise sequential Markovian coalescent (PSMC) method. We found a subset of populations declined in effective population size during the Late Pleistocene, while others had more stable demography. Genomes inferred to have undergone ancestral declines in effective population size, were autozygous at hundreds of short ROH (\u3c1 \u3eMb), reflecting high background relatedness due to coalescence of haplotypes deep within the pedigree. In contrast, longer and therefore younger ROH (\u3e1.5 Mb) were found in low latitude populations, and populations of known conservation concern. These include a Scottish killer whale, for which 37.8% of the autosomes were comprised of ROH \u3e1.5 Mb in length. The fate of this population, in which only two adult males have been sighted in the past five years, and zero fecundity over the last two decades, may be inextricably linked to its demographic history and consequential inbreeding depression

Evaluating the contribution of rare variants to type 2 diabetes and related traits using pedigrees

Significance Contributions of rare variants to common and complex traits such as type 2 diabetes (T2D) are difficult to measure. This paper describes our results from deep whole-genome analysis of large Mexican-American pedigrees to understand the role of rare-sequence variations in T2D and related traits through enriched allele counts in pedigrees. Our study design was well-powered to detect association of rare variants if rare variants with large effects collectively accounted for large portions of risk variability, but our results did not identify such variants in this sample. We further quantified the contributions of common and rare variants in gene expression profiles and concluded that rare expression quantitative trait loci explain a substantive, but minor, portion of expression heritability.</jats:p

A new strategy for enhancing imputation quality of rare variants from next-generation sequencing data via combining SNP and exome chip data

Background: Rare variants have gathered increasing attention as a possible alternative source of missing heritability. Since next generation sequencing technology is not yet cost-effective for large-scale genomic studies, a widely used alternative approach is imputation. However, the imputation approach may be limited by the low accuracy of the imputed rare variants. To improve imputation accuracy of rare variants, various approaches have been suggested, including increasing the sample size of the reference panel, using sequencing data from study-specific samples (i.e., specific populations), and using local reference panels by genotyping or sequencing a subset of study samples. While these approaches mainly utilize reference panels, imputation accuracy of rare variants can also be increased by using exome chips containing rare variants. The exome chip contains 250 K rare variants selected from the discovered variants of about 12,000 sequenced samples. If exome chip data are available for previously genotyped samples, the combined approach using a genotype panel of merged data, including exome chips and SNP chips, should increase the imputation accuracy of rare variants. Results: In this study, we describe a combined imputation which uses both exome chip and SNP chip data simultaneously as a genotype panel. The effectiveness and performance of the combined approach was demonstrated using a reference panel of 848 samples constructed using exome sequencing data from the T2D-GENES consortium and 5,349 sample genotype panels consisting of an exome chip and SNP chip. As a result, the combined approach increased imputation quality up to 11 %, and genomic coverage for rare variants up to 117.7 % (MAF < 1 %), compared to imputation using the SNP chip alone. Also, we investigated the systematic effect of reference panels on imputation quality using five reference panels and three genotype panels. The best performing approach was the combination of the study specific reference panel and the genotype panel of combined data. Conclusions: Our study demonstrates that combined datasets, including SNP chips and exome chips, enhances both the imputation quality and genomic coverage of rare variants

Genetic Drivers of Heterogeneity in Type 2 Diabetes Pathophysiology

Type 2 diabetes (T2D) is a heterogeneous disease that develops through diverse pathophysiological processes1,2 and molecular mechanisms that are often specific to cell type3,4. Here, to characterize the genetic contribution to these processes across ancestry groups, we aggregate genome-wide association study data from 2,535,601 individuals (39.7% not of European ancestry), including 428,452 cases of T2D. We identify 1,289 independent association signals at genome-wide significance (P \u3c 5 × 10-8) that map to 611 loci, of which 145 loci are, to our knowledge, previously unreported. We define eight non-overlapping clusters of T2D signals that are characterized by distinct profiles of cardiometabolic trait associations. These clusters are differentially enriched for cell-type-specific regions of open chromatin, including pancreatic islets, adipocytes, endothelial cells and enteroendocrine cells. We build cluster-specific partitioned polygenic scores5 in a further 279,552 individuals of diverse ancestry, including 30,288 cases of T2D, and test their association with T2D-related vascular outcomes. Cluster-specific partitioned polygenic scores are associated with coronary artery disease, peripheral artery disease and end-stage diabetic nephropathy across ancestry groups, highlighting the importance of obesity-related processes in the development of vascular outcomes. Our findings show the value of integrating multi-ancestry genome-wide association study data with single-cell epigenomics to disentangle the aetiological heterogeneity that drives the development and progression of T2D. This might offer a route to optimize global access to genetically informed diabetes care