The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exac...The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.展开更多
AIM:To compare the efficacies of patching and penalization therapies for the treatment of amblyopia patients.METHODS:The records of 64 eyes of 50 patients 7 to16y of age who had presented to our clinics with a diagnos...AIM:To compare the efficacies of patching and penalization therapies for the treatment of amblyopia patients.METHODS:The records of 64 eyes of 50 patients 7 to16y of age who had presented to our clinics with a diagnosis of amblyopia,were evaluated retrospectively.Forty eyes of 26 patients who had received patching therapy and 24 eyes of 24 patients who had received penalization therapy included in this study.The latencies and amplitudes of visual evoked potential(VEP)records and best corrected visual acuities(BCVA)of these two groups were compared before and six months after the treatment.RESULTS:In both patching and the penalization groups,the visual acuities increased significantly following the treatments(P【0.05).The latency measurements of the P100 wave obtained at 1.0°,15 arc min.Patterns of both groups significantly decreased following the 6-months-treatment.However,the amplitude measurements increased(P【0.05).CONCLUSION:The patching and the penalization methods,which are the main methods used in the treatment of amblyopia,were also effective over the age of 7y,which has been accepted as the critical age for the treatment of amblyopia.展开更多
Background:To date,compliance to atropine penalization in amblyopic children has only been assessed through self-report.The goal of this pilot study is to measure compliance to atropine penalization objectively.Method...Background:To date,compliance to atropine penalization in amblyopic children has only been assessed through self-report.The goal of this pilot study is to measure compliance to atropine penalization objectively.Methods:Seven amblyopic children(3-8 years;20/40-20/125 in the amblyopic eye) were enrolled.None had been treated with atropine previously.Children were prescribed either a twice per week or daily atropine regimen by their physicians.Compliance was defined as the percentage of days in which the atropine eye drop was taken compared to the number of doses prescribed.We used medication event monitoring system(MEMS) caps to objectively measure compliance.The MEMS caps are designed to electronically record the time and date when the bottle is opened.The parents of the children were provided a calendar log to subjectively report compliance.Participants were scheduled for return visits at 4 and 12 weeks.Weekly compliance was analyzed.Results:At 4 weeks,objective compliance averaged 88%(range,57-100%),while subjective compliance was 98%(range,90-100%).The actual dose in grams and visual acuity(VA) response relationship(r=0.79,P=0.03) was significantly better than the relationship between regimen and response(r=0.41,P>0.05),or the relationship between actual dose in drops and response(r=0.52,P>0.05).Conclusions:Objective compliance to atropine penalization instructions can be monitored with MEMS,which may facilitate our understanding of the dose-response relationship.Objective compliance with atropine penalization decreases over time and varies with regimen.On average,subjective parental reporting of compliance is overestimated.展开更多
The paper is directly motivated by the pricing of vulnerable European and American options in a general hazard process setup and a related study of the corresponding pre-default backward stochastic differential equati...The paper is directly motivated by the pricing of vulnerable European and American options in a general hazard process setup and a related study of the corresponding pre-default backward stochastic differential equations(BSDE)and pre-default reflected backward stochastic differential equations(RBSDE).The goal of this work is twofold.First,we aim to establish the well-posedness results and comparison theorems for a generalized BSDE and a reflected generalized BSDE with a continuous and nondecreasing driver A.Second,we study penalization schemes for a generalized BSDE and a reflected generalized BSDE in which we penalize against the driver in order to obtain in the limit either a constrained optimal stopping problem or a constrained Dynkin game in which the set of minimizer's admissible exercise times is constrained to the right support of the measure generated by A.展开更多
In this paper,we develop an advanced computational framework for the topology optimization of orthotropic materials using meshless methods.The approximation function is established based on the improved moving least s...In this paper,we develop an advanced computational framework for the topology optimization of orthotropic materials using meshless methods.The approximation function is established based on the improved moving least squares(IMLS)method,which enhances the efficiency and stability of the numerical solution.The numerical solution formulas are derived using the improved element-free Galerkin(IEFG)method.We introduce the solid isotropic microstructures with penalization(SIMP)model to formulate a mathematical model for topology opti-mization,which effectively penalizes intermediate densities.The optimization problem is defined with the numerical solution formula and volume fraction as constraints.The objective function,which is the minimum value of flexibility,is optimized iteratively using the optimization criterion method to update the design variables efficiently and converge to an optimal solution.Sensitivity analysis is performed using the adjoint method,which provides accurate and efficient gradient information for the optimization algorithm.We validate the proposed framework through a series of numerical examples,including clamped beam,cantilever beam,and simply supported beam made of orthotropic materials.The convergence of the objective function is demonstrated by increasing the number of iterations.Additionally,the stability of the iterative process is analyzed by examining the fluctuation law of the volume fraction.By adjusting the parameters to an appropriate range,we achieve the final optimization results of the IEFG method without the checkerboard phenomenon.Comparative studies between the Element-Free Galerkin(EFG)and IEFG methods reveal that both methods yield consistent optimization results under identical parameter settings.However,the IEFG method significantly reduces computational time,highlighting its efficiency and suitability for orthotropic materials.展开更多
We present an energy penalization method for isogeometric topology optimization using moving morphable components(ITO–MMC),propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetr...We present an energy penalization method for isogeometric topology optimization using moving morphable components(ITO–MMC),propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetric structures,and then extend the proposed energy penalization method to an ITO–MMC with a symmetric constraint.The energy penalization method can solve the problems of numerical instability and convergence for the ITO–MMC and the ITO–MMC subjected to the structural symmetric constraint with asymmetric loads.Topology optimization problems of asymmetric,bilateral symmetric,and periodic symmetric structures are discussed to validate the effectiveness of the proposed energy penalization approach.Compared with the conventional ITO–MMC,the energy penalization method for the ITO–MMC can improve the convergence rate from 18.6%to 44.5%for the optimization of the asymmetric structure.For the ITO–MMC under a bilateral symmetric constraint,the proposed method can reduce the objective value by 5.6%and obtain a final optimized topology that has a clear boundary with decreased iterations.For the ITO–MMC under a periodic symmetric constraint,the proposed energy penalization method can dramatically reduce the number of iterations and obtain a speedup of more than 2.展开更多
A new approach for reducing error of the volume penalization method is proposed.The mask function is modified by shifting the interface between solid and fluid by√νηtoward the fluid region,whereνandηare the visco...A new approach for reducing error of the volume penalization method is proposed.The mask function is modified by shifting the interface between solid and fluid by√νηtoward the fluid region,whereνandηare the viscosity and the permeability,respectively.The shift length√νηis derived from the analytical solution of the one-dimensional diffusion equation with a penalization term.The effect of the error reduction is verified numerically for the one-dimensional diffusion equation,Burgers’equation,and the two-dimensional Navier-Stokes equations.The results show that the numerical error is reduced except in the vicinity of the interface showing overall second-order accuracy,while it converges to a non-zero constant value as the number of grid points increases for the original mask function.However,the new approach is effective when the grid resolution is sufficiently high so that the boundary layer,whose width is proportional to√νη,is resolved.Hence,the approach should be used when an appropriate combination ofνandηis chosen with a given numerical grid.展开更多
Sonic Hedgehog Medulloblastoma(SHH-MB)is one of the four primary molecular subgroups of Medulloblastoma.It is estimated to be responsible for nearly one-third of allMB cases.Using transcriptomic and DNA methylation pr...Sonic Hedgehog Medulloblastoma(SHH-MB)is one of the four primary molecular subgroups of Medulloblastoma.It is estimated to be responsible for nearly one-third of allMB cases.Using transcriptomic and DNA methylation profiling techniques,new developments in this field determined four molecular subtypes for SHH-MB.SHH-MB subtypes show distinct DNAmethylation patterns that allow their discrimination fromoverlapping subtypes and predict clinical outcomes.Class overlapping occurs when two or more classes share common features,making it difficult to distinguish them as separate.Using the DNA methylation dataset,a novel classification technique is presented to address the issue of overlapping SHH-MBsubtypes.Penalizedmultinomial regression(PMR),Tomek links(TL),and singular value decomposition(SVD)were all smoothly integrated into a single framework.SVD and group lasso improve computational efficiency,address the problem of high-dimensional datasets,and clarify class distinctions by removing redundant or irrelevant features that might lead to class overlap.As a method to eliminate the issues of decision boundary overlap and class imbalance in the classification task,TL enhances dataset balance and increases the clarity of decision boundaries through the elimination of overlapping samples.Using fivefold cross-validation,our proposed method(TL-SVDPMR)achieved a remarkable overall accuracy of almost 95%in the classification of SHH-MB molecular subtypes.The results demonstrate the strong performance of the proposed classification model among the various SHH-MB subtypes given a high average of the area under the curve(AUC)values.Additionally,the statistical significance test indicates that TL-SVDPMR is more accurate than both SVM and random forest algorithms in classifying the overlapping SHH-MB subtypes,highlighting its importance for precision medicine applications.Our findings emphasized the success of combining SVD,TL,and PMRtechniques to improve the classification performance for biomedical applications with many features and overlapping subtypes.展开更多
In the development of linear quadratic regulator(LQR) algorithms, the Riccati equation approach offers two important characteristics——it is recursive and readily meets the existence condition. However, these attribu...In the development of linear quadratic regulator(LQR) algorithms, the Riccati equation approach offers two important characteristics——it is recursive and readily meets the existence condition. However, these attributes are applicable only to transformed singular systems, and the efficiency of the regulator may be undermined if constraints are violated in nonsingular versions. To address this gap, we introduce a direct approach to the LQR problem for linear singular systems, avoiding the need for any transformations and eliminating the need for regularity assumptions. To achieve this goal, we begin by formulating a quadratic cost function to derive the LQR algorithm through a penalized and weighted regression framework and then connect it to a constrained minimization problem using the Bellman's criterion. Then, we employ a dynamic programming strategy in a backward approach within a finite horizon to develop an LQR algorithm for the original system. To accomplish this, we address the stability and convergence analysis under the reachability and observability assumptions of a hypothetical system constructed by the pencil of augmented matrices and connected using the Hamiltonian diagonalization technique.展开更多
This paper proposes a novel method for estimating the sparse inverse covariance matrixfor longitudinal data with informative dropouts. Based on the modified Cholesky decomposition,the sparse inverse covariance matrix ...This paper proposes a novel method for estimating the sparse inverse covariance matrixfor longitudinal data with informative dropouts. Based on the modified Cholesky decomposition,the sparse inverse covariance matrix is modelled by the autoregressive regression model,which guarantees the positive definiteness of the covariance matrix. To account for the informativedropouts, we then propose a penalized estimating equation method using the inverse probabilityweighting approach. The informative dropout propensity parameters are estimated by the generalizedmethod of moments. The asymptotic properties are investigated for the resulting estimators.Finally, we illustrate the effectiveness and feasibility of the proposed method through Monte Carlosimulations and a practical application.展开更多
为获得高速动车齿轮箱最优结构设计方案,针对目前国产高速动车牵引齿轮箱箱体特点及存在的问题,基于SIMP(solid isotropic material with penalization)材料插值模型及应变能理论,利用软件HyperMesh中的拓扑优化与形状优化模块对动车齿...为获得高速动车齿轮箱最优结构设计方案,针对目前国产高速动车牵引齿轮箱箱体特点及存在的问题,基于SIMP(solid isotropic material with penalization)材料插值模型及应变能理论,利用软件HyperMesh中的拓扑优化与形状优化模块对动车齿轮箱箱体结构进行拓扑优化和局部形状优化。优化结果表明:优化后的动车齿轮箱结构的最大变形和最大应力有大幅度降低,能有效提高齿轮箱箱体的刚度和强度。文中结果可为设计性能优异的国产化高速动车齿轮箱提供数据支持。展开更多
Strabismic amblyopia is characterized by a distorted spatial perception.In this condition,the neurofunctional disorder occurring during first years of life provoke several monocular and binocular anomalies such as cro...Strabismic amblyopia is characterized by a distorted spatial perception.In this condition,the neurofunctional disorder occurring during first years of life provoke several monocular and binocular anomalies such as crowding,deficits in the accommodative response,contrast sensitivity,and ocular motility abilities.The inhibition of the binocular function of the brain by the misaligned amblyopic eye induces a binocular imbalance leading to interocular suppression and the reduction or lack of stereoacuity.Passive treatments such as occlusion,optical and/or pharmacological penalization,and Bangerter foils has been demonstrated to be potentially useful treatments for strabismic amblyopia.Recent researches have proved new pharmacological options to improve and maintain visual acuity af ter occlusion treatment in strabismic amblyopia.Likewise,the active vision therapy,in the last years,is becoming a very relevant therapeutic option in combination with passive treatments,especially during and after monocular therapy,in the attempt of recovering the imbalanced binocular vision.展开更多
In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where ...In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where △p is the p-Laplacian operator, 1 〈 p 〈 N, M ： R＋ → R＋ and V ： RN →R＋ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik- Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.展开更多
For the purpose of achieving high-resolution optimal solutions this paper proposes a nodal design variablebased adaptive method for topology optimization of continuum structures. The analysis mesh-independent density ...For the purpose of achieving high-resolution optimal solutions this paper proposes a nodal design variablebased adaptive method for topology optimization of continuum structures. The analysis mesh-independent density field, interpolated by the nodal design variables at a given set of density points, is adaptively refined/coarsened accord- ing to a criterion regarding the gray-scale measure of local regions. New density points are added into the gray regions and redundant ones are removed from the regions occupied by purely solid/void phases for decreasing the number of de- sign variables. A penalization factor adaptivity technique is employed-to prevent premature convergence of the optimiza- tion iterations. Such an adaptive scheme not only improves the structural boundary description quality, but also allows for sufficient further topological evolution of the structural layout in higher adaptivity levels and thus essentially enables high-resolution solutions. Moreover, compared with the case with uniformly and finely distributed density points, the proposed adaptive method can achieve a higher numerical efficiency of the optimization process.展开更多
We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operat...We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operator and the function is a nonlinear lower order and satisfy only the growth condition. The second term belongs to L1 （QT）. The proof of an existence solution is based on the penalization methods.展开更多
The sophisticated structures of flapping insect wings make it challenging to study the role of wing flexibility in insect flight.In this study,a mass-spring system is used to model wing structural dynamics as a thin,f...The sophisticated structures of flapping insect wings make it challenging to study the role of wing flexibility in insect flight.In this study,a mass-spring system is used to model wing structural dynamics as a thin,flexible membrane supported by a network of veins.The vein mechanical properties can be estimated based on their diameters and the Young's modulus of cuticle.In order to analyze the effect of wing flexibility,the Young's modulus is varied to make a comparison between two different wing models that we refer to as flexible and highly flexible.The wing models are coupled with a pseudo-spectral code solving the incompressible Navier–Stokes equations,allowing us to investigate the influence of wing deformation on the aerodynamic efficiency of a tethered flapping bumblebee.Compared to the bumblebee model with rigid wings,the one with flexible wings flies more efficiently,characterized by a larger lift-to-power ratio.展开更多
In this paper,we study the multiplicity and concentration of positive solutions for the following fractional Kirchhoff-Choquard equation with magnetic fields:(aε^(2s)+bε^(4 s-3)[u]_(ε)^(2),A/ε)(-Δ)_(A/ε)^(s)u+V(...In this paper,we study the multiplicity and concentration of positive solutions for the following fractional Kirchhoff-Choquard equation with magnetic fields:(aε^(2s)+bε^(4 s-3)[u]_(ε)^(2),A/ε)(-Δ)_(A/ε)^(s)u+V(x)u=ε^(-α)(Iα*F(|u|^(2)))f(|u|^(2))u in R^(3).Hereε>0 is a small parameter,a,b>0 are constants,s E(0,1),(-Δ)As is the fractional magnetic Laplacian,A:R^(3)→R^(3) is a smooth magnetic potential,Iα=Γ(3-α/2)/2απ3/2Γ(α/2)·1/|x|^(α) is the Riesz potential,the potential V is a positive continuous function having a local minimum,and f:R→R is a C^(1) subcritical nonlinearity.Under some proper assumptions regarding V and f,we show the multiplicity and concentration of positive solutions with the topology of the set M:={x∈R^(3):V(x)=inf V}by applying the penalization method and LjusternikSchnirelmann theory for the above equation.展开更多
A topology optimization method based on the solid isotropic material with penalization interpolation scheme is utilized for designing gradient coils for use in magnetic resonance microscopy.Unlike the popular stream f...A topology optimization method based on the solid isotropic material with penalization interpolation scheme is utilized for designing gradient coils for use in magnetic resonance microscopy.Unlike the popular stream function method,the proposed method has design variables that are the distribution of conductive material.A voltage-driven transverse gradient coil is proposed to be used as micro-scale magnetic resonance imaging(MRI)gradient coils,thus avoiding introducing a coil-winding pattern and simplifying the coil configuration.The proposed method avoids post-processing errors that occur when the continuous current density is approximated by discrete wires in the stream function approach.The feasibility and accuracy of the method are verified through designing the z-gradient and y-gradient coils on a cylindrical surface.Numerical design results show that the proposed method can provide a new coil layout in a compact design space.展开更多
The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basi...The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.展开更多
In this paper, we derive the existence and uniqueness theorem for the adapted solution to backward stochastic differential equations with two barriers under non-Lipschitz condition via penalization method.
文摘The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.
文摘AIM:To compare the efficacies of patching and penalization therapies for the treatment of amblyopia patients.METHODS:The records of 64 eyes of 50 patients 7 to16y of age who had presented to our clinics with a diagnosis of amblyopia,were evaluated retrospectively.Forty eyes of 26 patients who had received patching therapy and 24 eyes of 24 patients who had received penalization therapy included in this study.The latencies and amplitudes of visual evoked potential(VEP)records and best corrected visual acuities(BCVA)of these two groups were compared before and six months after the treatment.RESULTS:In both patching and the penalization groups,the visual acuities increased significantly following the treatments(P【0.05).The latency measurements of the P100 wave obtained at 1.0°,15 arc min.Patterns of both groups significantly decreased following the 6-months-treatment.However,the amplitude measurements increased(P【0.05).CONCLUSION:The patching and the penalization methods,which are the main methods used in the treatment of amblyopia,were also effective over the age of 7y,which has been accepted as the critical age for the treatment of amblyopia.
基金supported by a pilot grant from Indiana Clinical and Translational Sciences Institute Project Development Teams(PDT) to J Wanga Research to Prevent Blindness(RPB) unrestricted grant to the Glick Eye Institute at Indiana University
文摘Background:To date,compliance to atropine penalization in amblyopic children has only been assessed through self-report.The goal of this pilot study is to measure compliance to atropine penalization objectively.Methods:Seven amblyopic children(3-8 years;20/40-20/125 in the amblyopic eye) were enrolled.None had been treated with atropine previously.Children were prescribed either a twice per week or daily atropine regimen by their physicians.Compliance was defined as the percentage of days in which the atropine eye drop was taken compared to the number of doses prescribed.We used medication event monitoring system(MEMS) caps to objectively measure compliance.The MEMS caps are designed to electronically record the time and date when the bottle is opened.The parents of the children were provided a calendar log to subjectively report compliance.Participants were scheduled for return visits at 4 and 12 weeks.Weekly compliance was analyzed.Results:At 4 weeks,objective compliance averaged 88%(range,57-100%),while subjective compliance was 98%(range,90-100%).The actual dose in grams and visual acuity(VA) response relationship(r=0.79,P=0.03) was significantly better than the relationship between regimen and response(r=0.41,P>0.05),or the relationship between actual dose in drops and response(r=0.52,P>0.05).Conclusions:Objective compliance to atropine penalization instructions can be monitored with MEMS,which may facilitate our understanding of the dose-response relationship.Objective compliance with atropine penalization decreases over time and varies with regimen.On average,subjective parental reporting of compliance is overestimated.
基金supported by the Australian Research Council Discovery Project (Grant No.DP220103106).
文摘The paper is directly motivated by the pricing of vulnerable European and American options in a general hazard process setup and a related study of the corresponding pre-default backward stochastic differential equations(BSDE)and pre-default reflected backward stochastic differential equations(RBSDE).The goal of this work is twofold.First,we aim to establish the well-posedness results and comparison theorems for a generalized BSDE and a reflected generalized BSDE with a continuous and nondecreasing driver A.Second,we study penalization schemes for a generalized BSDE and a reflected generalized BSDE in which we penalize against the driver in order to obtain in the limit either a constrained optimal stopping problem or a constrained Dynkin game in which the set of minimizer's admissible exercise times is constrained to the right support of the measure generated by A.
基金supported by the Graduate Student Scientific Research Innovation Project through Research Innovation Fund for Graduate Students in Shanxi Province(Project No.2024KY648).
文摘In this paper,we develop an advanced computational framework for the topology optimization of orthotropic materials using meshless methods.The approximation function is established based on the improved moving least squares(IMLS)method,which enhances the efficiency and stability of the numerical solution.The numerical solution formulas are derived using the improved element-free Galerkin(IEFG)method.We introduce the solid isotropic microstructures with penalization(SIMP)model to formulate a mathematical model for topology opti-mization,which effectively penalizes intermediate densities.The optimization problem is defined with the numerical solution formula and volume fraction as constraints.The objective function,which is the minimum value of flexibility,is optimized iteratively using the optimization criterion method to update the design variables efficiently and converge to an optimal solution.Sensitivity analysis is performed using the adjoint method,which provides accurate and efficient gradient information for the optimization algorithm.We validate the proposed framework through a series of numerical examples,including clamped beam,cantilever beam,and simply supported beam made of orthotropic materials.The convergence of the objective function is demonstrated by increasing the number of iterations.Additionally,the stability of the iterative process is analyzed by examining the fluctuation law of the volume fraction.By adjusting the parameters to an appropriate range,we achieve the final optimization results of the IEFG method without the checkerboard phenomenon.Comparative studies between the Element-Free Galerkin(EFG)and IEFG methods reveal that both methods yield consistent optimization results under identical parameter settings.However,the IEFG method significantly reduces computational time,highlighting its efficiency and suitability for orthotropic materials.
基金This research was supported by the National Natural Science Foundation of China(Grant Nos.51675197 and 51705158)the National Engineering Research Center of Near-Net-Shape Forming for Metallic Materials,Ministry of Education Key Laboratory of High Efficient Near-Net-Shape Forming Technology and Equipment for Metallic Materials(Category B)Opening Foundation(Grant No.2018005)The support is gratefully acknowledged.
文摘We present an energy penalization method for isogeometric topology optimization using moving morphable components(ITO–MMC),propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetric structures,and then extend the proposed energy penalization method to an ITO–MMC with a symmetric constraint.The energy penalization method can solve the problems of numerical instability and convergence for the ITO–MMC and the ITO–MMC subjected to the structural symmetric constraint with asymmetric loads.Topology optimization problems of asymmetric,bilateral symmetric,and periodic symmetric structures are discussed to validate the effectiveness of the proposed energy penalization approach.Compared with the conventional ITO–MMC,the energy penalization method for the ITO–MMC can improve the convergence rate from 18.6%to 44.5%for the optimization of the asymmetric structure.For the ITO–MMC under a bilateral symmetric constraint,the proposed method can reduce the objective value by 5.6%and obtain a final optimized topology that has a clear boundary with decreased iterations.For the ITO–MMC under a periodic symmetric constraint,the proposed energy penalization method can dramatically reduce the number of iterations and obtain a speedup of more than 2.
文摘A new approach for reducing error of the volume penalization method is proposed.The mask function is modified by shifting the interface between solid and fluid by√νηtoward the fluid region,whereνandηare the viscosity and the permeability,respectively.The shift length√νηis derived from the analytical solution of the one-dimensional diffusion equation with a penalization term.The effect of the error reduction is verified numerically for the one-dimensional diffusion equation,Burgers’equation,and the two-dimensional Navier-Stokes equations.The results show that the numerical error is reduced except in the vicinity of the interface showing overall second-order accuracy,while it converges to a non-zero constant value as the number of grid points increases for the original mask function.However,the new approach is effective when the grid resolution is sufficiently high so that the boundary layer,whose width is proportional to√νη,is resolved.Hence,the approach should be used when an appropriate combination ofνandηis chosen with a given numerical grid.
基金funded by the Deanship of Graduate Studies and Scientific Research at Jouf University under grant No.(DGSSR-2024-02-01137).
文摘Sonic Hedgehog Medulloblastoma(SHH-MB)is one of the four primary molecular subgroups of Medulloblastoma.It is estimated to be responsible for nearly one-third of allMB cases.Using transcriptomic and DNA methylation profiling techniques,new developments in this field determined four molecular subtypes for SHH-MB.SHH-MB subtypes show distinct DNAmethylation patterns that allow their discrimination fromoverlapping subtypes and predict clinical outcomes.Class overlapping occurs when two or more classes share common features,making it difficult to distinguish them as separate.Using the DNA methylation dataset,a novel classification technique is presented to address the issue of overlapping SHH-MBsubtypes.Penalizedmultinomial regression(PMR),Tomek links(TL),and singular value decomposition(SVD)were all smoothly integrated into a single framework.SVD and group lasso improve computational efficiency,address the problem of high-dimensional datasets,and clarify class distinctions by removing redundant or irrelevant features that might lead to class overlap.As a method to eliminate the issues of decision boundary overlap and class imbalance in the classification task,TL enhances dataset balance and increases the clarity of decision boundaries through the elimination of overlapping samples.Using fivefold cross-validation,our proposed method(TL-SVDPMR)achieved a remarkable overall accuracy of almost 95%in the classification of SHH-MB molecular subtypes.The results demonstrate the strong performance of the proposed classification model among the various SHH-MB subtypes given a high average of the area under the curve(AUC)values.Additionally,the statistical significance test indicates that TL-SVDPMR is more accurate than both SVM and random forest algorithms in classifying the overlapping SHH-MB subtypes,highlighting its importance for precision medicine applications.Our findings emphasized the success of combining SVD,TL,and PMRtechniques to improve the classification performance for biomedical applications with many features and overlapping subtypes.
基金supported by the European Union’s Horizon Europe research and innovation programme (101120657)project ENFIELD (European Lighthouse to Manifest Trustworthy and Green AI), the Estonian Research Council (PRG658, PRG1463)the Estonian Centre of Excellence in Energy Efficiency, ENER (TK230) funded by the Estonian Ministry of Education and Research。
文摘In the development of linear quadratic regulator(LQR) algorithms, the Riccati equation approach offers two important characteristics——it is recursive and readily meets the existence condition. However, these attributes are applicable only to transformed singular systems, and the efficiency of the regulator may be undermined if constraints are violated in nonsingular versions. To address this gap, we introduce a direct approach to the LQR problem for linear singular systems, avoiding the need for any transformations and eliminating the need for regularity assumptions. To achieve this goal, we begin by formulating a quadratic cost function to derive the LQR algorithm through a penalized and weighted regression framework and then connect it to a constrained minimization problem using the Bellman's criterion. Then, we employ a dynamic programming strategy in a backward approach within a finite horizon to develop an LQR algorithm for the original system. To accomplish this, we address the stability and convergence analysis under the reachability and observability assumptions of a hypothetical system constructed by the pencil of augmented matrices and connected using the Hamiltonian diagonalization technique.
基金supported by the National Natural Science Foundation of China(Grant No.12171450).
文摘This paper proposes a novel method for estimating the sparse inverse covariance matrixfor longitudinal data with informative dropouts. Based on the modified Cholesky decomposition,the sparse inverse covariance matrix is modelled by the autoregressive regression model,which guarantees the positive definiteness of the covariance matrix. To account for the informativedropouts, we then propose a penalized estimating equation method using the inverse probabilityweighting approach. The informative dropout propensity parameters are estimated by the generalizedmethod of moments. The asymptotic properties are investigated for the resulting estimators.Finally, we illustrate the effectiveness and feasibility of the proposed method through Monte Carlosimulations and a practical application.
文摘为获得高速动车齿轮箱最优结构设计方案,针对目前国产高速动车牵引齿轮箱箱体特点及存在的问题,基于SIMP(solid isotropic material with penalization)材料插值模型及应变能理论,利用软件HyperMesh中的拓扑优化与形状优化模块对动车齿轮箱箱体结构进行拓扑优化和局部形状优化。优化结果表明:优化后的动车齿轮箱结构的最大变形和最大应力有大幅度降低,能有效提高齿轮箱箱体的刚度和强度。文中结果可为设计性能优异的国产化高速动车齿轮箱提供数据支持。
基金Supported by the Ministry of Economy,Industry and Competitiveness of Spain within the program Ramón y Cajal(RYC-2016-20471)。
文摘Strabismic amblyopia is characterized by a distorted spatial perception.In this condition,the neurofunctional disorder occurring during first years of life provoke several monocular and binocular anomalies such as crowding,deficits in the accommodative response,contrast sensitivity,and ocular motility abilities.The inhibition of the binocular function of the brain by the misaligned amblyopic eye induces a binocular imbalance leading to interocular suppression and the reduction or lack of stereoacuity.Passive treatments such as occlusion,optical and/or pharmacological penalization,and Bangerter foils has been demonstrated to be potentially useful treatments for strabismic amblyopia.Recent researches have proved new pharmacological options to improve and maintain visual acuity af ter occlusion treatment in strabismic amblyopia.Likewise,the active vision therapy,in the last years,is becoming a very relevant therapeutic option in combination with passive treatments,especially during and after monocular therapy,in the attempt of recovering the imbalanced binocular vision.
基金supported by Natural Science Foundation of China(11371159 and 11771166)Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT_17R46
文摘In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where △p is the p-Laplacian operator, 1 〈 p 〈 N, M ： R＋ → R＋ and V ： RN →R＋ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik- Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.
基金supported by the Key Project of Chinese National Programs for Fundamental Research and Development(2010CB832703)the National Natural Science Foundation of China(11072047 and 91130025)
文摘For the purpose of achieving high-resolution optimal solutions this paper proposes a nodal design variablebased adaptive method for topology optimization of continuum structures. The analysis mesh-independent density field, interpolated by the nodal design variables at a given set of density points, is adaptively refined/coarsened accord- ing to a criterion regarding the gray-scale measure of local regions. New density points are added into the gray regions and redundant ones are removed from the regions occupied by purely solid/void phases for decreasing the number of de- sign variables. A penalization factor adaptivity technique is employed-to prevent premature convergence of the optimiza- tion iterations. Such an adaptive scheme not only improves the structural boundary description quality, but also allows for sufficient further topological evolution of the structural layout in higher adaptivity levels and thus essentially enables high-resolution solutions. Moreover, compared with the case with uniformly and finely distributed density points, the proposed adaptive method can achieve a higher numerical efficiency of the optimization process.
文摘We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operator and the function is a nonlinear lower order and satisfy only the growth condition. The second term belongs to L1 （QT）. The proof of an existence solution is based on the penalization methods.
基金Financial support from the Agence Nationale de la Recherche(ANR)(Grant 15-CE40-0019)and Deutsche Forschungsgemeinschaft(DFG)(Grant SE 824/26-1),project AIFITHPC resources of IDRIS under the allocation No.2018-91664 attributed by Grand Equipement National de Calcul Intensif(GENCI)+2 种基金Centre de Calcul Intensif d'Aix-Marseille is acknowledged for granting access to its high performance computing resources financed by the project Equip@Meso(No.ANR-10-EQPX-29-01)financial support granted by the ministeres des Affaires etrangeres et du developpement international(MAEDI)et de l'Education nationale et l'enseignement superieur,de la recherche et de l'innovation(MENESRI),the Deutscher Akademischer Austauschdienst(DAAD)within the French-German Procope project FIFITfinancial support from the JSPS KAKENHI Grant No.JP18K13693。
文摘The sophisticated structures of flapping insect wings make it challenging to study the role of wing flexibility in insect flight.In this study,a mass-spring system is used to model wing structural dynamics as a thin,flexible membrane supported by a network of veins.The vein mechanical properties can be estimated based on their diameters and the Young's modulus of cuticle.In order to analyze the effect of wing flexibility,the Young's modulus is varied to make a comparison between two different wing models that we refer to as flexible and highly flexible.The wing models are coupled with a pseudo-spectral code solving the incompressible Navier–Stokes equations,allowing us to investigate the influence of wing deformation on the aerodynamic efficiency of a tethered flapping bumblebee.Compared to the bumblebee model with rigid wings,the one with flexible wings flies more efficiently,characterized by a larger lift-to-power ratio.
基金supported by National Natural Science Foundation of China(12161038)Science and Technology project of Jiangxi provincial Department of Education(GJJ212204)+1 种基金supported by Natural Science Foundation program of Jiangxi Provincial(20202BABL211005)supported by the Guiding Project in Science and Technology Research Plan of the Education Department of Hubei Province(B2019142)。
文摘In this paper,we study the multiplicity and concentration of positive solutions for the following fractional Kirchhoff-Choquard equation with magnetic fields:(aε^(2s)+bε^(4 s-3)[u]_(ε)^(2),A/ε)(-Δ)_(A/ε)^(s)u+V(x)u=ε^(-α)(Iα*F(|u|^(2)))f(|u|^(2))u in R^(3).Hereε>0 is a small parameter,a,b>0 are constants,s E(0,1),(-Δ)As is the fractional magnetic Laplacian,A:R^(3)→R^(3) is a smooth magnetic potential,Iα=Γ(3-α/2)/2απ3/2Γ(α/2)·1/|x|^(α) is the Riesz potential,the potential V is a positive continuous function having a local minimum,and f:R→R is a C^(1) subcritical nonlinearity.Under some proper assumptions regarding V and f,we show the multiplicity and concentration of positive solutions with the topology of the set M:={x∈R^(3):V(x)=inf V}by applying the penalization method and LjusternikSchnirelmann theory for the above equation.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51675506 and 51275504)the German Research Foundation(DFG)(Grant Nos.#ZA 422/5-1 and#ZA 422/6-1)
文摘A topology optimization method based on the solid isotropic material with penalization interpolation scheme is utilized for designing gradient coils for use in magnetic resonance microscopy.Unlike the popular stream function method,the proposed method has design variables that are the distribution of conductive material.A voltage-driven transverse gradient coil is proposed to be used as micro-scale magnetic resonance imaging(MRI)gradient coils,thus avoiding introducing a coil-winding pattern and simplifying the coil configuration.The proposed method avoids post-processing errors that occur when the continuous current density is approximated by discrete wires in the stream function approach.The feasibility and accuracy of the method are verified through designing the z-gradient and y-gradient coils on a cylindrical surface.Numerical design results show that the proposed method can provide a new coil layout in a compact design space.
基金support by Basic Science Research Program through the National Research Foundation(NRF)funded by Korea Ministry of Education(No.2016R1A6A1A0312812).
文摘The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.
基金Supported by the Key Science and Technology Project of Ministry of Education(207047)Supported by the Special Project Grants of Anhui Normal University(2006xzx08)+1 种基金Supported by the Project Grants for Younger Teachers of Anhui Normal University(2006xqn49)Supported by NSF of Anhui Educational Bureau(KJ2007A012)
文摘In this paper, we derive the existence and uniqueness theorem for the adapted solution to backward stochastic differential equations with two barriers under non-Lipschitz condition via penalization method.
