Solving Neumann Boundary Problem with Kernel-Regularized Learning Approach

We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.

Problem-solving model guided by stimulus-organism-response theory:State of mind and coping styles of depressed mothers after cesarean delivery

BACKGROUND The use of a problem-solving model guided by stimulus-organism-response(SOR)theory for women with postpartum depression after cesarean delivery may inform nursing interventions for women with postpartum depression.AIM To explore the state of mind and coping style of women with depression after cesarean delivery guided by SOR theory.METHODS Eighty postpartum depressed women with cesarean delivery admitted to the hospital between January 2022 and October 2023 were selected and divided into two groups of 40 cases each,according to the random number table method.In the control group,the observation group adopted the problem-solving nursing model under SOR theory.The two groups were consecutively intervened for 12 weeks,and the state of mind,coping styles,and degree of post-partum depression were analyzed at the end of the intervention.RESULTS The Edinburgh Postnatal Depression Scale and Hamilton Depression Scale-24-item scores of the observation group were lower than in the control group after care,and the level of improvement in the state of mind was higher than that of the control group(P<0.05).The level of coping with illness in the observation group after care(26.48±3.35)was higher than that in the control group(21.73±3.20),and the level of avoidance(12.04±2.68)and submission(8.14±1.15)was lower than that in the control group(15.75±2.69 and 9.95±1.20),with significant differences(P<0.05).CONCLUSION Adopting the problem-solving nursing model using SOR theory for postpartum depressed mothers after cesarean delivery reduced maternal depression,improved their state of mind,and coping level with illness.

A DUAL-RELAX PENALTY FUNCTION APPROACH FOR SOLVING NONLINEAR BILEVEL PROGRAMMING WITH LINEAR LOWER LEVEL PROBLEM

The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.

Complication rates after direct anterior vs posterior approach for hip hemiarthroplasty in elderly individuals with femoral neck fractures

BACKGROUND Dislocation rates after hemiarthroplasty reportedly vary from 1%to 17%.This serious complication is associated with increased morbidity and mortality rates.Approaches to this surgery are still debated,with no consensus regarding the superiority of any single approach.AIM To compare early postoperative complications after implementing the direct anterior and posterior approaches(PL)for hip hemiarthroplasty after femoral neck fractures.METHODS This is a comparative,retrospective,single-center cohort study conducted at a university hospital.Between March 2008 and December 2018,273 patients(a total of 280 hips)underwent bipolar hemiarthroplasties(n=280)for displaced femoral neck fractures using either the PL(n=171)or the minimally invasive direct anterior approach(DAA)(n=109).The choice of approach was related to the surgeons’practices;the implant types were similar and unrelated to the approach.Dislocation rates and other complications were reviewed after a minimum followup of 6 mo.RESULTS Both treatment groups had similarly aged patients(mean age:82 years),sex ratios,patient body mass indexes,and patient comorbidities.Surgical data(surgery delay time,operative time,and blood loss volume)did not differ significantly between the groups.The 30 d mortality rate was higher in the PL group(9.9%)than in the DAA group(3.7%),but the difference was not statistically significant(P=0.052).Among the one-month survivors,a significantly higher rate of dislocation was observed in the PL group(14/154;9.1%)than in the DAA group(0/105;0%)(P=0.002).Of the 14 patients with dislocation,8 underwent revision surgery for recurrent instability(posterior group),and one of them had 2 additional procedures due to a deep infection.The rate of other complications(e.g.,perioperative and early postoperative periprosthetic fractures and infection-related complications)did not differ significantly between the groups.CONCLUSION These findings suggest that the DAA to bipolar hemiarthroplasty for patients with femoral neck fractures is associated with a lower dislocation rate(<1%)than the PL.

An Improved Text-Based and Image-Based CAPTCHA Based on Solving and Response Time

CAPTCHA is an acronym that stands for Completely Automated Public Turing Test to tell Computers and Humans Apart(CAPTCHA),it is a good example of an authentication system that can be used to determine the true identity of any user.It serves as a security measure to prevent an attack caused by web bots(automatic programs)during an online transaction.It can come as text-based or image-based depending on the project and the programmer.The usability and robustness,as well as level of security,provided each of the varies and call for the development of an improved system.Hence,this paper studied and improved two different CAPTCHA systems(the text-based CAPTCHA and image-based CAPTCHA).The textbased and image-based CAPTCHAwere designed using JavaScript.Response time and solving time are the two metrics used to determine the effectiveness and efficiency of the two CAPTCHA systems.The inclusion of response time and solving time improved the shortfall of the usability and robustness of the existing system.The developed system was tested using 200 students from the Federal College of Animal Health and Production Technology.The results of each of the participants,for the two CAPTCHAs,were extracted from the database and subjected to analysis using SPSS.The result shows that textbased CAPTCHAhas the lowest average solving time(21.3333 s)with a 47.8%success rate while image-based CAPTCHA has the highest average solving time was 23.5138 s with a 52.8%success rate.The average response time for the image-based CAPTCHA was 2.1855 s with a 37.9%success rate lower than the text-based CAPTCHA response time(3.5561 s)with a 62.1%success rate.This indicates that the text-based CAPTCHA is more effective in terms of usability tests while image-based CAPTCHA is more efficient in terms of system responsiveness and recommended for potential users.

Qualia Role-Based Quantity Relation Extraction for Solving Algebra Story Problems

A qualia role-based entity-dependency graph(EDG)is proposed to represent and extract quantity relations for solving algebra story problems stated in Chinese.Traditional neural solvers use end-to-end models to translate problem texts into math expressions,which lack quantity relation acquisition in sophisticated scenarios.To address the problem,the proposed method leverages EDG to represent quantity relations hidden in qualia roles of math objects.Algorithms were designed for EDG generation and quantity relation extraction for solving algebra story problems.Experimental result shows that the proposedmethod achieved an average accuracy of 82.2%on quantity relation extraction compared to 74.5%of baseline method.Another prompt learning result shows a 5%increase obtained in problem solving by injecting the extracted quantity relations into the baseline neural solvers.

Time-dependent variational approach to solve multi-dimensional time-dependent Schr?dinger equation

We present an efficient approach to solve multi-dimensional time-dependent Schr?dinger equation(TDSE)in an intense laser field.In this approach,each spatial degree of freedom is treated as a distinguishable quasi-particle.The non-separable Coulomb potential is regarded as a two-body operator between different quasi-particles.The time-dependent variational principle is used to derive the equations of motion.Then the high-order multi-dimensional problem is broken down into several lower-order coupled equations,which can be efficiently solved.As a demonstration,we apply this method to solve the two-dimensional TDSE.The accuracy is tested by comparing the direct solutions of TDSE using several examples such as the strong-field ionization and the high harmonic generation.The results show that the present method is much more computationally efficient than the conventional one without sacrificing accuracy.The present method can be straightforwardly extended to three-dimensional problems.Our study provides a flexible method to investigate the laser-atom interaction in the nonperturbative regime.

A Variational Approach for Numerically Solving the Two-Component Radial Dirac Equation for One-Particle Systems

In this paper we propose a numerical approach to solve the relativistic Dirac equation suitable for computational calculations of one-electron systems. A variational procedure is carried out similar to the well-known Hylleraas computational method. An application of the method to hydrogen isoelectronic atoms is presented, showing its consistency and high accuracy, relative to the exact analytical eigenvalues.

Which approach of total hip arthroplasty is the best efficacy and least complication?

BACKGROUND Total hip arthroplasty is as an effective intervention to relieve pain and improve hip function.Approaches of the hip have been exhaustively explored about pros and cons.The efficacy and the complications of hip approaches remains inconclusive.This study conducted an umbrella review to systematically appraise previous meta-analysis(MAs)including conventional posterior approach(PA),and minimally invasive surgeries as the lateral approach(LA),direct anterior approach(DAA),2-incisions method,mini-lateral approach and the newest technique direct superior approach(DSA)or supercapsular percutaneouslyassisted total hip(SuperPath).AIM To compare the efficacy and complications of hip approaches that have been published in all MAs and randomized controlled trials(RCTs).METHODS MAs were identified from MEDLINE and Scopus from inception until 2023.RCTs were then updated from the latest MA to September 2023.This study included studies which compared hip approaches and reported at least one outcome such as Harris Hip Score(HHS),dislocation,intra-operative fracture,wound compliData were independently selected,extracted and assessed by two reviewers.Network MA and cluster rank and surface under the cumulative ranking curve(SUCRA)were estimated for treatment efficacy and safety.RESULTS Finally,twenty-eight MAs(40 RCTs),and 13 RCTs were retrieved.In total 47 RCTs were included for reanalysis.The results of corrected covered area showed high degree(13.80%).Among 47 RCTs,most of the studies were low risk of bias in part of random process and outcome reporting,while other domains were medium to high risk of bias.DAA significantly provided higher HHS at three months than PA[pooled unstandardized mean difference(USMD):3.49,95%confidence interval(CI):0.98,6.00 with SUCRA:85.9],followed by DSA/SuperPath(USMD:1.57,95%CI:-1.55,4.69 with SUCRA:57.6).All approaches had indifferent dislocation and intraoperative fracture rates.SUCRA comparing early functional outcome and composite complications(dislocation,intra-operative fracture,wound complication,and nerve injury)found DAA was the best approach followed by DSA/SuperPath.CONCLUSION DSA/SuperPath had better earlier functional outcome than PA,but still could not overcome the result of DAA.This technique might be the other preferred option with acceptable complications.

Attractive Multistep Reproducing Kernel Approach for Solving Stiffness Differential Systems of Ordinary Differential Equations and Some Error Analysis

In this paper,an efficient multi-step scheme is presented based on reproducing kernel Hilbert space(RKHS)theory for solving ordinary stiff differential systems.The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform formfor a rapidly convergent series in the posed Sobolev space.Using the Gram-Schmidt orthogonality process,complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction.Consequently,by applying the standard RKHS method to each subinterval,approximate solutions that converge uniformly to the exact solutions are obtained.For this purpose,several numerical examples are tested to show proposed algorithm’s superiority,simplicity,and efficiency.The gained results indicate that themulti-step RKHSmethod is suitable for solving linear and nonlinear stiffness systems over an extensive duration and giving highly accurate outcomes.

Minimalistic approach to left atrial appendage occlusion guided by cardiac computed tomography angiography

OBJECTIVE To assess the feasibility and safety of the minimalistic approach to left atrial appendage occlusion(LAAO) guided by cardiac computed tomography angiography(CCTA).METHODS Ninety consecutive patients who underwent LAAO, with or without CCTA-guided, were matched(1:2). Each step of the LAAO procedure in the computed tomography(CT) guidance group(CT group) was directed by preprocedural CT planning. In the control group, LAAO was performed using the standard method. All patients were followed up for 12 months, and device surveillance was conducted using CCTA.RESULTS A total of 90 patients were included in the analysis, with 30 patients in the CT group and 60 matched patients in the control group. All patients were successfully implanted with Watchman devices. The mean ages for the CT group and the control group were 70.0 ± 9.4 years and 68.4 ± 11.9 years(P = 0.52), respectively. The procedure duration(45.6 ± 10.7 min vs. 58.8 ± 13.0 min,P < 0.001) and hospital stay(7.5 ± 2.4 day vs. 9.6 ± 2.8 day, P = 0.001) in the CT group was significantly shorter compared to the control group. However, the total radiation dose was higher in the CT group compared to the control group(904.9 ± 348.0 m Gy vs.711.9 ± 211.2 m Gy, P = 0.002). There were no significant differences in periprocedural pericardial effusion(3.3% vs. 6.3%, P = 0.8) between the two groups. The rate of postprocedural adverse events(13.3% vs. 18.3%, P = 0.55) were comparable between both groups at 12 months follow-up.CONCLUSIONS CCTA is capable of detailed LAAO procedure planning. Minimalistic LAAO with preprocedural CCTA planning was feasible and safe, with shortened procedure time and acceptable increased radiation and contras consumption. For patients with contraindications to general anesthesia and/or transesophageal echocardiography, this promising method may be an alternative to conventional LAAO.

Virtual source approach for maximizing resolution in high-penetration gamma-ray imaging

High-energy gamma-ray radiography has exceptional penetration ability and has become an indispensable nondestructive testing(NDT)tool in various fields.For high-energy photons,point projection radiography is almost the only feasible imaging method,and its spatial resolution is primarily constrained by the size of the gamma-ray source.In conventional industrial applications,gamma-ray sources are commonly based on electron beams driven by accelerators,utilizing the process of bremsstrahlung radiation.The size of the gamma-ray source is dependent on the dimensional characteristics of the electron beam.Extensive research has been conducted on various advanced accelerator technologies that have the potential to greatly improve spatial resolution in NDT.In our investigation of laser-driven gamma-ray sources,a spatial resolution of about 90μm is achieved when the areal density of the penetrated object is 120 g/cm^(2).A virtual source approach is proposed to optimize the size of the gamma-ray source used for imaging,with the aim of maximizing spatial resolution.In this virtual source approach,the gamma ray can be considered as being emitted from a virtual source within the convertor,where the equivalent gamma-ray source size in imaging is much smaller than the actual emission area.On the basis of Monte Carlo simulations,we derive a set of evaluation formulas for virtual source scale and gamma-ray emission angle.Under optimal conditions,the virtual source size can be as small as 15μm,which can significantly improve the spatial resolution of high-penetration imaging to less than 50μm.

Debate on direct-anterior vs posterior approach for hip hemiarthroplasty:The authors’insights

We read and discussed the study entitled“Complication rates after direct anterior vs posterior approach for Hip Hemiarthroplasty in elderly individuals with femoral neck fractures”with great interest.The authors have done justice to the topic of comparison of anterior and posterior surgical approaches for bipolar hemiarthroplasty which has been an everlasting debate in the existing literature.However,there are certain aspects of this study that need clarification from the authors.

Direct anterior compared to posterior approach for hip hemiarthroplasty following femoral neck fractures

The differences in complication rates between the direct anterior and posterior approaches for hemiarthroplasty in elderly patients with femoral neck fractures are not yet fully understood.Dislocation,a severe complication associated with increased mortality and often requiring additional surgery,may occur less frequently with the direct anterior approach compared to the posterior approach.Careful consideration of patient demographics is essential when planning the surgical approach.Future research in this area should focus on robust randomized controlled trials involving elderly patients recovering from femoral neck fractures.

A FLEXIBLE OBJECTIVE-CONSTRAINT APPROACH AND A NEW ALGORITHM FOR CONSTRUCTING THE PARETO FRONT OF MULTIOBJECTIVE OPTIMIZATION PROBLEMS

In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.

A Deep Learning Based Broadcast Approach for Image Semantic Communication over Fading Channels

We consider an image semantic communication system in a time-varying fading Gaussian MIMO channel,with a finite number of channel states.A deep learning-aided broadcast approach scheme is proposed to benefit the adaptive semantic transmission in terms of different channel states.We combine the classic broadcast approach with the image transformer to implement this adaptive joint source and channel coding(JSCC)scheme.Specifically,we utilize the neural network(NN)to jointly optimize the hierarchical image compression and superposition code mapping within this scheme.The learned transformers and codebooks allow recovering of the image with an adaptive quality and low error rate at the receiver side,in each channel state.The simulation results exhibit our proposed scheme can dynamically adapt the coding to the current channel state and outperform some existing intelligent schemes with the fixed coding block.

Lychrel Numbers in Base 10: A Probabilistic Approach

For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel number in base 10 and provides some properties which enable a mathematical extraction of new Lychrel numbers from existing ones. This probabilistic approach has the advantage of being extendable to other bases. The results show that palindromes can also be Lychrel numbers.

Creative Problem-Solving and Music: Analyzing the Correlation between Music and Divergent Thinking Abilities

This research paper delves into the connection, between problem-solving and music. It’s a topic that has piqued the interest of scholars in fields, including science and neuroscience. The study explores how music can influence our ability to think divergently which is an aspect of creative thinking. It builds upon advancements in methods to investigate the relationship between music and divergent thinking aiming to uncover potential correlations. Doing it offers insights into the interplay between artistic expression and cognitive innovation. This research combines an analysis of existing literature with data collected from a group of participants shedding light on how music impacts our capacity for creative thinking. It demonstrates that music plays a role as a catalyst, for stimulating and enhancing thinking abilities.

Probabilistic Analysis of Slope Using Finite Element Approach and Limit Equilibrium Approach around Amalpata Landslide of West Central, Nepal

The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have different slope inclinations. The lower bench, located above the basement, consistently fails and sets others up for failure. The fluctuating water level of the slope, which travels down the slope masses, exacerbates the slide problem. The majority of these rocks are Amalpata landslide area experiences several structural disruptions. The area’s stability must be evaluated in order to prevent and control more harm from occurring to the nearby agricultural land and people living along the slope. The slopes’ failures increase the damages of house existing in nearby area and the erosion of the slope. Two modeling techniques the finite element approach and the limit equilibrium method were used to simulate the slope. The findings show that, in every case, the terrace above the basement is where the majority of the stress is concentrated, with a safety factor of near unity. Using probabilistic slope stability analysis, the failure probability was predicted to be between 98.90% and 100%.

Conformal Invariant Asymptotic Expansion Approach for Solving （3＋1）-Dimensional JM Equation

The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.