This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provi...This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provided that the uneven ground is concave to the fluid.展开更多
In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems...In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.展开更多
We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization p...We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.展开更多
This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By i...This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.展开更多
The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on...The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.展开更多
目的:探讨血清抗着丝粒蛋白F抗体(anti-centromere protein F antibody,anti-CENPF)在乳腺癌中的临床价值。方法:收集100例初诊乳腺癌(breast cancer,BC)患者、40例乳腺良性疾病(non breast cancer,non-BC)患者和40名健康体检者(healthy...目的:探讨血清抗着丝粒蛋白F抗体(anti-centromere protein F antibody,anti-CENPF)在乳腺癌中的临床价值。方法:收集100例初诊乳腺癌(breast cancer,BC)患者、40例乳腺良性疾病(non breast cancer,non-BC)患者和40名健康体检者(healthy control,HC)血清,采用酶联免疫吸附试验检测血清中的anti-CENPF水平,同时化学发光法测定血清糖类抗原153(carbohydrate antigen 153,CA153)的水平。结果:BC组血清anti-CENPF水平高于non-BC组和HC组,差异有统计学意义(P<0.05)。anti-CENPF和CA153诊断乳腺癌中的曲线下面积(area under the curve,AUC)分别为0.714和0.672,两者联合检测的AUC为0.739。有淋巴结转移、远处转移或者人表皮生长因子受体2(human epidermal growth factor receptor-2,HER-2)阴性的乳腺癌患者血清anti-CENPF浓度明显升高(P<0.05)。不同肿瘤大小、临床分期、分子分型乳腺癌患者血清anti-CENPF水平比较,差异有统计学意义(P<0.05)。组间比较显示Ⅳ期和Ⅲ期血清anti-CENPF浓度高于Ⅰ期和Ⅱ期,HER-2过表达型、Luminal B型血清anti-CENPF水平低于三阴性乳腺癌(triple negative breast cancer,TNBC)患者。雌激素受体(receptors estrogen,ER)阳性的乳腺癌患者中,HER-2阴性组的anti-CENPF浓度高于HER-2阳性组,差异有统计学意义(P=0.026)。结论:血清antiCENPF在乳腺癌的诊断、临床分期及分子分型中发挥了重要作用,其水平可能与乳腺癌预后呈负相关,有望成为乳腺癌潜在的疾病标志物。展开更多
Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded un...Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.展开更多
基金supported in part by the National Natural Science Foundation of China(12101088)the Natural Science Foundation of Sichuan Province(2022NSFSC1858)。
文摘This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provided that the uneven ground is concave to the fluid.
基金partially supported by the National Natural Science Foundation of China(52375238)Science and Technology Program of Guangzhou(202201020213,202201020193,202201010399)GZHU-HKUST Joint Research Fund(YH202109).
文摘In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.
基金supported in part by the Shanghai Natural Science Foundation under the Grant 22ZR1407000.
文摘We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.
基金the National Natural Science Foundation of China(62273058,U22A2045)the Key Science and Technology Projects of Jilin Province(20200401075GX)the Youth Science and Technology Innovation and Entrepreneurship Outstanding Talents Project of Jilin Province(20230508043RC)。
文摘This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.
基金supported by the National Natural Science Foundation of China(62176218,62176027)the Fundamental Research Funds for the Central Universities(XDJK2020TY003)the Funds for Chongqing Talent Plan(cstc2024ycjh-bgzxm0082)。
文摘The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.
文摘目的:探讨血清抗着丝粒蛋白F抗体(anti-centromere protein F antibody,anti-CENPF)在乳腺癌中的临床价值。方法:收集100例初诊乳腺癌(breast cancer,BC)患者、40例乳腺良性疾病(non breast cancer,non-BC)患者和40名健康体检者(healthy control,HC)血清,采用酶联免疫吸附试验检测血清中的anti-CENPF水平,同时化学发光法测定血清糖类抗原153(carbohydrate antigen 153,CA153)的水平。结果:BC组血清anti-CENPF水平高于non-BC组和HC组,差异有统计学意义(P<0.05)。anti-CENPF和CA153诊断乳腺癌中的曲线下面积(area under the curve,AUC)分别为0.714和0.672,两者联合检测的AUC为0.739。有淋巴结转移、远处转移或者人表皮生长因子受体2(human epidermal growth factor receptor-2,HER-2)阴性的乳腺癌患者血清anti-CENPF浓度明显升高(P<0.05)。不同肿瘤大小、临床分期、分子分型乳腺癌患者血清anti-CENPF水平比较,差异有统计学意义(P<0.05)。组间比较显示Ⅳ期和Ⅲ期血清anti-CENPF浓度高于Ⅰ期和Ⅱ期,HER-2过表达型、Luminal B型血清anti-CENPF水平低于三阴性乳腺癌(triple negative breast cancer,TNBC)患者。雌激素受体(receptors estrogen,ER)阳性的乳腺癌患者中,HER-2阴性组的anti-CENPF浓度高于HER-2阳性组,差异有统计学意义(P=0.026)。结论:血清antiCENPF在乳腺癌的诊断、临床分期及分子分型中发挥了重要作用,其水平可能与乳腺癌预后呈负相关,有望成为乳腺癌潜在的疾病标志物。
文摘Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.
