Optimal randomized multilevel algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition

In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decomposition of ANOVA-type. The weights model the relative importance of different groups of variables. We present new randomized multilevel algorithms to tackle this integration problem and prove upper bounds for their randomized error. Furthermore, we provide in this setting the first non-trivial lower error bounds for general randomized algorithms, which, in particular, may be adaptive or non-linear. These lower bounds show that our multilevel algorithms are optimal. Our analysis refines and extends the analysis provided in [F. J. Hickernell, T. M\"uller-Gronbach, B. Niu, K. Ritter, J. Complexity 26 (2010), 229-254], and our error bounds improve substantially on the error bounds presented there. As an illustrative example, we discuss the unanchored Sobolev space and employ randomized quasi-Monte Carlo multilevel algorithms based on scrambled polynomial lattice rules.Comment: 31 pages, 0 figure

Tractability of multivariate problems for standard and linear information in the worst case setting: part II

We study QPT (quasi-polynomial tractability) in the worst case setting for linear tensor product problems defined over Hilbert spaces. We assume that the domain space is a reproducing kernel Hilbert space so that function values are well defined. We prove QPT for algorithms that use only function values under the three assumptions: 1) the minimal errors for the univariate case decay polynomially fast to zero, 2) the largest singular value for the univariate case is simple and 3) the eigenfunction corresponding to the largest singular value is a multiple of the function value at some point. The first two assumptions are necessary for QPT. The third assumption is necessary for QPT for some Hilbert spaces

Beat length measurement in directional couplers by thermo-optic modulation

In integrated optical directional couplers formed by two parallel waveguides, we measure the difference Δβ = βeven - βodd between the propagation constants of the 'supermodes'. They are coupled locally by heating a fine spot on one of the guides. When the spot is scanned along the coupler the output power from one of the guides is found to vary periodically. The period of variation is the modal beat length λ = 2π/Δβ. We demonstrate this technique with directional couplers fabricated by K+-exchange in glass. Beat lengths in the range of 0.6 ... 2.2 mm are measured with an accuracy of ±0.3%.<br/

Renal Recovery after the Implementation of an Electronic Alert and Biomarker-Guided Kidney-Protection Strategy following Major Surgery

Background: The facilitation of early recovery of acute kidney injury (AKI) is an important step to improve outcome, particularly because of the limited therapeutic interventions currently available for AKI. The combination of an electronic alert and biomarker-guided kidney-protection strategy implemented in the routine care may have an impact on the incidence of early complete reversal of AKI after major non-cardiac surgery. Methods: We studied 294 patients in two cohorts before (n = 151) and after protocol implementation (n = 143). Data collection required 6 months for each cohort. The kidney-protection protocol included an electronic alert to detect patients who were eligible for urinary biomarker [TIMP2 × IGFBP7]-guided kidney-protection intervention. Intervention was stratified according to three levels of immediate AKI risk: low, moderate, and high. After intervention, postoperative changes in the glomerular filtration rate (eGFR) were identified with a tracking software that included an alert for nephrology consultation if the eGFR had declined by >25% from the preoperative reference value. Primary outcome was early AKI recovery, i.e., the complete reversal of any AKI stage to absence of AKI within the first 7 postoperative days. Results: Protocol implementation significantly increased the recovery of AKI (36/46, 78% compared to control 27/48, 56%, (p = 0.025)) and reduced the length of the ICU stay (p < 0.001). There was no significant difference in the overall incidence of all AKI and moderate and severe AKI in the first 7 postoperative days: 46/143 (32%) and 12/151 (8%) in the protocol implementation group compared to 48/151 (32%) and 18/151 (12%) in the historical control group. Patients with AKI reversal within the first 7 postoperative days had lower in-hospital mortality than patients without AKI reversal. Conclusions: Implementing a combined electronic alert and biomarker-guided kidney-protection strategy in routine care improved early recovery of AKI after major surgery

Genetic Determinants of Circulating Sphingolipid Concentrations in European Populations

Sphingolipids have essential roles as structural components of cell membranes and in cell signalling, and disruption of their metabolism causes several diseases, with diverse neurological, psychiatric, and metabolic consequences. Increasingly, variants within a few of the genes that encode enzymes involved in sphingolipid metabolism are being associated with complex disease phenotypes. Direct experimental evidence supports a role of specific sphingolipid species in several common complex chronic disease processes including atherosclerotic plaque formation, myocardial infarction (MI), cardiomyopathy, pancreatic beta-cell failure, insulin resistance, and type 2 diabetes mellitus. Therefore, sphingolipids represent novel and important intermediate phenotypes for genetic analysis, yet little is known about the major genetic variants that influence their circulating levels in the general population. We performed a genome-wide association study (GWAS) between 318,237 single-nucleotide polymorphisms (SNPs) and levels of circulating sphingomyelin (SM), dihydrosphingomyelin (Dih-SM), ceramide (Cer), and glucosylceramide (GluCer) single lipid species (33 traits); and 43 matched metabolite ratios measured in 4,400 subjects from five diverse European populations. Associated variants (32) in five genomic regions were identified with genome-wide significant corrected p-values ranging down to 9.08 x 10(-66). The strongest associations were observed in or near 7 genes functionally involved in ceramide biosynthesis and trafficking: SPTLC3, LASS4, SGPP1, ATP10D, and FADS1-3. Variants in 3 loci (ATP10D, FADS3, and SPTLC3) associate with MI in a series of three German MI studies. An additional 70 variants across 23 candidate genes involved in sphingolipid-metabolizing pathways also demonstrate association (p = 10(-4) or less). Circulating concentrations of several key components in sphingolipid metabolism are thus under strong genetic control, and variants in these loci can be tested for a role in the development of common cardiovascular, metabolic, neurological, and psychiatric diseases

Modeling of Environmental Effects in Genome-Wide Association Studies Identifies SLC2A2 and HP as Novel Loci Influencing Serum Cholesterol Levels

Genome-wide association studies (GWAS) have identified 38 larger genetic regions affecting classical blood lipid levels without adjusting for important environmental influences. We modeled diet and physical activity in a GWAS in order to identify novel loci affecting total cholesterol, LDL cholesterol, HDL cholesterol, and triglyceride levels. The Swedish (SE) EUROSPAN cohort (NSE = 656) was screened for candidate genes and the non-Swedish (NS) EUROSPAN cohorts (NNS = 3,282) were used for replication. In total, 3 SNPs were associated in the Swedish sample and were replicated in the non-Swedish cohorts. While SNP rs1532624 was a replication of the previously published association between CETP and HDL cholesterol, the other two were novel findings. For the latter SNPs, the p-value for association was substantially improved by inclusion of environmental covariates: SNP rs5400 (pSE,unadjusted = 3.6×10−5, pSE,adjusted = 2.2×10−6, pNS,unadjusted = 0.047) in the SLC2A2 (Glucose transporter type 2) and rs2000999 (pSE,unadjusted = 1.1×10−3, pSE,adjusted = 3.8×10−4, pNS,unadjusted = 0.035) in the HP gene (Haptoglobin-related protein precursor). Both showed evidence of association with total cholesterol. These results demonstrate that inclusion of important environmental factors in the analysis model can reveal new genetic susceptibility loci

Genomewide meta-analysis identifies loci associated with IGF-I and IGFBP-3 levels with impact on age-related traits

The growth hormone/insulin-like growth factor (IGF) axis can be manipulated in animal models to promote longevity, and IGF-related proteins including IGF-I and IGF-binding protein-3 (IGFBP-3) have also been implicated in risk of human diseases including cardiovascular diseases, diabetes, and cancer. Throug

A meta-analysis of genome-wide data from five European isolates reveals an association of COL22A1, SYT1, and GABRR2 with serum creatinine level

<p>Abstract</p> <p>Background</p> <p>Serum creatinine (S_CR) is the most important biomarker for a quick and non-invasive assessment of kidney function in population-based surveys. A substantial proportion of the inter-individual variability in S_CRlevel is explicable by genetic factors.</p> <p>Methods</p> <p>We performed a meta-analysis of genome-wide association studies of S_CRundertaken in five population isolates ('discovery cohorts'), all of which are part of the European Special Population Network (EUROSPAN) project. Genes showing the strongest evidence for an association with S_CR(candidate loci) were replicated in two additional population-based samples ('replication cohorts').</p> <p>Results</p> <p>After the discovery meta-analysis, 29 loci were selected for replication. Association between S_CRlevel and polymorphisms in the collagen type XXII alpha 1 (<it>COL22A1</it>) gene, on chromosome 8, and in the synaptotagmin-1 (<it>SYT1</it>) gene, on chromosome 12, were successfully replicated in the replication cohorts (p value = 1.0 × 10^-6and 1.7 × 10^-4, respectively). Evidence of association was also found for polymorphisms in a locus including the gamma-aminobutyric acid receptor rho-2 (<it>GABRR2</it>) gene and the ubiquitin-conjugating enzyme E2-J1 (<it>UBE2J1</it>) gene (replication p value = 3.6 × 10^-3). Previously reported findings, associating glomerular filtration rate with SNPs in the uromodulin (<it>UMOD</it>) gene and in the schroom family member 3 (<it>SCHROOM3</it>) gene were also replicated.</p> <p>Conclusions</p> <p>While confirming earlier results, our study provides new insights in the understanding of the genetic basis of serum creatinine regulatory processes. In particular, the association with the genes <it>SYT1 </it>and <it>GABRR2 </it>corroborate previous findings that highlighted a possible role of the neurotransmitters GABA_Areceptors in the regulation of the glomerular basement membrane and a possible interaction between GABA_Areceptors and synaptotagmin-I at the podocyte level.</p