inflexion point
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Author(s):  
P.L. de Andres ◽  
L. de Andres-Bragado ◽  
L. Hoessly

The COVID-19 pandemic has had worldwide devastating effects on human lives, highlighting the need for tools to predict its development. The dynamics of such public-health threats can often be efficiently analyzed through simple models that help to make quantitative timely policy decisions. We benchmark a minimal version of a Susceptible-Infected-Removed model for infectious diseases (SIR) coupled with a simple least-squares Statistical Heuristic Regression (SHR) based on a lognormal distribution. We derive the three free parameters for both models in several cases and test them against the amount of data needed to bring accuracy in predictions. The SHR model is ≈±2% accurate about 20 days past the second inflexion point in the daily curve of cases, while the SIR model reaches a similar accuracy a fortnight before. All the analyzed cases assert the utility of SHR and SIR approximants as a valuable tool to forecast the disease’s evolution. Finally, we have studied simulated stochastic individual-based SIR dynamics, which yields a detailed spatial and temporal view of the disease that cannot be given by SIR or SHR methods.


2021 ◽  
Vol 4 (2) ◽  
pp. 25-43

The article addresses the issue of standards of proof from a comparative perspective. The author sketches the conventional distinction between common law and civil law countries in this regard, as well as some approaches that query the validity of the rigid division. The main purpose of the article is to characterise the Ukrainian approach to the standards of proof against the background of comparative analysis. The author concludes that recent developments in Ukrainian law have paved the way for a distinction between criminal and civil standards of proof. However, the doctrine is not yet elaborate enough to warrant a coherent application of the two different standards. There is a view that in civil law countries, not much attention is paid to the standard of proof. We would rather not take the liberty of generalising about all civil law countries, but with regard to Ukrainian doctrine, the assertion seems rather justified. However, some recent developments in procedural legislation give reasons to believe that the approach is being gradually changed. The disregard of the issue, underpinned by the sacred belief in the attainability of absolute truth, fades in comparison to the acknowledgement that standards of proof may differ in civil (commercial) and criminal cases. It is this inflexion point in Ukrainian evidence law that may entail far-reaching repercussions. Therefore, open discussion of the issue is needed to elaborate a doctrinal approach that could serve as a basis for the development of a coherent jurisprudence.


2021 ◽  
Author(s):  
Gregory Kozyreff

A simple and explicit expression of the solution of the SIR epidemiological model of Kermack and McKendrick is constructed in the asymptotic limit of large basic reproduction numbers $\ro$. The proposed formula yields good qualitative agreement already when $\ro\geq3$ and rapidly becomes quantitatively accurate as larger values of $\ro$ are assumed. The derivation is based on the method of matched asymptotic expansions, which exploits the fact that the exponential growing phase and the eventual recession of the outbreak occur on distinct time scales. From the newly derived solution, an analytical estimate of the time separating the first inflexion point of the epidemic curve from the peak of infections is given.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yang Li ◽  
Jianmin Sun ◽  
Guodong Wang

AbstractThe retrospective study aimed to investigate the relationship between lumbar lordosis morphology, pelvic incidence and paraspinal muscle. It enrolled asymptomatic adult volunteers aged between 18 and 45 years old. Lumbar lordosis morphology, consisting of total lumbar lordosis (LL), proximal lumbar lordosis (PLL), distal lumbar lordosis (DLL), lumbar lordosis apex (LLA) and inflexion point, was evaluated, as well as pelvic incidence (PI) and muscularity of erector spinae (ES) and multifidus. Pearson correlation was performed to analyze the relationship between each other parameter. Cases were stratified according to pelvic incidence (very low < 30°, low 30°–45°, moderate 45°–60°, and high > 60°), comparison between groups was performed by univariance analysis. 87 asymptomatic adult volunteers (33 females and 54 males) were included in the study. PLL revealed a correlation with LLA (r = 0.603, p = 0.002) and inflexion point (r = 0.536, p = 0.004), but did not DLL with LL apex (r = 0.204, p = 0.058) or inflexion point (r = 0.210, p = 0.051). PI revealed a greater correlation with PLL (r = −0.673, p < 0.001) than with DLL (r = −0.237, p = 0.045). Linear stepwise regression analysis also exhibited the correlation between PI and PLL (R2 = 0.452, PLL = 16.2–0.61 * PI, p < 0.001). ES muscularity correlated with LL apex (r = −0.279, p = 0.014) and inflexion point (r = −0.227, p = 0.047). Stratification by PI demonstrated PLL increased across groups (p < 0.001), but DLL was comparable between low and moderate PI group (p = 0.329). Lumbar lordosis morphology appears to accommodate to pelvic incidence and erector spinae muscularity. Proximal lumbar lordosis has a bigger correlation with pelvic incidence than the distal lumbar lordosis. The results are helpful for restoring a rational lumbar lordosis shape in long fusion surgery.


2020 ◽  
Vol 12 (18) ◽  
pp. 3105
Author(s):  
Nicolas Lamquin ◽  
Ludovic Bourg ◽  
Sébastien Clerc ◽  
Craig Donlon

This study is a follow-up of a full methodology for the homogenisation and harmonisation of the two Ocean and Land Colour Instrument (OLCI) payloads based on the OLCI-A/OLCI-B tandem phase analysis. This analysis provided cross-calibration factors between the two instruments with a very high precision, providing a ‘truth’ from the direct comparison of simultaneous and collocated acquisitions. The long-term monitoring of such cross-calibration is a prerequisite for an operational application of sensors harmonisation along the mission lifetime, no other tandem phase between OLCI-A and OLCI-B being foreseen due to the cost of such operation. This article presents a novel approach for the monitoring of the OLCI radiometry based on statistics of Deep Convective Clouds (DCC) observations, especially dedicated to accurately monitor the full across-track dependency of the cross-calibration of OLCI-A and OLCI-B. Specifically, the inflexion point of DCC reflectance distributions is used as an indicator of the absolute calibration for each subdivision of the OLCI Field-of-View. This inflexion point is shown to provide better precision than the mode of the distributions which is commonly used in the community. Excess of saturation in OLCI-A high radiances is handled through the analysis of interband relationships between impacted channels and reference channels that are not impacted by saturation. Such analysis also provides efficient insights on the variability of the target’s response as well as on the evolution of the interband calibration of each payload. First, cross-calibration factors obtained over the tandem period allows to develop and validate the approach, notably for the handling of the saturated pixels, based on the comparison with the ‘truth’ obtained from the tandem analysis. Factors obtained out of (and far from) the tandem period then provides evidence that the cross-calibration reported over the tandem period (1–2% bias between the instruments) as well as inter-camera calibration residuals persist with very similar proportions, to the exception of the 400 nm channel and with slightly less precision for the 1020 nm channel. For all OLCI channels, relative differences between the cross-calibration factors obtained from the tandem analysis and the factors obtained over the other period are below 1% from a monthly analysis, even below 0.5% from a multi-monthly analysis). This opens the way not only to an accurate long-term monitoring of the OLCI radiometry but also, and precisely targeted for this study, to the monitoring of the cross-calibration of the two sensors over the mission lifetime. It also provides complementary information to the tandem analysis as the calibration indicators are traced individually for each sensor across-track, confirming and quantifying inter-camera radiometric biases, independently for both sensors. Assumptions used in this study are discussed and validated, also providing a framework for the adaptation of the presented methodology to other optical sensors.


2020 ◽  
Author(s):  
Guodong Wang ◽  
Yang Li ◽  
Jianmin Sun

Abstract Background It is still blank on the relationship between lumbar lordosis morphology and paraspinal muscle in asymptomatic Asian adults. The study aims to investigate the relationships. Methods 87 asymptomatic adults aged between 18 and 45 years old were enrolled in the retrospective study. Lumbar lordosis morphology, consisting of total lumbar lordosis (LL), proximal lumbar lordosis (PLL), distal lumbar lordosis (DLL), lumbar lordosis apex (LLA) and inflexion point (IP), was evaluated, as well as pelvic incidence (PI) and muscularity of erector spinae (ES) and multifidus (MF). Pearson correlation was performed to analyze the relationship between each other parameter. Cases were stratified according to pelvic incidence (very low < 30°, low 30°-45°, moderate 45°-60°, and high > 60°), comparison between groups was performed by univariance analysis. Results PLL revealed a correlation with LLA (r = 0.603, p = 0.002) and inflexion point (r = 0.536, p = 0.004), but did not DLL with LL apex (r = 0.204, p = 0.058) or inflexion point (r = 0.210, p = 0.051). PI revealed a greater correlation with PLL (r=-0.673, p < 0.001) than with DLL (r=-0.237, p = 0.045). Linear stepwise regression analysis also exhibited the correlation between PI and PLL (R2 = 0.452, PLL = 16.2–0.61*PI, p < 0.001). ES muscularity correlated with LL apex (r=-0.279, p = 0.014) and inflexion point (r=-0.227, p = 0.047). Stratification by PI demonstrated PLL increased across groups (p < 0.001), but DLL was comparable between low and moderate PI group (p = 0.329). Conclusion Lumbar lordosis morphology correlates to erector spinae muscularity. Proximal lumbar lordosis has a bigger correlation with pelvic incidence than the distal lumbar lordosis. The results are helpful for restoring a rational lumbar lordosis shape in long fusion surgery.


2020 ◽  
Author(s):  
Roschen Sasikumar ◽  
Ajit Haridas

AbstractPopulations are locked down during an epidemic to slow down the rate of infection so that epidemic trajectory is "flattened". This helps to keep cases at a manageable level. Given the enormous economic damage and misery caused by a lockdown, it is imperative to keep the lockdown period limited. A lockdown is useful only if it can be ensured that after the lockdown is lifted, the epidemic trajectory does not rise sharply again. We present here the results from a mathematical model of the epidemic which examines how the timing, strength and duration of the lockdown affects the post-lockdown epidemic trajectory. Our results show the following:A early lockdown (imposed when less than 1% of the population has been infected), of any reasonable duration, cannot prevent the return of the epidemic when the lockdown is lifted. The curve starts climbing soon after lifting the lockdown and reaches a peak of the same height as the no-lockdown curveThe post-lockdown trajectory can be flattened only if the lockdown is imposed after about 10% of the population has recovered after infection.The slope of the post-lockdown epidemic curve depends on the level of immunity built up in the population before and during the lockdown period. Application of lockdown around the inflexion point of the epidemic curve (the point of maximum slope of the curve) ensures that the post-lockdown curve is also flattened.


Author(s):  
Leonard V. Smith

Abstract The mandate system took shape at an inflexion point in the evolution from an international system based on rule over territories to one based on rule over peoples. Political compromises made at the Paris Peace Conference resulted in the creation of a new political agent, the League of Nations Mandate, with no clear sovereign. In seeking to systematize this political outcome, jurists located sovereignty with the victorious Great Powers, the League itself, and with the peoples of the mandate territories. Yet they never achieved a consensus, which created an absence at the centre of the mandate system that politics would have to fill throughout the interwar period.


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