A Full Predictor-Corrector Finite Element Method for the One-Dimensional Heat Equation with Time-Dependent Singularities

The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.

Predictors of Abnormal Vaginal Discharge among Women of Reproductive Age in Southeast Nigeria

Background: An abnormal vaginal discharge is a common complaint among women of reproductive age, and it can indicate serious conditions like pelvic inflammatory disease and cervical cancer. This study aimed to assess the predictors of abnormal vaginal discharge in women of reproductive age group in Imo State, Southeast Nigeria. Methods: A cross-sectional study was conducted among 368 women of reproductive age group attending the clinic at Federal University Teaching Hospital Owerri, in Imo State, Nigeria. Respondents were recruited using a systematic sampling technique. Data were collected using a pre-tested interviewer-administered questionnaire. Multivariable analysis was performed to determine predictors of abnormal vaginal discharge. Statistical significance was set at p Results: The mean age of the respondents was 30 ± 4.5 years. Predictors of abnormal vaginal discharge were: age 36 - 45 years (OR: 4.5;95% C.I: 1.023 - 8.967, p = 0.041), being a student (OR: 2.4: 95% C.I: 1.496 - 7.336, p = 0.003), use of oral contraceptives (OR: 3.4;95% C.I: 1.068 - 6.932, p = 0.010), use of water cistern (OR: 4.7;C.I: 1.654 - 5.210, p = 0.028) anal hygiene practices (OR: 2.7;95% C.I: 1.142 - 4.809, p Conclusion: These findings suggest that targeted sexual and reproductive health interventions should be provided to reduce the risk of abnormal vaginal discharge in women of reproductive age group.

Echocardiographic predictors and associated outcomes of multiple vegetations in infective endocarditis:A pilot study

BACKGROUND Infective endocarditis(IE)is a life-threatening infection with an annual mortality of 40%.Embolic events reported in up to 80%of patients.Vegetations of>10 mm size are associated with increased embolic events and poor prognosis.There is a paucity of literature on the association of multiple vegetations with outcome.AIM To study the echocardiographic(ECHO)features and outcomes associated with the presence of multiple vegetations.METHODS In this retrospective,single-center,cohort study patients diagnosed with IE were recruited from June 2017 to June 2019.A total of 84 patients were diagnosed to have IE,of whom 67 with vegetation were identified.Baseline demographic,clinical,laboratory,and ECHO parameters were reviewed.Outcomes that were studied included recurrent admission,embolic phenomenon,and mortality.RESULTS Twenty-three(34%)patients were noted to have multiple vegetations,13(56.5%)were male and 10(43.5%)were female.The mean age of these patients was 50.Eight(35%)had a prior episode of IE.ECHO features of moderate to severe valvular regurgitation[odds ratio(OR)=4],presence of pacemaker lead(OR=4.8),impaired left ventricle(LV)relaxation(OR=4),and elevated pulmonary artery systolic pressure(PASP)(OR=2.2)are associated with higher odds of multiple vegetations.Of these moderate to severe valvular regurgitation(P=0.028),pacemaker lead(P=0.039)and impaired relaxation(P=0.028)were statistically significant.These patients were noted to have an increased association of recurrent admissions(OR=3.6),recurrent bacteremia(OR=2.4),embolic phenomenon(OR=2.5),intensive care unit stay(OR=2.8),hypotension(OR=2.1),surgical intervention(OR=2.8)and device removal(OR=4.8).Of this device removal(P=0.039)and recurrent admissions(P=0.017)were statistically significant.CONCLUSION This study highlights the associations of ECHO predictors and outcomes in patients with IE having multiple vegetations.ECHO features of moderate to severe regurgitation,presence of pacemaker lead,impaired LV relaxation,and elevated PASP and outcomes including recurrent admissions and device removal were found to be associated with multiple vegetations.

Predictors of Fatal Outcome in Hospitalised Adult Patients with Acute Kidney Injury at Two Tertiary Hospitals in Sub-Saharan Africa

Introduction: Data on mortality in acute kidney injury (AKI) derives from high-income countries where AKI is hospital-acquired and occurs in elderly patients with a high burden of cardiovascular disease. In sub-Saharan Africa (SSA), AKI is community-acquired occurring in healthy young adults. We aimed to identify predictors of fatal outcomes in patients with AKI in two tertiary hospitals in Cameroon. Methods: Medical records of adults with confirmed AKI, from January 2018 to March 2020 were retrieved. The outcomes of interest were in-hospital deaths and presumed causes of death. We used multiple logistic regressions modeling to identify predictors of death. The study was approved by the ethics boards of both hospitals. Values were considered significant for a p-value of 0.05. Results: We included 285 patient records (37.2% females). The mean (SD) age was 50.1 (19.0) years. Hypertension (n = 97, 34.0%), organ failure (n = 88, 30.9%), and diabetes (n = 60, 21.1%) were the main comorbidities. The majority of patients had community-acquired AKI (78.6%, n = 224), were KDIGO stage 3 (88.8%, n = 253), and needed dialysis (52.6%, n = 150). Up to 16.7% (n = 25) did not receive what was needed. The in-hospital mortality rate was 29.1% (n = 83). Lack of access to dialysis (OR = 27.8;CI: 5.2 - 149.3, p = 0.001), hypotension (OR = 11.8;CI: 1.3 - 24.8;p = 0.001) and ICU admission (OR = 5.7;CI: 1.3 - 24.8, p = 0.001) were predictors of mortality. The presence of co-morbidities or underlying diseases (n = 46, 55%) were the main causes of death. Conclusions: In-hospital AKI mortality is high, as in other low- and middle-income economies. Lack of access to dialysis and the severity of the underlying illness are major predictors of death.

Predictors of portal vein thrombosis after splenectomy in patients with cirrhosis

BACKGROUND Portal vein thrombosis(PVT)is a commonthsn complication after splenectomy in patients with cirrhosis.However,the predictors of postoperative PVT are not known.AIM To investigate the predictors of PVT after splenectomy in patient with cirrhosis.METHODS A total of 45 patients with cirrhosis who underwent splenectomy were consecutively enrolled from January 2017 to December 2018.The incidence of PVT at 1 months,3 months,and 12 months after splenectomy in patients with cirrhosis was observed.The hematological indicators,biochemical and coagulation parameters,and imaging features were recorded at baseline and at each observation point.The univariable,multivariable,receiver operating characteristic curve and timedependent curve analyses were performed.RESULTS The cumulative incidence of PVT was 40.0%,46.6%,and 48.9%at 1 months,3 months,and 12 months after splenectomy.Multivariable analysis showed that portal vein diameter(PVD)≥14.5 mm and monthsdel end-stage liver disease(MELD)score>10 were independent predictors of PVT at 1 months,3 months,and 12 months after splenectomy(P<0.05).Time-dependent curve showed that the cumulative incidence of PVT was significantly different between patients with MELD score≤10 and>10(P<0.05).In addition,the cumulative incidence of PVT in the PVD≥14.5 mm group was significantly higher than that in the PVD<14.5 mm group(P<0.05).CONCLUSION Wider PVD and MELD score>10 were independent predictors of PVT at 1 months,3 months,and 12 months after splenectomy in patient with cirrhosis.

Rates, predictors, and causes of readmission after transcatheter aortic valve replacement in patients with chronic kidney disease

BACKGROUND Transcatheter aortic valve replacement(TAVR)is a revolutionary procedure for severe aortic stenosis.The coexistence of chronic kidney disease(CKD)and TAVR introduces a challenge that significantly impacts patient outcomes.AIM To define readmission rates,predictors,and causes after TAVR procedure in CKD stage 1-4 patients.METHODS We used the national readmission database 2018 and 2020 to look into readmission rates,causes and predictors after TAVR procedure in patients with CKD stage 1-4.RESULTS Out of 24758 who underwent TAVR and had CKD,7892(32.4%)patients were readmitted within 90 days,and had higher adjusted odds of being females(adjusted odds ratio:1.17,95%CI:1.02-1.31,P=0.02)with longer length of hospital stay>6 days,and more comorbidities including but not limited to diabetes mellitus,anemia,and congestive heart failure(CHF).CONCLUSION Most common causes of readmission included CHF(18.0%),sepsis,and complete atrioventricular block.Controlling readmission predictors with very close followup is warranted to prevent such high rate of readmission.

Heterogeneously elevated branched-chain/aromatic amino acids among new-onset type-2 diabetes mellitus patients are potentially skewed diabetes predictors

BACKGROUND The lack of specific predictors for type-2 diabetes mellitus(T2DM)severely impacts early intervention/prevention efforts.Elevated branched-chain amino acids(BCAAs:Isoleucine,leucine,valine)and aromatic amino acids(AAAs:Tyrosine,tryptophan,phenylalanine)show high sensitivity and specificity in predicting diabetes in animals and predict T2DM 10-19 years before T2DM onset in clinical studies.However,improvement is needed to support its clinical utility.AIM To evaluate the effects of body mass index(BMI)and sex on BCAAs/AAAs in new-onset T2DM individuals with varying body weight.METHODS Ninety-seven new-onset T2DM patients(<12 mo)differing in BMI[normal weight(NW),n=33,BMI=22.23±1.60;overweight,n=42,BMI=25.9±1.07;obesity(OB),n=22,BMI=31.23±2.31]from the First People’s Hospital of Yunnan Province,Kunming,China,were studied.One-way and 2-way ANOVAs were conducted to determine the effects of BMI and sex on BCAAs/AAAs.RESULTS Fasting serum AAAs,BCAAs,glutamate,and alanine were greater and high-density lipoprotein(HDL)was lower(P<0.05,each)in OB-T2DM patients than in NW-T2DM patients,especially in male OB-T2DM patients.Arginine,histidine,leucine,methionine,and lysine were greater in male patients than in female patients.Moreover,histidine,alanine,glutamate,lysine,valine,methionine,leucine,isoleucine,tyrosine,phenylalanine,and tryptophan were significantly correlated with abdominal adiposity,body weight and BMI,whereas isoleucine,leucine and phenylalanine were negatively correlated with HDL.CONCLUSION Heterogeneously elevated amino acids,especially BCAAs/AAAs,across new-onset T2DM patients in differing BMI categories revealed a potentially skewed prediction of T2DM development.The higher BCAA/AAA levels in obese T2DM patients would support T2DM prediction in obese individuals,whereas the lower levels of BCAAs/AAAs in NW-T2DM individuals may underestimate T2DM risk in NW individuals.This potentially skewed T2DM prediction should be considered when BCAAs/AAAs are to be used as the T2DM predictor.

Depression&Anxiety Among Women in Northern Kenya:Sociodemographic Predictors

This article documents socio-demographic predictors of anxiety and depression among Maasai women in resource poor settings in Northern Kenya.These findings emerged from the findings of a dissertation research that aimed to establish the treatment effectiveness of an eclectic model of psychoeducation(PE)in treating depressive and anxiety symptoms among the women.The study adopted a quasi-experimental research design which had an experimental group(EG)and control group(CG).The population for the study was 686 female members of Conservation Enterprise Groups(CEG)in Laikipia County,from which a sample of 200 were recruited for the study(EG,n=100 and CG,n=100),at 80%power and 30%effective size.The Beck’s Depression Inventory(BDI)and Beck’s Anxiety Inventory(BAI)tools were used to assess the symptoms of depression and anxiety,respectively.The PE was provided as an intervention treatment to the EG at the middle and end of the study,after which the respondents were tested for symptoms of depression.The study established the prevalence of depression as 26.7%and 31.3%for anxiety and disorders,among women in the region.Data was analyzed using SPSS Version 21.0.

凸二次规划的Predictor－Corrector算法

考虑凸二次规划问题，给出了一个新的算法。

AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM

A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.

A POLYNOMIAL PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING

This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O（√nL） iteration complexity which is the best result for convex quadratic programming so far.

Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

A predictor-corrector interior-point algorithmfor monotone variational inequality problems

Mehrotra' s recent suggestion of a predictor-eorrector variant of primal-dual interior-point method for linear programming is currently the interior-point method of choice for linear programming.In this work the authors give a predictor-corrector interior-point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented.

New Predictor-Corrector Methods Based on Exponential Time Differencing forSystems of Nonlinear Differential Equations

We present the new predictor-corrector methods for systems of nonlinear differential equations, based on themethod of esponential time differencing. We compare the present schemes with the explicit multistep exponential time differecing and Adams Bashforth-Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies.

An Explicit-Implicit Predictor-Corrector Domain Decomposition Method for Time Dependent Multi-Dimensional Convection Diffusion Equations

The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.

Two new predictor-corrector algorithms for second-order cone programming

Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton （AHO） directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O（rln（εo/ε）） is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.

Finite Volume Element Predictor-corrector Method for a Class of Nonlinear Parabolic Systems

A finite volume element predictor-corrector method for a class of nonlinear parabolic system of equations is presented and analyzed. Suboptimal L^2 error estimate for the finite volume element predictor-corrector method is derived. A numerical experiment shows that the numerical results are consistent with theoretical analysis.

Evaluating accuracy of Hessian-based predictor-corrector integrators

Direct dynamics simulations are a useful and general approach for studying the atomistic properties of complex chemical systems because they do not require fitting an analytic potential energy function.Hessian-based predictor-corrector integrators are a widely used approach for calculating the trajectories of moving atoms in direct dynamics simulations.We employ a monodromy matrix to propose a tool for evaluating the accuracy of integrators in the trajectory calculation.We choose a general velocity Verlet as a different object.We also simulate molecular with hydrogen(CO_2) and molecular with hydrogen(H_2O) motions.Comparing the eigenvalues of monodromy matrix,many simulations show that Hessian-based predictor-corrector integrators perform well for Hessian updates and non-Hessian updates.Hessian-based predictor-corrector integrator with Hessian update has a strong performance in the H_2O simulations.Hessian-based predictor-corrector integrator with Hessian update has a strong performance when the integrating step of the velocity Verlet approach is tripled for the predicting step.In the CO_2 simulations,a strong performance occurs when the integrating step is a multiple of five.

Predictor-corrector interior-point algorithm for linearly constrained convex programming

Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed. In eac h iteration, the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory. Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required. It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method. Numerical experiments on twenty-six standard test problems are made. The result s show that the proposed algorithm is stable and robust.

A PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING

The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off between expense and fast convergence by composing one Newton step with one simplified Newton step. Recently, Mehrotra suggested a predictor-corrector variant of primal-dual interior point method for linear programming. It is currently the interiorpoint method of the choice for linear programming. In this work we propose a predictor-corrector interior-point algorithm for convex quadratic programming. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require that the initial primal and dual points be feasible. Numerical experiments are made.