Monotone graph limits and quasimonotone graphs

The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences $(G_n)$ of graphs in terms of a limiting object which may be represented by a symmetric function $W$ on $[0,1]$, i.e., a kernel or graphon. In this context it is natural to wish to relate specific properties of the sequence to specific properties of the kernel. Here we show that the kernel is monotone (i.e., increasing in both variables) if and only if the sequence satisfies a `quasi-monotonicity' property defined by a certain functional tending to zero. As a tool we prove an inequality relating the cut and $L^1$ norms of kernels of the form $W_1-W_2$ with $W_1$ and $W_2$ monotone that may be of interest in its own right; no such inequality holds for general kernels.Comment: 38 page

Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience

Hierarchical organisation is a common feature of many directed networks arising in nature and technology. For example, a well-defined message-passing framework based on managerial status typically exists in a business organisation. However, in many real-world networks such patterns of hierarchy are unlikely to be quite so transparent. Due to the nature in which empirical data is collated the nodes will often be ordered so as to obscure any underlying structure. In addition, the possibility of even a small number of links violating any overall “chain of command” makes the determination of such structures extremely challenging. Here we address the issue of how to reorder a directed network in order to reveal this type of hierarchy. In doing so we also look at the task of quantifying the level of hierarchy, given a particular node ordering. We look at a variety of approaches. Using ideas from the graph Laplacian literature, we show that a relevant discrete optimization problem leads to a natural hierarchical node ranking. We also show that this ranking arises via a maximum likelihood problem associated with a new range-dependent hierarchical random graph model. This random graph insight allows us to compute a likelihood ratio that quantifies the overall tendency for a given network to be hierarchical. We also develop a generalization of this node ordering algorithm based on the combinatorics of directed walks. In passing, we note that Google’s PageRank algorithm tackles a closely related problem, and may also be motivated from a combinatoric, walk-counting viewpoint. We illustrate the performance of the resulting algorithms on synthetic network data, and on a real-world network from neuroscience where results may be validated biologically

Exome chip analyses identify genes affecting mortality after HLA-matched unrelated-donor blood and marrow transplantation

© 2018 by The American Society of Hematology Although survival outcomes have significantly improved, up to 40% of patients die within 1 year of HLA-matched unrelated-donor blood and marrow transplantation (BMT). To identify non-HLA genetic contributors to mortality after BMT, we performed the first exome-wide association study in the DISCOVeRY-BMT cohorts using the Illumina HumanExome BeadChip. This study includes 2473 patients with acute myeloid leukemia, acute lymphoblastic leukemia, or myelodysplastic syndrome and 2221 10/10 HLA-matched donors treated from 2000 to 2011. Single-variant and gene-level analyses were performed on overall survival (OS), transplantation-related mortality (TRM), and disease-related mortality (DRM). Genotype mismatches between recipients and donors in a rare nonsynonymous variant of testis-expressed gene TEX38 significantly increased risk of TRM, which was more dramatic when either the recipient or donor was female. Using the SKAT-O test to evaluate gene-level effects, variant genotypes of OR51D1 in recipients were significantly associated with OS and TRM. In donors, 4 (ALPP, EMID1, SLC44A5, LRP1), 1 (HHAT), and 2 genes (LYZL4, NT5E) were significantly associated with OS, TRM, and DRM, respectively. Inspection of NT5E crystal structures showed 4 of the associated variants affected the enzyme structure and likely decreased the catalytic efficiency of the enzyme. Further confirmation of these findings and additional functional studies may provide individualized risk prediction and prognosis, as well as alternative donor selection strategies

Legacy benefits of blood pressure treatment on cardiovascular events are primarily mediated by improved blood pressure variability: the ASCOT trial.

BACKGROUND AND AIMS: Visit-to-visit systolic blood pressure variability (BPV) is an important predictor of cardiovascular (CV) outcomes. The long-term effect of a period of blood pressure (BP) control, but with differential BPV, is uncertain. Morbidity and mortality follow-up of UK participants in the Anglo-Scandinavian Cardiac Outcomes Trial-Blood Pressure-Lowering Arm has been extended for up to 21 years to determine the CV impact of mean systolic blood pressure (SBP) control and BPV during the trial, and amongst those allocated to amlodipine- and atenolol-based treatment. METHODS: Eight thousand five hundred and eighty hypertensive participants (4305 assigned to amlodipine ± perindopril-based and 4275 to atenolol ± diuretic-based treatment during the in-trial period (median 5.5 years) were followed for up to 21 years (median 17.4 years), using linked hospital and mortality records. A subgroup of participants (n = 2156) was followed up 6 years after the trial closure with a self-administered questionnaire and a clinic visit. In-trial mean SBP and standard deviation of visit-to-visit SBP as a measure of BPV, were measured using >100 000 BP measurements. Cox proportional hazard models were used to estimate the risk [hazard ratios (HRs)], associated with (i) mean with SBP and BPV during the in-trial period, for the CV endpoints occurring after the end of the trial and (ii) randomly assigned treatment to events following randomization, for the first occurrence of pre-specified CV outcomes. RESULTS: Using BP data from the in-trial period, in the post-trial period, although mean SBP was a predictor of CV outcomes {HR per 10 mmHg, 1.14 [95% confidence interval (CI) 1.10-1.17], P < .001}, systolic BPV independent of mean SBP was a strong predictor of CV events [HR per 5 mmHg 1.22 (95% CI 1.18-1.26), P < .001] and predicted events even in participants with well-controlled BP. During 21-year follow-up, those on amlodipine-based compared with atenolol-based in-trial treatment had significantly reduced risk of stroke [HR 0.82 (95% CI 0.72-0.93), P = .003], total CV events [HR 0.93 (95% CI 0.88-0.98), P = .008], total coronary events [HR 0.92 (95% CI 0.86-0.99), P = .024], and atrial fibrillation [HR 0.91 (95% CI 0.83-0.99), P = .030], with weaker evidence of a difference in CV mortality [HR 0.91 (95% CI 0.82-1.01), P = .073]. There was no significant difference in the incidence of non-fatal myocardial infarction and fatal coronary heart disease, heart failure, and all-cause mortality. CONCLUSIONS: Systolic BPV is a strong predictor of CV outcome, even in those with controlled SBP. The long-term benefits of amlodipine-based treatment compared with atenolol-based treatment in reducing CV events appear to be primarily mediated by an effect on systolic BPV during the trial period

Predicting Risk of End-Stage Liver Disease in Antiretroviral-Treated HIV/Hepatitis C Virus-Coinfected Patients

Background. End-stage liver disease (ESLD) is an important cause of morbidity among HIV/hepatitis C virus (HCV)-coinfected patients. Quantifying the risk of this outcome over time could help determine which coinfected patients should be targeted for risk factor modification and HCV treatment. We evaluated demographic, clinical, and laboratory variables to predict risk of ESLD in HIV/HCV-coinfected patients receiving antiretroviral therapy (ART). Methods. We conducted a retrospective cohort study among 6,016 HIV/HCV-coinfected patients who received ART within the Veterans Health Administration between 1997 and 2010. The main outcome was incident ESLD, defined by hepatic decompensation, hepatocellular carcinoma, or liver-related death. Cox regression was used to develop prognostic models based on baseline demographic, clinical, and laboratory variables, including FIB-4 and aspartate aminotransferase-to-platelet ratio index, previously validated markers of hepatic fibrosis. Model performance was assessed by discrimination and decision curve analysis. Results. Among 6,016 HIV/HCV patients, 532 (8.8%) developed ESLD over a median of 6.6 years. A model comprising FIB-4 and race had modest discrimination for ESLD (c-statistic, 0.73) and higher net benefit than alternative strategies of treating no or all coinfected patients at relevant risk thresholds. For FIB-4 \u3e3.25, ESLD risk ranged from 7.9% at 1 year to 26.0% at 5 years among non-blacks and from 2.4% at 1 year to 14.0% at 5 years among blacks. Conclusions. Race and FIB-4 provided important predictive information on ESLD risk among HIV/HCV patients. Estimating risk of ESLD using these variables could help direct HCV treatment decisions among HIV/HCV-coinfected patients

Intravenous erythropoietin in patients with ST-segment elevation myocardial infarction - REVEAL: A randomized controlled trial

Context: Acute ST-segment elevation myocardial infarction (STEMI) is a leading cause of morbidity and mortality. In experimental models of MI, erythropoietin reduces infarct size and improves left ventricular (LV) function. Objective: To evaluate the safety and efficacy of a single intravenous bolus of epoetin alfa in patients with STEMI. Design, Setting, and Patients: A prospective, randomized, double-blind, placebo-controlled trial with a dose-escalation safety phase and a single dose (60 000 U of epoetin alfa) efficacy phase; the Reduction of Infarct Expansion and Ventricular Remodeling With Erythropoietin After Large Myocardial Infarction (REVEAL) trial was conducted at 28 US sites between October 2006 and February 2010, and included 222 patients with STEMI who underwent successful percutaneous coronary intervention (PCI) as a primary or rescue reperfusion strategy. Intervention: Participants were randomly assigned to treatment with intravenous epoetin alfa or matching saline placebo administered within 4 hours of reperfusion. Main Outcome Measure: Infarct size, expressed as percentage of LV mass, assessed by cardiac magnetic resonance (CMR) imaging performed 2 to 6 days after study medication administration (first CMR) and again 12±2 weeks later (second CMR). Results: In the efficacy cohort, the infarct size did not differ between groups on either the first CMR scan (n=136; 15.8% LV mass [95% confidence interval {CI}, 13.3-18.2% LV mass] for the epoetin alfa group vs 15.0% LV mass [95% CI, 12.6-17.3% LV mass] for the placebo group; P=.67) or on the second CMR scan (n=124; 10.6% LV mass [95% CI, 8.4-12.8% LV mass] vs 10.4% LV mass [95% CI, 8.5-12.3% LV mass], respectively; P=.89). In a prespecified analysis of patients aged 70 years or older (n=21), the mean infarct size within the first week (first CMR) was larger in the epoetin alfa group (19.9% LV mass; 95% CI, 14.0-25.7% LV mass) than in the placebo group (11.7% LV mass; 95% CI, 7.2-16.1% LV mass) (P=.03). In the safety cohort, of the 125 patients who received epoetin alfa, the composite outcome of death, MI, stroke, or stent thrombosis occurred in 5 (4.0%; 95% CI, 1.31%-9.09%) but in none of the 97 who received placebo (P=.04). Conclusions: In patients with STEMI who had successful reperfusion with primary or rescue PCI, a single intravenous bolus of epoetin alfa within 4 hours of PCI did not reduce infarct size and was associated with higher rates of adverse cardiovascular events. Subgroup analyses raised concerns about an increase in infarct size among older patients. Trial Registration: clinicaltrials.gov Identifier: NCT00378352. ©2011 American Medical Association. All rights reserved

Genome-wide mapping of IBD segments in an Ashkenazi PD cohort identifies associated haplotypes

The recent series of large genome-wide association studies in European and Japanese cohorts established that Parkinson disease (PD) has a substantial genetic component. To further investigate the genetic landscape of PD, we performed a genome-wide scan in the largest to date Ashkenazi Jewish cohort of 1130 Parkinson patients and 2611 pooled controls. Motivated by the reduced disease allele heterogeneity and a high degree of identical-by-descent (IBD) haplotype sharing in this founder population, we conducted a haplotype association study based on mapping of shared IBD segments. We observed significant haplotype association signals at three previously implicated Parkinson loci: LRRK2 (OR = 12.05, P = 1.23 x 10(-56)), MAPT (OR = 0.62, P = 1.78 x 10(-11)) and GBA (multiple distinct haplotypes, OR \u3e 8.28, P = 1.13 x 10(-11) and OR = 2.50, P = 1.22 x 10(-9)). In addition, we identified a novel association signal on chr2q14.3 coming from a rare haplotype (OR = 22.58, P = 1.21 x 10(-10)) and replicated it in a secondary cohort of 306 Ashkenazi PD cases and 2583 controls. Our results highlight the power of our haplotype association method, particularly useful in studies of founder populations, and reaffirm the benefits of studying complex diseases in Ashkenazi Jewish cohorts