Gradient Estimation Schemes for Noisy Functions

In this paper, we analyze different schemes for obtaining gradient estimates when the underlying functions are noisy. Good gradient estimation is important e.g. for nonlinear programming solvers. As error criterion, we take the norm of the difference between the real and estimated gradients. The total error can be split into a deterministic error and a stochastic error. For three finite-difference schemes and two design of experiments (DoE) schemes, we analyze both the deterministic errors and stochastic errors. We derive also optimal stepsizes for each scheme, such that the total error is minimized. Some of the schemes have the nice property that this stepsize minimizes also the variance of the error. Based on these results, we show that, to obtain good gradient estimates for noisy functions, it is worthwhile to use DoE schemes. We recommend to implement such schemes in NLP solvers.We thank our colleague Jack Kleijnen for useful remarks on an earlier version of this paper and Gül Gürkan for providing us with relevant literature. Moreover, we thank the anonymous referee for valuable remarks.     

可用硬币做的物理实验

介绍了用硬币做简易教具,演示水的表面张力、静电排斥斥力、电磁感应、磁化、磁屏蔽及光的全反射现象等力学、电磁学和光学实验.     

对设计性实验的讨论和体会

讨论了大学物理实验中设计性实验的内涵、外延和开课意义；介绍了我们的开课情况和教学体会。     

Numerical solutions of the Laplace’s equation

This paper uses the sinc methods to construct a solution of the Laplace’s equation using two solutions of the heat equation. A numerical approximation is obtained with an exponential accuracy. We also present a reliable algorithm of Adomian decomposition method to construct a numerical solution of the Laplace’s equation in the form a rapidly convergence series and not at grid points. Numerical examples are given and comparisons are made to the sinc solution with the Adomian decomposition method. The comparison shows that the Adomian decomposition method is efficient and easy to use.     

LED在物理演示实验中的应用

本文利用发光二极管对电磁感应现象、自感现象等演示实验进行了改进,并用多个发光二极管组成的阵列形式来模拟直流电流流动方向和对电容的充电、电容的放电现象的演示,加强学生对直流电流的方向性的认识,便于学生观察电容的充电、电容放电的整个过程,明显提高了实验的效果。     

新型趋肤效应演示仪

本文介绍了一个简单易制的演示装置,该装置结构简单、现象明显、演示内容全面,可加深学生对趋肤效应的理解,达到观察、研究趋肤效应的目的。     

大学物理课堂演示实验系统

用传感器、数据采集接口和数据采集分析软件,配合计算机建成大学物理课堂演示实验系统.该系统符合课堂演示实验要求,解决了一些物理现象、物理过程不能在课堂演示的难题.     

定性与半定量物理实验教学初探

近年来，复旦大学在物理实验教学中适当加入了一批定性与半定量实验，实践证明，该类实验有利于培养学生分析问题与解决问题的能力，增强科学洞察力与判断力，激发他们的求知欲与创新精神，提高其科学素质．本文介绍了开设这些实验的经验、体会及初步效果．     

The advantage of complexity in two 2 × 2 games

Competing populations of finite automata co‐evolve in an evolutionary algorithm to play two player games. Populations endowed with greater complexity do better against their less complex opponents in a strictly competitive constant sum game. In contrast, complexity determines efficiency levels, but not relative earnings, in a Prisoner's Dilemma game; greater levels of complexity result in mutually higher earnings. With reporting noise, advantages to complexity are lost and efficiency levels are reduced as relatively less complex strategies are selected. © 2004 Wiley Periodicals, Inc. Complexity 9: 71–78, 2004     

Studies on polymer concretes based on optimized aggregate mix proportion

Polymer concretes are composite materials made of polymeric binders with filler materials. The filler materials form the major component of the polymer concrete and the distribution of their particle size influences the properties of polymer concrete. Hence using an optimized aggregate mix proportion having least void content, a series of polymer concretes of different compositions were designed on the basis of mixture design concept of design of experiments. For each composition, compressive strength was checked at different intervals of time. The effects of variables such as binder content and curing time on the properties were discussed. Further, the compressive strength obtained were optimized and compared with the experimental data. The coefficient of correlation between the experimental values and predicted values was found to be high proving the fitness of the selected model.