Parametric error bounds for convex approximations of two-stage mixed-integer recourse models with a random second-stage cost vector

We consider two-stage recourse models with integer restrictions in the second stage. These models are typically non-convex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q. In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the ${?}_1$-norm of q.     

Stabilization of Parametric Vibrations of a Nonlinear Continuous System

The purpose of the present paper is to solve an active control problem of nonlinear continuous system parametric vibrations excited by the fluctuating force. The problem is solved using the concept of distributed piezoelectric sensors and actuators with a sufficiently large value of velocity feedback. The direct Liapunov method is proposed to establish criteria for the almost sure stochastic stability of the unperturbed (trivial) solution of the shell with closed-loop control. The distributed control is realized by the piezoelectric sensor and actuator, with the changing widths, glued to the upper and lower shell surface. The relation between the stabilization of nonlinear problem and a linearized one is examined. The fluctuating axial force is modeled by the physically realizable ergodic process. The rate velocity feedback is applied to stabilize the shell parametric vibrations.     

参数Kleene系统中的广义重言式

引入新的一组带对数ｐ（ｐ∈「０,１」的ｔ－范∧ｐ,ｔ－余范∨ｐ和蕴涵θｐ,讨论它们的基本性质。在此基础上参数Ｋｌｅｅｎｅ系统Ｋｐ与三值Ｋｌｅｅｎｅ系统Ｋ３,三值Ｌｕｋａｓｉｅｗｉｃｚ系统Ｌ３和经典二值系统Ｂ２关于（广义）重言式的相互关系,指出系统Ｋｐ对广义重言式而言是可判定的。     

A closed-form representation of mixed-integer program value functions

We identify a class of formulas computable in polynomial time such that the functions defined by these formulas are precisely the value functions of mixed-integer programs with rational constraint coefficients.     

电磁波的非线性动力理论

使用全动力途径，严格地推导了左旋圆极化电磁波的非线性色散关系。所得到的色散关系被用来分析电子Ｂｅｒｎｓｔｅｉｎ波和高杂波所激发的电磁辐射。结果表明：（１）电子Ｂｅｒｎｓｔｅｉｎ波可以激发频率上移辐射，也可以激发频率下移辐射，这取决于背景等离子体频率ｗｐｅ与电子回旋频率Ωｅ的比值大小；（２）高杂波只能激发频率下移辐射；（３）当电子Ｂｅｒｎｓｔｅｉｎ波位于高杂共振层时，频率上移辐射和频率下移辐射可以同     

Correlation receiver of below-noise pulsed signals based on parametric interactions of spin waves in magnetic films

A correlation receiver capable of receiving pulsed microwave signals having amplitudes substantially below the noise level is proposed and experimentally realized. The device is based on the parametric interaction of two contra-propagating spin waves excited by the received microwave signal and the reference pulsed signal, containing information about the received signal shape, in a ferrite film waveguide. The output nonlinear correlation signal having the doubled carrier frequency and the signal-to-noise ratio enhanced by several orders of magnitude is received by a dielectric resonator coupled to an output microwave transmission line.     

堆积脉冲光参量啁啾脉冲放大器

以自启动被动锁模掺镱光纤堆积脉冲激光器为种子源,采用非共线相位匹配的方法,进行了光参量啁啾脉冲放大器的实验研究,得到了两级放大总增益为1.1×107,单脉冲能量为11 mJ,能量稳定性小于2％ rms,8 nm的放大谱宽.实验结果表明,采用这种结构的光参量啁啾脉冲放大器,放大增益高,系统稳定、结构紧凑、便于调节,同时通过调节种子源中的堆积器,可以得到不同宽度的放大信号脉冲.     

On estimating model complexity and prediction errors in multivariate calibration: generalized resampling by random sample weighting (RSW)

The present paper focuses on determining the number of PLS components by using resampling methods such as cross validation (CV), Monte Carlo cross validation (MCCV), bootstrapping (BS), etc. To resample the training data, random non‐negative weights are assigned to the original training samples and a sample‐weighted PLS model is developed without increasing the computational burden much. Random weighting is a generalization of the traditional resampling methods and is expected to have a lower risk of getting an insufficient training set. For prediction, only the training samples with random weights less than a threshold value are selected to ensure that the prediction samples have less influence on training. For complicated data, because the optimal number of PLS components is often not unique or readily distinguished and there might exist an optimal region of model complexity, the distribution of prediction errors can be more useful than a single value of root mean squared error of prediction (RMSEP). Therefore, the distribution of prediction errors are estimated by repeated random sample weighting and used to determine model complexity. RSW is compared with its traditional counterparts like CV, MCCV, BS and a recently proposed randomization test method to demonstrate its usefulness. Copyright © 2010 John Wiley & Sons, Ltd.     

Stochastic resonance in circadian rhythms

The effect of fluctuations in the two-variable discrete delay model proposed earlier by us [1] for the circadian rhythm of the fungal species Neurospora Crassa is studied. We have investigated the effect of parametric and additive noise in two different regimes namely, steady-state and Period-1 regimes. It is found that under the influence of noise coherent oscillations are generated in the steady-state. Oscillations are preserved and robust to a wide range of noise intensity in the Period-1 regime. The oscillations in both these regimes are always found to be close to the circadian period (21.5 h). Coherence resonance is observed when parametric or velocity additive noise is added near the Hopf bifurcation. Finally, the implications of fluctuations in circadian rhythms are discussed. This article is dedicated to Professor Karl Jug on the occassion of his sixtyfifth birthday.     

On the interplay between interior point approximation and parametric sensitivities in optimal control

Infinite-dimensional parameter-dependent optimization problems of the form ‘minJ(u;p) subject to g(u)?0’ are studied, where u is sought in an L_∞ function space, J is a quadratic objective functional, and g represents pointwise linear constraints. This setting covers in particular control constrained optimal control problems. Sensitivities with respect to the parameter p of both, optimal solutions of the original problem, and of its approximation by the classical primal-dual interior point approach are considered. The convergence of the latter to the former is shown as the homotopy parameter μ goes to zero, and error bounds in various Lq norms are derived. Several numerical examples illustrate the results.