A geometric framework is proposed for multinomial nonlinear modelsbased on a modified version of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic infe...A geometric framework is proposed for multinomial nonlinear modelsbased on a modified version of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic inference in terms ofcurvatures for multinomial nonlinear models. Our previous results [15] for ordinarynonlinear regression models are extended to multinomial nonlinear models.展开更多
A modified Bates and Watts geometric framework is proposed for quasi\|likelihood nonlinear models in Euclidean inner product space.Based on the modified geometric framework,some asymptotic inference in terms of curvat...A modified Bates and Watts geometric framework is proposed for quasi\|likelihood nonlinear models in Euclidean inner product space.Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi\|likelihood nonlinear models is studied.Several previous results for nonlinear regression models and exponential family nonlinear models etc.are extended to quasi\|likelihood nonlinear models.展开更多
Efron and Amari (EA)studied curved exponential families first and presented a Riemannian geometric framework for these models. Bates and Watts (BW) proposed a geometric structure for nonlinear regression models in Euc...Efron and Amari (EA)studied curved exponential families first and presented a Riemannian geometric framework for these models. Bates and Watts (BW) proposed a geometric structure for nonlinear regression models in Euclidean space. Since then, many contributions have been made in these fields. In this note, we try to combine the advantages of both EA and BW approaches and present a new differential展开更多
本文对带寿命数据非线性随机效应模型,建立了微分几何框架,推广了Bates & Wates关于非线性模型几何结构.在此基础上,我们导出了关于固定效应参数和子集参数的置信域的曲率表示,这些结果是Bates and Wates(1980),Hamilton(1986)和Wei...本文对带寿命数据非线性随机效应模型,建立了微分几何框架,推广了Bates & Wates关于非线性模型几何结构.在此基础上,我们导出了关于固定效应参数和子集参数的置信域的曲率表示,这些结果是Bates and Wates(1980),Hamilton(1986)和Wei(1998)等的推广.展开更多
In order to understand how cells respond to concave and convex subcellular surface structures,colloidal crystal array and honeycomb-structured surfaces composed of highly ordered hexagonal units with completely invers...In order to understand how cells respond to concave and convex subcellular surface structures,colloidal crystal array and honeycomb-structured surfaces composed of highly ordered hexagonal units with completely inverse curvature were fabricated via facile self-assembly and breath figure approaches,respectively.The influence of hexagonal surface curvature on cell fate was subsequently investigated.Cells underwent more extensive spreading on the convex colloidal crystal array surface,while adhesive forces were higher on the concave honeycomb surface.The behaviors of cells on the different surfaces were investigated by comparing cell morphology,cellular adhesive force and cytoskeleton structure.The results revealed comprehensive differences in cell behavior between those on concave honeycomb surfaces and convex colloidal crystal arrays.展开更多
文摘A geometric framework is proposed for multinomial nonlinear modelsbased on a modified version of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic inference in terms ofcurvatures for multinomial nonlinear models. Our previous results [15] for ordinarynonlinear regression models are extended to multinomial nonlinear models.
基金The project supported by NSFC!(19631040)NSFJ!(BK99002)
文摘A modified Bates and Watts geometric framework is proposed for quasi\|likelihood nonlinear models in Euclidean inner product space.Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi\|likelihood nonlinear models is studied.Several previous results for nonlinear regression models and exponential family nonlinear models etc.are extended to quasi\|likelihood nonlinear models.
基金Project supported by the National Natural Science Foundation of China.
文摘Efron and Amari (EA)studied curved exponential families first and presented a Riemannian geometric framework for these models. Bates and Watts (BW) proposed a geometric structure for nonlinear regression models in Euclidean space. Since then, many contributions have been made in these fields. In this note, we try to combine the advantages of both EA and BW approaches and present a new differential
基金supported by the Major Program of Chinese National Programs for Fundamental Research and Development(973 Project,No.2012CB933803)the National Science Foundation of China(No.21574081)
文摘In order to understand how cells respond to concave and convex subcellular surface structures,colloidal crystal array and honeycomb-structured surfaces composed of highly ordered hexagonal units with completely inverse curvature were fabricated via facile self-assembly and breath figure approaches,respectively.The influence of hexagonal surface curvature on cell fate was subsequently investigated.Cells underwent more extensive spreading on the convex colloidal crystal array surface,while adhesive forces were higher on the concave honeycomb surface.The behaviors of cells on the different surfaces were investigated by comparing cell morphology,cellular adhesive force and cytoskeleton structure.The results revealed comprehensive differences in cell behavior between those on concave honeycomb surfaces and convex colloidal crystal arrays.
