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

Rischio sismico di Sistemi Urbani utilizzando l’analogia delle reti neuronali

L’obiettivo della ricerca è stata la messa a punto di un modello di rischio sismico per Sistemi Urbani con approccio multi-livello, utilizzando l’analogia con le reti neuronali, finalizzato sia ad una valutazione di confronto tra centri urbani, sulla base di indicatori di rischio, che ad una valutazione predittiva delle conseguenze di un evento sismico atteso. Lo studio dei Sistemi Urbani viene utilmente condotto per “livelli” di approfondimento del modello, con l’obiettivo di valutare dapprima sinteticamente (ad esempio attraverso le informazioni contenute in banche-dati esistenti) la propensione alla perdita di capacità di un numero elevato di centri urbani, da cui ricavare le situazioni di rischio più elevato, su cui occorra effettuare approfondimenti o stabilire priorità di ulteriori indagini (Livello 0). Qualora sia possibile effettuare studi di maggiore dettaglio sui centri urbani ad elevato rischio, si procederà con indagini e rilievi anche speditivi, valutando le perdite di capacità dei sistemi analizzati e rilevati, fino ad individuare parti dell’abitato a maggiore rischio (Livello 1). La ricerca è stata condotta nell’ambito del Task 5/7 del Progetto Reluis – Linea 10

Initial data for stationary space-times near space-like infinity

We study Cauchy initial data for asymptotically flat, stationary vacuum space-times near space-like infinity. The fall-off behavior of the intrinsic metric and the extrinsic curvature is characterized. We prove that they have an analytic expansion in powers of a radial coordinate. The coefficients of the expansion are analytic functions of the angles. This result allow us to fill a gap in the proof found in the literature of the statement that all asymptotically flat, vacuum stationary space-times admit an analytic compactification at null infinity. Stationary initial data are physical important and highly non-trivial examples of a large class of data with similar regularity properties at space-like infinity, namely, initial data for which the metric and the extrinsic curvature have asymptotic expansion in terms of powers of a radial coordinate. We isolate the property of the stationary data which is responsible for this kind of expansion.Comment: LaTeX 2e, no figures, 12 page

Inflammatory bowel disease, colorectal cancer and type 2 diabetes mellitus: The links.

The co-occurrence of the three disease entities, inflammatory bowel disease (IBD), colorectal cancer (CRC), type 2diabetes mellitus (T2DM) along with inflammation and dismicrobism has been frequently reported. Some authors have even suggested that dysbiosis could be the link through a molecular crosstalk of multiple inflammatory loops including TGFβ, NFKB, TNFα and ROS among others. This review focuses on the inflammatory process along with the role of microbiota in the pathophysiology of the three diseases. The etiology of IBD is multifactorial, and like CRC and T2DM, it is associated with a widespread and sustained GI inflammation and dismicrobism, whereby an array of pro-inflammatory mediators and other related biomolecules are up-regulated, both locally and systematically. Such a persistent or an inadequately resolved chronic inflammation may be a causative agent, in the presence other factors, leading to several pathologies such as IBD, CRC and T2DM. TGFβ plays a crucial role in pancreatic β cell malfunctioning as glucotoxicity stimulates its signaling cascade through smad 3, IL-6 and epithelial to mesenchymal transition. Such a cascade could lead to macrophages and other cells recruitment, inflammation, then IBD and CRC. NFkB is also another key regulator in the crosstalk among the pathways leading to the three disease entities. It plays a major role in linking inflammation to cancer development through its ability to up regulate several inflammatory and tumor promoting cytokines like: IL-6, IL-1 α and TNF α, as well as genes like BCL2 and BCLXL. It activates JAK/STAT signaling network via STAT3 transcription factors and promotes epithelial to mesenchymal transition. It also increases the risk for T2DM in obese people. In brief, NFKB is a matchmaker between inflammation, IBD, cancer and diabetes. In addition, TNFα plays a pivotal role in systemic inflammation. It is increased in the mucosa of IBD patients and has a central role in its pathogenesis. It also activates other signaling pathways like NFKB and MAPK leading to CRC. It is also overexpressed in the adipose tissues of obese patients thus linking it to T2DM, chronic inflammation and consequently CRC. On the other hand, increasing evidence suggests that dysbiosis plays a role in initiating, maintaining and determining the severity of IBD. Actually, among its functions, it modulates genotoxic metabolites which are able to induce CRC, a fact proven to be sustained by stool transfer from patients with CRC. Probiotics, however, may actively prevent CRC as well as IBD and results in a significant decrease in fasting glycemia in T2DM patients. In conclusion, IBD, CRC and T2DM are commonly occurring interrelated clinical problems. They share a common basis influenced by an inflammatory process, an imbalance in intestinal microbiota, and a crosstalk between various signaling pathways. Would probiotics interrupt the crosstalk or orient it in the physiological direction

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

Systematic review and literature appraisal on methodology of conducting and reporting critical-care echocardiography studies: a report from the European Society of Intensive Care Medicine PRICES expert panel

© 2020, The Author(s). Background: The echocardiography working group of the European Society of Intensive Care Medicine recognized the need to provide structured guidance for future CCE research methodology and reporting based on a systematic appraisal of the current literature. Here is reported this systematic appraisal. Methods: We conducted a systematic review, registered on the Prospero database. A total of 43 items of common interest to all echocardiography studies were initially listed by the experts, and other “topic-specific” items were separated into five main categories of interest (left ventricular systolic function, LVSF n = 15, right ventricular function, RVF n = 18, left ventricular diastolic function, LVDF n = 15, fluid management, FM n = 7, and advanced echocardiography techniques, AET n = 17). We evaluated the percentage of items reported per study and the fraction of studies reporting a single item. Results: From January 2000 till December 2017 a total of 209 articles were included after systematic search and screening, 97 for LVSF, 48 for RVF, 51 for LVDF, 36 for FM and 24 for AET. Shock and ARDS were relatively common among LVSF articles (both around 15%) while ARDS comprised 25% of RVF articles. Transthoracic echocardiography was the main echocardiography mode, in 87% of the articles for AET topic, followed by 81% for FM, 78% for LVDF, 70% for LVSF and 63% for RVF. The percentage of items per study as well as the fraction of study reporting an item was low or very low, except for FM. As an illustration, the left ventricular size was only reported by 56% of studies in the LVSF topic, and half studies assessing RVF reported data on pulmonary artery systolic pressure. Conclusion: This analysis confirmed sub-optimal reporting of several items listed by an expert panel. The analysis will help the experts in the development of guidelines for CCE study design and reporting

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