Dark Korteweg-De Vrise System and Its Higher-Dimensional Deformations

The new dimensional deformation approach is proposed to generate higher-dimensional analogues of integrable systems.An arbitrary(K+1)-dimensional integrable Korteweg-de Vries(Kd V)system,as an example,exhibiting symmetry,is illustrated to arise from a reconstructed deformation procedure,starting with a general symmetry integrable(1+1)-dimensional dark Kd V system and its conservation laws.Physically,the dark equation systems may be related to dark matter physics.To describe nonlinear physics,both linear and nonlinear dispersions should be considered.In the original lower-dimensional integrable systems,only liner or nonlinear dispersion is included.The deformation algorithm naturally makes the model also include the linear dispersion and nonlinear dispersion.

Model for liver hardness using two-dimensional shear wave elastography,durometer,and preoperative biomarkers

BACKGROUND Post-hepatectomy liver failure(PHLF)increases morbidity and mortality after liver resection for patients with advanced liver fibrosis and cirrhosis.Preoperative liver stiffness using two-dimensional shear wave elastography(2D-SWE)is widely used to evaluate the degree of fibrosis.However,the 2D-SWE results were not accurate.A durometer measures hardness by quantifying the ability of a material to locally resist the intrusion of hard objects into its surface.However,the durometer score can only be obtained during surgery.To measure correlations among 2D-SWE,palpation by surgeons,and durometermeasured objective liver hardness and to construct a liver hardness regression model.METHODS We enrolled 74 hepatectomy patients with liver hardness in a derivation cohort.Tactile-based liver hardness scores(0-100)were determined through palpation of the liver tissue by surgeons.Additionally,liver hardness was measured using a durometer.Correlation coefficients for durometer-measured hardness and preoperative parameters were calculated.Multiple linear regression models were constructed to select the best predictive durometer scale.Receiver operating characteristic(ROC)curves and univariate and multivariate analyses were used to calculate the best model’s prediction of PHLF and risk factors for PHLF,respectively.A separate validation cohort(n=162)was used to evaluate the model.RESULTS The stiffness measured using 2D-SWE and palpation scale had good linear correlation with durometer-measured hardness(Pearson rank correlation coefficient 0.704 and 0.729,respectively,P<0.001).The best model for the durometer scale(hardness scale model)was based on stiffness,hepatitis B virus surface antigen,and albumin level and had an R2 value of 0.580.The area under the ROC for the durometer and hardness scale for PHLF prediction were 0.807(P=0.002)and 0.785(P=0.005),respectively.The optimal cutoff value of the durometer and hardness scale was 27.38(sensitivity=0.900,specificity=0.660)and 27.87(sensitivity=0.700,specificity=0.787),respectively.Patients with a hardness scale score of>27.87 were at a significantly higher risk of PHLF with hazard ratios of 7.835(P=0.015).The model’s PHLF predictive ability was confirmed in the validation cohort.CONCLUSION Liver stiffness assessed by 2D-SWE and palpation correlated well with durometer hardness values.The multiple linear regression model predicted durometer hardness values and PHLF.

From decoupled integrable models to coupled ones via a deformation algorithm

By using a reconstruction procedure of conservation laws of different models,the deformation algorithm proposed by Lou,Hao and Jia has been used to a new application such that a decoupled system becomes a coupled one.Using the new application to some decoupled systems such as the decoupled dispersionless Korteweg–de Vries(Kd V)systems related to dispersionless waves,the decoupled KdV systems related to dispersion waves,the decoupled KdV and Burgers systems related to the linear dispersion and diffusion effects,and the decoupled KdV and Harry–Dym(HD)systems related to the linear and nonlinear dispersion effects,we have obtained various new types of higher dimensional integrable coupled systems.The new models can be used to describe the interactions among different nonlinear waves and/or different effects including the dispersionless waves(dispersionless KdV waves),the linear dispersion waves(KdV waves),the nonlinear dispersion waves(HD waves)and the diffusion effect.The method can be applied to couple all different separated integrable models.

Establish a normal fetal lung gestational age grading model and explore the potential value of deep learning algorithms in fetal lung maturity evaluation

Background:Prenatal evaluation of fetal lung maturity(FLM)is a challenge,and an effective non-invasive method for prenatal assessment of FLM is needed.The study aimed to establish a normal fetal lung gestational age(GA)grading model based on deep learning(DL)algorithms,validate the effectiveness of the model,and explore the potential value of DL algorithms in assessing FLM.Methods:A total of 7013 ultrasound images obtained from 1023 normal pregnancies between 20 and 41+6 weeks were analyzed in this study.There were no pregnancy-related complications that affected fetal lung development,and all infants were born without neonatal respiratory diseases.The images were divided into three classes based on the gestational week:class I:20 to 29+6 weeks,class II:30 to 36+6 weeks,and class III:37 to 41+6 weeks.There were 3323,2142,and 1548 images in each class,respectively.First,we performed a pre-processing algorithm to remove irrelevant information from each image.Then,a convolutional neural network was designed to identify different categories of fetal lung ultrasound images.Finally,we used ten-fold cross-validation to validate the performance of our model.This new machine learning algorithm automatically extracted and classified lung ultrasound image information related to GA.This was used to establish a grading model.The performance of the grading model was assessed using accuracy,sensitivity,specificity,and receiver operating characteristic curves.Results:A normal fetal lung GA grading model was established and validated.The sensitivity of each class in the independent test set was 91.7%,69.8%,and 86.4%,respectively.The specificity of each class in the independent test set was 76.8%,90.0%,and 83.1%,respectively.The total accuracy was 83.8%.The area under the curve(AUC)of each class was 0.982,0.907,and 0.960,respectively.The micro-average AUC was 0.957,and the macro-average AUC was 0.949.Conclusions:The normal fetal lung GA grading model could accurately identify ultrasound images of the fetal lung at different GAs,which can be used to identify cases of abnormal lung development due to gestational diseases and evaluate lung maturity after antenatal corticosteroid therapy.The results indicate that DL algorithms can be used as a non-invasive method to predict FLM.