Asympyotic behavior of Musielak-Orlicz-Sobolev modulars

In this article we study the asymptotic behavior of anisotropic nonlocal nonstandard growth seminorms and modulars as the fractional parameter goes to 1. This gives a so-called Bourgain-Brezis-Mironescu type formula for a very general family of functionals. In the particu\-lar case of fractional Sobolev spaces with variable exponent, we point out that our proof asks for a weaker regularity of the exponent than the considered in previous articles

Investigation on reconstruction methods applied to 3D terahertz computed tomography

International audience3D terahertz computed tomography has been performed using a monochromatic millimeter wave imaging system coupled with an infrared temperature sensor. Three different reconstruction methods (standard back-projection algorithm and two iterative analysis) have been compared in order to reconstruct large size 3D objects. The quality (intensity, contrast and geometric preservation) of reconstructed cross-sectional images has been discussed together with the optimization of the number of projections. Final demonstration to real-life 3D objects has been processed to illustrate the potential of the reconstruction methods for applied terahertz tomography

Mesoscale Equipartition of kinetic energy in Quantum Turbulence

The turbulence of superfluid helium is investigated numerically at finite temperature. Direct numerical simulations are performed with a "truncated HVBK" model, which combines the continuous description of the Hall-Vinen-Bekeravich-Khalatnikov equations with the additional constraint that this continuous description cannot extend beyond a quantum length scale associated with the mean spacing between individual superfluid vortices. A good agreement is found with experimental measurements of the vortex density. Besides, by varying the turbulence intensity only, it is observed that the inter-vortex spacing varies with the Reynolds number as $Re^{-3/4}$, like the viscous length scale in classical turbulence. In the high temperature limit, Kolmogorov's inertial cascade is recovered, as expected from previous numerical and experimental studies. As the temperature decreases, the inertial cascade remains present at large scales while, at small scales, the system evolves towards a statistical equipartition of kinetic energy among spectral modes, with a characteristic $k^2$ velocity spectrum. The accumulation of superfluid excitations on a range of mesoscales enables the superfluid to keep dissipating kinetic energy through mutual friction with the residual normal fluid, although the later becomes rare at low temperature. It is found that most of the superfluid vorticity can concentrate on these mesoscales at low temperature, while it is concentrated in the inertial range at higher temperature. This observation should have consequences on the interpretation of decaying turbulence experiments, which are often based on vortex line density measurements.Comment: 6 pages, 5 figure

Low penetrance in facioscapulohumeral muscular dystrophy type 1 with large pathological D4Z4 alleles: a cross-sectional multicenter study.

BackgroundFacioscapulohumeral muscular dystrophy type 1(FSHD1) is an autosomal dominant disorder associated with the contraction of D4Z4 less than 11 repeat units (RUs) on chromosome 4q35. Penetrance in the range of the largest alleles is poorly known. Our objective was to study the penetrance of FSHD1 in patients carrying alleles ranging between 6 to10 RUs and to evaluate the influence of sex, age, and several environmental factors on clinical expression of the disease. Methods A cross-sectional multicenter study was conducted in six French and one Swiss neuromuscular centers. 65 FSHD1 affected patients carrying a 4qA allele of 6¿10 RUs were identified as index cases (IC) and their 119 at-risk relatives were included. The age of onset was recorded for IC only. Medical history, neurological examination and manual muscle testing were performed for each subject. Genetic testing determined the allele size (number of RUs) and the 4qA/4qB allelic variant. The clinical status of relatives was established blindly to their genetic testing results. The main outcome was the penetrance defined as the ratio between the number of clinically affected carriers and the total number of carriers. Results Among the relatives, 59 carried the D4Z4 contraction. At the clinical level, 34 relatives carriers were clinically affected and 25 unaffected. Therefore, the calculated penetrance was 57% in the range of 6¿10 RUs. Penetrance was estimated at 62% in the range of 6¿8 RUs, and at 47% in the range of 9¿10 RUs. Moreover, penetrance was lower in women than men. There was no effect of drugs, anesthesia, surgery or traumatisms on the penetrance. Conclusions Penetrance of FSHD1 is low for largest alleles in the range of 9¿10 RUs, and lower in women than men. This is of crucial importance for genetic counseling and clinical management of patients and families

Response to COVID-19 in South Korea and implications for lifting stringent interventions

Background After experiencing a sharp growth in COVID-19 cases early in the pandemic, South Korea rapidly controlled transmission while implementing less stringent national social distancing measures than countries in Europe and the US. This has led to substantial interest in their “test, trace, isolate” strategy. However, it is important to understand the epidemiological peculiarities of South Korea’s outbreak and characterise their response before attempting to emulate these measures elsewhere. Methods We systematically extracted numbers of suspected cases tested, PCR-confirmed cases, deaths, isolated confirmed cases, and numbers of confirmed cases with an identified epidemiological link from publicly available data. We estimated the time-varying reproduction number, Rt, using an established Bayesian framework, and reviewed the package of interventions implemented by South Korea using our extracted data, plus published literature and government sources. Results We estimated that after the initial rapid growth in cases, Rt dropped below one in early April before increasing to a maximum of 1.94 (95%CrI; 1.64-2.27) in May following outbreaks in Seoul Metropolitan Region. By mid-June Rt was back below one where it remained until the end of our study (July 13th). Despite less stringent “lockdown” measures, strong social distancing measures were implemented in high incidence areas and studies measured a considerable national decrease in movement in late-February. Testing capacity was swiftly increased, and protocols were in place to isolate suspected and confirmed cases quickly however we could not estimate the delay to isolation using our data. Accounting for just 10% of cases, individual case-based contact-tracing picked up a relatively minor proportion of total cases, with cluster investigations accounting for 66%. Conclusions Whilst early adoption of testing and contact-tracing are likely to be important for South Korea’s successful outbreak control, other factors including regional implementation of strong social distancing measures likely also contributed. The high volume of testing and low number of deaths suggests that South Korea experienced a small epidemic relative to other countries. Caution is needed in attempting to replicate the South Korean response in populations with larger more geographically widespread epidemics where finding, testing and isolating cases that are linked to clusters may be more difficult

Report 26: Reduction in mobility and COVID-19 transmission

In response to the COVID-19 pandemic, countries have sought to control transmission of SARS-CoV-2 by restricting population movement through social distancing interventions, reducing the number of contacts. Mobility data represent an important proxy measure of social distancing. Here, we develop a framework to infer the relationship between mobility and the key measure of population-level disease transmission, the reproduction number (R). The framework is applied to 53 countries with sustained SARS-CoV-2 transmission based on two distinct country-specific automated measures of human mobility, Apple and Google mobility data. For both datasets, the relationship between mobility and transmission was consistent within and across countries and explained more than 85% of the variance in the observed variation in transmissibility. We quantified country-specific mobility thresholds defined as the reduction in mobility necessary to expect a decline in new infections (R<1). While social contacts were sufficiently reduced in France, Spain and the United Kingdom to control COVID-19 as of the 10th of May, we find that enhanced control measures are still warranted for the majority of countries. We found encouraging early evidence of some decoupling of transmission and mobility in 10 countries, a key indicator of successful easing of social-distancing restrictions. Easing social-distancing restrictions should be considered very carefully, as small increases in contact rates are likely to risk resurgence even where COVID-19 is apparently under control. Overall, strong population-wide social-distancing measures are effective to control COVID-19; however gradual easing of restrictions must be accompanied by alternative interventions, such as efficient contacttracing, to ensure control