Limits of detection and decision. Part 2

Extensive Monte Carlo studies of instrumental limits of detection (LODs) were performed on a simple univariate chemical measurement system having homoscedastic, Gaussian measurement noise and using ordinary least squares (OLS) processing of tens of millions of independent calibration curve data sets. It was found that experimental decision and detection limits in the content domain were distributed as scaled reciprocals of noncentral t variates. In the response domain, the decision and detection limits were distributed as scaled χ variates. Rates of false negatives were found to be as expected statistically and no bias was found. However, use of detection limit expressions based on critical values of the noncentrality parameter of the noncentral t distribution were found to be significantly biased, resulting in substantial bias in rates of false negatives.     

消偏光纤陀螺的理论和实验研究

本文首次在理论上导出消偏型光纤陀螺的零漂和标度因子表达式,并得出以下两个结论:1)在使用约 40 dB偏振器时,导致陀螺漂移的主要因素是强度误差而并不是振幅误差;2)由光学标度因子与各种器件参量关系表明开环解调时陀螺的线性误差较大.试验样机证明了以上结果,并找出减小漂移的方法.     

光纤CATV外调制发射机中的复合二次失真及其抑制

复合二次失真(CSO:Composite Second Order Distortion)是光纤CATV中最主要的非线性之一.理论分析表明:在外调制CATV中,将调制器偏置在最佳偏置点可以消除CSO,但外调制器最佳偏置点却随时间及环境温度等漂移,因而会导致CSO的严重恶化.本文提出了一种易于实现的调制器偏置点控制方案,并进行了详细的理论分析与实验研究,结果显示该方案能够将50～550MHz宽频带内电视信号CSO指标抑制在-65dB以下.     

Limits of detection and decision. Part 3

It has been shown that the MARLAP (Multi-Agency Radiological Laboratory Analytical Protocols) for estimating the Currie detection limit, which is based on ‘critical values of the non-centrality parameter of the non-central t distribution’, is intrinsically biased, even if no calibration curve or regression is used. This completed the refutation of the method, begun in Part 2. With the field cleared of obstructions, the true theory underlying Currie's limits of decision, detection and quantification, as they apply in a simple linear chemical measurement system (CMS) having heteroscedastic, Gaussian measurement noise and using weighted least squares (WLS) processing, was then derived. Extensive Monte Carlo simulations were performed, on 900 million independent calibration curves, for linear, “hockey stick” and quadratic noise precision models (NPMs). With errorless NPM parameters, all the simulation results were found to be in excellent agreement with the derived theoretical expressions. Even with as much as 30% noise on all of the relevant NPM parameters, the worst absolute errors in rates of false positives and false negatives, was only 0.3%.     

Programming configurational changes in systems of functionalised polymers using reversible intramolecular linkages

ABSTRACT

We study polymers functionalised by complexes forming intramolecular linkages. Simulations of chains forming reversible linkages are difficult due to entropic barriers that hamper the sampling of different connectivity states specified by the list of pairs of reacted complexes. We address this problem by devising Monte Carlo (MC) moves that change the connectivity state of the system by regrowing parts of the chain while simultaneously reacting bond-forming complexes. Along with moves that link/unlink pairs of complexes, we develop two types of bond-exchange moves. We use these algorithms to study self-assembly of single chain polymeric nanoparticles. When considering monofunctional precursors, we find branched and linear nanoparticle morphologies dominated by long and short intramolecular loops, respectively, along with hierarchical structures in which complexes belonging to different loops are cross-linked. In the strong association limit, equilibrium structures are only reached when using bond-exchange MC moves. We also consider bifunctional precursors in which two different types of complexes decorate the two halves of the chain. We find different types of morphologies featuring different amounts of linkages between complexes of different types. Such findings corroborate our method as a valuable tool to design and predict self-assembly of functional polymers.     

Testing Lack-of-fit for a Polynomial Errors-in-variables Model

When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial error-in-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables,we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the significance level well.The choice of weight functions involved in the test statistic and the related power study are also investigated.The application to two examples is illustrated. The approach can be readily extended to handle more general models.     

Marginal productivity index policies for scheduling a multiclass delay-/loss-sensitive queue

This paper addresses the problem of scheduling a Markovian multiclass queue with a finite dedicated buffer for each class, where class-dependent linear holding and rejection cost rates model differing levels of tolerance to delay and loss. The goal is to design well-grounded and tractable scheduling policies that nearly minimize expected total discounted or long-run average cost. New dynamic index policies are introduced, awarding higher priority to classes with larger index values, where a class’ index measures the marginal productivity of work at its current state. The results are obtained by deploying the work-cost analysis approach to marginal productivity indices (MPIs) for restless bandits developed by the author, which is extended to the bias criterion. The MPI furnishes new insights: for a loss-sensitive class, it is a decreasing function of the number of empty buffer spaces, independent of the buffer size; for a delay-sensitive class, it is a decreasing function of the queue length. Such opposite orderings show that preventive work is more valuable than reactive work for the latter classes, whereas the opposite holds for the former. The results of a computational study on two-class instances are reported, shedding light on how the MPI policy’s relative performance varies with each parameter. Parameter ranges are thus identified where the MPI policy is near optimal, and substantially outperforms conventional benchmark policies. 2000 Mathematics Subject Classification 90B22 · 90B36 · 90B18 · 60K25 · 60K30 · 68M20