Cliques in rank-1 random graphs: the role of inhomogeneity

We study the asymptotic behavior of the clique number in rank-1 inhomogeneous random graphs, where edge probabilities between vertices are roughly proportional to the product of their vertex weights. We show that the clique number is concentrated on at most two consecutive integers, for which we provide an expression. Interestingly, the order of the clique number is primarily determined by the overall edge density, with the inhomogeneity only affecting multiplicative constants or adding at most a $\log\log(n)$ multiplicative factor. For sparse enough graphs the clique number is always bounded and the effect of inhomogeneity completely vanishes.Comment: 29 page

Thermal Perception of Ventilation Changes in Full-Face Motorcycle Helmets: Subject and Manikin Study

We report the effects of full-face motorcycle helmet ventilation systems on heat, airflow, noise, and comfort perception for ventilation changes on the scalp. Eight subjects (aged 28.0 ± 5.4 years) underwent two experimental trials at ambient temperatures of 23.7 ± 0.4°C or 27.5 ± 0.3°C. In each trial, the thermally equilibrated subjects underwent two examination phases, during which four different helmets were assessed at wind speeds of 39.2 ± 1.9 km h−1 and 59.3 ± 1.4 km h−1. Vent-induced heat loss in the scalp ranged from −6.1 to 6.1 W, corresponding to vents being closed or opened, respectively. Perception of vent-induced changes was assessed immediately after the change. We find that the vent-induced heat loss, the subject, and the helmet are the most important response factors. In addition, comparison of two helmets with similar vent-induced heat loss suggests that internal airflow patterns may be important in explaining the observed perception difference

The Effect of Two Sock Fabrics on Perception and Physiological Parameters Associated with Blister Incidence: A Field Study

The goal of the present study was to investigate differences in perception and skin hydration at the foot of two sock fabrics with distinct moisture properties in a realistic military setting. Thirty-seven military recruits wore two different socks (PP: 99.6% polypropylene and 0.4% elastane, and BLEND: 50% Merino-wool, 33% polypropylene, and 17% polyamide), one on each foot. Measurements were carried out after a daily 6.5-km march on 4 days. Each participant rated temperature, dampness, friction, and comfort for each foot. On a daily selection of participants, skin hydration was measured on three sites of both feet using a corneometer, and moisture content of the socks was determined. BLEND was rated to be cooler, less damp, and more comfortable (P < 0.05). Two out of three skin sites were drier for BLEND than PP (P < 0.05). Moreover, BLEND stored 2.9 ± 0.3 times more moisture compared to PP. Thus, under the present conditions, socks such as BLEND are to be preferred over polypropylene sock

Detecting a planted community in an inhomogeneous random graph

We study the problem of detecting whether an inhomogeneous random graph contains a planted community. Specifically, we observe a single realization of a graph. Under the null hypothesis, this graph is a sample from an inhomogeneous random graph, whereas under the alternative, there exists a small subgraph where the edge probabilities are increased by a multiplicative scaling factor. We present a scan test that is able to detect the presence of such a planted community, even when this community is very small and the underlying graph is inhomogeneous. We also derive an information theoretic lower bound for this problem which shows that in some regimes the scan test is almost asymptotically optimal. We illustrate our results through examples and numerical experiments.Comment: 44 page

The Effect of Two Sock Fabrics on Physiological Parameters Associated with Blister Incidence: A Laboratory Study

The goal of the present study was to investigate physiological effects, mainly at the level of the foot, of two sock fabrics with distinct moisture properties. Twelve participants wore two different socks, one on each foot. The following two sock types were used: PP: 99.6% polypropylene and 0.4% elastane and BLEND: 50% Merino wool, 33% polypropylene, and 17% polyamide. The participants walked three times on a treadmill at 5 km h−1, with no gradient for the first and third phase and a 10% upward inclination for the second walking phase. The microclimate temperature between the boot and foot was measured during walking. Preceding and following the walking phases, additional measurements were carried out at the level of the foot, i.e. skin temperature and skin hydration on three locations and skin friction between the posterior surface of the calcaneus and a glass plate. In addition, the moisture absorption of boots and socks was determined. Differences between the sock fabrics were found for weight gain and microclimate temperature: (i) PP tended to hold less water compared to BLEND, (ii) the boot's microclimate temperature resulted in larger values for BLEND measured at the dorsal surface at the level of the third metatarsal, and (iii) warmer microclimates of the boot were measured for PP compared to BLEND at the distal anterior end of the tibia. The established differences in moisture behavior of both socks did not result in detectable differences in parameters measured on the skin of the foo

Aortic valve repair in neonates, infants and children:a systematic review, meta-analysis and microsimulation study

OBJECTIVES: To support clinical decision-making in children with aortic valve disease, by compiling the available evidence on outcome after paediatric aortic valve repair (AVr). METHODS: A systematic review of literature reporting clinical outcome after paediatric AVr (mean age at surgery &lt;18 years) published between 1 January 1990 and 23 December 2021 was conducted. Early event risks, late event rates and time-to-event data were pooled. A microsimulation model was employed to simulate the lives of individual children, infants and neonates following AVr. RESULTS: Forty-one publications were included, encompassing 2 623 patients with 17 217 patient-years of follow-up (median follow-up: 7.3 years; range: 1.0-14.4 years). Pooled mean age during repair for aortic stenosis in children (&lt;18 years), infants (&lt;1 year) or neonates (&lt;30 days) was 5.2 ± 3.9 years, 35 ± 137 days and 11 ± 6 days, respectively. Pooled early mortality after stenosis repair in children, infants and neonates, respectively, was 3.5% (95% confidence interval: 1.9-6.5%), 7.4% (4.2-13.0%) and 10.7% (6.8-16.9%). Pooled late reintervention rate after stenosis repair in children, infants and neonates, respectively, was 3.31%/year (1.66-6.63%/year), 6.84%/year (3.95-11.83%/year) and 6.32%/year (3.04-13.15%/year); endocarditis 0.07%/year (0.03-0.21%/year), 0.23%/year (0.07-0.71%/year) and 0.49%/year (0.18-1.29%/year); and valve thrombosis 0.05%/year (0.01-0.26%/year), 0.15%/year (0.04-0.53%/year) and 0.19%/year (0.05-0.77%/year). Microsimulation-based mean life expectancy in the first 20 years for children, infants and neonates with aortic stenosis, respectively, was 18.4 years (95% credible interval: 18.1-18.7 years; relative survival compared to the matched general population: 92.2%), 16.8 years (16.5-17.0 years; relative survival: 84.2%) and 15.9 years (14.8-17.0 years; relative survival: 80.1%). Microsimulation-based 20-year risk of reintervention in children, infants and neonates, respectively, was 75.2% (72.9-77.2%), 53.8% (51.9-55.7%) and 50.8% (47.0-57.6%). CONCLUSIONS: Long-term outcomes after paediatric AVr for stenosis are satisfactory and dependent on age at surgery. Despite a high hazard of reintervention for valve dysfunction and slightly impaired survival relative to the general population, AVr is associated with low valve-related event occurrences and should be considered in children with aortic valve disease.</p