Observational studies and Mendelian randomization experiments have been used to identify many causal factors for complex traits in humans. Given a set of causal factors, it is important to understand the extent to which these causal factors explain some, all, or none of the genetic heritability, as measured by single-nucleotide polymorphisms (SNPs) that are associated with the trait. Using the mediation model framework with SNPs as the exposure, a trait of interest as the outcome, and the known causal factors as the mediators, we hypothesize that any unexplained association between the SNPs and the outcome trait is mediated by an additional unobserved, hidden causal factor.We propose a method to infer the effect size of this hidden mediating causal factor on the outcome trait by utilizing the estimated associations between a continuous outcome trait, the known causal factors, and the SNPs. The proposed method consists of three steps and, in the end, implements Markov chain Monte Carlo to obtain a posterior distribution for the effect size of the hidden mediator. We evaluate our proposed method via extensive simulations and show that when model assumptions hold, our method estimates the effect size of the hidden mediator well and controls type I error rate if the hidden mediator does not exist. In addition, we apply the method to the UK Biobank data and estimate parameters for a potential hidden mediator for waist-hip ratio beyond body mass index (BMI), and find that the hidden mediator has a large effect size relatively to the effect size of the known mediator BMI.We develop a framework to infer the effect of potential, hidden mediators influencing complex traits. This framework can be used to place boundaries on unexplained risk factors contributing to complex traits.The online version contains supplementary material available at 10.1186/s12859-022-04977-4. One of the goals in studying the associations between heritable traits and disease outcomes is to identify which of these factors are truly causal for the outcome. Expansion of causal inference studies like Mendelian randomization studies  in recenThe classic mediation framework decomposes the associations between the exposures and the outcome into direct effect and indirect effect through a mediator  , 6. The In this work, we assume that the values of the SNPs, the known mediators, and the outcome trait are accurately measured and there are no unmeasured confounding variables in the model. Furthermore, we assume that the effect sizes of the SNPs on the standardized known and hidden mediators have the same distribution. This is reasonable due to the following: because there is little or no prior information about the hidden mediator, the unexplained genetic heritability can theoretically be decomposed by infinitely many combinations of the two parts. Thus, to limit the number of possible combinations of the two parts and infer a reasonable range of the hidden mediator’s effect size on the outcome, we propose to restrict the effect sizes of the SNPs on the hidden mediator to be similar to the effect sizes of the SNPs on the known mediators. Under this assumption, one part of the unexplained genetic heritability, that is, the SNP effects on the hidden mediator, can be learned from the SNP effects on the known mediators. Furthermore, the effect size of the hidden mediator on the outcome trait can be inferred by dividing the direct effects between the SNPs and the outcome trait by the inferred SNP effects on the hidden mediator.The rest of the report is organized as follows: In the "Y, the vector of SNPs associated with Y as G, and the two known mediating causal factors of Y as M1 and M2  come from the same distribution. Under this assumption, the true mean and standard deviation of a∗H can be consistently estimated by the SNP effects a∗1 and a∗2 if the sample size is large and a large number of SNPs are included in the model. We estimate the SNP effects a∗1 and a∗2 by fitting two linear regression models with the known mediators M1 and M2 as the dependent variables and G as the independent variable. Recognizing that assuming similar SNP effect sizes and variances on different mediators may be a strong assumption, we present a more general setting in which the SNP effects could vary according to a three-level structure , using a mixture model with a point mass at zero and a true effect size distribution that centers at a non-zero value. Because we estimate the SNPs effects on the known mediators (a∗) using linear regression models that come with estimation uncertainty, the distribution of a∗ will be a mixture of a distribution centered at zero and the true effect distribution with a non-zero mean and a variance that is larger than the true dispersion. Similarly, the SNP effects on the hidden mediator, aH, can also be modeled using a mixture model with a point mass at zero and a true effect distribution that centers at a non-zero value. For the same reason as in the case of a∗, the estimated c∗ will be the mixture of a point mass at zero and a true effect distribution not centered at zero and with a larger dispersion. Therefore, we utilize Gaussian mixture models (GMMs) to model the distributions of a∗ and c∗.One challenge in the decomposition of the direct effects of SNPs on a∗ and estimate the direct effects between the SNPs and the outcome trait to obtain c∗ by fitting a series of linear regression models. In Step 2, we fit GMMs on a∗ and c∗ using an Expectation–Maximization (EM) algorithm to separate the SNP effects on the known and hidden mediators from the zero-mean noises and estimate the GMM parameters from both distributions. In Step 3, we incorporate the estimated GMM parameters from Step 2 to a GMM Markov Chain Monte Carlo (MCMC) procedure to generate a posterior distribution for bH. Details of each step are presented below. All steps are implemented in R (version 3.6.1) [Our method consists of three major steps as shown in Fig. n 3.6.1) .Fig. 2Fla1 and a2, and direct effects between the SNPs by fitting linear regressions for each known mediator separately where the mediator  is the dependent variable and the elements of G are the independent variables. To estimate the direct effects between the SNPs and the outcome trait, c, we fit a linear regression with Y being the dependent variable and G, M1, M2, and other covariates being the independent variables. The resulting estimated effects are a∗ and c∗. We denote a∗ as the joint vector of a∗1 and a∗2.In Step 1, we estimate the SNP effects on the known mediators, c∗ from the zero-mean noise component by fitting a GMM. In addition, because it is possible that not all the SNPs are associated with the set of known mediators, we also fit a GMM on a∗ to capture the actual effects of the SNPs on the known mediators. Specifically, we use the EM algorithm to fit the GMMs on a∗ and c∗ via the normalmixEM function in the R package mixtools (version 1.2.0) [c∗ or the corresponding known mediators in the case of a∗).In Step 2, we separate the true effects in n 1.2.0) –11 with Xi for i = 1…n be random variables generated from a GMM consist of two normal distributions  [In Step 3, we specify a GMM as shown in Eq. on 4.10) , 13.6\doc∗. We denote the elements of c∗ as cj for j = 1…n, where n is the number of SNPs in the model. a∗ in Step 2; the value of bH and the binary indicator variables zj for j = 1…n, which indicate which Gaussian distribution in the GMM the corresponding cj belongs to. We specify the same categorical distribution prior for zj, where the weight parameters of the two categories are set to the corresponding estimated weights for the two Gaussian distributions in the fitted GMM in Step 2. Lastly, we specify a normal prior with mean zero and variance 100 for bH so its distribution is almost flat at small values close to 0, which is the potential region of the hidden mediator’s effect size.The data input into the GMM MCMC procedure are the elements of bH is equal to zero, the distribution for c∗ reduces to a single Gaussian distribution instead of a GMM, and the resulting GMM from EM will likely assign a very small weight to one of the Gaussian distributions in the GMM. If the Gaussian distribution that involves bH in the MCMC procedure happens to be the one that receives a very small weight, the posterior distribution of bH will span a very wide region around the true value of bH. This is because during each MCMC iteration, due to the small weight, very few or none of the elements in c∗ will be assigned to the Gaussian distribution that involves bH so that the MCMC procedure is uncertain about the estimation of bH. This situation can also occur when the true value of bH is very small such that the two Gaussian distributions in the GMM are not separable. Under these scenarios, the resulting interval estimators will be extremely wide and will not be useful in terms of giving a precise estimate of bH. Thus, if one observes an extremely wide posterior distribution of bH, we propose to flip the binary labeling of the fitted GMM from Step 2 and perform Step 3 again. Based on the results of the simulation study presented below, we observe that this adjustment generally results in more meaningful estimates of bH.When πH; in Setting 2, we allow two of the known mediators to have negative effects on the outcome trait; in Setting 3, we decrease the sample size ; in Setting 4, we consider cases where there are 1 and 10 known mediators of the outcome trait; in Setting 5, we consider four cases where some of the known mediators affect other known mediators; in Setting 6, we simulate two cases under the three-level SNP effect structure; in Setting 7, we simulate the case where bH is equal to zero ; in Setting 8, we vary the number of SNPs included in the model. For the base case and Settings 1–7, we consider a scenario where there are 70 SNPs associated with the outcome trait and another scenario where there are 500 SNPs associated with the outcome trait. We select the 500 SNP scenario because it is similar to the number of SNPs used in the data application example (522 SNPs) described in the next section. We also examine the 70 SNP scenario and repeated all the simulations done with 500 SNPs to access how our method behaves when there are a significantly smaller number of SNPs in the model. For both scenarios, we let the hidden mediator’s effect size on the outcome trait, bH, be 0.02, 0.25, and 0.5 and perform 1000 independent simulations for each of the three values of bH. Also, for Settings 1–6, we simulate data for 49 additional bH between 0.02 and 0.5 with a step size of 0.01 to show a behavior trend of our posterior distribution as bH increases. As previously mentioned, when the true value of bH is very small or equal to zero, the MCMC posterior distribution of bH may be too wide occasionally to make any meaningful inference about its true value. Therefore, we apply the labeling-switching adjustment if the width of the 90% quantile interval derived from the initial posterior distribution for bH is wider than 5. The detailed setting of the base case is presented in the next paragraph with its simulation results being presented in "R (version 3.6.1) [We conduct a simulation study to evaluate the proposed method. We consider a base case and eight additional settings Table . The basG, are simulated independently with minor allele frequencies generated from a uniform distribution between 0.1 and 0.5, and we assume the SNP effects are additive. The SNP effects on the mediators a1, a2, a3, a4, a5 and aH are generated from mixture distributions of zero point-masses and normal distributions with the mean being 0.2 and the standard deviation being 0.08 as shown in Eqs. M1; 60% of the SNPs associated with the outcome trait are associated with M2, and so forth. There are five known mediators of the outcome trait. The effect sizes of the five known mediators  on the outcome trait are . The known mediators are generated as Eqs. πH, is 0.8. The hidden mediator is generated as Eq. C1 and C2, in the outcome model. C1 is generated from a normal distribution with a mean of 7 and a standard deviation of 0.5; C2 is generated from a normal distribution with a mean of 4 and a standard deviation of 0.4. Their corresponding effect sizes on the outcome trait are 0.8 and -0.3. The outcome trait is generated based on Eq. M1, M2, M3, M4, and M5).The data for the base case are simulated as follows. The sample size is 100,000. The SNPs associated with the outcome trait, We apply the proposed method to UK Biobank data. We consider Waist-to-hip Ratio (WHR) as the outcome, the significant SNPs from the latest GWAS meta-analysis of WHR as the exposure, and body mass index (BMI) as the known causal mediator between WHR and the SNPs . The goa−9 when choosing the exposure SNPs. The resulting SNPs are clumped using the R package TwoSampleMR (version 0.5.6) with a clumping window of 250 kb and a cutoff for correlation due to linkage disequilibrium (LD r2 = 0.01) based on the 1000 Genomes Continental European groups reference [plink (version 2.0) [Because the GWAS meta-analysis used for identifying the exposure SNPs involves UK Biobank data, to minimize over-estimated SNP effect sizes in our analyses, we use a stringent p-value threshold of 5 × 10eference , 16. Aftion 2.0)  (Additioa∗) and the outcome (WHR) regression model (to obtain c∗), sex, age and the first ten principal components are adjusted for as covariates. For both a∗ and c∗, SNPs with effects that are greater than the 3rd quartile + 3 × interquartile range (IQR) and values that are smaller than the 1st quartile—3 × IQR are removed to avoid the downstream GMM methods to be driven by these outliers. A total of 12 SNPs were removed  and 90% quantile interval (QI) of bH are similar; both are close to the true value of bH, and slightly downward biased only when the true value of bH is 0.5. Both the median and the mean have a smaller variation for the cases with 500 SNPs compared to 70 SNPs   Fig. A. But webH when the true value of bH is large  and direct effects between the SNPs and WHR c∗ are shown in Fig. a∗ and c∗. The histograms with outliers removed are shown in Fig. a∗ with the mode on the left being approximately at zero suggesting a∗ follow a mixture model. It is less clear whether the distribution of c∗ has two modes. EM estimated means of a∗ and c∗ are indicated by the vertical red lines shown in Fig. a∗ estimates a mixture weight of 0.882 for the distribution on the left, and the fitted GMM on c∗ estimates a mixture weight of 0.836 to the distribution on the left. From the posterior distribution of bH, the point estimate for bH using the posterior median is 1.5556 and 1.5562 using the posterior mean; the HDI is ; the QI is . The whole procedure of the multi-step method on waist-hip-ratio  took 6.33 min on a MacBook Pro laptop with a 2.8 GHz Intel Core i7 processor and 16 GB memory. The runtime can be variable based on how long the MCMC chain is set to. In the sensitivity analysis that repeats the multi-step method 20 times with approximately 1/20 of the SNPs dropped each time, the median of the posterior median of bH from 20 repeats is 1.5486, the first quartile is 1.4483, the third quartile is 1.6355, the smallest value is 1.0511, and the largest value is 1.9575. For the posterior mean of bH, the median of the 20 repeats is 1.5494, the first quartile is 1.4492, the third quartile is 1.6368, the smallest value is 1.0511, and the largest value is 1.9584. The posterior median and mean from three repeats are relatively extreme  indicating that some SNPs are more influential than other SNPs. Finally, the effect of BMI on WHR conditional on sex, age and the first ten principal components is estimated to be 0.3834 .The regression estimated SNP effects on BMI . Lastly in Step 3, based on the EM estimated GMM parameters, a GMM MCMC procedure is applied to generate a posterior distribution for the hidden mediator’s effect size, bH well. We observe that if the model assumptions are correct, both using the posterior median and mean to estimate bH provides only small biases, and good coverage of the simulated true effect by the 90% HDI and QI. When there are more identified SNPs associated with the outcome trait, in general, both the point and the interval estimators perform better. Also, our posterior distribution estimates the hidden mediator’s effect size well if some of the known mediators have negative effects on the outcome trait while others have positive effects. Our method can also accommodate varying numbers of known mediators and the performance is not dramatically affected by decreasing sample size. In addition, our method estimates bH well even if the hidden mediator does not exist . However, we notice that when the hidden mediator is associated with all of the identified SNPs that are associated with the outcome trait, both the median and the mean are upward biased and both the HDI and the QI are less likely to include the true value of bH. This is expected because the assumed GMM distribution on the estimated direct effects between the SNPs and the outcome trait is wrong. On the other hand, if the hidden mediator is associated with too few identified SNPs, the point estimators have large biases and the interval estimators become wider. This is also expected as there are fewer SNPs that can provide information about bH. Also, if causal relationships exist among the known mediators, these effects need to be adjusted in the mediation regressions. Otherwise, the point estimators can have relatively large biases and the interval estimators are likely to include the true value if the causal relationships are large enough. Finally, our method assumes that the SNP effects on different mediators (including both the known and hidden mediators) are similar. The posterior distribution estimates bH poorly when the SNP effects on different mediators are very different, especially when the number of SNPs in the model is large. This is because little information can be borrowed from the observed SNP effects to infer the SNP effects on the hidden mediator, which can make it difficult to decompose the direct effects between the outcome trait and the associated SNPs to estimate bH.Through extensive simulation studies, we show that our method can produce a posterior distribution that captures bH  can be generated when the true value of bH is either zero or very close to zero such that the distribution of the estimated direct effects between the outcome trait and the associated SNPs follows a single Gaussian distribution around zero rather than a GMM. Under this scenario, by chance alone, the EM algorithm in Step 2 may assign a tiny weight to the distribution that involves bH in the MCMC model in Step 3 and assign a large weight to the other distribution in the GMM. As a result, little data can be used to infer bH in the MCMC procedure. To avoid this situation, we suggest one inspect the histogram of estimated direct effects and the EM fitted GMM from Step 2. If the histogram of estimated direct effects does not have two modes and is centered approximately at zero, and the EM fitted GMM assigns a tiny weight to the distribution that involves bH relative to the weight of the other distribution, then it is reasonable to flip the binary labeling of GMM and proceed to Step 3.Occasionally, a posterior distribution with little information about −9) for filtering SNPs associated with waist-hip ratio to mitigate biases from winner’s curse, some degree of biases from the winner’s curse is unavoidable. A more optimal approach is to identify SNPs associated with waist-hip ratio and perform the estimation in two independent populations with similar ancestries such that the effects are similar in the two populations but the biases from the winner’s curse are minimal. There are a couple of possible biological or physiological explanation for the hidden mediator identified in the current analysis that could contribute to the remaining association. For example, the distribution of brown fat (the cell type responsible for non-shivering thermogenesis) varies across individuals and could influence body size and weight, and studies have reported the negative association between WHR and having active brown fat in males [We applied our proposed method on UK Biobank data to estimate the effect size for a potential hidden mediator of waist-hip ratio. From the posterior distribution generated by our method, the posterior median estimates that a potential hidden mediator exists in the European population with an effect size of 1.56 . This result suggests that the hidden mediator has a larger effect on waist-hip ratio comparing to BMI (0.38). Some caution here is warranted, as we used the same UK Biobank data for both identifying SNPs associated with waist-hip ratio and for estimating the SNP effects. Although we used an extra stringent p-value threshold  and figures  including the discussion on a more generation assumption on the SNP effects (Section S1), additional simulation settings and results (Sections S2–S3), and a proof of the estimated SNP effect’s distribution (Section S4).Additional file 2. An Excel table containing the list of 535 independent SNPs associated with WHR.Additional file 3. An Excel table containing the simulation results for Settings 1–6 and 8Additional file 4. An Excel table containing the simulation results for Setting 7.


During a conventional measured resection using the posterior reference method for total knee arthroplasty (TKA) in varus knees, proximal tibia is resected from the lateral joint surface for the same thickness as the implant. Distal femur is resected from the worn medial surface for the same thickness as the implant. Posterior femur is resected using the posterior reference method with an external rotation for appropriate degrees. In this situation, although the joint line of the tibia is leveled to the height of lateral joint surface, the posterior joint line of the femur is leveled to the center of medial and lateral posterior condyle, which is a few millimeters lower than the lateral posterior condyle. This discrepancy between the proximal tibia‐posterior femoral joint line causes a tight flexion gap in cruciate‐retaining TKA. Therefore, downsizing of the femur is necessary to adjust the posterior joint line to the level of the lateral condyle.To avoid this circumstance, the postoperative joint line should be leveled to the center of the original medial and lateral joint surface. Proximal tibia is resected from the lateral joint surface 1 mm to 2 mm thicker than the implant. Distal femur is resected from the worn medial surface 1 mm to 2 mm thinner than the implant. Posterior femur is resected using the posterior reference method with an external rotation for appropriate degrees. In this situation, all the joint lines are leveled to the center of the medial and lateral joint surface. Otherwise, use of an anatomically shaped implant with a physiologic joint line is another option to avoid joint line discrepancy.Adopting joint line theory for bone resection can prevent the flexion gap tightness that likely occurs in cruciate‐retaining TKA.  A tight flexion gap is often encountered during cruciate‐retaining (CR) total knee arthroplasty (TKA). Methods to manage tension of the posterior cruciate ligament (PCL) have been frequently described, such as PCL release and the pie‐crusting methodThe joint line of the normal knee is medially inclined an average of 3° relative to the mechanical axis. After TKA, the joint line is altered to be perpendicular to the mechanical axis with the conventional mechanically aligned method. Many operations using the standard measured resection method indicate that the proximal tibia should be excised with the same thickness as the tibial implant from the lateral normal articular surface e.g. 10 mm). In that case, the joint line after implantation is leveled to the height of the original lateral joint surface . The distal femur is cut from the lateral articular cartilage surface, 1 mm to 2 mm thinner than the thickness of the implant (e.g. 8 mm for a 9‐mm implant). Therefore, the tibia joint line and the distal femoral joint line are set approximately 1 mm to 2 mm lower than the lateral joint surface. The femoral posterior condyle resection is determined by the posterior reference method, using a sizing guide measured at the femoral center. By doing so, the entire joint line is set to the center level between the medial and lateral joint levels. Therefore, the risk of a tight flexion gap can be avoided.In the second option, align the joint line of the tibia to the lateral joint surface and downsize the femur by 2 mm Fig. . HoweverThe previously mentioned theory and procedure are for use with a conventional implant with the same thickness as the medial and lateral condyles in the mechanical alignment method. Most implants accept this condition, but some implants have an anatomic shape that mimics the physiologic articular surface, such as the Journey II  and Fine  implants. When these implants are used, the bone should be resected at the same thickness as the lateral part of the implant from the lateral joint surface in the proximal tibia and distal femur. This adjusts the medial joint line to be in physiologic position with a 3° medial inclination. When femoral sizing is performed with the posterior reference, the posterior condyle line matches the original joint line Table . AlthougIn 30 consecutive patients with varus knee deformity , thickness of bone resection and intraoperative gap length were measured during TKA using Journey II CR. The proximal tibia was resected perpendicular to the mechanical axis for a thickness of 12 mm from the lateral joint surface . After assessment of the joint gap, the distal femur was resected perpendicular to the femoral mechanical axis for a thickness of 8 mm from the lateral femoral surface. After removal of all the osteophytes, femoral bone resection was completed using the posterior reference method aligned in 3° external rotation to the posterior condylar axis. Ligament balancing was limited to the removal of osteophytes and release of deep layer of medial collateral ligament (MCL). The superficial layers of MCL and PCL were preserved. Thickness of resected bone was measured by a caliper, considering the thickness of the bone saw (1.5 mm) for medial and lateral side of distal femur, posterior condyle, and proximal tibia. Intraoperative joint gap was measured after the bone preparation in extension and flexion using a tensor device that independently measured the bone distance at medial and lateral side under a constant distraction force of 120 N. Table The standard surgical procedure for CR‐TKA includes measured resection techniques, which principally resect bone at the same thickness as the implant. Using this technique and the posterior reference method with conventional implants, the joint line heights between the proximal tibia and posterior femur do not match. This joint line discrepancy risks a tight flexion gap. It is important to individually consider how the joint line is altered at the medial and lateral sides of the proximal tibia, distal femur, and posterior femoral condyle.Most surgical TKA instruments include a depth caliper to measure the resection level for the proximal tibia. The resection depth often is chosen at 10 mm, or 2 mm from the native cartilage or at the deepest point on the worn side, respectively. The 10‐mm resection from the lateral joint surface for a 10‐mm implant means that the postoperative joint line is set to the level of the lateral side. The distal femoral cut is usually set at the same thickness of the implant from the most distal end of the femur, which is usually on the worn medial side or the lateral cartilage. In most standard techniques, this means that the postoperative joint line is adjusted to the level of the lateral side in the coronal plane. In contrast, it is rare to primarily adjust the posterior joint line to the level of the lateral side with most TKA systems. This is why the flexion gap frequently becomes tight in CR‐TKA.The most reasonable way to avoid this joint line discrepancy between the proximal tibia and posterior femoral condyle is to adjust the joint line to the center level of the medial and lateral joint lines option 1). However, standard surgical instruments do not always allow the depth caliper to measure 1 mm to 2 mm deeper than the implant thickness for the tibial side. In such cases, surgeons can remove remaining cartilage from the lateral tibial surface to deepen the joint line for 1 mm to 2 mm. Standard instruments also do not have a way to resect the distal femur 1 mm to 2 mm thinner than the implant from the lateral side. Surgeons must manually estimate the bone thickness to be removed. The only method that most standard surgical instruments possess is downsizing the femur and placing it anteriorly on the posterior reference guide to reduce the posterior joint line to the same level as the lateral femoral condyle (option 2). This is usually used as an option when the sizing guide shows an in‐between size or when the tight flexion gap is encountered. However, some CR‐TKA systems adopt a 1 mm to 2 mm thinner posterior condyle compared to the thickness of bone resection to automatically downsize the posterior condyle . Informed consent was obtained using the opt‐out form on our center's website.The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable requestNo financial support was obtained for this study.KO conceived the concepts, wrote the manuscript, performed surgery, and analyzed the data.The author declares that they have no competing interests.


Moreover, we detected a clear association between the size of the rice paddy fields and the decrease in leptospirosis incidence in provinces . This study shows that the Livestock Manure Control Policy had significantly reduced human leptospirosis incidence in the Republic of Korea, in particular, in rural regions.Leptospirosis is a zoonotic disease that the pathogen can be transmitted to humans through the excretions of infected animals. In the Republic of Korea, the Livestock Manure Control Act was enforced in September 2007 to improve underground water hygiene. The objective of this study was to evaluate the impact of Livestock Manure Control Policy on the incidence and the trend of human leptospirosis. An interrupted time series analysis using the monthly incidence of leptospirosis was conducted based on data derived from the Korean National Surveillance System between January 1999 and January 2015. We used a Spearman correlation method to compare the level of leptospirosis incidence decrease between the metropolitan cities and rural provinces. The annual incidence of leptospirosis in South Korea decreased by 33% after policy enforcement of the policy. A significant change in the slope of human leptospirosis cases was observed after the policy enforcement ( Leptospirosis is a zoonotic disease commonly reported in tropical and sub-tropical countries , 2. PathPrevious studies have shown that the incidence of leptospirosis follows distinct seasonal patterns and is strongly associated with high rainfall amounts and flooding, when leptospires are widely dispersed in the environment , 6. OccuIn September 2007, the Korean Ministry of Environment enforced the Livestock Manure Control Act, which makes it compulsory for livestock farmers to be equipped with appropriate sludge process facilities on their farms . Since tIn this study, we aimed to evaluate the effect of the Livestock Manure Control Policy on the incidence of human leptospirosis in the Republic of Korea.We conducted a retrospective interrupted time series analysis using national surveillance data. Since the Livestock Manure Control Act came into effect in September 2007, data were divided into two sets: those from January 1999 to September 2007 (before policy roll out), and those from October 2007 to December 2014 (after policy roll out) . For furMonthly data of leptospirosis and HFRS incidence were collected from the Database of National Notifiable Infectious Diseases of the Korea Centers for Disease Control and Prevention between 1999 and 2015. The criteria mandating a notification for leptospirosis included clinically and epidemiologically suspicious cases, as well as laboratory-confirmed cases. Suspicious cases were defined as patients with the following criteria: (1) experiencing influenza-like illness with jaundice and/or renal failure, and/or hemorrhages, or (2) having occupations that put them at risk for direct contact with potentially infected animals  , 18. LabEnvironmental data, including the total areas (hectare) of rice paddy field of provinces and metropolitan cities were derived from the Institution of Korean National Statistics . The meaYt is the independent outcome variable of human leptospirosis incidence. T is the number of months starting in January 1999. β0 estimates the baseline level of the outcome at the beginning of the time series. β1 estimates the linear trend of the pre-intervention period where T is a continuous variable indicating the time in months at time t from the initiation of the study period. β2 estimates the changes in incidence where policyt = 0 is before policy intervention and policyt = 1 is after the intervention. β3 estimates the mean monthly trend in post-intervention period, where time after policy enforcement is a continuous variable indicating the number of months after implementation at time t and is coded as zero before the policy intervention. et is the random error at time t.We calculated the annual incidence of leptospirosis and compared data from before and after the enforcement of the Livestock Manure Control Act using segmented regression analysis of time series data . We consU test and a Poisson regression analysis were used. The statistical package R version 3.2·4  was used for all analyses.We utilized a Spearman correlation method to evaluate the association the mean areas of rice paddy field and the leptospirosis incidence at the provincial level. To evaluate differences in possible confounders  between before and after the policy roll out, the Mann–Whitney P < 0·01). The interrupted time series analysis showed that the leptospirosis incidence was 2·23 per 10 million at the beginning of study period (January 1999). No significant changes before and immediately after the policy roll out were observed. However, a significant decrease in leptospirosis incidence (0·02 per 10 million per month) after policy enforcement  and 0·32 per 10 million people in the nine provinces (with a mean rice paddy field area of 1 12 414 hectare). Although we found no significant association between the effect of the policy on leptospirosis incidence and the area of rice paddy fields in metropolitan cities, a statistically significant association was observed for the nine provinces (P = 0·06). In addition, no significant differences were seen in the amount of rainfall between pre- and post-enforcement periods  1·15, 95% CI 1·07–1·15,  periods .Fig. 3.Our study has shown that enforcement of the Livestock Manure Control Act in the Republic of Korea was associated with a decrease in human leptospirosis incidence. We found strong positive correlation between the decrease in leptospirosis incidence and the mean area of rice paddy fields in the provinces. No significant change was found in environmental factors such as the amount of rainfall and exposure to rodents.In 1990s, South Korean government promoted the use of organic waste including livestock manure to curb the excessive use of chemical fertilizers that had caused an imbalanced of nutrients in the soil . Previour = 0·94, P < 0·01). Thus, this supports our finding that the decrease in human leptospirosis incidence after the policy enforcement was larger in the provinces, which had larger rice paddy field sizes.Moreover, several studies have shown that there is a positive association between water logged land, which provides a favorable environment to sustain leptospires, and leptospirosis incidence , 6. ThisThis study has several limitations. First, the Database of National Notifiable Infectious Diseases includes clinically and epidemiologically defined cases that have not been laboratory confirmed. However, these data provide the best proxy measure of the leptospirosis cases through a nationally trusted institution. Second, we used HFRS data as a proxy for exposure to rodent. A proxy measure is not in itself directly relevant; yet, it can be used for statistical analysis in place of immeasurable variables. Several studies have shown that HFRS and rodent density exhibit a significant correlation as HFRS is caused by Hantaan or Seoul viruses, of which mice are the main carriers , 24. ThiThis is the first study to quantify the effect of a Livestock Manure Control Policy on the incidence of zoonotic disease in humans using standardized national data spanning 15 years. Furthermore, our data identified a statistically significant association between the policy's effect and the mean rice paddy field size on the provincial level.Our study found a significant decrease in the human leptospirosis incidence after the enforcement of the National Livestock Manure Control Act in South Korea, in particular in the nine provinces. Our study suggests that livestock manure control could be an important strategy for the leptospirosis control and prevention.


EU MECI is defined upon the economic complexity methodology, exploiting the network’s centrality metrics to calculate aggregate scores of the capacity of Member States to ‘ I will not rest when it comes to building a Union of equality.         — President von der Leyen, The State of the European Union 2020Building a Union of equality requires extensive knowledge of prevailing inequalities across multiple life domains, from material living conditions to health and from environmental conditions to political participation, social life, knowledge and education. Inequalities pose a major threat to social cohesion and the COVID-19 pandemic has inflated these by attacking the global society at its core UN, . The gloAlthough inequality has been the focus of a vast amount of research aiming to identify policy recommendations and solutions, the consensus regarding goals, priorities and methods is often limited ’s Joint Research Centre (JRC) has undertaken a pilot research project to develop a Multidimensional Inequality Monitoring Framework for the EU (EU MIMF) that provides a novel and comprehensive dashboard of 346 indicators for the 28 Member States.1The JRC researchers refrain from computing a composite inequality index leading to a single EU inequality ranking, due to the correlation structure of the indicators used. They offer instead an analysis based on the set of 346 indicators, recognizing though, the importance of a country-ranking methodology and providing a way to compare countries’ performances based on a double-sorting algorithm , based on linear-algebra tools within a bipartite-networks framework to measure economic complexity, reconciling the established methodologies of Economic Complexity Index  and a minimum value (0 indicating the poorest performance) to ensure comparability and enable the aggregation of measurements. Then, indicators with missing values are dropped. The final list of 177 indicators considered in the computation of the EU MECI is shown in Table Figure 4c’s achievement in equality indicator i .A central role in our analysis is played by the bipartite network of Member States and equality indicators. Several examples of bipartite or bi-modal networks appear in the scientific literature  is ‘Knowledge and skills’The matrix mentclass2pt{minimmentclass2pt{minimRelative gap in average hours of of full-time employment worked per week ’ in the ‘Working life’ dimension, followed by code 199, ‘Odds ratio of practising artistic activities as a hobby ’ in the ‘Cultural life and recreation’ dimension and code 105, ‘Odds ratio of household not being able to afford an unexpected expense ’ in the ‘Material living conditions’ dimension are relatively ‘easy to accomplish’ equality goals at the EU level. On the other hand, equality measures such as the ‘Odds ratio of people rating their satisfaction with leisure time as high ’ (code 190) in the ‘Cultural life and recreation’ dimension and the ‘Odds ratio of feeling depressed ’ in the ‘Health’ dimension, seem to require more effort and better strategies from the policy side.Figure GENEPY methodology described in Sciarra et al.  accounting for the relative performance of countries and the synergies and trade-offs across Goals, and (b) providing useful insights of the policy actions required to be undertaken by the countries to achieve sustainable development. It does so by assigning higher GENEPY scores to the few countries that have relatively more capabilities in implementing policy interventions towards achieving the Goals within the Agenda 2030.Sciarra et al.  take theGENEPY methodology can be directly applicable to equality indicators. The system of 28 countries and 346 indicators within the EU MIMF is complex and characterised by high heterogeneity and disordered interactions, and any attempt to assess multidimensional equalities is not compatible with the absence of a complex networks approach  the complex interconnections between the equality indicators and (b) the high heterogeneity of Member States performance across the equality goals.To consolidate the multidimensional information available for the Member States into a single composite equality indicator, we devise and introduce the EU MECI, defined upon the GENEPY framework is set in a linear algebra framework and embeds the interplay between Member States and equality indicators  in the ‘Knowledge and skills’ dimension is the measure with the biggest limitations in terms of improvement when chasing a more equitable Union. On the other end of the spectrum is ‘Relative gap in average hours of full-time employment worked per week ’ (code 151) in the ‘Working life’ dimension, which reflects a  good performance by all Member States.Table These findings are of high importance in guiding policy making both at the EU and the national level. More effort through policy interventions is needed in improving the EU’s performance in PISA scores and this effort should be initiated and focused on the Member States with low EU MECI scores (see next Section).Figure Sweden appears at the top of the ranking of the most equal countries, followed by Denmark, Finland and the Netherlands. These top four Member States show relatively good performance on the indicators with the top three weights  compared to the low EU MECI countries: Portugal, Bulgaria, Croatia and Slovakia  the interactions across the equality indicators and (b) the interplay between Member States and equality measures, while the corresponding weights of countries and indicators are determined endogenously by the data.Our ranking of indicators, based on the data-driven weights, reveals the equality goals, and implicitly the key life dimensions, that policy makers should concentrate their efforts on in order to devise action plans towards a more equitable European society. What is more, the EU MECI, offers a comprehensive tool for monitoring and analysing multidimensional inequalities in the EU, that allows for a geographical prioritization of the corresponding policy interventions, where EU and Member State strategies should align and collaborate. Our aggregate ranking captured by the EU MECI verifies the geographical two-tier segregation of EU countries, while highlights the advantages, in terms of actionable insights, that the network science offers as compared to traditional approaches with neutral weights.From a policy perspective, the proposed analysis complements the EU MIMF by introducing an additional arrow into the policymaker’s quiver of effective policies to tackle unfair social inequalities. It does so by identifying—through data-driven techniques—the areas in which Member States find it more difficult to reduce existing inequalities.Building a Union of equality is a core topic in the von der Leyen Commission’s policy debate, and the analysis presented in this work can play an important role in the formulation of evidence-based policy responses to rising social disparities.The information and views set out in this paper are those of the authors and do not necessarily state or reflect the official opinion of the European Commission. The scientific output expressed does not imply a policy position of the European Commission. Neither the European Union institutions and bodies nor any person acting on their behalf may be held responsible for the use, which may be made of the information contained therein.


The study employed Fick’s second law of diffusion to discover some unknown aspect of carbon diffusion in grey cast iron during carburisation process. Emphasis on the experiments and theoretical modelling were established for better accomplishments. Pulverised palm kernel and eggshell additives of 70 (wt.%) and 30 (wt.%) according to the Voige law of mixture was considered as a continuous medium without considering the atomic nature of the mixture. Furthermore, a kinetic approach was described where a physical model of the substrate immersed in the carbon mixture was established while diffusion equations were modelled to establish the mechanism of carbon diffusion during carburisation. Initial composition and concentration of diffused atom remained constant which are 2.68 and 6.67% carbon. While the carburizing time used varied from 60 min, 90 min, 120 min, 150 min, 180 min and 210 min respectively at constant carburising temperature of 900° The results revealed varying composition gradient of carbon atom ranging from 5.4%, 5.42%, 5.44%, 5.46%, 5.51%, and 5.65 compared to the initial carbon content of 2.68%. The concentration of carbon atom on the substrate surface at varying time implies that the process was non-steady state diffusion which verified Fick’s second law of diffusion. Hence, the composition achieved is a function of boundary conditions such as time position and temperature. This novel study will enhance the understanding of heat treat treatment of metals such that their applications in the industry will be numerous. They are basically modified for advanced engineering applications using diffusion mechanism2. Diffusion involved the squeezing of carbon atoms past its surrounding atoms in other to reach a new position. Diffusion process can be best understood from the equation parameter of Fick’s law as well as the knowledge of the activation energy required for the diffusion process3. For instance, Fick’s second law established a non-steady state diffusion of atoms as described by the differential equation 4.Metallic materials which have undergone heat treatment via carburisation process have surfaces characterised with improved mechanical properties5. Recent study on the diffusion of palm kernel and eggshell additives to grey cast iron resulted in increase in the hardness of the material6. The tribological properties of the treated material via diffusion process was excellent which made it suitable for advanced engineering material8. The principle of Fick’s second law had been limitedly used in evaluating the depth of the mechanical properties that had been diffused into these materials, thus making the analysis or establishing the statistical significance of the diffused carbon atom a major problem11. One major problem in diffusion analysis is the determination of the temperature field and depth of carbon imposed on the surroundings of the substrate metal13. Study has shown that the knowledge of the temperature distribution could be a pointer to understanding the carbon diffusion mechanism as well as the depth of diffusion14. For grey cast iron material, knowledge of the carbon diffusion is important in analysing the structural integrity. Also, knowledge of carbon diffusion is critical to the optimisation of the coating thickness as well as the compatibility of the carburising agents20. However, movement of atoms is an essential factor for the diffusion process to take place in metals. Therefore, understanding the dynamics of the diffusion process remain a crucial problem in the determination of the carbon depth in solid materials21.The solution to Fick’s second law permits the evaluation of concentration of an atom diffused near the surface of the coupon material as a function of time and distance, provided that the coefficient of diffusion D remains constant and the concentration of the atom at the surface 22. To address these problems and improve on the applications of these organic materials, various material, methods and concepts have been designed and developed. For instance, Chen et al.23 developed a light-weight thermal energy concrete and reinforced it with carbon from palm kernel shell. This helped in improving the thermal lag and lowered the peak temperature as a composite. More so, alloying of steel with borides under high temperature resulted in increase in the hardness of the substrate24 and the thickness of the layers increased with increased temperature as reported by Hu et al.25. It has also been reported that carbon diffuses into the surface and settles at the face centred cubic region during the carburisation of austenitic steel. This therefore, caused an increase in the hardness of the layers formed and leaving chromium in its free form and allows an increase in corrosion resistance as well as improvements in tribological and mechanical properties. However, it is important to understand that in an ideal diffusion process, a diffusing atom squeezes past the surrounding atoms to get to the new position. This implies that energy will be utilized to force the atom to its new position. Thus, the energy barrier needed to move the atom to its new position is referred to as the activation energy30.Furthermore, carbon content such as that from palm kernel, coconut, wood charcoal and eggshells have been the major carbon content that are usually deployed during carburisation process. The eco-friendliness and their environmental friendliness make them most promising materials for advanced heat treatment applications. However, the commercial applications of these organic materials are limited by some drawbacks including the determination of the depth of carbon diffusionIn our present research, diffusion in grey cast iron using pulverised palm kernel and eggshell additives showed an increase in the hardness of the substrate material. Therefore, the aim of this study is to deploy the Fick’s Second Law in the determination of the depth of carbon in the material that resulted in increased hardness after the carburisation process. This method had become prominent in the understanding of diffusion in solids, liquids and gases.The experimental approach involved the use of pulverised palm kernel and eggshell additives of 70 (wt.%) of pulverised palm kernel and 30 (wt.%) of pulverised eggshells according to the Voige law of mixture. Grey cast iron substrates of dimensions (20 mm × 20 mm × 10 mm) and chemical composition (wt.%) of 2.68 C, 1.42 Si, 0.63 Mn, 0.13 S, 0.28 P was prepared using different grades of silicon carbide abrasives to obtain a polished and smooth surface for easy carbon diffusion. Prepared grey cast iron substrate were embedded into some stainless steel containers to reduce the rate of carbon absorption and were finally charged into a muffle furnace of 1200 ℃ capacity. The carburisation process was carried out at a temperature of 900 ℃ for 60, 90,120, 150, and 180 min after which it was stopped and cooling was done using water. Water was used as a quenching medium due to its natural convective heat transfer ability and the tendency of increasing the hardness property of the substrate. Initial composition and concentration of diffused atom remained constant which are 2.68 and 6.67%. This is to be able to determine the percentage of carbon atom diffused into the material surface, depth of diffusion at a particular time.The main aim of this analyses is to determine the temperature field impacted by the surrounding medium (carburisers) on the carburised material (grey cast iron). Since, conduction process takes place for proper diffusion of carbon into the material, it is important to understand and analyse the temperature distribution around the material. To achieve this, Fourier’s law of heat conduction was employed.Consider a grey cast iron substrates of dimensions (20 mm × 20 mm × 10 mm) immersed in a homogenous medium in which there is no bulk motion as demonstrated in Fig. Therefore, the rate of heat conduction is given by the equations;The thermal energy generated within the medium is given by;Based on the thermal energy generated, there was variation in the internal thermal energy stored by the grey cast iron material which is being carburised. However, in the absence of phase transformation, latent energy is minimal and the stored energy is given by;The conservation energy required within the medium is given by;Since the rate of heat conduction involve energy input and output and substituting Eqs. Substituting from Eqs. Assuming that the material become isotropic after the carburisation process, then the conduction heat rate can be established from Fourier’s law;Each equation from Eq. Substituting the heat flux Eqs. 11, 12, and 13 into Eq. 9 and dividing through the control volume Equation Assuming the temperature distribution across the substrate is ven by the equation;This equation is expressed as a function of time and also establishes the energy conservation. Thus, The same can be expressed in the y- and z-coordinates to obtain Eqs. 19Therefore, for a constant thermal conductivity, Eq. According to Fick’s Second law, carbon atom diffused during the carburisation can be defined by the differential equation in the form [32];3C), containing 6.67% carbon. −11 (m2 s−1) of carbon in FCC iron interstitial carbon diffusion [33].And the boundary conditions for the carburisation process depends on the equation [32];Thus, based on these conditions, the solution to Fick’s second law enabled the study to determine the concentration of a diffused carbon atom as a function of carburising time and distance (depth). erf = error function which is given by 0.71 [34], t = time of carburisation which is given as 3600 s, x = is the depth (mm)?Substituting the values into Eq. 22Figures In addition, Fig. Similarly, Figs. Hence, carburisation was defined in this study as the diffusion of carbon into the substrate metal. The purpose was to determine the concentration gradient of carbon at varying time since the entire process involved thermal effects. Thus, the processing parameters such as temperature and time are the key influencers of diffused carbon potentials. From the results, it is noteworthy to say that irrespective of the interaction between the carbon and other alloying elements present in the carbon, diffusion of carbon into the substrate (grey cast iron) was a perfect description of Fick’s Second Law of diffusion. This is because the composition gradient of carbon atom near the surface of the substrate vary with time due to carbon accumulation. This is the reason why it is called a non-steady state diffusion as expressed in the modelled equations.Figure The initial micro-hardness of the as-received cast iron was 288.41HV, which increased to 355.8 HV after carburisation at 180 min. This showed that there was an increase of about 67.39HV compared to the initial hardness value. This increment is a function of the adjustment in the characteristic parameters of the carburised material. Furthermore, the fatigue and wear resistance of grey cast iron component has been improved.From the study, it was established that atoms of the carbon used during carburisation moved in different fashion to eliminate concentration differences and eventually produce a homogeneous deposit on the grey cast iron material. These deposits are of varying composition. Thus, the understanding of atomic movements during the diffusion process has been established. More so, it was established that a diffusing atom of the carbon squeezed past the other surrounding atoms until it is deposited on the material. This process requires energy supply to force the atom to be deposited. This the reason for the temperature of carburisation.In addition, the presence of graphite in the microstructures as observed in the carburised samples would help in the improvement of wear resistance because graphite presence serves as lubricant to the material. Thus, thermal fatigue is reduced. More so, increase in microhardness will help in reduction of surface abrasion of the grey cast iron during application.Furthermore, Fick’s second law had been used to establish the non-steady state diffusion of carbon atoms into the substrate material (grey cast iron). However, a consequence of Fick’s second law is the possibility of achieving the constant composition profile for varying conditions, provided Dt remain constant. For several heat treatment and for most industrial applications, it will be possible to determine the temperature effect at varying time.


Multimode fibers (MMF) have been extensively investigated for transmitting images. The transmitting images are distorted into speckle patterns by MMFs, which can be reconstructed by neural networks. We studied the information distribution of MMF speckle patterns for image reconstruction. The speckle patterns, segmented by three methods of segmentation, as Centering (1), Quartering (2) and Surrounding (3), are reconstructed into input images by Complex Artificial Neural Network (CANN). Experimental results show that only about one third of full speckle patterns is enough to reconstruct the original images. The quality of reconstructed image is related to the cropping method with different frequency components in speckle patterns, under the same cropped size, Centering segmentation has 4% performance improvement compared to Surrounding segmentation. Optimized segmentation will improve the quality of reconstructed images. The croThe transmission matrix is complex, which needs both the amplitude and the phase of the output patterns corresponding to those of the input patterns . A lot oThe ideas of using neural networks on MMFs has been proposed for almost three decades . As for The input lights are decomposed into separate guiding modes to transmit through the MMFs. Therefore, the speckle patterns at distal end of MMFs contain the spatial characteristics information. Understanding the distribution characteristics of speckle patterns is meaningful, which may effectively reduce the calculation of redundant information in the training of neural networks. If only part of speckle information can be used to reconstruct the original image, the speed of image reconstruction will be enhanced. Accordingly, the time costs will be reduced.In this paper, the cropped speckle patterns in different areas from the original are used for image reconstruction through neural network. The distribution of original image information in speckle patterns is studied, part of speckle information can be utilized for reconstruction, which is intuitive for the accurate and real-time imaging of MMFs based on neural network.22.1u and angular index v respectively, MMF imaging experiments are demonstrated with step-index MMFs. Through MMFs, the relation between the input light field The digital images can be regarded as discrete pixel matrix, which are stored as one-dimensional vectors for simplicity. The coordinates of object plane and image plane are In eq. After transmitting in MMFs, the light waves on each object point are mixed with each other, and the image plane is completely distorted. At the same time, each object point contributes to all image points on the image plane.2.2The single multimode fiber image transmission system is built on an air floating vibration isolation platform. To avoid external stray light interference and air disturbance, the experimental platform is shielded by a shading cloth. The entire experimental system is illustrated in A laser beam with a wavelength of 650 nm, generated by a semiconductor laser , is collimated to a beam with a diameter of 7 mm by a telescope and is split by a Polarization Beam splitter (PBS). The reflected beam illuminates on Spatial light Modulator (SLM) that reflects the light with image information as the object light for imaging. The object light is coupled into single MMF by a fiber coupler (FC). After transmitting through the MMF, the emitted light forms the speckles, recorded by a charge couple device (CCD).2.3The transmission of light wave in MMFs is commonly described by complex functions in mathematics. To improve the fitting accuracy with the same number of hidden layers compared to traditional ANN networks, and to be able to implement equivalent complex operations in real neural networks with less original information lost. We need to change the node values and weight parameters of traditional networks in the form of real values, equivalent complex neurons are represented from that of real numbers in neural network. Followingly, Complex Artificial Neural Network (CANN) is designed on the basis of single-layer fully connected layer Neural Network . In form2.4In order to fit the transmission matrix, which is closer to the real transmission characteristics of optical fiber, it is necessary to train the neural network with a large amount of data with different features. In this paper, the open-source ImageNet natural scene sample set are loaded on SLM for training. The structural features of ImageNet set are complicated, which can ensure the feasibility of training. The speckle pattern resolution of the ImageNet set is set as 120 × 120 pixels.There are three methods of segmentation, as Centering (1), Quartering (2) and Surrounding (3), to study the distribution of effective information in different regions of speckle patterns.Centering (1), shown in Quartering (2), shown in Surrounding (3), shown in For the speckle patterns with resolution of 120 × 120 pixels imaged by ImageNet natural scene sample set, the cropped sizes of region 1 to 4 are set as 40 × 40, 60 × 60, 80 × 80 and 100 × 100 pixels, respectively. The cropped size of region 5 to 8 are all set as 60 × 60 pixels. And the resolution of speckle shielding areas of region 9 to 12 are set as 60 × 60, 70 × 70, 80 × 80 and 90 × 90 pixels, respectively.3Based on the MMF imaging setup in Based on the MMF imaging setup in The speckle patterns are cropped by the above three methods in Section The reconstruction results of the Centering (1) are shown in From eq. The reconstruction results of Quartering (2) are shown in 4To further investigate the information distribution in different cropped regions. The experimental results demonstrate that the information, carried by cropped speckle patterns, is almost proportional to the available speckle area, which can be seen from the improvements of IQA in The results of image reconstruction using speckle patterns cropped by Quartering segmentation is almost the same, which can also be reflected from IQA. The four regions from different quadrants play almost the same role in image reconstruction tasks. To further illustrate the influence of cropped location on image reconstruction effect, we compared the image quality using region 5 to 8 with that using region 2, and all the five cropped speckle patterns have the same resolution of 60 × 60 pixels. The image quality of the cropped speckle patterns from the quadrants is slightly lower than that from the center, which can be explained by the different speckle information that is available for training neural networks. We can see that the energy of the target image used for reconstruction is mainly concentrated in the low-frequency region, which corresponds to the low-frequency components distributed in the central region of speckle patterns. Besides, not all the cropped regions of region 5 to 8 contain image information, only a quarter of the circle is available to extract information. There is a difference in effective area of In The reconstruction quality of full original speckle patterns is slightly lower than that of Centering (1) with cropped pattern 4. This phenomenon can be explained by the distribution of information from different frequency components in full speckle patterns. The noises with high frequency components are concentrated in the edge of the original speckle patterns, which affects the image reconstruction in this part of the area. As the available area of speckle patterns reducing, the edge contour of the main body of the reconstructed image is still well preserved. Meanwhile, because of removing the region with more noises, the reconstruction quality of Centering (1) is better than that of full speckle patterns. The phenomena further indicate that the low-frequency components of the image are mainly concentrated at the center of the speckle patterns (image information), while the high-frequency components are mainly concentrated at the edge of the speckle patterns.The larger the proportion of the input speckle pattern to the original pattern, the more available feature information can be used to enhance the quality of image reconstruction. But in 5In this paper, we study the original image information carried by the local speckles in different locations. The training set and test set are made by cropped speckle patterns from different locations of the original speckle patterns. The original image is reconstructed successfully by neural network. The results show that the reconstruction effect is mainly related to the available speckle size. The smaller the speckle size as the input, the smaller the number of parameters and computation required by neural network. However, it is worth mentioning that there are frequency components that differ in different speckle locations. By cropping the original speckle pattern in a proper way with the knowledge of frequency distribution in target image, we can effectively reduce the time complexity of network algorithm, and the time required for single speckle reconstruction, which is of great significance for the development of endoscopy real-time video imaging.Shenyi Liu: Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.Yunxu Sun: Conceived and designed the experiments; Analyzed and interpreted the data; Wrote the paper.Wei Liu: Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data.FuChen Xiao: Conceived and designed the experiments; Performed the experiments.Haoyang Song: Performed the experiments.Science and Technology Planning Project of Shenzhen Municipality [JCYJ20190806142610885].Yunxu Sun was supported by Data will be made available on request.The authors declare no competing interests


Ice cliffs are common on debris‐covered glaciers and have relatively high melt rates due to their direct exposure to incoming radiation. Previous studies have shown that their number and relative area can change considerably from year to year, but this variability has not been explored, in part because available cliff observations are irregular. Here, we systematically mapped and tracked ice cliffs across four debris‐covered glaciers in High Mountain Asia for every late ablation season from 2009 to 2019 using high‐resolution multi‐spectral satellite imagery. We then quantified the processes occurring at the feature scale to train a stochastic birth‐death model to represent the cliff population dynamics. Our results show that while the cliff relative area can change by up to 20% from year to year, the natural long‐term variability is constrained, thus defining a glacier‐specific cliff carrying capacity. In a subsequent step, the inclusion of external drivers related to climate, glacier dynamics, and hydrology highlights the influence of these variables on the cliff population dynamics, which is usually not a direct one due to the complexity and interdependence of the processes taking place at the glacier surface. In some extreme cases , these external drivers may lead to a reorganization of the cliffs at the glacier surface and a change in the natural variability. These results have implications for the melt of debris‐covered glaciers, in addition to showing the high rate of changes at their surface and highlighting some of the links between cliff population and glacier state. The proportion of ice cliffs on debris‐covered glaciers can change by up to 20% from 1 year to the nextThere is no direct influence of external drivers on cliff variability due to the complexity and interdependence of glacier surface processesThe long‐term variability of the cliff population is constrained unless it is modified by an extreme climatic and/or glacier change Additionally, there needed to be a continuous and relatively long time series of satellite images to map ice cliffs over large portions of the glacier. Upon inspection of the Planet Labs RapidEye, we therefore identified four sites with sufficient suitable data.We derived the long‐term evolution of ice cliffs for four debris‐covered glaciers located in the Karakoram , Garhwal Himalaya , and Nepal Himalaya (Langtang Glacier) Figure . The gla−1 (Table −1 for 2009–2018 on average) and evidence of a previous surge in the 1990s  and were thus considered negligible in everything that follows.To look at the controls of cliff dynamics we accessed the annual velocities for the years 2009–2018 from the NASA MEaSUREs—ITS_LIVE project  for the 2011 and 2016 images  to make sure that there was a good agreement in the resulting changes Figure . The cha3.3−1 threshold is conservative relative to observed cliff backwasting rates that are usually less than 15 m.yr−1  or disappeared (death events) every year. We also quantified the split events, when one cliff splits into two cliffs or more Figure , and mer44.1The cliff relative area and the cliff number change considerably from one year to the next Figure . These tFor all four glaciers, the cliff relative area is higher than the pond area by a factor ranging between 2.4 for Langtang and 7.3 for Bhagirath Kharak over the whole time series. For each glacier, the pond relative area and number appear to be uncorrelated with the cliff area and number, except for Satopanth where both pond and cliff relative area exhibit a decreasing trend. The pond relative area is much higher for Urdok  than for the other glaciers, for which the average pond relative area is between 0.6% and 1.3%. The pond relative area on Urdok also has very strong variations and can more than double in a single year Figure . The num4.2The tracking of the individual cliffs allowed us to count the birth, death, split, merge, and persist events over time Figures  and S4. For all four glaciers, the change in cliff number is centered around zero and the standard deviation varies between 10% and 20% of the total cliff number. For the four glaciers, the change in number is driven by the birth and death events. Split and merge events contribute respectively positively and negatively to the change in number, mix events can cause changes in both directions Figure , and perChanges in cliff area are mostly positive for Urdok, and negative for Satopanth, thus highlighting an increase and a decrease in cliff area, respectively. These changes are centered around zero for Bhagirath Karak and Langtang Figure . Their s4.32, which corresponds to four RapidEye pixels and can therefore be considered as the cliff detectability threshold, to ∼10,000 m2 (400 pixels), and even to more than 20,000 m2 (800 pixels) for some cliffs in Urdok  and after the event (Sf), is given by the area ratio α:For split, merge, mix and persist events, the relationship between the sum of cliff sizes before  is the number of individuals (cliffs) in a given year, B(t) and D(t) are the birth and death rate in cliffs/year, respectively. In the case of ice cliffs, we include merge, split, and mix events, and the governing equation for the stochastic cliff population dynamics becomes:S(t), M(t), and Mi(t) are the split, merge, and mix rates in cliffs/year, respectively. Mi(t) can be positive or negative while the other terms are all positive. All the terms are described by their probability density functions (mean and variance) estimated from data. There is a linear dependency between the death rate and the population size D can be written following a similar equation as Equation BA, DA, SA, MA, MiA, and PeA are the changes in size from the birth, death, split, merge, mix, and persist events which can be positive or negative, except for BA and DA which are always positive.Since the processes controlling the size changes of the cliffs are also stochastic for each event, the cliff area (dP/dt)=0and(dA/dt)=0), the mean changes from the different events compensate each other and force the mean population P¯ to a given value that is independent of the initial conditions:Note that if we combine Equations Equation .P(t) will converge in time to its steady‐state value P¯. However, these probability distributions can also be time‐dependent with individual annual rates as a function of external driving forces.In this first version of the model, the probability distributions of the different terms of Equations 5.2R2 value by more than 0.1, which guarantees that the new terms improve the model more than they would be expected by chance  as a function of the eight external drivers Di using the coefficients ai,j and RMSE from the multivariate regression:λj(t) is a stochastic term drawn at each time step from a discrete normal distribution of mean zero and standard deviation equal to the RMSE of the multivariate regression. δi,j is equal to zero or one depending on the inclusion or exclusion of the external driver in the multivariate regression , which means that what we count here as birth or death events may just be persist events, but involving features that have passed beyond the satellite images' limit of detectability. The area ratio of persist events is centered around 1 but there are cases where the cliff size is multiplied or reduced by a factor up to 10, which can happen when the cliff expands laterally on the nearby slopes. This expansion or reduction probably depends on the stability of the debris on an ice slope, which is linked to the slope angle but also to the debris water content and the presence of a pond or stream at the base of the slope (Moore, The size of the cliff also plays a role in its evolution. We found that cliffs tend to follow a lognormal distribution with regards to their size, which is consistent with what has been found on Khumbu Glacier (Watson, Quincey, Carrivick & Smith, e Moore, .Merge, split or mix events also contribute to the interannual variability of the cliff population, especially for the change in cliff relative area. Their contribution to cliff area change follows the same general pattern as the contribution of persist events Figure , which mAll these events contribute to increasing the interannual variability of the cliff population, except for death events, which to some extent compensate for strong variations in cliff number and as a result, relative area. Indeed, at all sites, an increase in the number of cliffs usually results in an increase in the number of death events the year after. Such feedback is the basis of most birth‐death models in a closed system with limited resources Bailey, .6.3Determining the controls of the variability of the cliff population is important to understand the observed patterns and relate this to processes happening at the glacier surface, but also in a broader sense to understand whether these variations are purely stochastic or on the contrary are representative of a particular glacier state or evolution. The stochastic model runs provide new insights into the natural internal variability of the cliff population at the glacier scale based on the observed variability of the system. This gives a first approximation of the system bounds in the long term, assuming that the glacier surface does not undergo major changes. Our stochastic model outputs a distribution of cliffs that depends on the initial conditions for the first few years but rapidly converges to a steady state that depends on the parameters of the different events and that has an internal variability that is proportional to its mean value. We estimated the parameters over a period of 10 Figure  and 5 yeThe stochastic assumption enables us to calculate the internal variability of the system but does not tell us if this variability can be influenced by external drivers. Adding the influence of external drivers in the model reduces the variability and improves the fit with the observations, which shows that these external drivers do have an influence on the variability of the system. The results from the multivariate regression help explain some of the observed variability and link it with climate, glacier velocity, or pond evolution. None of the tested variables stands out as a principal driver and all contribute to some extent to the observed changes. They are, however, all related to the melt at the surface of the glacier, since climate variables influence melt and this melt will increase the amount of water circulating at the surface of the glacier via ponds and streams, while enhancing basal sliding and therefore glacier velocity (Kraaijenbrink, Meijer, et al., Urdok is an interesting study site as its cliff population undergoes extreme variations, and shows a major increase in cliff relative area between years 2012 and 2015 that the internal variability fails to explain. This change results from an increase in cliff size from merge, mix and persist events Figure  and coinOur stochastic model lets us quantify the possible range of the number and relative area of ice cliffs and our observations fall within the model bounds in all cases except for Urdok. There, the glacier is undergoing a major change which results in the complete rearrangement of the cliffs at its surface. We interpret the variability bounds given by the model as a physical constraint on the system. These bounds define the cliff carrying capacity of a glacier. Indeed, the number and relative area of cliffs are constrained by the availability of steep slopes, which are in turn constrained by the number of hummocks and cryo‐valleys (Bartlett et al., The fact that none of the tested variables stands out as a main driver of the cliff variability highlights the complexity underlying ice cliff evolution, due to a number of competing and interlinked processes happening at the glacier surface Figure . Indeed,6.4The significant variability of ice cliffs that we observed shows that cliff population dynamics need to be taken into account for distributed glacier melt models operating at multi‐year timescales. Indeed, for example on Langtang, an increase in cliff relative area of 20% could translate into 4% of additional volume loss of the debris‐covered area (Buri et al., This study also shows that there can be very different ice cliff population dynamics for different glaciers, which depend at least partially on the mechanisms that drive cliff birth and organization. However, this variability is difficult to constrain due to the lack of large‐scale observations of ice cliffs. The emergence of semi‐automated approaches to map these features from remote sensing data (Anderson et al., 7In this study, we combined systematic mapping of ice cliffs at yearly intervals with a method to track individual cliffs to quantify and characterize the cliff population variability of four HMA glaciers. Our results show that the cliff relative area can commonly change by 20% and up to 80% from one year to the next at the surface of a glacier. Due to the melt enhancement effect of the cliffs, this variability will have large implications for the melt of debris‐covered glaciers and should therefore be accounted for in glacier and glacio‐hydrological models, at least in a stochastic way in a first step to include this additional uncertainty from natural cliff variability in the melt rates.This interannual variability is driven by a combination of contributions from different events occurring at the cliff scale and that rule the cliff life cycle. Birth and death events dominate the variability in the number of ice cliffs. Death events constrain the number of ice cliffs, thus defining the cliff carrying capacity of a glacier while birth events are stochastic, with some dependence on the pond interannual variability. These ponds promote cliff persistence but affect less than 50% of the population and thus are not the main driver of the cliff population's interannual variability. The changes in cliff relative area are also driven by the net contributions of persist events in addition to net contributions from split, merge, or mix events that vary consistently.These events can be represented in a stochastic birth‐death model to constrain the long‐term natural variability of the number and area of cliffs. Some of the changes are however not entirely stochastic and our results show that they can be influenced by climate, supraglacial ponds and/or surface velocity, in spite of the complexity of all the interdependent processes occurring at the glacier surface. As a result, major climatic or glaciological changes, such as we have seen in the case of a surge, may lead to a reorganization of ice cliffs at the glacier surface and a change in the natural variability of the system.Supporting Information S1Click here for additional data file.


In Japan, the criteria of the latent and active phases of the first stage of labor have not been decided. The Japan Society of Obstetrics and Gynecology (JSOG) Perinatal Committee conducted a study to construct a spontaneous labor curve in order to determine the point of onset of the active phase.The participants were women who had spontaneous deliveries at four health facilities in Japan between September 1, 2011, and September 31, 2019. Spontaneous delivery was defined as the spontaneous onset of labor at term  with vaginal delivery of a mature fetus in a cephalic position without uterotonic agents or epidural analgesia. The time points for each “cm” of dilation were collected starting from the time of full dilation retrogradely. The relationship between time since labor onset and cervical dilation was expressed as a curve using a smoothing B‐spline.A total of 4215 primiparous and 5266 multiparous women were included in this study. The spontaneous labor curve showed that in both primiparous and multiparous women, labor progress was slow until 5 cm cervical dilation, accelerating between 5 and 6 cm dilation, and steadily progressed after 6 cm dilation.We propose that the active phase of the first stage of labor be defined as starting at 5 cm dilation of the cervix, and that it be divided into an acceleration phase (5–6 cm dilation) and a maximal phase (>6 cm dilation). The first stage of labor is divided into a latent phase, characterized by a slow cervical dilation rate, and an active phase, with an accelerated progression of labor. If the progression of labor is slower than the standard, interventions such as oxytocin augmentation are considered. Proposed in the 1950s, the Friedman curve has been widely used in Japan as the standard progression.Both the ACOGIn this retrospective, multi‐center study, data were collected from existing medical records. The study was conducted as an initiative of the JSOG with the approval of the Ethics Committee of Yokohama City University . The subjects of this study were primiparous and multiparous women who had spontaneous deliveries at four health facilities  in Japan between September 1, 2011, and September 31, 2019. Spontaneous delivery was defined as the spontaneous onset of labor at term  and the vaginal delivery of a mature fetus in a cephalic position without the use of interventions such as uterotonic agents or epidural analgesia, with exception of routine episiotomies. Since the progression of delivery differs greatly between primiparous and multiparous women, these were analyzed separately. Maternal characteristics such as age at delivery, height, pre‐pregnancy and delivery weight, BMI, gestational age at delivery, infant birthweight, and infant sex were collected. Data related to the progress of labor were collected, as follows: (1) the time of hospital admission for the onset of labor; (2) the degree of cervical dilation upon admission; (3) the degree of cervical dilation at a certain time, as evaluated using internal examination by a physician or midwife; (4) the time of delivery; and (5) the number of internal examinations before the cervix reached full dilation.The period between admission for the onset of labor and full dilation of the cervix was defined as the time required for the first stage of labor. The period between full dilation of the cervix to the delivery of the baby was defined as the time required for the second stage of labor. The time of full cervical dilation was set as the baseline, and the time points before full cervical dilation were collected retrogradely for each cm of dilation. The degree of cervical dilation (from 0 to 10 cm) was plotted on the vertical axis against time on the horizontal axis to create a scatter plot. In addition, the relationship between time and cervical dilation was expressed as a curve using a smoothing B‐spline for primiparous and multiparous women. The degree of the B‐spline function was determined using the Akaike information criterion (AIC) method. The time required for the cervix to open by 1 cm was calculated using an inverse estimation approach based on the estimated labor curve for each degree of opening on the labor curve. We used a bootstrap method with 3000 replications to calculate 95% confidence intervals (CI).There was a total of 9481 eligible patients, of whom, 4215 were primiparous women and 5266 were multiparous women. Maternal characteristics are shown in Table Table Figure In this study, the first stage of labor for deliveries without medical interventions, such as uterotonic agents or epidural anesthesia, was illustrated as a spontaneous labor curve. The spontaneous labor curve was different in shape from either Friedman'sIn the Friedman curve, the active phase of the first stage of labor is subdivided into three phases: acceleration, maximal slope, and deceleration phases. The acceleration phase is a short period that bridges the latent phase and the maximal. The maximal slope phase is the period in which labor progresses most quickly, with cervical dilation ranging from about 3–4 cm to 8–9 cm. The deceleration phase is the period from 9 cm dilation to full dilation. On the other hand, the curve of Zhang et al.At 3–4 cm of cervical dilation, which was already in the active phase in the Friedman curve, the spontaneous labor curve in this study was almost horizontal and the progress of delivery was very slow. Furthermore, in the Friedman curve, there is a deceleration phase in which the progression slows down when the cervical dilation is 9–10 cm, but no deceleration phase was observed in the spontaneous labor curve. As pointed out by Zhang et al.,In comparison with Zhang et al.'s) The investigators constructed a labor curve for a total of 3172 primiparous and multiparous mothers who delivered at one university hospital and six primary medical facilities. The curve suggested that the onset of the active stage of labor was at 6 cm cervical dilation in primiparous women and 5 cm cervical dilation in multiparous women. On the other hand, unlike our study, their report was limited to cases with maternal age of 20–39 years, BMI of less than 30, and infant birthweight of appropriate for dates. However, it is notable that their insights on the shape of the curve and the starting point of the active phase were generally consistent with the results of the present study.There is only one report that analyzed a population without oxytocin augmentation or analgesia similar to the present study.) In addition, by collecting data from multiple university hospitals, we were able to reduce policy bias among institutions. However, this study also has several limitations. First, the participating facilities are biased toward tertiary referral hospital, and second, the duration and frequency of internal examinations are not based on a uniform protocol because of the retrospective nature of the study. Related to this, the criteria for oxytocin augmentation were also not standardized. Therefore, it cannot be denied that only patients with short labor times were included in the study, especially if oxytocin augmentation was performed at an earlier time. Further studies considering with the perinatal outcomes at various facilities including the maternity houses are needed.A strength of this study is the reduced variation in delivery time due to the retrospective examination of only deliveries with a smooth course. It is also favorable that the active phase could be further divided into the accelerated phase and the maximal phase, unlike the curve of Zhang et al.In conclusion, in spontaneous labor without medical intervention, the active phase began at 5 cm of cervical dilation and labor progressed more rapidly after 6 cm in both primiparous and multiparous women. We, the JSOG Perinatal Committee, propose that the active phase of the first stage of labor is defined as cervical dilation after 5 cm and that the active phase is further divided into an accelerated phase , in which the progression of labor begins to accelerate, and a maximal phase , in which labor progresses more rapidly.The authors have no conflicts of interest to disclose.Ryosuke Shindo wrote the initial draft of the manuscript. Sayuriu Nakanishi assisted writing the manuscript. Toshihiro Misumi contributed to analysis and interpretation of data. Shigeru Aoki designed the study and assisted in the preparation of the manuscript. Hisashi Masuyama,Takeshi Nagamatsu, and Takeshi Umazume contributed to collect data. Astuo Itakura and Tomoaki Ikeda contributed to review the manuscript and final approval pf the version to be published.Figure S1. Friedman's curve for primiparous women.Click here for additional data file.Figure S2. Zhang's labor curve.Click here for additional data file.


Clinical Neuroradiology had seen over the course of the past three decades [Last year, we reported on the enormous success  decades . The jouJournal metrics, such as article accesses and submissions, showcase a journal’s development within its field; as such, the journal impact factor receives much attention as one of the most prominent journal metrics.Clinical Neuroradiology has risen continuously in recent years, we are seeing a drop for the first time on publication of the journal impact factors in mid-2022 , the number of citable items, while additional citations stem from the inclusion of additional early access content in 2021 contributing to the numerator [Clinical Neuroradiology this year, we are positive that the quality of our submissions and publications continues to increase.This change in calculation, along with the enormous impact of COVID-19 on publications and citations has caused many shifts in citation numbers and rankings. While this has affected a dip in impact factor and ranking for We are looking forward to your continued support of the journal as readers, authors and reviewers and will take all measures to continue to offer a just and profound peer review process and to serve as an excellent publication home for research of the international neuroradiological community.László SolymosiEditor-in-Chief