Nonmonotone gradient methods generally perform better than their monotone counterparts especially on unconstrained quadratic optimization.However,the known convergence rate of the monotone method is often much better ...Nonmonotone gradient methods generally perform better than their monotone counterparts especially on unconstrained quadratic optimization.However,the known convergence rate of the monotone method is often much better than its nonmonotone variant.With the aim of shrinking the gap between theory and practice of nonmonotone gradient methods,we introduce a property for convergence analysis of a large collection of gradient methods.We prove that any gradient method using stepsizes satisfying the property will converge R-linearly at a rate of 1-λ_(1)/M_(1),whereλ_(1)is the smallest eigenvalue of Hessian matrix and M_(1)is the upper bound of the inverse stepsize.Our results indicate that the existing convergence rates of many nonmonotone methods can be improved to 1-1/κwithκbeing the associated condition number.展开更多
为倡导绿色出行理念,解决以往研究在处理重复观测数据时容易忽视的潜在相关性和个体异质性问题,针对如何利用智能手机APP提供的多模式出行信息引导小汽车出行者转向停车换乘(Park-and-Ride,P+R)模式进行了探究,同时引入广义线性混合模型...为倡导绿色出行理念,解决以往研究在处理重复观测数据时容易忽视的潜在相关性和个体异质性问题,针对如何利用智能手机APP提供的多模式出行信息引导小汽车出行者转向停车换乘(Park-and-Ride,P+R)模式进行了探究,同时引入广义线性混合模型(Generalized Linear Mixed Model,GLMM)分析了多模式出行信息对小汽车出行者转向P+R意向的影响。首先,基于上海市路网设计意向调查问卷,整合了自驾和P+R两种出行方式的道路拥堵程度、出行时间、停车费用及地铁车厢座位情况等信息,并运用全因子设计法构建了24种不同信息水平组合的假设情景。然后,通过智能手机APP界面示意图向小汽车出行者展示这些多模式出行信息,并收集其转向P+R的意向数据。最后,运用GLMM方法处理同一个体重复决策数据中潜在的相关性和捕捉个体间的异质性。结果显示,GLMM的应用不仅解决了同一个体重复决策间的相关性,还揭示了不同个体对道路拥堵程度和地铁车厢座位情况的差异化关注;智能手机APP整合的多模式出行信息显著提升了小汽车出行者转向P+R的意愿,且这一转变占比达29.2%;高收入、长驾龄以及对P+R政策不了解的出行者转向P+R的意愿较低。研究表明,通过智能手机APP整合自驾和P+R的多模式出行信息能显著增强P+R方式的吸引力,可为提升P+R的普及率提供新思路,有效促进小汽车出行者向绿色出行方式的转变。展开更多
大数据时代的到来使得时空轨迹数据的规模和复杂度迅速增长,这对如何高效管理和查询时空轨迹数据提出了新的需求和挑战。图数据库在处理时空轨迹数据的建模、存储和管理方面具有独特优势。然而,随着路网时空轨迹数据规模的不断扩大,图...大数据时代的到来使得时空轨迹数据的规模和复杂度迅速增长,这对如何高效管理和查询时空轨迹数据提出了新的需求和挑战。图数据库在处理时空轨迹数据的建模、存储和管理方面具有独特优势。然而,随着路网时空轨迹数据规模的不断扩大,图数据库的查询性能也会随之下降。为应对这一挑战,本文提出了一种基于图数据库的路网时空轨迹建模与高效索引方法。该方法采用压缩线性参考(Compressed Linear Reference,CLR)模型对路网时空轨迹进行建模,并将其存储于图数据库中,在此基础上,进一步构建了一种高效的路网时空轨迹索引机制。该索引体系采用了三层时空索引结构,包括路网空间索引、时间索引和时空路径段索引。路网空间索引主要负责底层路段的高效检索,而时间索引与时空路径段索引则针对轨迹数据的时空特征进行精确定位和高效查询。该结构能够有效减少图数据库查询中节点的遍历,提高查询效率。此外,基于该索引结构的2种时空查询方法被开发以满足不同应用场景的需求。为验证所提出时空索引的有效性,本文基于人工合成的不同数量级路网时空轨迹数据进行了2种时空查询效率的对比。实验结果显示,本文提出的高效时空索引相比Nebula Graph原生图数据库索引,在时空窗口-时空路径相交查询中效率提升至少16.59倍,在时空路径-时空路径相交查询中效率提升至少2.74倍。这项研究为路网时空轨迹数据的高效管理和实时查询提供了新的解决方案,具有重要的理论和实际意义。展开更多
In basketball, each player’s skill level is the key to a team’s success or failure, the skill level is affected by many personal and environmental factors. A physics-informed AI statistics has become extremely impor...In basketball, each player’s skill level is the key to a team’s success or failure, the skill level is affected by many personal and environmental factors. A physics-informed AI statistics has become extremely important. In this article, a complex non-linear process is considered by taking into account the average points per game of each player, playing time, shooting percentage, and others. This physics-informed statistics is to construct a multiple linear regression model with physics-informed neural networks. Based on the official data provided by the American Basketball League, and combined with specific methods of R program analysis, the regression model affecting the player’s average points per game is verified, and the key factors affecting the player’s average points per game are finally elucidated. The paper provides a novel window for coaches to make meaningful in-game adjustments to team members.展开更多
基金supported by the National Natural Science Foundation of China(No.11701137)the Natural Science Foundation of Hebei Province(No.A2021202010).
文摘Nonmonotone gradient methods generally perform better than their monotone counterparts especially on unconstrained quadratic optimization.However,the known convergence rate of the monotone method is often much better than its nonmonotone variant.With the aim of shrinking the gap between theory and practice of nonmonotone gradient methods,we introduce a property for convergence analysis of a large collection of gradient methods.We prove that any gradient method using stepsizes satisfying the property will converge R-linearly at a rate of 1-λ_(1)/M_(1),whereλ_(1)is the smallest eigenvalue of Hessian matrix and M_(1)is the upper bound of the inverse stepsize.Our results indicate that the existing convergence rates of many nonmonotone methods can be improved to 1-1/κwithκbeing the associated condition number.
文摘为倡导绿色出行理念,解决以往研究在处理重复观测数据时容易忽视的潜在相关性和个体异质性问题,针对如何利用智能手机APP提供的多模式出行信息引导小汽车出行者转向停车换乘(Park-and-Ride,P+R)模式进行了探究,同时引入广义线性混合模型(Generalized Linear Mixed Model,GLMM)分析了多模式出行信息对小汽车出行者转向P+R意向的影响。首先,基于上海市路网设计意向调查问卷,整合了自驾和P+R两种出行方式的道路拥堵程度、出行时间、停车费用及地铁车厢座位情况等信息,并运用全因子设计法构建了24种不同信息水平组合的假设情景。然后,通过智能手机APP界面示意图向小汽车出行者展示这些多模式出行信息,并收集其转向P+R的意向数据。最后,运用GLMM方法处理同一个体重复决策数据中潜在的相关性和捕捉个体间的异质性。结果显示,GLMM的应用不仅解决了同一个体重复决策间的相关性,还揭示了不同个体对道路拥堵程度和地铁车厢座位情况的差异化关注;智能手机APP整合的多模式出行信息显著提升了小汽车出行者转向P+R的意愿,且这一转变占比达29.2%;高收入、长驾龄以及对P+R政策不了解的出行者转向P+R的意愿较低。研究表明,通过智能手机APP整合自驾和P+R的多模式出行信息能显著增强P+R方式的吸引力,可为提升P+R的普及率提供新思路,有效促进小汽车出行者向绿色出行方式的转变。
文摘大数据时代的到来使得时空轨迹数据的规模和复杂度迅速增长,这对如何高效管理和查询时空轨迹数据提出了新的需求和挑战。图数据库在处理时空轨迹数据的建模、存储和管理方面具有独特优势。然而,随着路网时空轨迹数据规模的不断扩大,图数据库的查询性能也会随之下降。为应对这一挑战,本文提出了一种基于图数据库的路网时空轨迹建模与高效索引方法。该方法采用压缩线性参考(Compressed Linear Reference,CLR)模型对路网时空轨迹进行建模,并将其存储于图数据库中,在此基础上,进一步构建了一种高效的路网时空轨迹索引机制。该索引体系采用了三层时空索引结构,包括路网空间索引、时间索引和时空路径段索引。路网空间索引主要负责底层路段的高效检索,而时间索引与时空路径段索引则针对轨迹数据的时空特征进行精确定位和高效查询。该结构能够有效减少图数据库查询中节点的遍历,提高查询效率。此外,基于该索引结构的2种时空查询方法被开发以满足不同应用场景的需求。为验证所提出时空索引的有效性,本文基于人工合成的不同数量级路网时空轨迹数据进行了2种时空查询效率的对比。实验结果显示,本文提出的高效时空索引相比Nebula Graph原生图数据库索引,在时空窗口-时空路径相交查询中效率提升至少16.59倍,在时空路径-时空路径相交查询中效率提升至少2.74倍。这项研究为路网时空轨迹数据的高效管理和实时查询提供了新的解决方案,具有重要的理论和实际意义。
文摘In basketball, each player’s skill level is the key to a team’s success or failure, the skill level is affected by many personal and environmental factors. A physics-informed AI statistics has become extremely important. In this article, a complex non-linear process is considered by taking into account the average points per game of each player, playing time, shooting percentage, and others. This physics-informed statistics is to construct a multiple linear regression model with physics-informed neural networks. Based on the official data provided by the American Basketball League, and combined with specific methods of R program analysis, the regression model affecting the player’s average points per game is verified, and the key factors affecting the player’s average points per game are finally elucidated. The paper provides a novel window for coaches to make meaningful in-game adjustments to team members.
