Model recovery for Hammerstein systems using the auxiliary model based orthogonal matching pursuit method

This article investigates parameter and order identification of a block-oriented Hammerstein system by using the orthogonal matching pursuit method in the compressive sensing theory which deals with how to recover a sparse signal in a known basis with a linear measurement model and a small set of linear measurements. The idea is to parameterize the Hammerstein system into the linear measurement model containing a measurement matrix with some unknown variables and a sparse parameter vector by using the key variable separation principle, then an auxiliary model based orthogonal matching pursuit algorithm is presented to recover the sparse vector.The standard orthogonal matching pursuit algorithm with a known measurement matrix is a popular recovery strategy by picking the supporting basis and the corresponding non-zero element of a sparse signal in a greedy fashion. In contrast to this, the auxiliary model based orthogonal matching pursuit algorithm has unknown variables in the measurement matrix. For a K-sparse signal, the standard orthogonal matching pursuit algorithm takes a fixed number of K stages to pick K columns (atoms) in the measurement matrix, while the auxiliary model based orthogonal matching pursuit algorithm takes steps larger than K to pick K atoms in the measurement matrix with the process of picking and deleting atoms, due to the gradually accurate estimates of the unknown variables step by step.The auxiliary model based orthogonal matching pursuit algorithm can simultaneously identify parameters and orders of the Hammerstein system, and has a high efficient identification performance.     

高维空间中数据的相似性度量

高维空间中数据之间的相似性度量是目前数据挖掘、信息处理与检索等领域所面临的一个重要问题.文章在总结分析了高维数据的特点以及现有的一些度量方法的基础上,提出了一种新的度量方式,该方法在对高维数据进行相似性度量之前,首先对原始数据空间进行网格划分.文章的最后对其有效性作了定量分析,实验证明,该方式是行之有效的.     

The impact of mismeasurement in performance benchmarking: A Monte Carlo comparison of SFA and DEA with different multi-period budgeting strategies

Performance-based budgeting has received increasing attention from public and for-profit organizations in an effort to achieve a fair and balanced allocation of funds among their individual producers or operating units for overall system optimization. Although existing frontier estimation models can be used to measure and rank the performance of each producer, few studies have addressed how the mismeasurement by frontier estimation models affects the budget allocation and system performance. There is therefore a need for analysis of the accuracy of performance assessments in performance-based budgeting. This paper reports the results of a Monte Carlo analysis in which measurement errors are introduced and the system throughput in various experimental scenarios is compared. Each scenario assumes a different multi-period budgeting strategy and production frontier estimation model; the frontier estimation models considered are stochastic frontier analysis (SFA) and data envelopment analysis (DEA). The main results are as follows: (1) the selection of a proper budgeting strategy and benchmark model can lead to substantial improvement in the system throughput; (2) a “peanut butter” strategy outperforms a discriminative strategy in the presence of relatively high measurement errors, but a discriminative strategy is preferred for small measurement errors; (3) frontier estimation models outperform models with randomly-generated ranks even in cases with relatively high measurement errors; (4) SFA outperforms DEA for small measurement errors, but DEA becomes increasingly favorable relative to SFA as the measurement errors increase.     

一类带有感染年龄SIR模型最优化免疫策略的存在性

对于一个免疫策略来讲,付出(单位时间内接种疫苗的数量)和效果(再生数的大小)是两个重要概念.在给定的费用下找到带有最小再生数的策略和在给定的再生数下找到最小费用的策略是两个最优问题.对一个确定的免疫策略来说,人群中的易感群体和染病群体会趋于相对稳定的状态.当一种疾病侵袭已免疫人群时,用带有感染年龄的SIR模型去描述这类疾病的传播更为准确.因此,本文研究了一类带有感染年龄的SIR模型,得到了最优化策略的存在性.     

Strategy,performance and operational research

This paper explores the nature of operational research and its interactions with performance measurement and strategy. It is argued that operational research (OR) is well fitted to handle strategic issues as the modelling approach of OR facilitates understanding and learning, and the evaluation of strategies prior to action. The development of problem structuring methods is also a key aid to strategy and policy formulation. OR is also beginning to play a role in performance measurement and there is an opportunity for OR to lead in the improvement of performance measurement systems.     

不确定性自私路由模型的理论和应用

为了更加准确地描述现实生活中的交通情况,以经典的自私路由模型为基础,在边的费用函数上引入不确定性,从而定义了具有不确定性的自私路由模型.对于不确定性自私路由模型,采用三种费用衡量标准,风险厌恶型（保守型）、风险折衷型（理智型）、风险偏好型（乐观型）,分别对应着不同人群在现实中的选择.进而定义了在不同衡量标准下所形成的稳定策略,即纳什均衡策略,并且证明了在任何一种衡量标准下,纳什均衡策略总是存在并且本质是唯一的.接着对三种费用衡量标准下的纳什均衡费用进行了比较,发现了一种反直观的现象：风险厌恶型（保守型）衡量标准下的纳什均衡费用可能严格低于风险偏好型（乐观型）衡量标准下的纳什均衡费用,即有可能会出现高风险低回报,低风险高回报的情况,这与经济学中高风险高回报,低风险低回报的原则是相违背的.以此为基础,进而提出了一种自私路由风险性悖论,并证明了这种自私路由风险回报悖论本质上是传统布雷斯悖论的推广.最后,刻画出了不会发生自私路由风险回报悖论的网络结构,证明了一个单对始终点网络不会发生自私路由风险回报悖论当且仅当它是序列-平行网络.     

On regularization and discretization control for the numerical solution of inverse problems in parabolic equations

In this paper, the influence of modelling, a priori information, discretization and measurement error to the numerical solution of inverse problems is investigated. Given an a priori approximation of the unknown parameter function in a parabolic problem, we propose a strategy for the regularized determination of a skeleton solution to the inverse problem. This strategy is based on a discretization control of the forward problem in order to find a trade-off between accuracy and computational efficiency. Numerical results with regard to a nonlinear inverse heat conduction problem illustrate the study.     

Infinite-Dimensional Compressed Sensing and Function Interpolation

We introduce and analyse a framework for function interpolation using compressed sensing. This framework—which is based on weighted \(\ell ^1\) minimization—does not require a priori bounds on the expansion tail in either its implementation or its theoretical guarantees and in the absence of noise leads to genuinely interpolatory approximations. We also establish a new recovery guarantee for compressed sensing with weighted \(\ell ^1\) minimization based on this framework. This guarantee conveys several benefits. First, unlike existing results, it is sharp (up to constants and log factors) for large classes of functions regardless of the choice of weights. Second, by examining the measurement condition in the recovery guarantee, we are able to suggest a good overall strategy for selecting the weights. In particular, when applied to the important case of multivariate approximation with orthogonal polynomials, this weighting strategy leads to provably optimal estimates on the number of measurements required, whenever the support set of the significant coefficients is a so-called lower set. Finally, this guarantee can also be used to theoretically confirm the benefits of alternative weighting strategies where the weights are chosen based on prior support information. This provides a theoretical basis for a number of recent numerical studies showing the effectiveness of such approaches.     

Children's understanding of length measurement using a ruler in preschool and primary education: A cross-national longitudinal study

Measuring length is a practice of everyday life and a mathematical principle shared across cultures. A cross-national and longitudinal study was designed to analyse the evolution of the strategies used by Spanish and Portuguese preschoolers and 1st graders when measuring length. The instruments were rulers designed to discriminate between the strategies demonstrated by young children in previous research, taking as variables the number of correct measurements and the strategy used to measure, and country as a covariate. Neither country nor age influenced correct measurements while the ruler used affected the strategy developed by the children. No significant differences were found in the strategies used from preschool to 1st grade, except for the ruler with numbered units and marks. Considering the sequence of sophistication of the strategies, our results reinforce the scaffolding role of discrete units for the understanding of length measurement towards the use of the standard ruler.     

Facilitated modelling in strategy development: measuring the impact on communication,consensus and commitment

Facilitated modelling is used in supporting the resolution of strategic issues mainly because it is expected to improve communication between decision makers, foster consensus and create commitment. Researchers in both the strategy and facilitated modelling fields call for more systematic research on how strategy development works in practice and how outcomes are created. In this paper, three facilitated modelling cases on strategic issues are studied using both written questionnaires, developed in the strategy and decision support fields, and semi-structured interviews. Results of both measurement approaches are compared to determine (a) to what extent outcomes in participants’ own terms are similar to concepts in the questionnaire and (b) whether changes measured by both methods are similar. Interview results are used to assess (c) which elements of the intervention contribute to outcomes. Findings suggest that questionnaires offer clear benefits as standardized measurement of facilitated modelling outcomes.     

具有不确定项的高阶非完整系统的反馈控制问题的研究

针对一类具有不确定性的高阶非完整系统,通过引入观测器,采用状态-输入转换、反推方法,设计了反馈控制器.同时为了处理初值为0的情况,提出了一种新的基于第一个子系统输出值的切换控制策略,提出的切换控制策略能有效的防止系统的状态发生有限时间逃逸现象.     

基于无线通信基站三维定位问题的求解模型

基于无线通信基站的三维定位相比于传统GPS定位有着诸多优势,技术有着广阔的应用前景和巨大的商业价值.针对基于无线通信基站的三维定位问题,首先分析建立TOA定位的初步模型.其次,基于对模型时钟误差、非视距传播误差、测量误差的分析,优化方程组的建立策略,基站排序,方程组系数修正的方式,使误差项的影响降到最小.最终由最小二乘法计算出定位结果.实验表明,定位模型的定位精度在1米左右,并且定位精度随基站数目的增多而增高.     

Shrinkage strategy in stratified random sample subject to measurement error

The empirical likelihood estimation approach has been used in statistical applications. In this paper, we consider a stratified random sample subject to measurement error and with this framework, we propose a shrinkage estimation strategy that improves the performance of the maximum empirical likelihood estimator (MELE). Further, we generalize some recent findings that demonstrate the superiority of the shrinkage strategy over the MELE. Monte Carlo simulation results corroborate the established theoretical findings.     

Robust inference strategy in the presence of measurement error

In this paper, we consider a statistical model where samples are subject to measurement errors. Further, we propose a shrinkage estimation strategy by using the maximum empirical likelihood estimator (MELE) as the base estimator. Our asymptotic results clearly demonstrate the superiority of our proposed shrinkage strategy over the MELE. Monte Carlo simulation results show that such a performance still holds in finite samples. We apply our method to real data set.     

Noniterative solution of inverse problems by the linear least square method

In this paper, a noniterative linear least-squares error method developed by Yang and Chen for solving the inverse problems is re-examined. For the method, condition for the existence of a unique solution and the error bound of the resulting inverse solution considering the measurement errors are derived. Though the method was shown to be able to give the unique inverse solution at only one iteration in the literature, however, it is pointed out with two examples that for some inverse problems the method is practically not applicable, once the unavoidable measurement errors are included. The reason behind this is that the so-called reverse matrix for these inverse problems has a huge number of 1-norm, thus, magnifying a small measurement error to an extent that is unacceptable for the resulting inverse solution in a practical sense. In other words, the method fails to yield a reasonable solution whenever applied to an ill-conditioned inverse problem. In such a case, two approaches are recommended for decreasing the very high condition number: (i) by increasing the number of measurements or taking measurements as close as possible to the location at which the to-be-estimated unknown condition is applied, and (ii) by using the singular value decomposition (SVD).     

Multivariate nonparametric control chart with variable sampling interval

This paper proposes an adaptive, multivariate, nonparametric, exponentially weighted moving average control chart with variable sampling interval. A number of studies have discussed multivariate nonparametric control charts. However, the proposed multivariate nonparametric control charts usually have strict requirements. In this paper, we construct a control chart for multivariate processes that is based on the Mahalanobis depth. Specifically, we use the concept of the Mahalanobis depth to reduce each multivariate measurement to a univariate index. It is worth mentioning that this approach is completely nonparametric. We also discuss the optimal strategy for the parameters. This chart is an adaptive chart and has a variable sampling interval. A simulation study demonstrates that the proposed chart is efficient in detecting various magnitudes of shifts. A gravel data and a wine quality detection example are given to introduce the proposed control chart.     

具有模糊支付的Moran过程演化博弈动态

以往对演化博弈的研究都假设个体从博弈中获得的支付是确定的并以精确的数来表示。然而由于受环境中各种不确定因素的影响,个体博弈时所获得的支付并不是一个精确的数值,而需要用一个模糊数来表示。本文研究模糊支付下2×2的对称博弈, 利用模糊数的运算, 分析具有模糊支付的有限种群Moran过程演化动态。在弱选择下以梯形模糊数和三角模糊数表示博弈支付,计算策略的模糊扎根概率,分析自然选择有利于策略扎根及策略成为模糊演化稳定策略的条件。将经典博弈推广到模糊环境中丰富了演化博弈理论,更具有现实意义。     

The Minimal Measurement Number Problem in Phase Retrieval: A Review of Recent Developments

Phase retrieval is to recover the signals from phaseless measurements which is raised in many areas. A fundamental problem in phase retrieval is to determine the minimal measurement number $m$ so that one can recover $d$-dimensional signals from $m$ phaseless measurements. This problem attracts much attention of experts from different areas. In this paper, we review the recent development on the minimal measurement number and also raise many interesting open questions.     

A robust optimization approach to experimental design for model discrimination of dynamical systems

A high-ranking goal of interdisciplinary modeling approaches in science and engineering are quantitative prediction of system dynamics and model based optimization. Quantitative modeling has to be closely related to experimental investigations if the model is supposed to be used for mechanistic analysis and model predictions. Typically, before an appropriate model of an experimental system is found different hypothetical models might be reasonable and consistent with previous knowledge and available data. The parameters of the models up to an estimated confidence region are generally not known a priori. Therefore one has to incorporate possible parameter configurations of different models into a model discrimination algorithm which leads to the need for robustification. In this article we present a numerical algorithm which calculates a design of experiments allowing optimal discrimination of different hypothetic candidate models of a given dynamical system for the most inappropriate (worst case) parameter configurations within a parameter range. The design comprises initial values, system perturbations and the optimal placement of measurement time points, the number of measurements as well as the time points are subject to design. The statistical discrimination criterion is worked out rigorously for these settings, a derivation from the Kullback-Leibler divergence as optimization objective is presented for the case of discontinuous Heaviside-functions modeling the measurement decision which are replaced by continuous approximations during the optimization procedure. The resulting problem can be classified as a semi-infinite optimization problem which we solve in an outer approximations approach stabilized by a suggested homotopy strategy whose efficiency is demonstrated. We present the theoretical framework, algorithmic realization and numerical results.