On the optimality of gluing over scales

We show that for every $\alpha > 0$, there exist $n$-point metric spaces (X,d) where every "scale" admits a Euclidean embedding with distortion at most $\alpha$, but the whole space requires distortion at least $\Omega(\sqrt{\alpha \log n})$. This shows that the scale-gluing lemma [Lee, SODA 2005] is tight, and disproves a conjecture stated there. This matching upper bound was known to be tight at both endpoints, i.e. when $\alpha = \Theta(1)$ and $\alpha = \Theta(\log n)$, but nowhere in between. More specifically, we exhibit $n$-point spaces with doubling constant $\lambda$ requiring Euclidean distortion $\Omega(\sqrt{\log \lambda \log n})$, which also shows that the technique of "measured descent" [Krauthgamer, et. al., Geometric and Functional Analysis] is optimal. We extend this to obtain a similar tight result for $L_p$ spaces with $p > 1$.Comment: minor revision

Discovery of biomarkers for glycaemic deterioration before and after the onset of type 2 diabetes: rationale and design of the epidemiological studies within the IMI DIRECT Consortium

Aims/hypothesis The DIRECT (Diabetes Research on Patient Stratification) Study is part of a European Union Framework 7 Innovative Medicines Initiative project, a joint undertaking between four industry and 21 academic partners throughout Europe. The Consortium aims to discover and validate biomarkers that: (1) predict the rate of glycaemic deterioration before and after type 2 diabetes onset; (2) predict the response to diabetes therapies; and (3) help stratify type 2 diabetes into clearly definable disease subclasses that can be treated more effectively than without stratification. This paper describes two new prospective cohort studies conducted as part of DIRECT. Methods Prediabetic participants (target sample size 2,200-2,700) and patients with newly diagnosed type 2 diabetes (target sample size similar to 1,000) are undergoing detailed metabolic phenotyping at baseline and 18 months and 36 months later. Abdominal, pancreatic and liver fat is assessed using MRI. Insulin secretion and action are assessed using frequently sampled OGTTs in non-diabetic participants, and frequently sampled mixed-meal tolerance tests in patients with type 2 diabetes. Biosamples include venous blood, faeces, urine and nail clippings, which, among other biochemical analyses, will be characterised at genetic, transcriptomic, metabolomic, proteomic and metagenomic levels. Lifestyle is assessed using high-resolution triaxial accelerometry, 24 h diet record, and food habit questionnaires. Conclusinos/interpretation DIRECT will yield an unprecedented array of biomaterials and data. This resource, available through managed access to scientists within and outside the Consortium, will facilitate the development of new treatments and therapeutic strategies for the prevention and management of type 2 diabetes

Clinical profiles of post-load glucose subgroups and their association with glycaemic traits over time: an IMI-DIRECT study

Aim To examine the hypothesis that, based on their glucose curves during a seven-point oral glucose tolerance test, people at elevated type 2 diabetes risk can be divided into subgroups with different clinical profiles at baseline and different degrees of subsequent glycaemic deterioration.Methods We included 2126 participants at elevated type 2 diabetes risk from the Diabetes Research on Patient Stratification (IMI-DIRECT) study. Latent class trajectory analysis was used to identify subgroups from a seven-point oral glucose tolerance test at baseline and follow-up. Linear models quantified the associations between the subgroups with glycaemic traits at baseline and 18 months.Results At baseline, we identified four glucose curve subgroups, labelled in order of increasing peak levels as 1-4. Participants in Subgroups 2-4, were more likely to have higher insulin resistance (homeostatic model assessment) and a lower Matsuda index, than those in Subgroup 1. Overall, participants in Subgroups 3 and 4, had higher glycaemic trait values, with the exception of the Matsuda and insulinogenic indices. At 18 months, change in homeostatic model assessment of insulin resistance was higher in Subgroup 4 (beta = 0.36, 95% CI 0.13-0.58), Subgroup 3 (beta = 0.30; 95% CI 0.10-0.50) and Subgroup 2 (beta = 0.18; 95% CI 0.04-0.32), compared to Subgroup 1. The same was observed for C-peptide and insulin. Five subgroups were identified at follow-up, and the majority of participants remained in the same subgroup or progressed to higher peak subgroups after 18 months.Conclusions Using data from a frequently sampled oral glucose tolerance test, glucose curve patterns associated with different clinical characteristics and different rates of subsequent glycaemic deterioration can be identified.Molecular Epidemiolog

The role of physical activity in metabolic homeostasis before and after the onset of type 2 diabetes: an IMI DIRECT study.

AIMS/HYPOTHESIS: It is well established that physical activity, abdominal ectopic fat and glycaemic regulation are related but the underlying structure of these relationships is unclear. The previously proposed twin-cycle hypothesis (TC) provides a mechanistic basis for impairment in glycaemic control through the interactions of substrate availability, substrate metabolism and abdominal ectopic fat accumulation. Here, we hypothesise that the effect of physical activity in glucose regulation is mediated by the twin-cycle. We aimed to examine this notion in the Innovative Medicines Initiative Diabetes Research on Patient Stratification (IMI DIRECT) Consortium cohorts comprised of participants with normal or impaired glucose regulation (cohort 1: N ≤ 920) or with recently diagnosed type 2 diabetes (cohort 2: N ≤ 435). METHODS: We defined a structural equation model that describes the TC and fitted this within the IMI DIRECT dataset. A second model, twin-cycle plus physical activity (TC-PA), to assess the extent to which the effects of physical activity in glycaemic regulation are mediated by components in the twin-cycle, was also fitted. Beta cell function, insulin sensitivity and glycaemic control were modelled from frequently sampled 75 g OGTTs (fsOGTTs) and mixed-meal tolerance tests (MMTTs) in participants without and with diabetes, respectively. Abdominal fat distribution was assessed using MRI, and physical activity through wrist-worn triaxial accelerometry. Results are presented as standardised beta coefficients, SE and p values, respectively. RESULTS: The TC and TC-PA models showed better fit than null models (TC: χ2 = 242, p = 0.004 and χ2 = 63, p = 0.001 in cohort 1 and 2, respectively; TC-PA: χ2 = 180, p = 0.041 and χ2 = 60, p = 0.008 in cohort 1 and 2, respectively). The association of physical activity with glycaemic control was primarily mediated by variables in the liver fat cycle. CONCLUSIONS/INTERPRETATION: These analyses partially support the mechanisms proposed in the twin-cycle model and highlight mechanistic pathways through which insulin sensitivity and liver fat mediate the association between physical activity and glycaemic control.S.Bra. was funded by the UK Medical Research Council [MC_UU_12015/3]

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

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele