Multiple Periodic Solutions for a Class of Fourth-order Difference Systems

By using critical point theory,we study periodic solutions for a class of fourthorder difference systems with partially periodic potential and linear nonlinearity.Some sufficient conditions for the existence of multiplicity of periodic solutions are obtained via generalized saddle point theorem.

Beyond statistical significance:Embracing minimal clinically important difference for better patient care

The minimal clinically important difference(MCID)represents a pivotal metric in bridging the gap between statistical significance and clinical relevance,addressing the direct impact of medical interventions from the patient's perspective.This comprehensive review analyzes the evolution,applications,and challenges of MCID across medical specialties,emphasizing its necessity in ensuring that clinical outcomes not only demonstrate statistical significance but also offer genuine clinical utility that aligns with patient expectations and needs.We discuss the evolution of MCID since its inception in the 1980s,its current applications across various medical specialties,and the methodologies used in its calculation,highlighting both anchor-based and distribution-based approaches.Furthermore,the paper delves into the challenges associated with the application of MCID,such as methodological variability and the interpretation difficulties that arise in clinical settings.Recommendations for the future include standardizing MCID calculation methods,enhancing patient involvement in setting MCID thresholds,and extending research to incorporate diverse global perspectives.These steps are critical to refining the role of MCID in patient-centered healthcare,addressing existing gaps in methodology and interpretation,and ensuring that medical interventions lead to significant,patient-perceived improvements.

High Accurate Fourth-Order Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinate

In this work, by extending the method of Hockney into three dimensions, the Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly. The Poisson equation is approximated by fourth-order finite differences and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The accuracy of this method is tested for some Poisson’s equations with known analytical solutions and the numerical results obtained show that the method produces accurate results.

SECOND-ORDER ACCURATE DIFFERENCE METHOD FOR THE SINGULARLY PERTURBED PROBLEM OF FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we construct a uniform second-order difference scheme for a class of boundary value problems of fourth-order ordinary differential equations. Finally, a numerical example is given.

Two Energy-Preserving Compact Finite Difference Schemes for the Nonlinear Fourth-Order Wave Equation

In this paper,two fourth-order compact finite difference schemes are derived to solve the nonlinear fourth-order wave equation which can be viewed as a generalized model from the nonlinear beam equation.Differing from the existing compact finite difference schemes which preserve the total energy in a recursive sense,the new schemes are proved to per-fectly preserve the total energy in the discrete sense.By using the standard energy method and the cut-off function technique,the optimal error estimates of the numerical solutions are established,and the convergence rates are of O(h^(4)+τ^(2))with mesh-size h and time-step τ.In order to improve the computational efficiency,an iterative algorithm is proposed as the outer solver and the double sweep method for pentadiagonal linear algebraic equations is introduced as the inner solver to solve the nonlinear difference schemes at each time step.The convergence of the iterative algorithm is also rigorously analyzed.Several numerical results are carried out to test the error estimates and conservative properties.

Compact Difference Method for Time-Fractional Neutral Delay Nonlinear Fourth-Order Equation

In this paper, we present a compact finite difference method for a class of fourth-order nonlinear neutral delay sub-diffusion equations in two-dimensional space. The fourth-order problem is first transformed into a second-order system by a reduced-order method. Next by using compact operator to approximate the second order space derivatives and L2-1σ formula to approximate the time fractional derivative, the difference scheme which is fourth order in space and second order in time is obtained. Then, the existence and uniqueness of solution, the convergence rate of and the stability of the scheme are proved. Finally, numerical results are given to verify the accuracy and validity of the scheme.

Domain-based noise removal method using fourth-order partial differential equation

Due to the fact that the fourth-order partial differential equation （PDE） for noise removal can provide a good trade-off between noise removal and edge preservation and avoid blocky effects often caused by the second-order PDE, a domain-based fourth-order PDE method for noise removal is proposed. First, the proposed method segments the image domain into two domains, a speckle domain and a non-speckle domain, based on the statistical properties of isolated speckles in the Laplacian domain. Then, depending on the domain type, different conductance coefficients in the proposed fourth-order PDE are adopted. Moreover, the frequency approach is used to determine the optimum iteration stopping time. Compared with the existing fourth-order PDEs, the proposed fourth-order PDE can remove isolated speckles and keeps the edges from being blurred. Experimental results show the effectiveness of the proposed method.

Age-specific differences in the association between prediabetes and cardiovascular diseases in China:A national cross-sectional study

BACKGROUND Cardiovascular disease(CVD)is a leading cause of morbidity and mortality worldwide,the global burden of which is rising.It is still unclear the extent to which prediabetes contributes to the risk of CVD in various age brackets among adults.To develop a focused screening plan and treatment for Chinese adults with prediabetes,it is crucial to identify variations in the connection between prediabetes and the risk of CVD based on age.AIM To examine the clinical features of prediabetes and identify risk factors for CVD in different age groups in China.METHODS The cross-sectional study involved a total of 46239 participants from June 2007 through May 2008.A thorough evaluation was conducted.Individuals with prediabetes were categorized into two groups based on age.Chinese atherosclerotic CVD risk prediction model was employed to evaluate the risk of developing CVD over 10 years.Random forest was established in both age groups.SHapley Additive exPlanation method prioritized the importance of features from the perspective of assessment contribution.RESULTS In total,6948 people were diagnosed with prediabetes in this study.In prediabetes,prevalences of CVD were 5(0.29%)in the younger group and 148(2.85%)in the older group.Overall,11.11%of the younger group and 29.59% of the older group were intermediate/high-risk of CVD for prediabetes without CVD based on the Prediction for ASCVD Risk in China equation in ten years.In the younger age group,the 10-year risk of CVD was found to be more closely linked to family history of CVD rather than lifestyle,whereas in the older age group,resident status was more closely linked.CONCLUSION The susceptibility to CVD is age-specific in newly diagnosed prediabetes.It is necessary to develop targeted approaches for the prevention and management of CVD in adults across various age brackets.

Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.

POSITIVE SOLUTIONS OF FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Under suitable conditions on h(x) and f(u), the authors show that the following boundary value problem has at least one positive solution. Moreover, the authors also establish several existence theorems of multiple positive solutions.

Extraction of Acoustic Normal Mode Depth Functions Using Range-Difference Method with Vertical Linear Array Data

Data-derived normal mode extraction is an effective method for extracting normal mode depth functions in the absence of marine environmental data.However,when the corresponding singular vectors become nonunique when two or more singular values obtained from the cross-spectral density matrix diagonalization are nearly equal,this results in unsatisfactory extraction outcomes for the normal mode depth functions.To address this issue,we introduced in this paper a range-difference singular value decomposition method for the extraction of normal mode depth functions.We performed the mode extraction by conducting singular value decomposition on the individual frequency components of the signal's cross-spectral density matrix.This was achieved by using pressure and its range-difference matrices constructed from vertical line array data.The proposed method was validated using simulated data.In addition,modes were successfully extracted from ambient noise.

Differential pressure difference based altitude control of a stratospheric satellite

An autonomous altitude adjustment system for a stratospheric satellite(StratoSat)platform is proposed.This platform consists of a helium balloon,a ballonet,and a two-way blower.The helium balloon generates lift to balance the platform gravity.The two-way blower inflates and deflates the ballonet to regulate the buoyancy.Altitude adjustment is achieved by tracking the differential pressure difference(DPD),and a threshold switching strategy is used to achieve blower flow control.The vertical acceleration regulation ability is decided not only by the blower flow rate,but also by the designed margin of pressure difference(MPD).Pressure difference is a slow-varying variable compared with altitude,and it is adopted as the control variable.The response speed of the actuator to disturbance can be delayed,and the overshoot caused by the large inertia of the platform is inhibited.This method can maintain a high tracking accuracy and reduce the complexity of model calculation,thus improving the robustness of controller design.

TSCND:Temporal Subsequence-Based Convolutional Network with Difference for Time Series Forecasting

Time series forecasting plays an important role in various fields, such as energy, finance, transport, and weather. Temporal convolutional networks (TCNs) based on dilated causal convolution have been widely used in time series forecasting. However, two problems weaken the performance of TCNs. One is that in dilated casual convolution, causal convolution leads to the receptive fields of outputs being concentrated in the earlier part of the input sequence, whereas the recent input information will be severely lost. The other is that the distribution shift problem in time series has not been adequately solved. To address the first problem, we propose a subsequence-based dilated convolution method (SDC). By using multiple convolutional filters to convolve elements of neighboring subsequences, the method extracts temporal features from a growing receptive field via a growing subsequence rather than a single element. Ultimately, the receptive field of each output element can cover the whole input sequence. To address the second problem, we propose a difference and compensation method (DCM). The method reduces the discrepancies between and within the input sequences by difference operations and then compensates the outputs for the information lost due to difference operations. Based on SDC and DCM, we further construct a temporal subsequence-based convolutional network with difference (TSCND) for time series forecasting. The experimental results show that TSCND can reduce prediction mean squared error by 7.3% and save runtime, compared with state-of-the-art models and vanilla TCN.

Deep reinforcement learning using least-squares truncated temporal-difference

Policy evaluation(PE)is a critical sub-problem in reinforcement learning,which estimates the value function for a given policy and can be used for policy improvement.However,there still exist some limitations in current PE methods,such as low sample efficiency and local convergence,especially on complex tasks.In this study,a novel PE algorithm called Least-Squares Truncated Temporal-Difference learning(LST2D)is proposed.In LST2D,an adaptive truncation mechanism is designed,which effectively takes advantage of the fast convergence property of Least-Squares Temporal Difference learning and the asymptotic convergence property of Temporal Difference learning(TD).Then,two feature pre-training methods are utilised to improve the approximation ability of LST2D.Furthermore,an Actor-Critic algorithm based on LST2D and pre-trained feature representations(ACLPF)is proposed,where LST2D is integrated into the critic network to improve learning-prediction efficiency.Comprehensive simulation studies were conducted on four robotic tasks,and the corresponding results illustrate the effectiveness of LST2D.The proposed ACLPF algorithm outperformed DQN,ACER and PPO in terms of sample efficiency and stability,which demonstrated that LST2D can be applied to online learning control problems by incorporating it into the actor-critic architecture.

Study on sex differences and potential clinical value of threedimensional computerized tomography pelvimetry in rectal cancer patients

BACKGROUND Laparoscopic rectal cancer radical surgery is a complex procedure affected by various factors.However,the existing literature lacks standardized parameters for the pelvic region and soft tissues,which hampers the establishment of consistent conclusions.AIM To comprehensively assess 16 pelvic and 7 soft tissue parameters through computerized tomography(CT)-based three-dimensional(3D)reconstruction,providing a strong theoretical basis to address challenges in laparoscopic rectal cancer radical surgery.METHODS We analyzed data from 218 patients who underwent radical laparoscopic surgery for rectal cancer,and utilized CT data for 3D pelvic reconstruction.Specific anatomical points were carefully marked and measured using advanced 3D modeling software.To analyze the pelvic and soft tissue parameters,we emp-loyed statistical methods including paired sample t-tests,Wilcoxon rank-sum tests,and correlation analysis.RESULTS The investigation highlighted significant sex disparities in 14 pelvic bone parameters and 3 soft tissue parameters.Males demonstrated larger measurements in pelvic depth and overall curvature,smaller measurements in pelvic width,a larger mesorectal fat area,and a larger anterior-posterior abdominal diameter.By contrast,females exhibited wider pelvises,shallower depth,smaller overall curvature,and an increased amount of subcutaneous fat tissue.However,there were no significant sex differences observed in certain parameters such as sacral curvature height,superior pubococcygeal diameter,rectal area,visceral fat area,waist circumference,and transverse abdominal diameter.CONCLUSION The reconstruction of 3D CT data enabled accurate pelvic measurements,revealing significant sex differences in both pelvic and soft tissue parameters.This study design offer potential in predicting surgical difficulties and creating personalized surgical plans for male rectal cancer patients with a potentially“difficult pelvis”,ultimately improving surgical outcomes.Further research and utilization of these parameters could lead to enhanced surgical methods and patient care in laparoscopic rectal cancer radical surgery.

Analysis of Extended Fisher-Kolmogorov Equation in 2D Utilizing the Generalized Finite Difference Method with Supplementary Nodes

In this study,we propose an efficient numerical framework to attain the solution of the extended Fisher-Kolmogorov(EFK)problem.The temporal derivative in the EFK equation is approximated by utilizing the Crank-Nicolson scheme.Following temporal discretization,the generalized finite difference method(GFDM)with supplementary nodes is utilized to address the nonlinear boundary value problems at each time node.These supplementary nodes are distributed along the boundary to match the number of boundary nodes.By incorporating supplementary nodes,the resulting nonlinear algebraic equations can effectively satisfy the governing equation and boundary conditions of the EFK equation.To demonstrate the efficacy of our approach,we present three numerical examples showcasing its performance in solving this nonlinear problem.

Keep in mind sex differences when prescribing psychotropic drugs

Women represent the majority of patients with psychiatric diagnoses and also the largest users of psychotropic drugs.There are inevitable differences in efficacy,side effects and long-term treatment response between men and women.Psychopharmacological research needs to develop adequately powered animal and human trials aimed to consider pharmacokinetics and pharmacodynamics of central nervous system drugs in both male and female subjects.Healthcare professionals have the responsibility to prescribe sex-specific psychopharmacotherapies with a priority to differentiate between men and women in order to minimize adverse drugs reactions,to maximize therapeutic effectiveness and to provide personalized management of care.

Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.

Three-dimensional analysis of age and sex differences in femoral head asphericity in asymptomatic hips in the United States

BACKGROUND The sphericity of the femoral head is a metric used to evaluate hip pathologies and is associated with the development of osteoarthritis and femoral-acetabular impingement.AIM To analyze the three-dimensional asphericity of the femoral head of asymptomatic pediatric hips.We hypothesized that femoral head asphericity will vary significantly between male and female pediatric hips and increase with age in both sexes.METHODS Computed tomography scans were obtained on 158 children and adolescents from a single institution in the United States(8-18 years;50%male)without hip pain.Proximal femoral measurements including the femoral head diameter,femoral head volume,residual volume,asphericity index,and local diameter difference were used to evaluate femoral head sphericity.RESULTS In both sexes,the residual volume increased by age(P<0.05).Despite significantly smaller femoral head size in older ages(>13 years)in females,there were no sex-differences in residual volume and aspherity index.There were no age-related changes in mean diameter difference in both sexes(P=0.07)with no significant sex-differences across different age groups(P=0.06).In contrast,there were significant increases in local aspherity(maximum diameter difference)across whole surface of the femoral head and all quadrants except the inferior regions in males(P=0.03).There were no sex-differences in maximum diameter difference at any regions and age group(P>0.05).Increased alpha angle was only correlated to increased mean diameter difference across overall surface of the femoral head(P=0.024).CONCLUSION There is a substantial localized asphericity in asymptomatic hips which increases with age in.While 2D measured alpha angle can capture overall asphericity of the femoral head,it may not be sensitive enough to represent regional asphericity patterns.

Application of the Adomian Decomposition Method (ADM) for Solving the Singular Fourth-Order Parabolic Partial Differential Equation

In this paper, the ADM method is used to construct the solution of the singular fourth-order partial differential equation.