When developing models there is always a trade-off between model complexity and model fit. In this paper, a measure of learning model complexity based on VC dimension is presented, and some relevant mathematical theor...When developing models there is always a trade-off between model complexity and model fit. In this paper, a measure of learning model complexity based on VC dimension is presented, and some relevant mathematical theory surrounding the derivation and use of this metric is summarized. The measure allows modelers to control the amount of error that is returned from a modeling system and to state upper bounds on the amount of error that the modeling system will return on all future, as yet unseen and uncollected data sets. It is possible for modelers to use the VC theory to determine which type of model more accurately represents a system.展开更多
In this paper, through symbolic computations, we obtain two exact solitary wave solitons of the (2 + l)-dimensional variable-coefficient Caudrey-Dodd- Gibbon-Kotera-Sawada equation. We study basic properties of l-peri...In this paper, through symbolic computations, we obtain two exact solitary wave solitons of the (2 + l)-dimensional variable-coefficient Caudrey-Dodd- Gibbon-Kotera-Sawada equation. We study basic properties of l-periodic solitary wave solution and interactional properties of 2-periodic solitary wave solution by using asymptotic analysis.展开更多
叙述了复杂地质体三维建模在Adina中自下而上依次建立点、线、面和体的方法,其中面和体的定义需要手工完成,费时费力。用VC编写了AutoCAD To Adina三维建模程序,实现了点、线、面和体的自动定义,大大缩短了Adina三维建模的周期。实例表...叙述了复杂地质体三维建模在Adina中自下而上依次建立点、线、面和体的方法,其中面和体的定义需要手工完成,费时费力。用VC编写了AutoCAD To Adina三维建模程序,实现了点、线、面和体的自动定义,大大缩短了Adina三维建模的周期。实例表明,该方法具有较大的实用价值。展开更多
文摘When developing models there is always a trade-off between model complexity and model fit. In this paper, a measure of learning model complexity based on VC dimension is presented, and some relevant mathematical theory surrounding the derivation and use of this metric is summarized. The measure allows modelers to control the amount of error that is returned from a modeling system and to state upper bounds on the amount of error that the modeling system will return on all future, as yet unseen and uncollected data sets. It is possible for modelers to use the VC theory to determine which type of model more accurately represents a system.
文摘In this paper, through symbolic computations, we obtain two exact solitary wave solitons of the (2 + l)-dimensional variable-coefficient Caudrey-Dodd- Gibbon-Kotera-Sawada equation. We study basic properties of l-periodic solitary wave solution and interactional properties of 2-periodic solitary wave solution by using asymptotic analysis.
